DOCUMENT RESUME
ED 330 566
SE 052 076
TITLE
The State of Mathematics Achievement in Minnesota:
The Trial State Assessment at Grade Eight.
INSTITUTION
Educational Testing Service, Princeton, N.J.;
National Assessment of Educational Progress,
Princeton, NJ.
SPONS AGENCY
National Center for Education Statistics (ED),
Washington, DC.
REPORT NO
ETS-21-ST-02; ISBN-0-88685-14-9
PUB DATE
Jun 91
NOTE
146p.; The entire Report consists of a composite
report, an executive summary, and 40 separate reports
for 37 states, DC, Guam, and the Virgin Islands,
respectively; see SE 052 055-096.
AVAILABLE FROM
Individual state reports are available directly from
the assessment division of the appropriate State
Department of Education.
PUB TYPE
Statistical Data (110) -- Reports -
Research/Technical (143)
EDRS PRICE
MF01/PC06 Plus Postage.
DESCRIPTORS
Academic Achievement; Calculators; *Educational
Assessment; Family Environment; *Grade 8; Homework;
Junior High Schools; *Mathematics Achievement;
Mathematics Instruction; Mathematics Skills;
Mathcatics Tests; National Programs; Problem
Solving; Public Schools; *State Programs; Student
Attitudes; Teacher Attitudes; Teacher Qualifications;
Television Viewing
IDENTIFIERS
*Minnesota; National Assessment of Educational
Progress; *Numeracy; State Mathematics Assessments;
Trial State Assessment (NAEP)
ABSTRACT
In 1990, the National Assessment of Educational
Progress (NAEP) included a Trial State Assessment (TSA); for the
first time in the NAEP's history, voluntary state-by-state
assessments (37 states, the District of Columbia, Guam, and the
Virgin Islands) were made. The sample was designed to represent the
8th grade public school population in a state or territory. The 1990
TSA covered five mathematics content areas (numbers and operations;
measurement; geometry; data analysis, statistics, and probability;
and algebra and functions). In Minnesota, 2,584 students in 97 public
so;lools were assessed. This report describes the mathematics
proficiency of Minnesota eighth-graders, compares their overall
performance to students in the Central region of the United States
and the nation (using data from the NAEP national assessments),
presents the average proficiency separately for the five content
areas, and summarizes the performance of subpopulations
(race/ethnicity, type of community, parents' educational level, and
gender). To provide a context for the assessment data, participating
students, their mathematics teachers, and principals completed
questionnaires which focused on: instructional content (curriculum
coverage, amount of homework); delivery of math instruction
(availability of resources, type); use of calculators; educational
background of teachers; and conditions facilitating math learning
(e.g., hours of television watched, absenteeism). On the NAEP math
scale, Minnesota students had an average proficiency of 276 compared
to 261 nationwide. Many fewer students (Minnesota-20%; U.S.-12%)
appear to have acquired reasoning and problem solving skil.s.
(JJN/CRW)
NATIONAL CENTER FOR EDUCATION STATISTICS
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Prepared by Educational Testing Service under Contract with the National Center for Education Statistics
Office of Educational Research and Improvement
U.S. Department of Education
What is The Nation's Report Card?
THE NATION'S REPORT CARD. the National Assessment of Educational Progress (NAFP) is the only nationally representative and
continuing assessment of what America's students know and can do in various subject areas. Since 1969, assessments have been conducted
periodically in reading, mathematics, science, writing, history/geography. and other fields. By making objective information on student
performance available to policymakers at the national, state, and local levels. NAEP is an integral part of our nation's evaluation of the
condition and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees
the privacy of individual students and their families.
NAEP is a congressionally mandated project of the National Center for Education Statistics. the U.S. Department of Education. The
Commissioner of Education Statistics is responsible. by law, for carrying out the NAEP project through competitive award.s to qualified
organizations. NAEP rt_ports directly to the Commissioner, who is also responsible for providing continuing reviews, including validation
studies and solicitation of public comment, on NAEP's conduct and usefulness.
In 1988. Congress created the National Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The board is
resisible for set:A:ling the subject areas to he assessed, which may include adding to those specified by Congress; identifying appropriate
achievement goals for each age and grade; developing assessment objectives; developing test specifications; designing the assessment
methodology; developing guidelines and standards for data analysis and for reporting and disseminating results; developing standards and
procedures for interstate. regional. and national comparisons; improving the form and use of the National Assessment; and ensuring that all
items selected for use in the National Assessment are free from racial, cultural, gender. or regional bias.
The National Assessment Governing Board
Richard A. Boyd, Chairman
Executive Director
Martha Holden Jennings Foundation
Cleveland, Ohio
Phyllis Williamson Aldrich
Curriculum Coordinator
Saratoga-Warren B.O,C.E.S.
Saratoga Springs. New York
Franck Alexander
Associate Superintendent
California Department of Education
Sacramento. California
David P. Battini
High School History Teacher
Cairo.Durham High School
Cairo, New York
Parris C. Rattle
Teacher
Horace Mann Elementary School
Miami, Florida
Mary R. Blanton
Attorney
Cromweil, Porter. Blanton 15z. Blanton
Salisbury. North Carolina
Boyd W. Rochije
Attorney
Gaass.
Bochlje
Pella, Iowa
Linda R. Bryant
Teacher
Greenway Middle School Teaeher Cone,
Pittsburgh. Pennsylvania
Honorabk Michael N. Castle
Governor of Delaware
Carve! State Office Building
Wilmington, Delaware
Honorable Naomi K. Cohen
State of Connecticut
House of Representatives
Legislative Office Building
Hartford, Connecticut
Chester E. Finn, Jr.
Professor of Education and Public Pohey
Vanderbilt University
Washington, D.C.
Michael S. Glade
Wyoming State Board of Educatiim
Saratoga, Wyoming
t llristine Johnson
Principal
Abraham Lincoln High School
Denver. Colorado
John Lindley
Principal
South Colby Elementary School
Port Orefr,u, Washington
Carl J. Moser
Director of Schools
Pre Lutheran Church
Missouri Synod
International Center
St. Louis, Missouri
Mark D. Muskk
President
Southein Regional Education Board
Atlanta. Georgia
Honorable Carolyn Pollan
Arkansas House of Representatives
Fort Smith, Arkansas
Matthew W. Prophet, Jr.
Superintendent
Portland Oregon School District
Portland. Oregon
Honorabk William T. Randall
Commissioner of Education
State Department of Education
Denver, Colorado
Dorothy K. Rich
President
Home and School Institute
Special Projects Office
Washington. D.C.
Howrable Richard W. Riley
Attorney
Nelson. Mullins, Riley and
Scarborough
Columbia, South Carolina
Thomas Topuzes
Attorney
Law Offices of Frank Rogozienski
Coronado, California
Herbert J. Walberg
Professor of Education
University of Illinois
Chicago, Illinois
Assistant Secretary for
Educational Research and
Improvement (Fs-Officio)
1.7.S. Department of Education
Washington, DC.
Rny Truby
Executive Director, NAGB
Washington, D.C.
NATIONAL CENTER FOR EDUCATION
STATISTICS
The STATE of
M thematics
Achievement
in MINNESOTA
The Trial State Assessment at Grade Eight
THE NATION'S
REPORT
CARO
Report No: 21-ST-02
June 1 9g1
Prepared by Educational Testing Service under Contract with the National Center for Education Statistics
Office of Educational Research and Improvement
U.S. Department of Education
U.S. Department of Education
Lamar Alexander
Secretary
Office of Educational Research and Improvement
Bmno V. Mdnno
Acting Assistant Sectetary
National Center for Education Statistics
Emerson J. Elliott
Acting Commissioner
FOR MORE INFORMATION:
Copies of the 1990 NAEP Trial State Assessment's individual State reports are available directly from the participating
States. For ordering information, please contact the assessment division of your State Department of Education. For
ordering information on the composite report of results for the Nation and all State participants, or for single copies
of the Executive Summary while supplies last, write:
Education Information Branch
Office of Educational Research and Improvement
U.S. Department of Education
555 New Jersey Avenue, NW
Washington, D.C. 20208-5641
or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651).
Library of Cccgress, Catalog Card Number: 91-61478
ISBN: 0-88685-14-9
The work upon which this publication is based was performed for the National Center for Education Statistics,
Office of Educational Research and Improvement, by Educational Testing Service.
Educational Testing Service is an equal opportunity/affirmative action employer.
Educational Testing Service, ETS, and
ars registered trademarks of Educational Testing Servio
Table of Contents
EXECUTIVE SUMMARY
1
INTRODUCTION
7
Overview of the 1990 Trial State Assessnient
8
This Report
9
Guidelines for Analysis
12
Profile of Minnesota
14
Eighth-Grade School and Student Characteristics
14
Schools and Students Assessed
15
PART ONE
How Proficient in Mathematics Are Eighth-Grade Students
in Minnesota Public Schools?
17
Chapta 1.
Students' Mathematics Performance
18
I Awe ls of Mathematics Proficiency
19
Content Area Performance
19
Chapter 2.
Mathematics Performance by Subpopulations
24
Race / Ethnicity
24
Type of Community
27
Parents' Education Level
19
Gender
Content Area Performance
33
THE 1990 NAEP TRIAL STATE ASSESSMENT
III
PART TWO
Finding a Context for Understanding
Students' Mathematics Proficiency
37
Chapter 3.
What Are Students Taught in Mathematics'
39
Cuniculum Coverage
41
Mathematics Homework
42
Instructional Emphasis
45
Summary
48
Chapter 4.
How Is Mathematics Instruction Delivered'
49
Availability of Resources
49
Patterns in Classroom Instruction
51
Collaborating in Small Groups
54
Using Mathematical Objects
55
Materials for Mathematics Instruction
56
Summary
59
Chapter 5.
How Are Calculators Used"
60
The Availability of Calculators
62
The Use of Calculators
63
When To Use a Calculator
64
Summary
66
Chapter 6.
Who Is Teaching Lighth-Grade Mathematics?
67
Educational Backgound
68
Summaly
71
Chapter 7.
The Conditions Beyond School that Facilitate Mathematics Learning and Teaching
73
Amount of Reading Materials in the Home
74
Hours of Television Watched per Day
75
Student Absenteeism
76
Students' Perceptions of Mathematics
78
Summary
79
PROCEDURAL APPENDIX
si
DATA APPENDIX
97
iv
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
ME NATION'S
REPORT
CARO
EXECUTIVE SUMMARY
In 1988, Congress passed new legislation for the National Assessment of Hucational
Progress (NAFP), which included -- for the first time in the projeci's history -- a provision
authorizing voluntary state-by-state :1essments on a tria1 basis, in addition to continuing
its primary mission, the national
inents that NALP has conducted since its inception.
As a result of the leslation, the 1990 NALP progfam included a Trial State Assessment
Program in eighth-grade mathematics. National assessments in mathematics, reading,
writing, and science were conducted simultaneously in 1990 at grades four, eight, and
twelve.
For the Trial State Assessment, eighth-grade public-school students were assessed in each
of 37 states, the District of Columbia. and two territories in February 1990. The sample
was carefully designed to represent the eighth-grade public-school population in a state or
territory. Within each selected school, students were randomly chosen to participate in the
progam. Local school district personnel administered all assessment sessions, and the
contractor's staff monitored 50 percent of the sessions as part of the quality assurance
program designed to ensure that the sessions were being conducted uniformly. The results
of the monitoring indicated a high degree of quality and uniformity across sessions.
THE 1990 NAEP TRIAL STATE ASSESSMENT
1
Minnesota
In Minnesota, 97 public schools participated in the assessment. The weighted school
participation rate was 93 percent, which means that all of the eighth-grade students in this
sample of schools were representative of 93 percent of the eighth-grade public-school
students in Minnesota.
In each school, a random sample of students was selected to participate in the assessment.
As estimated by the sample, 1 percent of the eighth-grade public-school population was
classified as Limited English Proficient (LEP), while S percent had an Individualized
Education Plan (IEP). An IEP is a plan, written for a student who has been determined
to be eligible for special education, that typically sets forth goals and objectives for the
student and describes a program of activitits and/or related services necessary to achieve the
goals and objectives.
Schools were permitted to exclude certain students from the assessment. To be excluded
from the assessment, a student had to be categorized as Limited English Proficient or had
to have an Individualized Education Plan and (in either case) be judged incapable of
participating in the assessment. The students who were excluded from the assessment
because they were categorized as LEP or had an IEP represented 0 percent and 3 percent
of the population, respectively. In total, 2,584 eighth-grade Minnesota public-school
students were assessed. The weighted student participation rate was 95 percent. This
means that the sample of students who took part in the assessment was representative of
95 percent of the eligible eighth-grade public-school student population in Minnesota.
Students' Mathematics Performance
The average proficiency of eighth-grade public-school students from Minnesota on the
NAEP mathematics scale is 276. This proficiency is higher than that of students across the
nation (261).
Average proficiency on the NAEP scale provides a global view of eighth graders'
mathematics achievement; however, it does not reveal specifically what the students know
and can do in the subject. To describe the nature of students' proficiency in greater detail,
NAM) used the results from the 1990 national assessments of fourth-, eighth-, and
twelfth-grade students to define the skills, knowledge, and understandings that characterize
four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAM'
scale.
2
THE 1990 NAEP TRIAL STATE ASSTSSMENT
Minnesota
In Minnesota, 99 percent of the eighth graders, compared to 97 percent in the nation,
appear to have acquired skills involving simple additive reasoning and problem solving wifn
whole numben (level 200). However, many fewer students in Minnesota (20 percent) and
12 percent in the nation appear to have acquired reasoning and problem-solving skills
involving fractions, decimals, percents, elementary geometric properties, and simple
algebraic manipulations (level 300).
The Trial State Assessment included five content areas -- Numbers and Operations;
Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and
Functions. Students in Minnesota performed higher than students in the nation in all of
these five content areas.
Subpopulation Performance
In addition to the overall results, the 1990 Thal State Assessment permits reporting on the
performance of various subpopulations of the Minnesota eighth-grade student population
defined by raceiethnicity, type of community, parents' education level, and gender. In
Minnesota:
White students had higher average mathematics proficiency than did Black.
Hispanic, or Asian students.
Further, a geater percentage of White students than Black or Hispanic
students and about thc same percentage of White as Asian students attained
level 300.
The results by type of community indicate that the average mathematics
performance of the Minnesota students attending schools in advantaged
urban areas was about the same as that of students attending schools in
extreme rural areas and areas classified as "other".
In
Minnesota,
the
average mathematics proficiency of eighth-grade
public-school students having at least one parent who graduated from
college was approximately 30 points higher than that of students whose
parents did not graduate fwm high school.
The results by gender show that there appears to be no difference in the
average mathematics proficiency
of eighth-grade
males and females
attending public schools in Minnesota. In addition, there was no difference
between the percentages of males and females in Minnesota who attained
level
300,
Compared to the national results, females in Minnesota
performed higher than females across the country; males in Minnesota
performed higher than males across the countr.
1, 0
THE 1990 NAEP TRIAL STATE ASSESSMENT
3
Minnesota
A Context for Understanding Students' Mathematics Proficiency
Information on students' mathematics proficiency is valuable in and of itself, but it
becomes more useful for improving instruction and setting policy when supplemented with
contextual information about schools, teachers, and students.
To gather such information, the students participating in the 1990 Trial State Assessment,
their mathematics teachers, and the principals or other administrators in their schools were
asked to complete questionnaires on policies, instruction, and programs. Taken together,
the student, teacher, and school data help to describe some of the current practices and
emphases in mathematics education, illuminate some of the factors that appear to be
related to eighth-grade public-school students' proficiency in the subject, and provide an
educational context for understanding information about student achievement.
Some of the salient results for the public-school students in Minnesota are as follows:
About half of the students in Minnesota (52 percent) were in schools
where mathematics was identified as a special priority.
This is about the
same percentage as that for the nation (63 percent).
In Minnesota, 80 percent of the students could take an algebra course in
eighth grade for high-school course placement or credit.
A greater percentage of students in Minnesota were taking eighth-grade
mathematics (54 percent) than were taking a course in pre-algebra or
algebra (42 percent).
Across
the
nation,
62 percent
were taking
eighth-grade mathematics and 34 percent were taking a
course
in
pre-algebra or algebra.
According to their teachers, the greatest percentage of eighth-grade students
in public schools in Minnesota spent either 15 or 30 minutes doing
mathematics homework each day; according to the students, most of them
spent either 15 or 30 minutes doing mathematics homework each day.
Across the nation, teachers reported that the largest percentage of students
spent either 15 or 10 minutes doing mathematics homework each day,
while students reported either 15 or 30 minutes daily.
Students whose teachers placed heavy instructional emphasis on Algebra
and Functions had higher proficiency in this content area than students
whose teachers placed little or no emphasis on Algebra and Functions
Students whose teachers placed heavy instructional emphasis on Numbers
and Operations had lower proficiency in this content area than students
whose teachers placed little or no emphasis on Numbers and Operations.
4
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
In Minnesota, 12 percent of the eighth-grade students had mathematics
teachers who reported getting all of the resources they needed. while
23 percent of the students were taught by teachers who got only some or
nooe of the resources they needed. Across the nation, these figures were
13 percent and 31 percent, respectively.
In Minnesota, 20 percent of the students never used a calculator to work
problems in class, while 45 percent almost always did.
In
Minnesota, 44 percent of the students were being taught
by
mathematics teachers who reported having at least a master's or education
specialist's degree.
This compares to 44 percent for students across the
nation.
About three-quarters of the students (76 percent) had teachers who had the
highest level of teaching certification available. This is similar to the figure
for the nation, where 66 percent of students were taught by teachers who
were certified at the highest level available in their states.
Students in Minnesota who had four types of reading materials (an
encyclopedia, newspapers, magazines, and more than 25 books) at home
showed higher mathematics proficiency than did students with zero to two
types of these materials. This is similar to the results for the nation, where
students who had all four types of materials showed higher mathematics
proficiency than did students who had zero to two types.
Some of the eighth-grade public-school students in Minnesota (15 percent)
watched one hour or less of television each day; 7 percent watched six
hours or more. Average mathematics proficiency was lowest for students
who spent six hours or more watching television each day.
4
A
THE 1990 NAEP TRIAL STATE ASSESSMENT
5
Minnesorq
THE NATION'S
REPORT
CARD
INTRODUCTION
As a result of legislation enacted in 1988, the 1990 National Assessment of Educational
Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics.
The Trial State Assessment was conducted in February 1990 with the following
participants:
Alabama
Iowa
Ohio
Arizona
Kentucky
Oklahoma
Louisiana
Arkansas
Oregon
California
Maryland
Pennsylvania
Colorado
Michigan
Rhode Island
Connecticut
Minnesota
Texas
Delaware
Montana
Virginia
District of Columbia
Nebraska
West Virginia
Florida
New Hampshire
Wisconsin
Georgia
New Jersey
Wyoming
Hawaii
New Mexico
Idaho
New York
Illinois
North Carolina
Guam
Indiana
North Dakota
Virgin Islands
THE 1990 NAEP TRIAL STATE ASSESSMENT
7
Minnesota
This repc t describes the performance of the eighth-grade public-school students in
Minnesota and consists of three sections:
This Introduction provides background information about the Trial State
Assessment and this report. It also provides a profile of the eighth-grade
public-school students in Minnesota,
Part One describes the mathematics performance of the eighth-grade
public-school students in Minnesota, the Central region, and the nation.
Part Two relates students' mathematics performance to
contextual
information about the mathematics policies and instruction in schools in
Minnesota, the Central region, and the nation.
Overview of the 1990 Trial State Assessment
In 1988, Congress passed new legislation for the National Assessment of Educational
Progress (NAEP), which included -- for the first time in the project's history -- a provision
authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing
its primary mission, the national assessments that NAEP has conducted since its inception:
The National Assessment shall develop a trial mathematics assessment survey
instrument for the eighth grade and shall conduct a demonstration of the
instrument in 1990 in States which wish to participate, with the purpose of
determining whether such an assessment yields valid, reliable State representative
data.
(Section 406 (i)(2)(C)(i) of the General Education Provisions Act, as
amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(i)))
As a result of the legislation, the 1990 NAFP program included a Trial State Assessment
Program in eighth-grade mathematics. National assessments in mathematics, reading,
writing, and science were conducted simultaneously in 1990 at grades four, eight, and
twelve.
For the Trial State Assessment, eighth-grade public-school students were assessed in each
state or territory. The sample was carefully designed to represent the eighth-grade
public-school population in the state or territory. Within each selected school, students
were randomly chosen to participate in the program. Local school district personnel
administered all assessment sessions, and the contractor's staff monitored 50 percent of the
sessions as part of the quality assurance program designed to ensure that the sessions were
being conducted uniformly. The results of the monitoring indicated a high degree of quality
and uniformity across sessions.
14
8
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
The Trial State Assessment was based on a set of mathematics objectives newly developed
for the program and patterned after the consensus process described in Public Law 98-511,
Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988
legislation that auth.)rized the Trial State Assessment, the federal government arranged for
the National Science Foundation and the U.S. Department of Education to issue a special
grant to the Council of Chief State School Officers in mid-1987 to develop the objectives.
The development process included careful attention to the standards developed by the
National Council of Teachers of Mathematics,'
the formal mathematics objectives of
states and of a sampling of local districts, and the opinions of practitioners at the state and
local levels as to what content should be assessed.
There was an extensive review by mathematics educators, scholars, states' mathematics
supervisors, the National Center for Education Statistics (NCES), and the Assessment
Policy Committee (APC), a panel that advised on NAEP policy at that time. The
objectives were further refined by NAEP's Item Development Panel, reviewed by the Task
Force on State Comparisons, and resubmitted to NCES for peer review. Because the
objectives needed to be coordinated across all the grades for the national program, the final
objectives provided specifications for the 1990 mathematics assessment at the fourth,
eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight.
An overview of the mathematics objectives is provided in the Procedural Appendix.
This Report
This is a computer-generated report that describes the performance of eighth-grade
public-school students in Minnesota, in the Central region, and for the nation. Results also
are provided for groups of students defined by shared characteristics -- race/ethnicity, type
of community, parents' education level, and gender. Definitions of the subpopulations
referred to in this report are presented below. The results for Minnesota are based only
on the students included in the Trial State Assessment Program. However, the results for
the nation and the region of the country are based on the nationally and regionally
representative samples of public-school students who were assessed in January or February
as part of the 1990 national NAEP program. lise of the regional and national results from
the 1990 national NAEP program was necessary because the voluntary nature of the Trial
State Assessment Program did not guarantee representative nat.nal or regional results,
since not every state participated in the program.
National Council of Teachers of Mathernancs, Curricuhim and Evaluation Standardv pr School Mathematics
(Reston, VA: National Council of Teaclrrs of Mathematics, 1989).
THE 1990 NAEP TRIAL STATE ASSESSMENT
9
Minnesota
RACE/ETIENICITY
Results are presented for students of different racial/ethnic groups based on the students'
self-identification of their race/ethnicity according to the following mutually exclusive
categories: White, Black, Hispanic, Asian (including Pacific Islander), and American
Indian (including Alaskan Native). Based on criteria described in the Pmcedural Appendix,
there must be at least 62 students in a particular subpopulation in order for the results for
that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with
fewer than 62 students are not reported. However, the data for all students, regardless of
whether their racial/ethnic group was reported separately, were included in computing
overall results for Minnesota.
TYPE OF COMMUNITY
Results are provided for four mutually exclusive community types -- advantaged urban,
disadvantaged urban, extreme rural, and other -- as defined below:
Advantaged Urban: Students in this group live in metropolitan statistical areas
and attend schools where a high proportion of the students' parents are in
professional or managerial positions.
Disadvantaged Urban:
Students in this group live in metropolitan statistical
areas and attend schools where a high proportion of the students' parents are
on welfare or are not regularly employed.
Extreme Rural:
Students in this group live outside metropolitan statistical
areas, live in areas with a population below 10,000, and ittend schools where
many of the students' parents are farmers or farm workers.
Other: Students in this category attend schools in areas other than those defined
as advantaged urban, disadvantaged urban, or extreme rural.
The repo:ting of results by each type of community was also subject to a minimum student
samplc size of 62.
PARENTS' EDUCATION LEVEL
Students were asked to indicate the extent of schooling for each of their parents -- did not
finish high school, graduated high school, some education after high school, or gaduated
college. The response indicating the higher level of education was selected for reporting.
10
l'HE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
GENDER
Results are reported .-.,eparately for males and females.
REGION
The United States has been divided into four regions: Northeast, Southeast, Central, and
West. States included in each region are shown in Figure 1. All SO states and the District
of Columbia are listed, with the participants in the Trial State Assessment highlighted in
boldface type, Territories were not assigned to a region. Further, the part of Virginia that
is included in the Washington, DC, metropolitan statistical area is included in the
Northeast region; the remainder of the state is included in the Southeast region. Because
most of the students are in the Southeast region, regional comparisons for Virginia will be
to the Southeast.
FIGURF 1
I
Regions of the Country
THE NATION'S
REPORT
CARD
NORTHEAST
SOUTHEAST
CENTRAL
WEST
Connecticut
Alabama
Illinois
Alaska
Delaware
Arkansas
Indiana
Arizona
District of Columbia
Florida
Iowa
California
Maine
Gaorgia
Kansas
Colorado
Maryland
Kentucky
Michigan
Hawaii
Massachusetts
Louisiana
Minnesota
Idaho
New Hampshire
Mississippi
Missouri
Montana
New Jersey
North Carolina
Nebraska
Nevada
New York
South Carolina
North Dakota
New Mexico
Pennsylvania
Tennessee
Ohio
Oklahoma
Rhode Island
Virginia
South Dakota
Oregon
Vermont
West Virginia
Wisconsin
Texas
Virginia
Utah
Washington
Wyoming
THE 1990 NAEP TRIAL STATE ASSESSMENT
11
Minnesota
Guidelines for Analysis
This report describes and compares the mathematics proficiency of various subpopulations
of students -- for example, those who have certain demographic characteristics or who
responded to a specific background question in a particular way. The report examines the
results for individual subpopulations and individual background questions.
It does not
include an analysis of the relationships among combinations of these subpopulations or
background questions.
Because the proportions of students in these subpopulations and their average proficiency
are based on samples -- rather than the entire population of eighth graders in public schools
in the state or territory -- the numbers reported are necessarily estimates. As such, they are
subject to a measure of uncertainty, reflected in the standard error of the estimate. When
the proportions or average proficiency of certain subpopulations are compared, it is
essential that the standard error be taken into account, rather than relying solely on
observed similarities or differences. Therefore, the comparisons discussed in this report are
based on statistical tests that consider both the magnitude of the difference between the
means or proportions and the standard errors of those statistics.
The statistical tests determine whether the evidence -- based on the data from the groups
in the sample -- is strong enough to conclude that the means or proportions are really
different for those goups in the population.
If the evidence is strong (i.e., the difference is
statistically significant), the report describes the group means or proportions as being
different (e.g., one group performed higher than or lower than another group) -- regardless
of whether the sample means or sample proportions appear to be about the same or not.
If the evidence is not sufficiently strong (i.e., the difference is not statistically significa.nt),
the means or proportions are described as being about the same -- again, regardless of
whether the sample means or sample proportions appear to be about the same or widely
discrepant.
The reader is cautioned to rely on the results of the statistical tests -- rather than on the
apparent magnitude of the difference between sample means or proportions -- to determine
whether those sample differences are likely to represent actual differences between the
groups in the population. If a statement appears in the report indicating that a particular
goup had higher (or lower) average proficiency than a second group, the 95 percent
confidence interval for the difference between groups did not contain the value zero. When
a statement indicates that the average proficiency or proportion of some attribute was about
the same for two p-oups, the confidence interval included zero, and thus no difference could
be assumed between the goups. When three or more groups are being compared, a
Bonferroni procedure is also used, The statistical tests and Bonferroni procedure are
discussed in geater detail in the Procedural Appendix.
S
12
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
It is also important to note that the confidence intervals pictured in the figures in Part One
of this report are approximate 95 percent confidence intervals about the mean of a
particular population of interest. Comparing such confidence intervals for two populations
is not equivalent to examining the 95 percent confidence interval for the difference between
the means of the populations. If the individual confidence intervals for two populations
do not overlap, it is true that there is a statistically significant difference between the
populations. However, if the confidence intervals overlap, it is not always true that there
is not a statistically significant difference between the populations.
Finally, in several places in this report, results (mean proficiencies and proportions) are
reported in the text for combined groups of students. For example, in the text, the
percentage of students in the combined group taking either algebra or pre-algebra is giver.
and compared to the percentage of students enrolled in eighth-grade mathematics.
However, the tables that accompany that text report percentages and proficiencies
separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The
combined-group percentages reported in the text and used in all statistical tests are based
on unrounded estimates (i.e., estimates calculated to several decimal places) of the
percentages in each group. The percentages shown in the tables are rounded to integers.
Hence, the percentage for a combined group (reported in the text) may differ slightly from
the sum of the separate percentages (presented in the tables) for each of the groups that
were combined. Similarly, if statistical tests were to be conducted based on the rounded
numbers in the tables, the results might not be consonant with the results of the statistical
tests that are reported in the text (based on unrounded numbers).
THE 1990 NAEP TRIAL STA' E ASSESSMENT
13
Minnesota
Profile of Minnesota
EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS
Table 1 provides a profile of the demographic characteristics of the eighth-grade
public-school students in Minnesota, the Central region, and the nation. This profile is
based on data collected from the students and schools participating in the Trial State
Assessment.
TABLE 1
I Profile of Minnesota Eighth-Grade
I
Public-School Students
PERCENTAGE OF STUDENTS
-
WOO NAV TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
-
DEMOGRAPHIC SUBGROUPS
1
Race/Ethnicity
White
Black
Hispamc
Asian
American Indian
Type of Community
Advantaged urban
Disadvantaged urban
Extreme rural
Other
Parents' Education
Did not finish high school
Graduated high school
Some education after high school
Graduated college
Gender
Male
Female
Percentap
Porcentage
Percentage
90 ( 0.9)
79 ( 2.6)
70 ( 0.5)
2 ( 0.5)
13 ( 3.2)
16 ( 0.3)
3 ( 0.4)
5 ( 1.0)
10 ( 0.4)
3 ( 0.4)
1
( 0.4)
2 ( 0.5)
2 ( 0.5)
1 ( 0.4)
2 ( 0.7)
24 ( 3.3)
3 ( 3.1)
10 ( 3.3)
0 ( 0.0)
10 ( 4.3)
10 ( 2.8)
29 ( 4.6)
8 ( 6.0)
10 ( 3.0)
47 ( 5.3)
79 ( 7.7)
70 ( 4.4)
4 ( 0.3)
7 ( 0.9)
10 ( 0.8)
27 ( 1.0)
33 ( 2.1)
25 ( 1.2)
22 ( 0.8)
19 ( 0.9)
17 ( 0.9)
42 ( 1-2)
35 ( 1.8)
39 ( 1.9)
50 ( 1.0)
50 ( 1.4)
51 ( 1.1)
50 ( 1.0)
50 ( 1.4)
49 ( 1.1)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample. The percergages for Race/Ethnicity may not add to 100 percent because some
students categorized themselves as "Other."
This may also be true of Parents' Education, for which some
students responded "I don't know." Throughout this report, percentages less than 0.5 percent are reported as
0 percent.
14
:20
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
SCHOOLS AND STUDENIS ASSESSED
Table 2 provides a profile summarizing participation data for Minnesota schools and
students sampled for the 1990 Trial State Assessment. In Minnesota, 97 public schools
participated in the assessment. The weighted school participation rate was 93 percent,
which means that all of the eighth-grade students in this sample of schools were
representative of 93 percent of the eighth-grade public-school students in Minnesota.
TABLE 2
j
Profile of the Population Assessed in Minnesota
EIGHTH-GRADE PUBLIC SCHOOL
PARTICIPATION
Weighted school participation
rate before Substitution
Weighted school participation
rate after substitution
Number of schools originally
sampled
Number of schools not eligible
Number of schools in original
sample participating
Number of substitute schools
provided
Number of substitute schools
participating
Total number of participating
schools
108
3
94
5
3
97
EIGHTH-GRADE PUBLIC-SCHOOL STUDENT
PARTICIPATION
Weighted student participation
rate after make-ups
Number of students selected to
part!cipate in the assessment
Number of students withdrawn
from the assessment
Percentage of students who were
of Limited English Proficiency
Percentage of students excluded
from the assessment due to
Limited English Proficiency
Percentage of students who had
an Individualized Education Plan
Percentage of students excluded
from the assessment due to
Individualized Education Plan status
Number of students to be assessed
Number of students assessed
95%
2,907
105
1%
0%
8%
3°Ai
2,715
2,584
TH E 1990 NAEP TRIAL STATE ASSESSMENT
15
Minnesota
!n each school, a random sample of students was selected to participate in the assessment.
As estimated by the sample, 1 percent of the eighth-grade public-school population was
classified as Limited English Proficient (LEP), while 8 percent had an Individualized
Education Plan (IEP). An IEP is a plan, written for a student who has been determined
to be eligible for special education, that typically sets forth goals and objectives for the
student and describes a program of activities and/or related services necessary to achieve the
goals and objectives.
Schools were permitted to exclude certain students from the assessment. To be excluded
from the assessment, a student had to be categorized as Limited English Proficient or had
to have an Individualized Education Plan and (in either case) be judged incapable of
participating in the assessment. The students who were excluded from the assessment
because they were categorized as LEP or had an IEP represented 0 percent and 3 percent
of the population, respectively.
In total, 2,584 eighth-grade Minnesota public-school students were assessed. The weighted
student participation rate was 95 percent. This means that the sample of students who
took part in the assessment was representative of 95 percent of the eligible eighth-grade
public-school student population in Minnesota.
16
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
THE NATION'S
REPORT
CARD
PART ONE
How Proficient in Mathematics Are Eighth-Grade
Students in Minnesota Public Schools?
The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and
Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and
Algebra and Functions. Students' overall performance in these content areas was
summarized on the NAEP mathematics scaie, which ranges from 0 to 500.
This part of the report contains two chapters that describe the mathematics proficiency of
eighth-wade public-school students in Minnesota. Chapter 1 compares the overall
mathematics performance of the students in Minnesota to students in the Central region
and the nation. It also presents the students' average proficiency separately for the five
mathematics content areas. Chapter 2 summarizes the students' overall mathematics
performance for subpopulations defined by race/ethnicity, type of community, parents'
education level, and gender, as well as their mathematics performance in the five content
areas.
4. LI
THE 1990 NAEP TRIAL STATE ASSESSMENT
17
Minnesota
CHAPTER 1
Students' Mathematics Performance
As shown in Figure 2, the average proficiency of eighth-grade public-school students from
Minnesota on the NAEP mathematics scale is 276. This proficiency is higher than that
of students across the nation (261).2
FIGURE 2
I
Average Eighth-Grade Public-School
I
Mathematics Proficiency
NALP Mathematics Scale
200
225
250
275
300
500
n.-
Average
Proficiency
1-1,04
Minnesota
Central
Nation
216
265
261
(
(
(
0.9)
2.8)
1.4)
The standard errors are presented in parentheses.
With about 95 percent certainty, the average mathematics
proficiency for each population of interest is within
7±- 2 standard errors of the esnmated mean (95 percent
confidence interval, denoted by P44).
If the confidence intervals for the populations do not overlap, there is a
statistically significant difference between the populations.
2 Differences reported are statistically different at about the 95 percent certainty level. This moans that with
about 95 percvnt certainty there is a real difference in the average mathematics proficiency between the two
populations of interest.
18
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
LEVELS OF MATHEMATICS PROFICIENCY
Average proficiency on the NAEP scale provides a global view of eighth graders'
mathematics achievement; however, it does not reveal the specifics of what the students
know and can do in the subject. To describe the nature of students' proficiency in greater
detail, NAEP used the result! from the 1990 national assessments of fourth-, eighth-, and
twelfth-grade students to define the skills, knowledge, and understandings that characterize
four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP
scale.
To define the skills, knowledge, and understandings that characterize each proficiency level,
mathematics specialists studied the questions that were typically answered correctly by
most students at a particular level but answered incorrectly by a majority of students at thc
next lower level. They then summarized the kinds of abilities needed to answer each set
of questions. While defining proficiency levels below 200 and above 350 is theoretically
possible, so few students performed at the extreme ends of the scale that it was =practical
to define meaningful levels of mathematics proficiency beyond the four presented here.
Definitions of the four levels of mathematics proficiency are Oven in Figure 3.
It is
important to note that the definitions of these levels are based solely on student
performance on the 1990 mathematics assessment. The levels arc not judgmental standards
of what ought to bc achieved at a particular grade. Figure 4 provides the percentages of
students at or above each of these proficiency levels.
In Minnesota, 99 percent of the
eighth graders, compared to 97 percent in the nation, appear to have acquired skills
involving simple additive reasoning and problem solving with whole numbers (level 200).
However, many fewer students in Minnesota (20 percent) and 12 percent in the nation
appear to have acquired reasoning and problem-solving skills involving fractions, decimals,
percents, elementary geometric properties, and simple algebraic manipulations (level 300).
CONTENT AREA PERFORMANCE
As previously indicated, the questions comprising the Trial State Assessment covered five
content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis,
Statistics, and Probability; and Algebra and Functions. Figure 5 provides the Minnesota,
Central region, and national results for each content area. Students in Minnesota
performed higher than students in the nation in all of these five content areas.
THE 1990 NAEP TRIAL STATE ASSESSMENT
29
Minnesota
FIGURE 3
I
Levels of Mathematics Proficiency
THE NATION'S
REPORT Nip
CARD
I
200
Simple Additive Reasoning and Problem Solving with Whole
Numbers
Students at this level have some degree of understanding of simple quantitative relationships involving
whole numbers. They can solve simple addition and subtraction problems with and without regrouping.
Using a calculator, they can extend these abilities to multiplication and division problems. These students
can identify solutions to one-step word problems and seleCt the greatest four-diglt number in a list.
In measurement, these students can read a ruler as well as common weight and graduated scales. They
also can make volume comparisons based on visualization and determine the value of coins.
In geometry,
these students can recognize simple figures.
In data analysis, they are able to read simple bar graphs. In
the algebra dimension, these siudents can recognize translations of word problems to numerical sentences
and extend simple pattern sequences.
LEVEL 250 I Simple Multiplicative Reasoning and Two-Step Problem Solving
Students at this level have extended their understanding of quantitative reasoning with whole numbers from
additive to multiplicative settings.
They can solve routine one-step multiplication and division problems
involving remainders and two-step addition and subtraction problems involving money. Using a calculator,
they can identify solutions to other elementary two-step word problems.
In these basic problem-solving
situations, they can identify missing or extraneous information and have some knowledge of when to use
computational estimation. They have a rudimentary understanding of such concepts as whole number place
value, "even," "factor," and "multiple."
in measurement, these students can use a ruler to measure objects, convert units within a system when the
conversions require multiplication, and recognize a numerical expression solving a measurement word
problem.
In geometry, they demonstrate an initial understanding of basic terms and properties, such as
parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use
information from graphs to solve simple prnblems.
They are beginning to understand the relationship
between proportion and probability.
In algebra, they are beginning to deal informally with a variable
through numerical substitution in the evaluation of simple expressions.
20
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
FIGURE 3
I
Levels of Mathematics Proficiency
(continued)
I
LEVEL 300
Reasoning and Problem Solving involving Fractions, Docimals,
Percents, Elementary Geometric Properties, and Simple Algebraic
Manipulations
Students at this level are able to represent, interpret, and perform simple operations with fractions and
decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, and
recognize the equivalence between common fractions and decimals, including pictorial representations.
They can interpret the meaning of percents less than and greater than 100 and apply the concepts of
percentages to solve simple problems. These students demonstrate some evidence of using mathematical
notation to interpret expressions, including those with exponents and negative integers.
In measurement, these students can find the perimeters and areas of rectangles, recognize relationships
among common units of measure, and use proportional relationships to solve routine problems involving
similar triangles and scale drawings.
In geometry, they have some mastery of the definitions and
properties of geometric figures and solids.
In data analysis, these students can Calculate averages, Select and interpret data from tabular displays,
pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding
of sample bias.
In algebra, they can graph points in the Cartesian plane and perform simple algebraic
manipulations suCh as simplifying an expression by collecting like terms, identifying the solution to open
linear sentences and inequalities by substitution, and checking and graphing an interval representing a
compound Inequality when it is described in words.
They can determine and apply a rule for simple
functional relations and extend a numerical pattern.
LEVEL 350
Reasoning and Problem Solving Involving Geometric Relationships,
Algebraic Equations, and Beginning Statistics and Probability
Students at this level have extended their knowledge of nurntier and algebraic understanding to include
some properties of exponents.
They can recognize scientific notation on a calculator and make the
transition between scientific notation and decimal notation.
In measurement, they can apply their
knowledge of area and perimeter of rectangles and triangles to solve problems.
They can find the
circumferences of circles and the surface areas of solid figures.
In geometry, they can apply the
Pythagorean theorem to solve problems involving indirPct measurement. These students alSo can apply
their knowledge of the properties of geometric figures
)Ive problems, such as determining the slope of
a line.
in data analysis, these students can compute means from frequency tables and determine the probability
of a simple event. In algebra, they can identify an equation describing a linear relation provided in a table
and solve literal equations and a system of two linear equations. They are developing an understanding
of linear functions and their graphs, as well as functional notation, including the composition of functions.
They can determine the nth term of a sequence and give counterexamples to disprove an algebraic
generalization.
THE 3990 NAEP TRIAL STATE ASSESSMENT
21
Minnesota
FIGURE 4
I Levels of Eighth-Grade Public-School
Mathematics Proficiency
LEVEL 350
State
Region
Nation
LEVEL 300
State
Region
Nation
LEVEL 250
State
Region
Nation
LEVEL 200
State
Region
Nation
1-4.4
1.01"'""rni
1-1041
1-4.0.04
Hal
0-1,0
PM
20
40
so
80
100
Percentage at or Above Proficiency Levels
The standard errors are presented in parentheses. With about 95 percent certainty, the value
for each population of interest is within i 2 standard errors of the estimated percentage (95
percent confidence interval, denoted by P+1),
If the confidence intervals for the populations
da not overlap, there is a statistically significant difference between the populations.
22
THE 1990 NAEP TRIAL STATE ASSESSM ENI
Percantage
0 ( 0.1)
( 0.2)
( 0.2)
20 ( 1,1)
12 ( 2.5)
12 (
1.2)
82 (
1.0)
70 ( 3.2)
64 (
1.6)
99 ( 0.3)
90 ( 0.9)
97 ( 0.7)
Minnesota
FIGURE 5
I Eighth-Grade Public-School Mathematics
Content Area Performance
State
Region
Nation
State
Region
Nation
State
Region
Nation
State
Region
Nation
State
Region
Nation
0
200
225
250
275
300
Average
Prolicleicy
279 ( 1.0)
270 ( 2.7)
266 ( 1.4)
272 ( 1.1)
263 ( 3.4)
256 ( 1.7)
273 ( 1.1)
262 ( 3.1)
259 ( 1.4)
279 ( 0.9)
265 ( 3.2)
262 ( 1.8)
274 ( 0.9)
263 ( 2.1)
260 ( 1.3)
500
Mathematics Subscale Proficiency
The standard errors are presented in parentheses.
With about 95 percent certainty, the
average mathematics proficiency for each population of interest is within + 2 standard
errors of the estimated mean (95 percent confidence interval, denoted by 14-4).
If the
confidence intervals for the populations do not overlap, there is a statisucally sigrnficant
difference between the populations.
THE 1990 NAEP TRIAL STATE ASSESSMENT
23
CHAPTER 2
Mathematics Performance by Subpopulations
In addition to the overall state results, the 1990 Trial State Assessment included reporting
on the performance of various subgroups of the student population defined by
race/ethnicity, type of community, parents' education level, and gender.
RACE/ETHNICITY'
The Trial State Assessment results can be compared according to the different racialjethnic
groups when the number of students in a raciaLethnic group is sufficient in size to be
reliably reported (at least 62 students). Average mathematics performance results for
White, Black, Hispanic, and Asian students from Minnesota are presented in Figure 6.
As shown in Figure 6, White students demonstrated higher average mathematics
proficiency than did Black, Hispanic, or Asian students.
Figure 7 presents mathematics perfbrmance by proficiency levels. The figure shows that a
geater percentage of White students than Black or Hispanic students and about the same
percentage of White as Asian students attained level 300.
24
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
FIGURE 6
I Average Eighth-Grade Public-School
I Mathematics Proficiency by Race/Ethnicity
NAEP Mathematics Scale
200
225
250
275
300
500
Tie
NOWT
CMO
Average
Proficiency
1111,004
0-001
1formsw4
Minnesota
Wtilte
-VS (
Black
2*
4.9$
Hispanic
( 3:7)
Asian
IN ( 44)
Central
White
272 ( 2.6)
Black
231
3.6)f
Hispanic
14" ( a")
Asian
( ***)
Nation
White
IN ( 1.5)
Black
2
( 2.8)
Hispanic
243 ( 2A)
Asian
200 ( 5.6)1
The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics
proficiency for each population of interest is within
t 2 standard errors of the estimated mean (95 percent
confidence interval, denoted byI-4-4). If the confidence intervals for the populations do not overlap, there is a
statistically significant difference between the populations.
! Interpret with caution -- the nature of the sample
does not allow accurate determination of the variability of this estimated mean proficiency. *1" Sample size is
insufficient to permit a reliable estimate (fewer than 62 students).
0")
THE 1990 NAEP TRIAL STATE ASSESSMENT
25
Minnesota
FIGURE 7
I
Levels of Eighth-Grade Public-School
I Mathematics Proficiency by Race/Ethnicity
LEVEL 300
State
White
Black
Hispanic
Asian
Region
White
Black
Hispanic
Asian
Nation
White
Black
Hispanic
Asian
LEVEL 250
State
White
Black
Hispanic
Asian
Region
White
Black
Hispanic
Asian
Nation
White
Black
Hispanic
Asian
LEVEL 200
Stat.
White
Black
Hispanic
Asian
Region
White
Black
Hispanic
Asian
Nation
White
Black
Hispanic
Asian
1-0-00mq
111141
20
40
60
80
Percentage at or Above Proficiency Levels
The standard errors are presented in parentheses. With about 95 percent certainty, the value
for each population of interest is within
t 2 standard errors of the estimated percentage (95
percent confidence interval, denoted by 1-+4).
If the confidence intervals for the populations
do not overlap, there is a statistically significant difference between the populations.
Proficiency level 350 is not presented in this figure because so few students attained that level.
t Interpret with caution -- the nature of the sample does not allow accurate determination
of the variability of this estimated mean proficiency. "* Sample size is insufficient to permit
a reliable estimate (fewer than 62 students).
100
26
THE 1990 NAEP TRIAL STATE ASSESSMENT
22 (
1.2)
6 ( 2.8)1
3
( 2.5)
13 ( 5.7)
15 (
1.5)
2 (
1.3)
3
(
1.1)
31
(
6.2)1
85 ( 0.9)
34
(
7.4)1
37
( 5.8)
71
( 5.8)
75
(
3.1 )
23 (
4,7)1
:us )
puot
**)
74
( 1.8)
30 (
3.4)
41
( 4.5)
SO ( 5.6)1
100 (
0.2)
87 ( 6.5)1
92 ( 3.3)
$118
(
1.9)
100 ( 0.4)
91
( 4.4)i
mut )
'4"
ea
( 0.4)
1118
( 3.1)
93 (
1.6)
97 ( 2.5)1
Minnesota
TYPE OF COMMUNITY
Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students
attending public schools in advantaged urban areas, extreme mai areas, and arms
classified as "other". (These are the "type of community" groups in Minnesota with
student samples large enough to be reliably reported.) The results indicate that the average
mathematics performance of the Minnesota students attending schools in advantaged urban
areas was about the same as that of students attending schools in extreme rural areas and
areas classified as "other".
FIGURE 8
Average Eighth-Grade Public-School
Mathematics Proficiency by Type of
Community
wwwAr
NAEP Mathematics Scale
200
225
250
275
300
SOO
WC
INONT
CAM
Average
Proficiency
Minnesota
tr
Advantaged urban
277
1.7)
til
Extreme rural
1.45)
144
Other
271
( 1.3)
Central
Advantaged urban
.molg ( *el
Extreme rural
w
1--1004
Other
1111
( 3.4)
Nation
Advantaged urban
211
( 3AI
1-4144.04
Extreme rural
201
(
Other
2111
( 1.6)
The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics
proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent
confidence interval, denoted 'by 1-4-1).
If the confidence intervals for the populations do not overlap, there is a
statistically significant difference between the populations.
Interpret with caution -- the nature of the sample
does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is
insufficient to permit a re:,able estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
27
Minnesota
FIGURE 9
LEVEL 300
State
Adv. urban
Ext. rural
Other
Region
My. urban
Ext. rural
Other
Nation
Mv. urban
Ext. rural
Other
LEVEL 250
State
Adv. urban
Ext. rural
Other
Region
Adv. urban
Ext. rural
Other
Nation
Mv, urban
Ext. rural
Other
LEVEL 200
state
Adv. urban
Ext. rural
Other
Region
Mv. urban
Ext. rural
Other
Nation
Mv. urban
Ext. rural
Other
Levels of Eighth-Grade Public-School
Mathematics Proficiency by Type of
Community
20
40
60
80
Percentage at or Above Proficiency Levels
The standard errors are presented in parentheses. With about 95 percent certainty, the value
for each population of interest is within ± 2 standard errors of the estimated percentage (95
percent confidence interval, denoted by 1-44).
If the coi-.fidence intervals for the populations
do not overlap, there
is a statistically significant difference between the populations.
Proficiency level 350 is not presented in this figure because so few students attained that level.
! Interpret with caution -- the nature of the sample does not allow accurate determination
of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit
a reliable estimate (fewer than 62 student.$).
Percentage
22
( 2.3)
18
( 2.1)
23 ( 1.9)
*)
13
( 2.9)
4.8))
(
2.3)1
12
( 1.2)
82
( 1.8)
84
( 1.9)
85
( 1.7)
.** )
pm*
* )
73 ( 4.2)
83
(
4.6)1
58
( 6.2)1
$4
( 2.3)
90
( 0.6)
100
( 0.3)
100
( 0.2)
*Am )
RI* )
90
( 0.9)
100
( 0.0)
97
(
2.8)1
97
( 1.0)
100
25
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
PARENTS' EDUCATION LEVEL
Previous NAEP findings have shown that students whose
parents are better educated tend
to have higher mathematics pmficiency (see Figures 10 and 11). In Minnesota, the average
mathematics proficiency of eighth-grade public-school students having at least one parent
who graduated from college was approximately 30 points higber than that of students who
reported that neither parent graduated from high school. As shown in Table 1 in the
Introduction, about the same percentage of students in Minnesota (42 percent) and in the
nation (39 percent) had at least one parent who graduated from college. In comparison,
the percentage of students who reported that neither parent graduated from high school
was 4 percent for Minnesota and 10 percent for the nation.
FIGURE 10
I Average Eighth-Grade Public-School
i Mathematics Proficiency by Parents' Education
Minnosota
HS non-graduate
HS graduate
Some college
College graduate
Cntral
HS non-graduate
HS graduate
Some college
College graduate
Nation
HS non-graduate
HS graduate
Some college
College graduate
The standard errors are presented m parentheses. With about 95 percent certainty, the average mathematics
proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent
confidence interval, denoted by 14-9. If the confidence intervals for the populations do not overlap, there is a
statistically significant difTerence between the populations. *** Sample size is insufficient to permit a reliable
esumate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
29
Minnesota
r-v NATION'S
IOW
FIGURE 11
I
Levels of Eighth-Grade Public-School
CARD
Mathematics Proficiency by Parents' Education
LEVEL 300
State
HS non-grad.
HS graduate
Some college
College grad.
Region
HS non-grad.
HS graduate
SOO* COltege
College grad.
Nation
HS non-grad.
HS graduate
Some college
College grad.
LEVEL 250
State
HS non-grad.
HS graduate
Some college
College grad.
Region
HS non-grad.
HS graduate
Some college
College grad.
Nation
HS non-grad,
HS graduate
Some college
College WV.
LEVEL 200
State
HS non-grad.
HS graduate
Some college
College grad.
Region
HS non-grad.
HS graduate
Some college
College grad.
Nation
HS non-grad.
HS graduate
Some college
College grad.
5 ( 2.8)
( 1.7)
25 ( 2.0)
30 ( 1.7)
PIXCX
( ***)
( 3.9)
14 ( 3.4)
17 ( 3.7)
1
( 0.9)
5 ( 1.5)
12 ( 1.4)
21
( 1.9)
59 ( 6.7)
72
( 2.1)
92 ( 1.5)
99 (
1.4)
ROM
( Ad)
96 ( 4.1)
75 ( 5.1)
79 ( 3.9)
37 ( 4.6)
56 ( 2,7)
71
( 2.6)
75 ( 2.0)
97 ( 2.3)
99 ( 0.5)
100 ( 0.0)
100 (
0,3)
nom ( .)
( 1.2)
100 ( 0.0)
99 ( 0.9)
96 ( 1.9)
( 0.8)
0
20
40
60
80
Percentage at or Above Proficiency Levels
The standard errors are presented in parentheses. With about 95 percent certainty, the value
for each population of interest is within ±
2 standard errors of the estimated percentage (95
percent confidence interval, denoted by 1-4-4).
If the confidence intervals for the populations
do not overlap, there is a
statistically significant difference between the populations.
Proficiency level 350 is not presented in this figure because so few students attained that level,
*** Sample size is msufficient to permit a reliable estimate (fewer than 62 students).
100
g.)
30
THE 1990 NAEP TRIAL STATE ASSESSMENT
99 ( 0.7)
SO ( 0.7)
Minnesota
GENDER
As shown in Figure 12, there appears to be no difference in the average mathematics
proficiency of eighth-grade males and females attending public schools in Minnesota.
Compared to the national results, females in Minnesota performed higher than females
across the country; males in Minnesota performed higher than males across the country.
FIGURE 12
I Average Eighth-Grade Public-School
Mathematics Proficiency by Gender
Minnesota
Male
Female
Central
Nate
Female
Nation
Male
Female
The nandard errors are presented in parentheses. With about 95 percent certainty, the average mathematics
proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent
corfidence interval, denoted by 1-4-1).
If the confidence intervals for the populations do not overlap, there is a
statistically significant difference between the populations.
As shown in Figure 13, the= was no difference between the percentages of males and
females in Minnesota who attained level 200. The percentage of females in Minnesota who
attained level 200 was greater than the percentage of females in the nation who attained
level 200. Also, the percentage of males in Minnesota who attained level 200 was greater
than the percentage of males in the nation who attained level 200.
THE 1940 NAEP TRIAL STATE ASSESSMENT
31
Minnesota
FIGURE 13
I
Levels of Eighth-Grade Public-School
I Mathematics Proficiency by Gender
LEVEL 300
State
Male
Female
Region Male
Female
Nation
Male
Female
LEVEL 250
State
Male
Female
Region Male
Female
Nation
Male
Female
LEVEL 200
State
Male
Female
Region Male
Female
Nation
Male
Female
20
40
ea
80
100
Percentage at or Above Proficiency Levels
The standard errors are presented in parentheses. With about 95 percent certainty, the value
for each population of interest is within
2 standard errors of the estimated percentage (95
percent confidence interval, denoted by 1-0-4). If the confidence intervals for the populations
do not overlap, there is a statistically significant difference between the populations.
Proficiency level 350 is not presented in this figure because so few students attained that level.
32
THE 1990 NAEP TRIAL STATE ASSESSMENT
22 ( 1.5)
19
( 1.2)
14
( 4.8)
( 2.3)
14
( 1.7)
10
( 1.3)
811
( 1.3)
92 ( 1.3)
( 3.3)
71
( 4.0)
64
( 2.0)
54
( 1.8)
91) ( 0.4)
99
( 0.3)
99
( 0.6)
011
( 1.2)
97
( 0.9)
97
( 0.8)
Minnesota
In addition, there was no difference between the percentages of males and females L.1
Minnesota who attained level 300. The percentage of females in Minnesota who attained
level 300 was geater than the percentage of females in the nation who attained level 300.
Also, the percentage of males in Minnesota who attained level 300 was greater than the
percentage of males in the nation who attained level 300.
CONTENT AREA PERFORMANCE
Table 3 provides a summary of content area performance by race/ethnicity, type of
community, parents' education level, and gender.
THE 1990 NAEP TRIAL STATE ASSESSMENT
33
Minnesota
TABLE 3
I Eighth-Grade Public-School Mathematics
I Content Area Performance by Subpopulations
AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS
1910 NAEP TRIAL
STATE ASSESSMENT
Numbers and
Operations
Massursat"
1
"saw"
Data Analysis,
Statistics' ana
Probability
"IbraFixoctkomand
TOTAL
PraNciancy
Pnaliciancy
Prattolancy
Prods:lam
Prodloisncy
State
279 ( 1.0)
272 ( 1.1)
273 ( 1.1)
279 ( 0.9)
274
0.9)
Region
270 ( 2/)
263 ( 3.4)
262 ( 3.1)
265 ( 3.2)
263
2.1)
Nation
208 ( 1.4)
2W ( 1.7)
259 ( 1.4)
262 ( 1.8)
240
1.3)
RACE/ETItNICITY
11111 its
State
262 ( 1.0)
275 ( 1.1)
275 ( 1.0)
282 ( 0.8)
278 ( 0.0)
Region
276 ( 2.9)
271 ( 3.7)
268 ( 3.0)
273 ( 3.1)
289 ( 2.3)
Nation
273 ( 1.6)
267 ( 2.0)
267 ( 1.5)
272 ( 1.8)
268 ( 1.4)
Slack
State
242 ( 4.6)1
233 ( 7.8)1
235 ( 5.7)1
245 ( 5.8)1
240 ( 6.0)1
Region
241 ( OS)!
223 ( 3.5)1
231 ( 4.2)1
225 ( 7.0)1
231 ( 1.9)1
Nation
244 ( 3.1)
227 ( 3.6)
234 ( 2.8)
231 ( 3.8)
237 ( 2.7)
Hispanic
State
Region
245 (
( 4.7)
...)
228 (
( 4.7)
...)
241 (
( 3.6)
...)
240 (
( 4.5)
...)
239 (
(
4.2)
***)
Nation
248 ( 2.7)
238 ( 3.4)
243 ( 3.2)
239 ( 3.4)
243 ( 3.1)
Asian
State
Region
271 (
( 5.0)
252 (
( 6.3)
...)
267 ( 4.9)
261 (
( 52)
270 (
( 82)
Nation
285 ( 5.9)1
278 ( 6.3)1
275 ( 5.9)1
282 ( 6.9)1
278 ( 6.7)1
TYPE Of COMMUNITY
Advantagad urban
State
Region
280 (
(
1.9)
"")
272 (
( 2.1)
...)
273 ( 1.8)
282 (( 1.8)
...)
Nation
283 ( 3.2)!
281 ( 3.2)1
277 ( 5.2)1
285 ( 4.8)1
277 ( 4.8)1
Extrema rural
State
Region
280 (
( 2.1)
...)
( ...)
273 (
( 2.1)
...)
278 (
( 1.7)
.4.)
.4.
( ...)
Nation
258 ( 4.3)1
254 ( 4.2)1
253 ( 4.5)1
257 ( 5.0)I
256 ( 44)1
Other'
State
282 ( 1,4)
275 ( 1.7)
276 ( 1.6)
282 ( 1.7)
277 ( 1.3)
Region
273 ( .3.5)
266 ( 4.3)
264 ( 3.7)
267 ( 4.1)
265 ( 2.8)
Nation
288 ( 1.9)
257 ( 2A)
259 ( 1.7)
261 ( 2.2)
261 ( 1.7)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
34
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE 3
I Eighth-Grade Public-School Mathematics
(continued)
I Content Area Performance by Subpopuiations
AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS
1900 NAEP TRIAL
STATE ASSESSMENT
Nuatdael add
Operations
Meaurement
Geometry
Ana
Data
lysis,
Statistics, and
Probability
and
Functions
TOTAL
Proaciency
Proficiency
Proncioncy
!Widow/
Preadincy
State
279 ( 1.0)
272 ( 1.1)
273 ( 1.1)
279 ( 0.9)
274 ( 0.9)
Region
270 ( 2.7)
263 ( 3.4)
262 ( 3.1)
265 ( 3.2)
263 ( 2.1)
Nation
266 ( 1.4)
258 ( 1.7)
256 ( 1.4)
202 ( 1.8)
200 ( 1.3)
PARENTS' EDUCATION
NS nort-graduate
State
Region
258
(
251 ( 3.9)
.44)
257 (
Mk* ( 4.0)
Man
253 ( 4.0)
Nation
247 ( 2.4)
237 ( 3.6)
242 ( 2.2)
240 ( 3.1)
242 ( 3.0)
HS graduate
State
268 ( 1.8)
258 ( 2.0)
262 ( 1.8)
267 ( 1.5)
262 ( 1.4)
Region
289 ( 2.5)
258 ( 3.8)
257 ( 9.4)
200 ( 3.2)
250 ( 3.4)
Nation
259 ( 1.8)
248 ( 2.1)
252 ( 1.6)
253 ( 22)
253 ( 2.0)
Some college
State
285 ( 1.4)
284 ( 1.8)
278 ( 1.3)
266 ( 1.3)
280 ( 1.3)
Region
275 ( 32)
270 ( 5.7)
264 ( 4.9)
273 ( 4.7)
266 ( 3.7)
Nation
270 ( 1.5)
264 ( 2.7)
262 ( 2.0)
269 ( 2.4)
2621 2.2)
College graduate
State
288 ( 1.4)
281 ( 1.3)
281 ( 1.2)
269 ( 1.2)
263 ( 1$)
Region
277 ( 4.2)
270 ( 4.4)
270 ( 4.3)
273 ( 4.5)
271 ( 3-1)
Nation
278 ( 1.8)
272 ( 2.0)
270 ( 1.6)
276 ( 2.2)
273 ( 1.7)
GENDER
Male
State
279 ( 1.2)
278 ( 1.3)
273 ( 1.4)
279 ( 1.2)
272 ( 1.2)
Region
271 ( 3.9)
.287 ( 4.8)
264 ( 3.7)
265 ( 3.4)
263 ( 2.2)
Nation
266 ( 2.0)
262 ( 2.3)
260 ( 1.7)
2e2 ( 2.1)
260( 1.8)
Female
State
279 (
1.2)
268 (
1.4)
272 (
1.2)
279 ( 1.2)
275 ( 1.1)
Region
270 ( 2.7)
259 ( 3.4)
200 ( 3.1)
26$ ( 4.0)
262 ( 2.8)
Nation
266 ( 1.4)
253 ( 1.6)
258 ( 1.5)
281 ( 1.9)
260 ( 1.4)
The standard errors of the estimated statistics appear in parentheses.
It can be said with a
certainty that, for each population of interest, the value for the entire population is within ± 2
of the estimate for the sample.
*** Sample size is insufficient to permit a reliable estimate
students).
bout 95 percent
standard errors
(fewer than 62
ft I
THE 1990 NAEP TRIAL STATE ASSESSMENT
35
Minnesota
THE NATION'S
REPORT
CARD
PART TWO
Finding a Context for Understanding Students'
Mathematics Proficiency
Information on students' mathematics proficiency is valuable in and of itself, but it
becomes more useful for improving instruction and setting policy when supplemented with
contextual information about schools, teacher
'students.
To gather such information, the students participating in the 1990 Trial State Assessment,
their mathematics teachers, and the principals or other administrators in their schools were
asked to complete questionnaires on policies, instruction, and programs. Taken together,
the student, teacher, and school data help to describe some of the current practices and
emphases in mathematics education, illuminate some of the factors that appear to be
related to eighth-grade public-school students' proficiency in the subject, and provide an
educational context for understanding information on student achievement. It is important
to note that the NAEP data cannot establish cause-and-effect links between various
contextual factors and students' mathematics proficiency. However, fir results do provide
information about important relationships between the contextual factors and proficiency.
The contextual information provided in Part Two of this report focuses on four major
areas: instructional content, instructional practices, teacher qualifications, and conditions
beyond school that facilitate learning and instruction -- fundamental aspects of the
educational process in the country.
THE 1990 NAEP TRIAL STATF: ASSESSMENT
37
Minnesota
Through the questionnaires administered to students, teachers, and principals, NAEP is
able to provide a broad picture of educational practices prevalent in American schools and
classrooms. In many instances, however, these findings contradict our perceptions of what
school is like or educational researchers' suggestions about what stratesOes work best to help
students learn.
For example, research has indicated new and more successful ways of teaching and learning,
incorporating more hands-on activities and student-centered learning techniques; however,
as described in Chapter 4, NAEP data indicate that classroom work is still dominated by
textbooks or worksheets. Also, it is widely recognized that home environment has an
enormous impact on future academic achievement. Yet, as shown in Chapters 3 and 7,
large proportions of students report having spent much more time each day watching
television than doing mathematics homework.
Part Two consists of five chapters. Chapter 3 discusses instnictional content and its
relationship to students' mathematics proficiency. Chapter 4 focuses on instructional
practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter
6 provides information about teachers, and Chapter 7 examines students' home support for
learning.
4 3
38
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
CHAPTER 3
What Are Students Taught in Mathematics?
In response to the continuing swell of information about the poor mathematics
achievement of American students, educators and policymakers have recommended
widespread reforms that are changing the direction of mathematics education. Recent
reports have called for fundamental revisions in curriculum, a reexamination of tracking
practices, improved textbooks, better assessment, and an increase in the proportions of
students in high-school mathematics programs.' This chapter focuses on curricular and
instructional content issues in Minnesota public schools and their relationship to students'
proficiency.
Table 4 provides a profile of the eighth-grade public schools' policies and staffmg. Some
of the salient results are as follows:
About half of the eighth-grade students in Minnesota (52 percent) were in
public schools where mathematics was identified as a special priority. This
compares to 63 percent for the nation.
3 Curtis McKnight, ci al., The Underachieving Curriculum. Assessing U.S. School Mathematks from an
International Perspective, A Nati(' -al Report on the Second International Mathematics Study (Champaign,
Stipes Publishing Company, 1987).
Lynn Steen, Ed. Everybody Counts
A Report to the Nation on the Future of Mathematics Education
(Washington, DC: National Academy Press, 1989).
THE 1990 NAEP TRIAL STATE ASSESSMENT
19
Minnesota
In Minnesota, 80 percent of the students could take an algebra course in
eighth grade for high school course placement or credit.
Many of the students in Minnesota (84 percent) were taught mathematics
by teachers who teach only one subject.
a
More than half (63 percent) of the students in Minnesota were typically
taught mathematics in a class that was grouped by mathematics ability.
Ability grouping was equally prevalent across the nation (63 percent).
TABLE 4
I Mathematics Policies and Practices in
I Minnesota Eighth-Grade Public Schools
PERCENTAGE OF STUDENTS
1900 NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
_
Percentage of eighth-grade students in public
schools that identified mathematics as
recelvklg special emphasis in school-wide
goals and objectives, instruction, In-service
training, etc.
Percentage of eighth-grade public-school students
who are offered a course in algebra for
high school course placement or credit
Percentage of eighth-grade students in public
schools who are taught by teachees who teach
only mathematics
Percentage of eighth-grade students in public
schools who are assigned to a mathematics
dan by their abNity in mathematics
Percentage of eighth-grade students in public
schools who receive four or more hours of
mathematics Instruction per week
Percentage
Parcente90
Penentage
52 ( 4.5)
70 (13.8)
83 ( 6.9)
80 ( 4.1)
89 (15.4)
76 ( 4.6)
84 ( 3.1)
$7 ( 7.8)
91 ( 3.3)
63 ( 4.0)
00 ( 5.7)
63 ( 4.0)
42 ( 4.0)
25 ( 8.6)
30 ( 4.4)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
40
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
CURRICULUM COVERAGE
To place students' mathematics proficiency in a curriculum-related context, it is necessary
to examine the extent to which eighth graders in Minnesota are taking mathematics
courses. Based on their responses, shown in Table 5:
A greater percentage of students in Minnesota were taking eighth-grade
mathematics (54 percent) than were taking a course in pre-algebra or
algebra
(42 percent).
Across the
nation,
62 percent were
taking
eighth-grade mathematics and 34 percent were taking a course
in
pm-algebra or algebra.
Students in Minnesota who were enrolled in pre-algebra or algebra courses
exhibited higher average mathtmatics proficiency than did those who were
in eighth-grade mathematics courses. This result is not unexpected since
it is assumed that students enrolled in pm-algebra and algebra courses may
be the more able students who have already mastered the general
eiegh-grade mathematics curriculum.
TABLE 5
I Students' Reports on the Mathematics Class
I They Are Taking
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL STATE ASSESSMENT
Mkinesota
Central
Nation
_
Percentage
and
Proficiency
Percentage
and
Proficiency
Percentage
and
Proficiency
What kind of mathematics class are you
taking this year?
Eighth-grade mathematics
54 ( 3.0)
si
4.8)
62 ( 2.1)
266 ( 1.3)
255 ( 3.1)
251 ( 1.4)
Pre-aigebra
25 ( 2.4)
22 ( 4.3)
19 ( 1.9)
281 ( 1.1)
276 ( 3.1)1
272 ( 2.4)
Algebra
17 ( 1.4)
15 ( 2.8)
15 ( 1.2)
303 ( 1.6)
289 ( 5.4)
296 ( 2.4)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because a small number of students
reported taking other mathematics courses.
! Interpret with caution -- the nature of the sample does not allow
accurate determination of the variability of this estimated mean proficiency.
THE 1990 NAEP TRIAL STATE ASSESSMENT
41
Minnesota
Further, from Table A5 in the Data Appendix:4
About the same percentage of females (42 percent) and males (42 percent)
in Minnesota were enrolled in pre-algebra or algebea courses.
In Minnesota, 43 percent of White students, 29 percent of Black students,
30 percemt of Hispanic students, and 46 percent of Asian students were
enrolled in pre-algebra or algebra courses.
Similarly, 41 percent of students attending schools in advantaged urban
areas, 40 percent in schools in extreme rural areas, and 41 percent in
schools in areas classified as "other" were enrolled in pre-algebra or algebra
courses.
MATHEMATICS HOMEWORK
To illuminate the relationship between homework and proficiency in mathematics, the
assessed students and their teachers were asked to report the amount of time the students
spent on mathematics homework each day. Tables 6 and 7 report the teachers' and
students' responses, respectively.
According to their teachers, the greatest percentage of eighth-grade students in public
schools in Minnesota spent either 15 or 30 minutes doing mathematics homework each
day; according to the students, the greatest percentage spent either 15 or 30 minutes doing
mathematics homework each day. Across the nation, according to their teachers, the
largest percentage of students spent either 15 or 30 minutes doing mathematics homework
each day, while students reported spending either 15 or 30 minutes daily.
Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix):
In Minr,esota, 2 percent of the students spent no time each day on
mathematics homework, compared to 1 percent for the nation. Moreover,
2 percent of the students in Minnesota and 4 percent of the students in the
nation spent an hour or more on mathematics homework each day.
4 For every table in the body of the report that includes estimates of average proficiency, the Data Appendix
provides a corresponding table presenting the results for the four subpopulations -- race ethnicity, type of
community, parents' education level, and gender.
4 7
42
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
The itsults by race/ethnicity show that 2 percent of White students,
1 percent of Black students, 1 percent of Hispanic students, and 8 percent
of Asian students spent an hour or more on mathematics homework each
day.
In comparison, 2 percent of White students, 2 percent of Black
students, 6 percent of Hispanic students, and 6 percent of Asian students
spent no time doing mathematics homework.
In addition, 1 percent of students attending schools in advantaged urban
areas, 1 percent in schools in extreme rural areas, and 4 percent in schools
in areas classified as "other" spent an hour or more on mathematics
homework daily. In cnmparison, 2 percent of students attending schools
in advantaged urban areas, 0 percent in schools in extreme rural areas, and
2 percent in schools in areas classified as "other" spent no time doing
mathematics homework.
TABLE 6
Teachers' Reports on the Amount of Time
Students Spent on Mathematics Homework
Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
,
10 NAEP TRIAL STATE ASSESSMENT
Mktnesota
Central
Nation
Percents,.
and
Pro lidera*
2 ( 0.5)
Percentage
and
Prollicloncy
1 ( 0.8)
*IS ( Mel
Percentage
and
Pr*: fancy
( 0.3)
4.1
About how much time do students spend
on mathematics homework each day?
None
15 minutes
48 ( 3.4)
34 ( 7.1)
43 ( 4.2)
273 ( 1.5)
255 ( 4.1)
250 ( 2.3)
30 minutes
42 ( 3.3)
48 ( 9.8)
43 ( 43)
278 ( 1.8)
272 ( 3.5)
203 ( 2.6)
45 minutes
7 ( 1.6)
13 ( 6.0)
10 ( 1.9)
290 ( 4.0)I
261 (12.5)I
272 ( 5.7)1
An hour or more
2 ( 1.1)
6 ( 2.3)
4 ( 0.9)
287 ( 8.3)!
( 44)
276 ( 5.1)1
The standard errors of the estimated statistics appear M parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the valt, for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
43
Minnesota
TABLE 7
I Students' Reports on the Amount of Time They
I Spent on Mathematics Homework Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
_
.
1900 NAEP TRIAL STATE ASSESSMENT
Minnesota
Centre!
Nation
,
Porto Idw
and
lreackagy
Peewits.
Mid
Pnifisieney
Percentage
Wel
Proliamey
About how much time do you usually
spend
ach
day
on
mathematics
homework?
None
10 (
271 (
0.7)
2.4)
7 (1.4)
441
(
251 (
0.5)
2.5)
15 minutes
33 ( 1.3)
34 ( 4.8)
31 ( 2.0)
278 ( 1.2)
2e0 ( 3.8)
264 ( 1.9)
30 minutes
30 ( 1.0)
32 ( 2.3)
32 ( 1.2)
278 ( 1.3)
264 ( 3.8)
263 ( 1.9)
45 minutes
15 ( 1.0)
15 ( 1.2)
18 ( 1.0)
278 ( 1.8)
285(4.0)
288 ( 1.9)
An hoar or more
12 ( 1.0)
12 ( 3.4)
12 ( 1.1)
214 ( 1.8)
262 ( 8.2)1
25$ ( 3.1)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
And, according to the students (Table 7 and Table A7 in the Data Appendix):
In Minnesota, relatively few of the students (10 percent) reported that they
spent no time each day on mathematics homework, compared to 9 percent
for the nation.
Moreover, 12 percent of the students in Minnesota and
12 percent of students in the nation spent an hour or more each day on
mathematics homework.
The results by race/ethnicity show that 11 percent of White students,
14 percent of Black students, 15 percent of Hispanic students, and
22 percent of Asian students spent an hour or more on mathematics
homework each day.
In comparison, 10 percent of White students,
10 percent of Black students, 7 percent of Hispanic students, and
4 percent of Asian students spent no time doing mathematics homework.
4 :4
44
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
In addition, 11 percent of students attending schools in advantaged urban
areas, 14 percent in schools in extreme rural areas, and 10 percent in
schools in areas classified as "other" spent an hour or more on mathematics
homework daily.
In comparison, 9 percent of students attending schools
in advantaged urban areas, 9 percent in schools in extreme rural areas, and
11 percent in schools in areas classified as "other" spent no time doing
mathematics homework.
INSTRUCTIONAL EMPHASIS
According to the approach of the National Council of Teachers of Mathematics (NCTM),
students should be taught a broad range of mathematics topics, including number concepts,
computation, estimation, functions, algebra, statistics, probability, geometry, and
measurement.'
Because the Trial State Assessment questions were designed to measure
students' knowledge, skills, and understandings in these various content areas -- regardless 4.
of the type of mathematics class in which they were enrolled -- the teachers of the assessed
students were asked a series of questions about the emphasis they planned to give specific
mathematics topics during the school year. Their responses provide an indication of the
students' opportunity to learn the various topics covered in the assessment.
For each of 10 topics, the teachers were asked whether they planned to place "heavy,"
"moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to
skills that were measured in one of the five mathematics content areas included in the Trial
State Assessment:
Numbers and Operations. Teachers were asked about emphasis placed on
five topics:
whole number operations, common fractions,
decimal
fractions, ratio or proportion, and percent.
Measurement. Teachers were asked about emphasis placed on one topic:
measurement.
Geometry.
Teachers were asked about emphasis placed on one topic:
geometry.
Data Analysis, Statistics, and Probability.
Teachers were asked about
emphasis placed on two topics:
tables and graphs, and probability and
statistics.
Algebra and Functions.
Teachers were asked about emphasis placed on
one topic: algebra and functions.
National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics
(Reston, VA: National Council of leachers of Mathematics, 1989).
50
THE 1990 NAEP TRIAL STATE ASSESSMENT
45
Minnesota
The responses of the assessed students' teachers to the topic emphasis questions for each
content area were combined to create a new variable. For each question in a particular
content area, a value of 3 was given to "heavy emphasis" responses, 2 to "moderate
emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses
were then averaged over all questions related to the particular content area.
Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or
no emphasis" -- and the average student proficiency in each content area. For the emphasis
questions about numbers and operations, for example, the proficiency reported is the
average student performance in the Numbers and Operations content area.
Students whose teachers placed heavy instructional emphasis on Algebra and Functions
had higher proficiency in this content area than students whose teachers placed little or no
emphasis on Algebra and Functions. Students whose teachers placed heavy instructional
emphasis on Numbers and Operations had lower proficiency in this content area than
students whose teachers placed little or no emphasis on Numbers and Operations.
46
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE 8
I Teachers' Reports on the Emphasis Given to
I Specific Mathematics Content Areas
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL STATE ASSESSMENT
1
Minnesota I
Central
Nation
Teacher
"emphasis"
categories
by
content areas
Percentage
and
Pattie:henry
Percentage
and
Proficiency
Percentage
end
Proficiency
Numbers and Operations
Heavy emphasis
36 ( 3.3)
S4 ( 7,2)
4$ ( 3..)
275 ( 1.8)
264 ( 4.3)
200 ( 1i)
Little or no emphasis
13 ( 1,7)
13 ( 4.5)
15 ( 2.1)
301 ( 22)
285 ( 6.5)1
287 ( 3.4)
Measurement
Heavy emphasis
12 ( 2.2)
15 ( 5.7)
17 ( 3.0)
208 ( 4.1)
247 (12.5)1
250 ( $.8)
Little or no emphasis
47 ( 3.8)
42 ( 9.7)
33 ( 4.0)
277 ( 1.8)
270 (
7.7)1
272 ( 4.0)
Geometry
Heavy emphasis
19 ( 3.0)
26 ( 7.0)
2$ ( 3.8)
270 ( 2.5)
261 ( 7.9)I
260 ( 3.2)
Little or no emphasis
27 (
275 (
2.9)
2,1)
3.5 (
261 (
7.2)
9.0)1
21
264
( 3.3)
( 5.4)
Data Analysis, Statistics, and Probability
Heavy emphasis
8 ( 1.8)
12 ( 2.5)
14 ( 2.2)
287 ( 3.3)1
262 ( 7.5)
269 ( 4.3)
Little or no emphasis
89 ( 2.6)
57 ( 8.8)
53 ( 4.4)
279 (
1.3)
264 ( 5.6)1
261 ( 2.9)
Algebra and Functions
Heavy emphasis
50 ( 32)
50 ( 7.6)
48 ( 3.8)
285 ( 13)
273 ( 3.6)
275 ( 2.5)
Little or no emphasis
8 ( 1.3)
19 ( 3.9)
20 ( 3.0)
248 ( 3.4)
242 ( 5.5)1
243 ( 3.0)
The standard errors of the estimated stausucs appear m parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within
2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis"
category is not included.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency.
THE 1990 NAEP TRIAL STATE ASSESSMENT
47
Mbutesota
SUMMARY
Although many types of mathematics learning can take place outside of the school
environment, there are some topic areas that students are unlikely to study unless they are
covered in school. Thus, what students are taught in school becomes an important
determinant of their achievement.
The information on curriculum coverage, mathematics homework, and instructional
emphasis has revealed the following:
About half of the eighth-grade students in Minnesota (52 percent) were in
public schools where mathematics was identified as a special priority. This
compares to 63 percent for the nation.
In Minnesota, 80 percent of the students could take an algebra course in
eighth grade for high-school course placement or credit.
A greater percentage of students in Minnesota were taking eighth-grade
mathematics (54 percent) than were taking a course in pre-algebra or
algebra
(42 percent).
Across the
nation,
62 percent were taking
eighth-pude mathematics and 34 percent were taking a course
in
pre-algebra or algebra.
According to their teachers, the greatest percentage of eighth-grade students
in public schools in Minnesota spent either 15 or 30 minutes doing
mathematics homework each day; according to the students, most of them
spent either 15 or 30 minutes doing mathematics homework each day.
Across the nation, teachers reported that the largest percentage of students
spent either 15 or 30 minutes doing mathematics homework each day,
while students reported either 15 or 30 minutes daily.
In Mimiesota, relatively few of the students (10 percent) reported that they
spent no time each day on mathematics homework, compared to 9 percent
for the nation.
Moreover, 12 percent of the students in Minnesota and
12 percent of students in the nation spent an hour or more each day on
mathematics homework.
Students whose teachers placed heavy instructional emphasis on Algebra
and Functions had higher proficiency in this content area than students
whose teachers placed little or no emphasis on Algebra and Functions.
Students whose teachers placed heavy instructional emphasis on Numbers
and Operations had lower proficiency in this content area than students
whose teachers placed little or no emphasis on Numbers and Operations.
48
THE 1990 NAEP
STATE. ASSESSMENT
Minnesota
CHAPTER 4
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How Is Mathematics Instruction Delivered?
Teachers facilitate learning through a variety of instructional practices. Because a particular
teaching method may not be equally effective with all types of Ftudents, selecting and
tailoring methods for students with different styles of learning or for those who come from
different cultural backgrounds is an important aspect of teaching.°
An inspection of the availability and use of resources for mathematics education can
provide insight into how and what students are learning in mathematics. To provide
information about how instruction is delivered, students and teachers participating in the
Trial State Assessment were asked to report on the use of various teaching and learning
activities in their mathematics classrooms.
AVAILABILITY OF RESOURCES
Teachers' use of resources is obviously constrained by the availability of those resources.
Thus, the assessed students' teachers were asked to what extent they were able to obtain
all of the instructional materials and other resources they needed.
° National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematks
(Reston, VA: National Council of Teachers of Mathematics, 1991).
THE 1990 NAEP TRIAL STATE ASSESSMENT
49
Minnesota
From Table 9 and Table A9 in the Data Appendix:
In Minnesota, 12 percent of the eighth-grade students had mathematics
teachers who reported getting all of the resources they needed, while
23 percent of the students were taught by teachers who got only some or
none of the resources they needed. Across the nation, these figures were
13 percent and 31 percent, respectively.
In Minnesota, 13 percent of students attending schools in advantaged
urban areas, 16 percent in schools in extreme rural areas, and 10 percent
in schools in areas classified as "other" had mathematics teachers who got
all the resources they needed.
By comparison, in Minnesota, 9 percent of students attending schools in
advantaged urban areas, 23 percent in schools in extreme rural areas, and
26 percent in schools in areas classified as "other" were in classrooms
where only some or no resources were available.
Students whose teachers got all the resources they needed had higher
mathematics achievement levels than those whose teachers got only some
or none of the resources they needed.
TABLE 9
I Teachers' Reports on the Availability of
Resources
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1S00 NAEP TRIM_ STATE ASSESSMENT
Minnesota
Central
Nation
Which of the following statements is true
about how well supplied you are by your
school system
with
the
Instructional
materials and other resources you need
to teach your class?
I get ad the resources I need.
I get most of the resources I need.
I get some or none of the
ources I need
Percentage
and
Proficiency
Percentage
Percentage
and
and
Proficiency
Proaciency
12 (
281 (
2.1)
2.8)
8 (
.0*
( 2.4)
13 (
265 (
2.4)
42)
65 ( 3.7)
45 ( 7.8)
56 ( 4.0)
276 ( 12)
271 ( 2.2)1
265 ( 2.0)
23 (
3.8)
47 ( 7.3)
31 ( 4.2)
273 (
1.9)
259 ( 3.5)
261 ( 2.9)
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
er the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
r J
50
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
PATTERNS IN CLASSROOM INSTRUCTION
Research in education and cognitive psychology has yielded many insights into the types
of instructional activities that facilitate students' mathematics learning. Increasing the use
of "hands-on" examples with concrete materials and placing problems in real-world
contexts to help children construct useful meanings for mathematical concepts are among
the recommended approaches.'
Students' responses to a series of questions on their
mathematics instruction provide an indication of the extent to which teachers are making
use of the types of student-centered activities suggested by researchers. Table 10 presents
data on patterns of classroom practice and Table 11 provides information on materials used
for classroom instruction by the mathematics teachers of the assessed students.
According to their teachers:
Less than half of the students in Minnesota (43 percent) worked
mathematics problems in small groups at least once a week; relatively few
never worked mathematics pmblems in small groups (7 percent).
The largest percentage of the students (72 percent) used objects like nilers,
counting blocks, or geometric shapes less than once a week; relatively few
never used such objects (9 percent).
In Minnesota, 73 percent of the students were assigned problems from a
mathematics textbook almost every day; 4 percent worked textbook
problems about once a week or less.
Less than half of the students (39 percent) did problems from worksheets
at least several times a week; about one-quarter did worksheet problems
less than weekly (29 percent).
7 Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common
Curriadum. Eighty-second Yearbook of the National Society for the Study of Education (Chicago, I L:
University of Chicago Press, 1983).
G
THE 1990 NAEP TRIAL STATE ASSESSMENT
51
Minnesota
TABLE 10
I Teachers' Reports on Patterns of Mathematics
Instruction
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
_
1900 NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
A
Percentage
end
Percents.
Ind
Penisniese
and
About how often do students work
problems in small groups?
Preidency
Pralicioncy
Proficiency
At least once a week
43 ( 3.0)
50 ( 7.8)
50 ( 4A)
279 ( 111)
258 ( 4.1)
280 ( 2.2)
Less than once a week
50 ( 3.1)
43 ( 8.6)
43 ( 4.1)
273 ( t4)
2138 ( 4.0)1
284 ( 2.3)
Never
7 ( 12)
( 4.3)
8 ( 2.0)
279 ( 3.6)1
***)
277 ( 5.4$
About how often do students use objects
Percentage
Percentage
Percentage
like rulers, counting blocks, Or geometric
and
and
solids?
Proficiency
Proficiency
PranameY
At least once a week
19 ( 3.3)
15 ( 5.1)
22 ( 3.7)
271 ( 2.1)
255 ( 4.9)1
254 ( 32)
Less than once a wopak
72 ( 3.4)
81 ( 8.0)
89 ( 3.9)
276 ( 0.9)
284 ( 3.3)
263 ( 1.9)
Now
9 ( 1.8)
290 ( 4S)
4 ( 2.3)
9 ( 2.6)
282 ( 5.9)1
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
52
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE 11
I Teachers' Reports on Materials for
I Mathematics Instruction
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL STATE ASSESSMENT
klinnoseta
Central
Nation
Percentage
Percentage
Percentage
About how often do students do problems
and
Mid
end
from textbooks?
Prelioirstay
Prelkienay
Madam
Almost every day
73 ( 3.9)
82 ( 5.8)
82 ( 3.4)
279 ( 1.2)
269 ( 3-11)
267 ( 1.8)
Several tknes a week
23 ( 3.9)
32 ( 4.2)
31 ( 3.1)
271 ( 1.8)
252 ( 53)
254 ( 2.9)
Alma once a week or less
4 ( 1.3)
250 ( 6.1)I
( 2.7)
.4* ( 41
7 ( 1.8)
200 ( 5.1)1
About how often do students do problems
Percentage
Percentage
Percentage
on worksheets?
and
and
end
Proficiency
Prelidoncy
Prolkimmy
At least several times a week
39 ( 15)
38 ( 83)
34 ( 3.5)
271 ( 15)
252 ( 5.5)1
256 ( 2.3)
About once a week
32 ( 3.5)
23 ( 4.8)
33 ( 3.4)
275 ( 1.9)
261 ( 8.1)
2e0 ( 2.3)
Lass Man %resift
29 ( 3.8)
39 ( 7.0)
32 ( 3.5)
284 ( 2.2)
278 ( 4.1)
274 ( 2.7)
The standard errors of the estimated statistics appear in psrentheses.
lt can be said with about 95 percent
certainty that, for each population of' interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
1. Interpret with caution
the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
The next section presents the students' responses to a corresponding set of questions, as
well as the relationship of their responses to their mathematics proficiency.
It also
compares the responses of the students to those of their teachers.
THE 1990 NAEP TRIAL STATE ASSESSMENT
53
Minnesota
COLLABORATING IN SMALL GROUPS
In Minnesota, 45 percent of the students reported never working mathematics problems
in small groups (see Table 12); 26 percent of the students worked mathematics problems
in small groups at least once a week.
TABLE 12
I Students' Reports on the Frequency of Small
1 Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1000 ttAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
Percentage
and
Proficiency
Percentage
and
Proficiency
Percentage
and
Prnficiency
How often do you work in small groups
in your mathematics class?
At toast once a weak
26 ( 2.0)
23 ( 4.6)
23 ( 2.5)
277 ( 1.7)
206 ( 8.5)
258 ( 2.7)
Less than once
a week
28 ( 1.7)
32 ( 3.3)
2$ ( 1.4)
279 ( 12)
206 ( 3.0)
267 ( 2.0)
Nem
45 ( 2.3)
45 ( 8.3)
44( 2.9)
273 ( 1.3)
264 (
3.4)
261 ( 1.6)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standarderrors
of the estimate for the sample.
Examining the subpopulations (Table Al2 in tbf Data Appendix):
In Minnesota, 19 percent of students attending schools in advantaged
urban areas, 26 percent in schools in extreme rural areas, and 27 percent
in schools in areas classified as "other" worked in small groups at least once
a week.
Further, 26 percent of White students, 39 percent of Black students,
28 percent of Hispanic students, and 25 percent of Asian students worked
mathematics problems in small groups at least once a week.
Females were as likely as males to work mathematics problems in small
groups at least once a week (25 percent and 28 percent, respectively).
54
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
USING MATHEMATICAL OBJECTS
Students west asked to report on the frequency with which they used mathematical objects
such as rulers, counting blocks, or geometric solids. Table 13 below and Table A13 in the
Data Appendix summarize these data:
Less than half of the students in Minnesota (39 percent) never used
mathematical objects; 23 percent used these objects at least once a week.
Mathematical objects were used at least once a week by 21 percent of
students attending schools in advantaged urban areas, 29 percent in schools
in extreme rural arms, and 20 percent in schools in areas classified as
"other".
Males were as likely as females to use mathematical objects in their
mathematics classes at least once a week (26 percent and 20 percent,
respectively).
In addition, 23 percent of White students, 28 percent of Black students,
22 percent of Hispanic students, and 27 percent of Asian students used
mathematical objects at least once a week.
TABLE 13
I Students' Reports on the Use of Mathematics
1 Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
1
Central
Nation
How often do you work with objects like
rulers,
counting blocks, or geometric
solids In your mathematics class?
At least once a wed(
Less than once a week
Never
Percentage
Pervontage
and
and
Proficiency
!roadway
23 ( 2.1)
23 ( 2.9)
Percentage
and
ringielaney
28 ( 1.8)
270 ( 1.5)
260 ( 3.5)
258 ( 2,6)
38 (
1.5)
36 ( 2.5)
31 ( 1.2)
280 ( 1.1)
272 ( 2.9)
269 ( 1.5)
39 ( 22)
41 ( 4.6)
41 ( 2.2)
275 ( 1.3)
262 ( 2.8)
259 ( 1.6)
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
certairty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
f;
THE 1990 NAEP TRIAL STATE ASSESSMENT
55
Minnesota
MATERIALS FOR MATHEMATICS INSTRUCTION
The percentages of eighth-grade public-school students in Minnesota who frequently
worked mathematics problems from textbooks (Table 14) or worksheets (Table 15)
indicate that these materials play a major role in mathematics teaching and learning
Regarding the frequency of textbook usage (Table 14 and Table A 14 in the Data
Appendix):
Many of the students in Minnesota (81 percent) worked mathematics
problems from textbooks almost every day, compared to 74 percent of the
students in the nation.
Textbooks were used almost every day by 81 percent of students attending
schools in advantaged urban areas, 81 percent in schools in extreme rural
areas, and 84 percent in schools in areas classified as "other".
TABLE 14
I Students' Reports on the Frequency of
Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
-
MO NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
How often
do
you do
mathematics
problems
from
textbooks
Ifr
your
mathematics class?
Percentage
and
Proficiency
Porcentage
and
Proficiency
Isercontage
and
Proficiency
Almost every day
81 ( 1.5)
74 ( 4.7)
74 ( 1.9)
279 ( 0.9)
271 ( 2.2)
287 ( 12)
Several times a wiook
12 ( 1.2)
15 ( 1.8)
14 ( 0.8)
2SS ( 1.8)
250 ( 4.2)
252 ( 1.7)
About once a week or less
7 ( 12)
11 ( 4.3)
12 ( 1.8)
257 ( 4.4)
250 ( 4.7)1
242 ( 4.5)
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution
the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency.
56
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
And, for the frequency of worksheet usage (Table 15 and Table Al 5 in the Data
Appendix);
Less than half of the students in Minnesota (33 percent) used worksheets
at least several times a week, compared to 38 percent in the nation.
Worksheets were used at least several times a week by 35 percent of
students attending schools in advantaged urban areas, 33 percent in schools
in extreme nwal areas, and 33 percent in schools in areas classified as
othert%
TABLE 15
I Students' Reports on the Frequency of
1 Mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
_
1880 MAEP TRIAL STATE ASSE5SIMENT
Illnnesot&
Central
nation
Percentage
and
Infoficiency
Percentage
and
Proildatcy
Percentage
anti
Proficiency
How often
do you do mathematics
problems
on
worksheets
in
your
mathematics class?
At least several times a week
33 ( 2.2)
38 ( CO)
38 ( 2.4)
269 ( 1.5)
257 ( 4.9)
253 ( 2.2)
About once a week
29 ( 1.6)
23 ( 2.3)
25 ( 1.2)
275 ( 1.3)
204 ( 2.8)
281 ( 1.4)
Less than wieldy
37 ( 2.4)
40 ( 5.8)
37 ( 2.5)
282 ( 1.5)
273 ( 4.0)
272 ( 1.9)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certaMty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
Table 16 compares students' and teachers' responses to questions about the patterns of
classroom instruction and materials for mathematics instruction.
62
THE 1990 NAEP TRIAL STATE ASSESSMENT
57
Minnesota
TABLE 16
Comparison of Students' and Teachers' Reports
on Patterns of and Materials for Mathematics
Instrucfion
PERCENTAGE OF STUDENTS
1990 NAEP TRIAL STATE
ASSESSMENT
masata
Central
Nation-,-.
Patterns
of
classroom
Instruction
Percentele
Students Teachers
PeTcentege
Shades* Teachets
Porcudefe
Students Teaches
Percentage of students who
work mathematics problems in
small groups
At least once a week
26 ( 2.0)
43 ( 3.0)
23 ( 4.8)
50 ( 7.8)
28 ( 2.5)
SO ( 4.4)
Less than once a week
28 ( 1.7)
50 ( 11)
32 ( 3.3)
43 ( 8.8)
28 ( 1.4)
43 ( 4.1)
Never
45 ( 2.3)
7 ( 1.9)
45 ( 6.3)
7 ( 4.3)
44 ( 2.9)
6 ( 2.0)
Percentage of students who
use objects like rulers, counting
blocks, or geometric solids
At least once a week
23 ( 2.1)
19 ( 3.3)
23 ( 2.9)
15 ( 5.1)
28 ( 1.8)
22 ( 3.7)
Less then once a week
30 ( 15)
72 ( 3.4)
Se ( 2.5)
81 ( 6.0)
( 1.2)
SO ( 3.9)
Never
39 ( 2.2)
9 ( 1.8)
41 ( 4.6)
4 ( 2.3)
41 ( 22)
0 ( 2.8)
Admeria Is for mathematics
Percentage
Percentege
Percentage
inttruction
Students Teachers
Students Teacher"
Students Teachers
Pemntage of students who
us* a mathematics textbook
Almost every day
31 ( 1.5)
73 ( 3.9)
74 ( 4.7)
82 ( 5.8)
74 ( 1.9)
62 ( 3.4)
Several times a week
12 ( 1.2)
23 ( 3,9)
15 ( 1.8)
32 ( 4.2)
14 ( 04)
31 ( 3.1)
About once a week or less
7 ( 1.2)
4 ( 1.3)
11 ( 4.3)
( 2.7)
12 ( 1,8)
7 ( 1.8)
Percentage of students who
use a mathematics worksheet
At least several times a week
33 ( 2,2)
39 ( 3.5)
36 ( 8.0)
38 ( 8.3)
3$ ( 2.4)
34 ( 3.8)
About once a week
29 ( 1.6)
32 ( 3$)
23 ( 2.3)
23 ( 4.8)
25 ( 1.2)
13 ( 34)
Less than weekly
37 ( 24)
29 ( 3.6)
40 ( 5.6)
39 ( 7.0)
37 ( 2.5)
32 ( 3.6)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
58
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
SUMMARY
Because classroom instructional time is typically limited, teachers need to make the best
possible use of what is known about effective instructional delivery pradiees and resources.
It appears that mathematics textbooks and worksheets continue to play a major role in
math matics teaching. Although there is some evidence that other instructional resources
and practices are emerging, they are not yet commonplace.
According to the students' mathematics teachers:
Less than half of the students in Minnesota (43 percent) worked
mathematics problems in small groups at least once a week; relatively few
never worked in small groups (7 percent).
The largest percentage of the students (72 percent) used objects like rulers,
counting blocks, or geometric shapes less than once a week, and relatively
few never used such objects (9 percent).
In Minnesota, 73 percent of the students were assigned problems from a
mathematics textbook almost every day; 4 percent worked textbook
problems about once a week or less.
"Less than half of the students (39 percent) did problems from worksheets
at least several times a week; about one-quarter did worksheet problems
less than weekly (29 percent).
And, according to the students:
In Minnesota, 45 percent of the students never worked mathematics
problems in small groups; 26 percent of the students worked mathematics
problems in small groups at least once a week.
Less than half of the students in Minnesota (39 percent) never used
mathematical objects; 23 percent used these objects at least once a week.
Many of the students in Minnesota (81 percent) worked mathematics
problems from textbooks almost every day, compared to 74 percent of
students in the nation.
Less than half of the students in Minnesota (33 percent) used worksheets
at least several times a week, compared to 38 percent in the nation.
THE 1990 NAEP TRIAL STATE ASSESSMENT
59
Minnesota
CHAPTER 5
How Are Calculators Used?
Although computation skills are vital, calculators -- and, to a lesser extent, computers --
have drastically changed the methods that can be used to perform calculations. Calculators
are important tools for mathematics and students need to be able to use them wisely. The
National Council of Teachers of Mathematics and many other educators believe that
mathematics teachers should help students become proficient in the use of calculators to
free them from time-consuming computations and to permit them to focus on more
challenging tasks.8 The increasing availability of affordable calculators should make it
more likely and attractive for students and schools to acquire and use these devices.
Given the prevalence and potential importance of calculators, part of the Trial State
Assessment focused on attitudes toward and uses of calculators. Teachers were asked to
report the extent to which they encouraged or permitted calculator use for various activities
in mathematics class and students were asked about the availability and use of calculators.
National Assessment of Educational Progress, Mathematics Objectives.
1990 Assessment (Princeton, NJ:
Educational Testing Service, 1988).
National Council of Teachers of Mathematics, Curriculwn and Evaluation Standards jor School Mathematics
(Reston, VA: National Council of Teachers of Mathematics, 1989).
60
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
Table 17 provides a profile of Minnesota eighth-grade public schools' policies with regard
to calculator use:
In comparison to 33 percent across the nation, 47 percent of the students
in Minnesota had teachers who allowed calculators to be used for tests.
A greater percentage of students in Minnesota than in the nation had
teachers who permitted unrestricted use of calculators (31 percent and
18 percent, respectively).
1 ABLE 17
I Teachers' Reports of Minnesota Policies on
Calculator Use
PERCENTAGE OF STUDENTS
MO NAEP TRIAL. STATE ASSESSMENT
Mkomoota
Percentage of elghth-grade students in public
schools whose teachers permit the unrestricted
um of calculators
Percentage of eighth-grade stueePts in public
schools whose teachers permit the use of
calculator* for teats
Percentage of eighth-grade students in public
schools whose teachers report that students
have access to calculators owned by the school
Percentage
Pommel,'
Percentage
31 ( 3.1)
27 ( 8.1)
18 ( 3.4)
47 ( 3.9)
44 ( 7.9)
33 ( 4.5)
58 ( 4.4)
55 ( 8.2)
58 ( 4.8)
41.
The standard errors of the estimated stitilliCs appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
THE 1990 NAEP TRIAL STATE ASSESSMENT
61
Minnesota
THE AVAILABILITY OF CALCULATORS
In Minnesota, most students or their families (99 percent) owned calculators (Table 18);
however, fewer students (51 percent) had teachers who explained the use of calculators to
them. From Table A18 in the Data Appendix:
In Minnesota, 50 percent of White students, 67 percent of Black students,
58 percent of Hispanic students, and 48 percent of Asian students had
teachers who explained how to use them.
Females were as likely as males to have the use of calculators explained to
them (48 percent and 54 percent, respectively).
TABLE 18
Students' Reports on Whether They Own a
Calculator and Whether Their Teacher Explains
How To Use One
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
_
MO NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
Do you of your family own a calculator?
Percentage
and
Proficiency
99 ( 0.2)
276 ( 0.8)
1
( 0.2)
v. (
Percentage
and
Profidency
Percentage
and
Proficierwy
98 ( 0.6)
266 ( 2.5)
2 ( 0.6)
( ".)
Percentage
and
Proficiency
Percentage
and
Proficiency
97 ( 0.4)
263 ( 1.3)
3 ( 0.4)
234 ( 3.8)
Percentage
and
Proficiency
Yes
No
Does your mathematics teacher explain
how to use a calculator for mathematics
problems?
Yrs
51 ( 2.1)
56 ( 4,9)
49 ( 2.3)
274 ( 1.3)
263 ( 3.0)
258 ( 1,7)
No
49 ( 2.1)
44 ( 4.9)
51 ( 2.3)
278 ( 1.1)
269 ( 3.4)
266 ( 1.5)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample,
*** Sample size is insufficient to permit a reliable estimate (fewer than 62
students).
62
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
THE USE OF CALCULATORS
As previously noted, calculators can free students from tedious computations and allow
them to concentrate instead on problem solving and other important skills and content.
As part of the Trial State Assessment, stue-ms were asked how frequently (never,
sometimes, almost always) they used calL..
ars for working problems in class, doing
problems at home, and taking quizzes or tests. As repotted in Table 19:
In Minnesota, 20 percent of the students never used a calculator to work
problems in class, while 45 percent almost always did.
Some of the students (15 percent) never used a calculator to work
problems at home, compared to 29 percent who almost always used one.
Less than half of the students (31 percent) never used a calculator to take
quizzes or tests, while 21 percent almost always did.
TABLE 19
Students' Reports on the Use of a Calculator
I for Problem Solving or Tests
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
_
1960 NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
Percentage
and
Predictor";
Pareentege
and
Madam/
Portents.
and
Prolldenry
How often do you use a calculator for the
following tasks?
Working problems In class
Almost always
45 ( 1.5)
51 ( 3.8)
46 ( 1.5)
26a ( 1.2)
260 ( 2.8)
254 ( 14)
Never
20 ( 1.6)
18 ( 3,6)
23 ( 1.9)
285 ( 1.2)
270 ( 4.111
272 ( 1.4)
Doing problems at home
Almost always
29 ( 1.3)
36 ( 22)
30 ( 1.3)
275 ( 1.3)
266 ( 2.8)
261 ( 1.8)
Never
15 ( 0.8)
16 ( 2.1)
19 ( 02)
277 ( 1.7)
283 ( 3.3)
263 ( 14)
Taking quizzes or tests
Almost always
21 ( 1.5)
22 ( 4,5)
27 ( 1.4)
272 ( 2.1)
200 ( 4.0)
253 ( 2.4)
Never
31 ( 1.6)
22 ( 4.8)
30 ( 2.0)
236 ( 1.2)
271 ( 3.4)1
274 ( 1.3)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within 7i 2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category
is not included.
1 Interpret with caution -- the nature of the sample does not allow accurate determination of
the variability of this estimated mean proficiency.
THE 1990 NAEP TRIAL STATE ASSESSMENT
63
Minnesota
WHEN TO USE A CALCULATOR
Part of the Trial State Assessment was designed to investigate whether students know when
the use of a calculator is helpful and when it is not. There were seven sections of
mathematics questions in the assessment; however, each student took only three of those
sections. For two of the seven sections, students were given calculators to use. The test
administrator provided the students with instructions and practice on how to use a
aculator prior to the assessment. During the assessment, students were allowed to choose
whether or not to use a calculator for each item in the calculator sections, and they were
asked to indicate in their test booklets whether they did or did not use a calculator for each
item.
Certain items in the calculator sections were defined as "calculator-active" items -- that is,
items that required the student to use the calculator to determine the coffect response.
Certain other items were defined as "calculator-inactive" items -- items whose solution
neither required nor suggested the use of a calculator. The remainder of the items were
"calculator-neutral" items, for which the solution to the question did not require the use
of a calculator.
In total, there were eight calculator-active items, 13 calculator-neutral items, and 17
calculator-inactive items across the two sections. However, because of the sampling
methodology used as part of the Trial State Assessment, not every student took both
sections. Some took both sections, some took only one section, and some took neither.
To examine the characteristics of students who generally knew when the use of the
calculator was helpful and those who did not, the students who responded to one or both
of the calculator sections were categorized into two groups:
High -- students who used the calculator appropriately (i.e., used it for the
calculator-active items and did not use it for the calculator-inactive items)
at least 85 percent of the time and indicated that they had used the
calculator for at least half of the calculator-active items they were presented.
Other -- students who did not use the calculator appropriately at least 85
percent of the time or indicated that they had used the calculator for less
than half of the calculator-active items they were presented.
G
64
THE 1990 NAEP TRIAL STkTE ASSESSMENT
Minnesota
The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below:
About the same percentage of students in Minnesota were in the High
group as were in the Other group.
A smaller percentage of males than females were in the High group.
In addition, SO percent of White students, 40 percent of Black students,
40 percent of Hispanic students, and 45 percent of Asian students were in
the High group.
TABLE 20
I Students' Knowledge of Using Czkulators
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1AINI NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
Perandage
and
Proficiency
Piemonte AN
aid
Proficiency
Pareettiles
and
Pnificiency
"Calculator-use" group
High
50 ( 1.0)
45 ( 1.8)
42 ( 1.3)
252 ( 1.0)
272 ( SA)
272 ( 1.8)
Other
50 ( 1.0)
54 ( 1.$)
55 ( 1.31
( 1.2)
2f10 ( 2.7)
255 ( 1.5)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
7 ( )
THE 1990 NAEP TRIAL STATE ASSESSMENT
65
Minnesota
SUMMARY
Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to
devote large portions of instructional time to teaching students how to perform routine
calculations by hand. Using calculators to replace this time-consuming process would
create more instructional time for other mathematical skill topics, such as problem solving,
to be emphasized.
The data related to calculators and their use show that:
In comparison to 33 percent across the nation, 47 percent of the students
in Minnesota had teachers who allowed calculators to be used for tests.
A greater percentage of students in Minnesota than in the nation had
teachers who permitted unrestricted use of calculators (31 percent and
18 percent, respectively).
In Minnesota, most students or their
families (99 percent) owned
calculators; however, fewer students (51 percent) had teachers who
explained the use of calculators to them.
In Minnesota, 20 percent of the students never used a calculator to work
problems in class, while 45 percent almost always did.
Some of the students (15 percent) never used a calculator to work
problems at home, compared to 29 percent who almost always used one.
Less than half of the students (31 percent) never used a calculator to take
quizzes or tests, while 21 percent almost always did.
71
66
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
CHAPTER 6
Who Is Teaching Eighth-Grade Mathematics?
In recent years, accountability for educational outcomes has become an issue of increasing
importance to federal, state, and local governments. As part of their effort to improve the
educational process, policymakers have reexamined existing methods ofeducating and
certifying teachers.9 Many states have begun to raise teacher certification standards and
strengthen teacher training programs. As shown in Table 21:
In
Minnesota,
44 percent of the
students
were
being taught
by
mathematics teachers who reported having at least a master's or education
specialist's degree. This compares to 44 percent '..r students across the
nation.
About three-quarters of the students (76 percent) had mathematics
teachers who had the highest level of teaching certification available. This
is similar to the figure for the nation, where 66 percent of the students were
taught by mathematics teachers who were certified at the highest level
available in their states.
Almost all of the students (98 percent) had mathematics teachers who had
a mathematics (middle school or secondary) teaching certificate.
This
compares to 84 percent for the nation.
9 National Council of Teachers of Mathematics, Professional Standards for the 'leaching of Mathematics
(Reston, VA: National Council of Teachers of Mathematics, 1991).
THE 1990 NAEP TRIAL STATE ASSESSMENT
67
Minnesota
TABLE 21
I Profile of Eightb-Grade Public-School
Mathematics Teachers
PERCENTAGE OF STUDENTS
1900 NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
,
Percentage
Percentage
Percentage
Percentage of students whose mathematics teachers
reported having the Mowing degrees
Bachelor's degree
56 ( 3.4)
4 ( 0.1)
56 ( 4,2)
Master's or specialist's degree
44 ( 3.4)
4 ( SA)
42 ( 4.2)
Doctorate or professional degree
( 0.0)
4 ( 2.7)
2 ( 1.4)
Percentage et students whose mathematics teachers have
the Mowing types of teaching certificates that are
recognized by Minnesota
No regular certification
2 ( 1.0)
4 ( 2.7)
4 ( 1.2)
Regular certification but less than the highest available
22 ( 3.5)
25 ( 7.3)
29 ( 4$)
Highest certification available (permanent Of long-term)
76 ( SS)
TI ( 7.3)
90(4.3)
Percentage of students *lose mathematics teachers have
the bellowing types of teaching certificates that are
recognized by Minnesota
Mathematics (middle school or secondary)
90 ( 0.9)
77 ( 4.5)
( 2.2)
Education (elementary or middle school)
1 ( 0.4)
17 ( 7.5)
12 ( 2.6)
Other
2 ( 0.6)
( 4.6)
4 ( 1.5)
The standard errors of the estimated statipiCE appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
EDUCATIONAL BACKGROUND
Although mathematics teachers are held responsible for providing high-quality instruction
to their students, there is a concern that many teachers have had limited exposure to
content and concepts in the subject area. Accordingly, the Trial State Assessment gathered
details on the teachers' educational backgrounds
more specifically, their undergraduate
and graduate majors and their in-service training.
7 3
68
i e.F. 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
Teachers' responses to questions concerning their undergraduate and graduate fields of
study (Table 22) show that:
In Minnesota, 88 percent of the eighth-grade public-school students were
being taught mathematics by teachers who had an undergraduate major in
mathematics. In comparison, 43 percent of the students across the nation
had mathematics teachers with the same major.
Less than half of the eighth-grade public-school students in Minnesota
(40 percent) were taught mathetaatics by teachers who had a graduate
major in mathematics. Across the nation, 22 percent of the students were
taught by teachers who majored in mathematics in graduate school.
TABLE 22
I Teachers' Reports on Their Undergraduate and
I Graduate Fields of Study
PERCENTAGE OF STUDENTS
1990 NAEP TRIAL STATE ASSENIMENT
Minnesota
Central
Nation
What was your undergraduate major?
Mathematics
Education
Other
What was your graduate major?
Mathematics
Education
Other or no graduat Wei study
Perapetage
Pareenta.
Pewees.
111 ( 2.0)
9 ( 1.6)
4 ( 1.6)
ST ( 7.1)
29 ( 8.4)
14 ( 5.4)
43 ( 3.9)
35 ( 3.3)
22 ( 3.3)
Percentage
Percentage
Percentage
40 ( 3.8)
23 ( 3.0)
37 ( 3.1)
34 ( 9.1)
34 ( 6.2)
32 ( 8.5)
22 ( 3.4)
36 ( 34)
40( 3.4)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
74
THE 1990 NAEP TRIAL STATE ASSESSMENT
59
Minnesota
Teachers' responses to questions concerning their in-service training for the year up to the
Trial State Assessment (Table 23) show that:
In Minnesota, 34 percent of the eighth-grade public-school students had
teachers who spent at least 16 hours on in-service education dedicated to
mathematics or the teaching of mathematics.
Across the nation,
39 percent of the students had teachers who spent at least that much time
on similar types of in-service training.
Some of the students in Minnesota (11 percent) had mathematics teachers
who spent no time on in-service education devoted to mathematics or the
teaching of mathematics.
Nationally, I I percent of the students had
mathematics teachers who spent no time on similar in-service training.
TABLE 23
I Teachers' Reports on Their In-Service Training
PERCENTAGE OF STUDENTS
1900 KAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
During the last year, how much time in
total have you
spent
on
in-service
eOucation in mathematics or the teaching
of mathematics?
None
One to 15 hours
115 hours or more
Percentage
Percentage
Percentage
11 ( 2$)
( 1.3)
11 ( 2.1)
55 ( 3.5)
71 ( 5.4)
51 ( 4.1)
34 ( 3.4)
26 ( 5.0)
39 ( 3.8)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
70
THE 1940 NAEP TRIAL STATE ASSESSMENT
Minnesota
SUMMARY
Recent results from international studies have shown that students from the United States
do not compare favorably with students from other nations in mathematics and science
achievement.'°
Further, results from NAEP assessments have indicated that students'
achievement in mathematics and science is much lower than educators and the public
would like it to be."
In curriculum areas requiring special attention and improvement,
such as mathematics, it is particularly important to have well-qualified teachers. When
performance differences across states and territories are described, variations in teacher
quAlifications and practices may point to areas worth further exploration. There is no
guarantee that individuals with a specific set of credentials will be effective teachers;
however, it is likely that relevant training and experience do contribute to better teaching.
The information about teachers' educational backgrounds and experience reveals that:
In Minnesota, 44 percent of the assessed students were being taught by
mathematics teachers who reported having at least a master's or education
specialist's degree. This compares to 44 percent for students across the
nation.
About three-quarters of the students (76 percent) had mathematics
teachers who had the highest level of teaching certification available. This
is similar to the figure for the nation, where 66 percent of students were
taught by mathematics teachers who were certified at the highest level
available in their states.
In Minnesota, 88 percent of the eighth-grade public-school students were
being taught mathematics by teachers who had an undergraduate major in
mathematics. In comparison, 43 percent of the students across the nation
had mathematics teachers with the same major.
Less than half of the eighth-fgade public-school students in Minnesota
(40 percent) were taught mathematics by teachers who had a graduate
major in mathematics. Across the nation, 22 percent of the students were
taught by teachers who majored in mathematics in graduate school.
Archie E. Lapomte, Nancy A. Mead, and Gary W. Phillips, A World of Differences An International
Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress,
Educational Testing Service, 1988).
Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of ,fathematks
Achievement
NA EP's 1990 Assessment of the Nation and the Thal Assessment of the States (Prinmton, NJ:
Nutional Assessment of Educational Progress, Educational Testing Service, 1991).
THE 1990 NAEP TRIAL STATE ASSESSMENT
71
Minnesota
In Minnesota, 34 percent of the eighth-grade public-school students had
teachers who spent at least 16 hours on in-service education dedicated to
mathematics or the teaching of mathematics.
Across the nation,
39 percent of the students aad teachers who spent at least that much time
on similar types of in-service training.
Some of the students in Minnesota (11 percent) had mathematics teachers
who spent no time on in-service education devoted to mathematics or the
teaching of mathematics.
Nationally, 11 percent of the students had
mathematics teachers who spent no time on similar in-service training
0°1
72
THE 1990 NAEP TRIAL STATE ASSESSMENT
CHAPTER 7
The Conditions Beyond School that Facilitate
Mathematics Learning and Teaching
Because students spend much more time out of school each day than they do in school, it
is reasonable to expect that out-of-school factors greatly influence students' attitudes and
behaviors in school. Parents and guardians can therefore play an important rolc in the
education of their children. Family expectations, encouragement, and participation in
student learning experiences arc powerful influences. Together, teachers and parents can
help build students' motivation to learn and can broaden their interest in mathematics and
other subjects.
To examine the relationship between home environment and mathematics proficiency,
students participating in the Trial State Assessment were asked a series of questions about
themselves, their parents or guardians, and home factors related to education.
'7 S
THE 1990 NAEP TRIAL STATE ASSESSMENT
73
Minnesota
AMOUNT OF READING MATERIALS IN THE HOME
The number and types of reading and reference materials in the home may be an indicator
of the value placed by parents on learning and schooling. Students participating in the Trial
State Assessment were asked about the availability of newspapers, magazines, books, and
an encyclopedia at home. Average mathematics proficiency associated with having zero to
two, three, or four of these types of materials in the home is shown in Table 24 and Table
A24 in the Data Appendix.
TABLE 24
I Students' Reports on Types of Reading
Materials in the Home
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
11190 NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
r Does your family have, or receive on a
regular basis, any of the following items:
.more than 25 books, an encyclopedia,
newspapers, magazines?
Zero to two types
Pm PAW
Fotr typos
Ihralfltife
and
Proficiency
Percentage
and
Prolkiency
Percentage
mei
PreSciency
12 ( 0.7)
19 ( 2.1)
21 ( 1.0)
258 ( 1.9)
250 ( 3.4)
244 ( 2.0)
31 ( 0.7)
31 ( 2.2)
30 ( 1.0)
274 ( 13)
285 ( 3.8)
258 ( 1.7)
57 ( 1.0)
50 ( 1.8)
48 ( 1,3)
281 ( 0.9)
272 ( 2.1)
272 ( 1$)
The standard errors of the esumated statistics appear in parentheses,
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
The data for Minnesota reveal that:
Students in Minnesota who had all four of these types of materials in the
home showed higher mathematics proficiency than did students with zero
to two types of materials. This is similar to the results for the nation, where
students who had all four types of materials showed higher mathematics
proficiency than did students who had zero to two types.
74
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
A smaller percentage of Black and Asian students and about the same
percentage of Hispanic students had all four types of these reading materials
in their homes as did White students.
About the same percentage of students attending schools in advantaged
urban areas as in extreme rural areas and areas classified as "other" had all
four types of these reading materials in their homes.
HOURS OF TELEVISION WATCHED PER DAY
Excessive television watching is generally seen as detracting from time spent on educational
pursuits. Students participating in the Trial State Assessment were asked to report on the
amount of television they watched each day (Table 25).
TABLE 25
1 Students' Reports on the Amount of Time Spent
I Watching Television Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
-
19.0 NAEP TRIAL STATE ASSESSMENT
Minnesota
Central
Nation
11,
How much television do you usually
watch each day?
Percentage
and
Proficiency
Percentage
and
Proficiency
Percentage
and
Proficiency
One hour or less
15 ( 0.8)
11 ( 1.6)
12 ( 0.8)
281 ( 1.7)
270 ( 3.5)
269 ( 2.2)
Two hours
27 (
0.8)
22 (
1.7)
21 (
0.9)
281 ( 1.5)
274 ( 3.2)
268 ( 1.8)
Tire* ha"
26 ( 0.9)
25 ( 2.4)
22 ( 0.8)
277 ( 1.1)
271 ( 4,0)
265 ( 1.7)
Four to five hors
25 ( 0.7)
27 ( 3.0)
28 ( 1.1)
271 ( 1.4)
261 ( 2.9)
260 ( 1.7)
Six hours or more
7 ( 0.5)
14 (
1.6)
16 (
1.0)
260 ( 2.3)
247 ( 3.4)
245 ( 1.7)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard prors
of the estimate for the sample.
r r-t)
THE 1990 NAEP TRIAL STATE ASSESSMENT
75
Minnesota
From Table 25 and Table A25 in the Data Appendix:
In Minnesota, average mathematics proficiency was lowest for students
who spent six hours or more watching television each day.
Some of the eighth-grade public-school students in Minnesota (15 percent)
watched one hour or less of television each day; 7 percent watched six
hours or more.
A greater percentage of males than females tended to watch six or more
hours of television daily.
However, a smaller percentage of males than
females watched one hour or less per day.
In addition, 6 percent of White students, 20 percent of Black students,
10 percent of Hispanic students, and 14 percent of Asi,an students watched
six hours or more of television each day.
In comparison, 15 percent of
White students, 3 percent of Black students, 16 percent of Hispanic
students, and 12 percent of Asian students tended to watch only an hour
or less.
STUDENT ABSENTEEISM
Excessive absenteeism may also be an obstacle to students' success in school. To examine
the relationship of student absenteeism to mathematics proficiency, the students
participating in the Trial State Assessment were asked to report on the number of days of
school they missed during the one-month period preceding the assessment.
From Table 26 and Table A26 in the Data Appendix:
In Minnesota, average mathematics proficiency was lowest for students
who missed three or more days of school.
Less than half of the students in Minnesota (44 percent) did not miss any
school days in the month prior to the assessment, while 20 percent missed
three days or more.
In addition, 20 percent of White students, 33 percent of Black students,
29 percent of Hispanic students, and 11 percent of Asian students missed
three or more days of school.
S 1
76
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
Similarly, 22 percent of students attenditg, schools in advantaged urban
areas, 19 percent in schools in extreme rural areas, and 19 percent in
schools in areas classified as "other" missed three or more days of school.
TABLE 26
I Students' Reports on the Number of Days of
I School Missed
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
OM NAEP TRIAL II A '':. VISESSMENT
Atkin's*: la
How many days of school did you miss
last month?
One or two days
Three days or more
Panmdase
and
Pro Odeon
44 ( 1.0)
280 ( 1.0)
38 ( 1.0)
276 ( 1.3)
20 ( 0.9)
265 ( 1.4)
Poivonlass
Paroardap
wed
and
Proficiency
Proficiency
47 ( 1.7)
286 ( 2.5)
( 2.0)
271 ( 3.4)
23 ( 2.0)
252 ( 3.3)
45 ( 1.1)
285 ( 1.8)
32 ( 0.9)
246 ( 1.5)
23 ( 1.1)
250 ( 1.9)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
L.'
THE 1990 NAEP TRIAL STATE ASSESSMENT
77
Minnesota
'TUDENTS' PERCEPTIONS OF MATHEMATICS
According to the National Council of Teachers of Mathematics, learning mathematics
should require students not only to master essential skills and concepts but also to develop
confidence in their mathematical abilities and to value mathematics as a discipline."
Students were aued if they agreed or disagreed with five statements designed to elicit their
perceptions of mathematics. These included statements about:
Personal experience with mathematics, including students' enjoyment of
mathematics and level of confidence in their mathematics abilities: I like
mathematics; I am good in mathematics.
Value of mathematics, including students' perceptions of its present utility
and its expected relevance to future work and life requirements: Almost all
people use mathematics in their jobs; mathematics is not more for boys than
for girls.
The nature of mathematics, including students' ability to identify the salient
features of the discipline:
Mathematics is useful for solving everyday
problems.
A student "perception index" was developed to examine students' perceptions of and
attitudes toward mathematics. For each of the five statements, students who responded
"strongly agree" were given a value of I (indicating very positive attitudes about the
subject), those who responded "agree" were given a value of 2, and those who responded
"unoecided," "disagree," or "strongly disagree" were given
value of 3. Each student's
responses were averaged over the five statements. The students were then assigned a
perception index according to whether they tended to strongly agree with the.statements
(an index of I), tended to agree with the statements (an index of 2), or tended to be
undecided, to disagree, or to strongly disagree with the statements `san indl..x of 3).
Table 27 provides the data for the students' attitudes toward mathematics as defined by
their perception index. The following results were observed for Miunesota:
Average mathematics proficiency was highest for students wh.1 were in the
"strongly agree" category and lowest for students who were in the
"undecided, disagee, strongly disagTee" category.
About one-quarter of the students (26 percent) were in the "strongly
agree" category (perception index of l).
This compares to 27 percent
across the nation.
About one-quarter of the students in Minnesota (23 percent), compared
to 24 percent across the nation, were in the "undecided, disagyee, or
strongly disagree" category (perception index of 3).
" National Council of Teachers of Mathematics, Currkulum and Evaluation Standards for Sclwol Mathematics
(Reston, VA: National Council of Teachers of Mathematics, 1989).
(,(.3 3
78
THE 1990 NAEP TRIAL STATE ASSESFMENT
Minnesota
TABLE 27
I Students' Perceptions of Mathematics
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL STATE ASSESSMENT
Minnesota
Centrai
Nation
Student "perception index" groups
Percentage
and
Prelicienqf
Penentaga
and
Prodeleacar
Pereadage
and
Prellakmay
Strongly agree
28 ( 1.3)
25 ( 1.0)
271 1.3)
(' perceptIon index" of 1)
289 ( 1.3)
272
3.5)
271 ( 1.9)
Aare*
51 ( 1.3)
50 ( 1.8)
49 ( 1.0)
("perception index" of 2)
276 ( 1.1)
267 ( 3.1)
2112 ( 1.7)
Undooldotl, clisagreo, strongly tilsagrso
23 ( 1.2)
2$ ( 2.2)
24 ( 1.2)
("perception Index" of 3)
263 ( 1.3)
258 ( 2.3)
251 ( 1.8)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
SUMMARY
Some out-of-school factors cannot be changed, but others can be altered in a positive way
to influence a student's learning and motivation.
Partnerships among students, parents,
teachers, and the larger community can affect the educational environment in the home,
resulting in more out-of-school reading and an increased value placed on educational
achievement, among other desirable outcomes.
The data related to out-of-school factors show that:
Students in Minnesota who had four types of reading matnials (an
encyclopedia, newspapers, magazines, and more than 25 books) at home
showed higher mathematics proficiency than did students with zero to two
types of materials.
This is similar to the results for the nation, where
students who had all four types of materials showed higher mathematics
proficiency than did students wl.;) had zero to two types.
THE 1990 NAEP TRIAL STATE ASSESSMENT
79
Minnesota
Some of the eighth-grade public-school students in Minnesota (15 percent)
watched one hour or less of television each day; 7 percent watched six
hours or more. Average mathematics proficiency was lowest for students
who spent six hours or more watching television each day.
Less than half of the students in Minnesota (44 percent) did not miss any
school days in the month prior to the assessment, while 20 percent missed
three days or more.
Average mathematics proficiency was lowest for
students who missed three or more days of school.
About one-quarter of the students (26 percent) were in the "strongly
agree" category relating to students' perceptions of mathematics. Average
mathematics proficiency was highest for students who were in the "strongly
agree" categorj and lowest for students who were in the "undecided,
disagree, strongly disagree" category.
80
THE 1990 NAEP TRIAL STAIL ASSESSMENT
Minnesota
ME NATION'S
REPORT
CARD
PROCEDURAL APPENDIX
This appendix provides an overview of the technical details of the 1990 Trial State
Assessment Program. It includes a discussion of the assessment desigy, the mathematics
framework and objectives upon which the assessment was based, and the procedures used
to analyze the trsults.
The objectives for the assessment were developed through a consensus process managed
by the Council of Chief State School Officers, and the items were developed through a
similar process managed by Et:...,i-ational Testing Service. The development of the Trial
State Assessment Program benetitted from the involvement of hundreds of representative
from State Education Agencies who attended numerous NETWORK meetings, served on
committees, reviewed the framework, objectives, and questions, and, in general, provided
important suggestions on all aspects of the program.
Assessment Design
The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB)
spiral matrix design -- a design that enables broad coverage of mathematics content while
minimizing the burden for any one student.
In total, 137 cognitive mathemaiics items wem developed for the assessment, including 35
open-ended items. The first step in implementing the BIB design required dividing the
entire set of mathematics items into seven units called blocks. Each block was designed to
be completed in 15 minutes.
THE 1990 NAEP TRIAL STATE ASSESSMENT
81
Minnesota
The blocks were then assembled into assessment booklets so that each booklet contained
two background questionnaires -- the first consisting of general background questions and
the second consisting of mathematics background questions -- and three blocks of cognitive
mathematics items. Students were given five minutes to complete each of the background
questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics
items. Thus, the entire assessment required approximately 55 minutes of student time.
In accordance with the BIB design, the blocks were assigned to the assessment booklets so
that each block appeared in exactly three booklets and each block appeared with every
other block in one booklet. Seven assessment booklets were used in the Trial State
Assessment Program. The booklets were spiraled or interleaved in a systematic sequence
so that each booklet appeared an appropriate number of times in the sample. The students
within an assessment session were assigned booklets in the order in which the booklets were
spiraled. Thus, students in any given session received a variety of different booklets and
only a small number of students in the session received the same booklet.
Assemment Content
The framework and objectives for the Trial State Assessment Program were developed
using a broad-based consPisus process, as described in the introduction to this report.'
The assessment framework consisted of two dimensions: mathematical content areas and
abilities. The five content areas assessed were Numbers and Operations; Measurement;
Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see
Figure Al). The three mathematical ability areas assessed were Conceptual Understanding,
Procedural Knowledge, and Problem Solving (see Figure A2).
Data Analysis and Scales
Once the assessments had been conducted and information from the assessment booklets
had been compiled in a database, the assessment data were weighted to match known
population proportions and adjusted for nonresponse. Analyses were then conducted to
determine the percentages of students who gave various responses to each cognitive and
background question.
Item response theory (I RT) was used to estimate average mathematics proficiency for each
jurisdiction and for various subpopulations, based on students' performance on the set of
mathematics items they received. IRT provides a common scale on which performance
can be reported for the nation, each jurisdiction, and subpcpulations, even when all
students do not answer the same set of questions. This common scale makes it possible
to report on relationships between students' characteristics (based on their responses to the
background questions) and their overall performance in the assessment.
National Assessment of Priueational Progress, Mathematics Objectives 1990 Asse.ssment (Princeton, NJ:
EAucational Testing Service. 1988).
-/
0
82
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
FIGURE Al I
Content Areas Assessed
THE NNW'S
REPORT
CARD
111,
Numbers and Operations
This content area focuses on Students' understanding of numbers (whole numbers, fractions, decimals,
integers) and their application to real-world situations, as well as computational and estimation situations.
Understanding numerical relationships as expressed in ratios, proportions, and percents is emphasized.
Students' abilities in estimation, mental computation, use ot calculators, generalization of numerical
patterns, and verification of results are also included.
Measurement
This content area focuses on students' ability to describe real-world objects 'sing numbers. Students are
asked to identify attribute% Select appropriate units, apply measurement concepts, and communicate
measurement-related ideas to Others. Questions are included that require an ability to read instruments
using metric, customary, or nonstandard units, with emphasis on precision and accuracy. Questions
requiring
estimation,
measurements, and
applications
of
measurements of
length,
time,
money,
temperature, mass/welght, area, volume, capacity, and angles are also included in this content area.
Geometry
This content area focuses on students' knowledge of geometric figures and relationships and on their skills
in working with this knowledge. These siolls are important at all levels of schooling as well as in practical
applications.
Students need to be able to model and viStafIZe geometric figures in one, two, and three
dimensions and to communicate geometric ideas. In addition, students should be able to use informal
reasoning to establish geometric relationships.
Data Analysis, Statistics, and Probability
This content area focuses on data representation and analysis across all disciplines and reflects the
Importance and prevalence of these activities in our society. Statistical knowledge and the ability to
interpret data are necessary skills in the contemporary world. Questions emphasize appropriate methods
for gathering data, the visual exploration of data, and the development and evaluation of arguments based
on data analysis.
Algebra and Functions
This content area is broad in Scope, covering algebraic and functional concepts in more informal,
exploratory ways for the eighth-grade Trial State Assessment. Proficiency in this concept area requires
both manipulative facility and Conceptual understanding: it involves the ability to use algebra as a means
of representation and algebraic processing as a problem-solving tool. Functions are viewed not only in
terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs.
88
THE 1990 NAEP TRIAL STATE ASSESSMENT
83
Minnesota
FIGURE A2
I Mathematical Abilities
The following three categories of mathematical billtles are not to be coast
i as hierarchical.
For
example, probiern solving Involves interactions between conceptual knowledge.
procedural 'skills, but
what is considered complex problem solving at one grade level
may be considered conceptual
understanding or procedural knowledge at another.
Conceptual Understanding
Students demonstrate conceptual understanding in mathematics when they provide evidenGe that they can
recognize, label, and generate examples and counterexamples of concepts; can use arid interrelate models,
diagrams, and varied representations of concepts; can identify and apply principles; know and can aPPly
facts and definitions; can compare, contrast, and integrate related concepts and principles; can recognize,
interpret, and apply the signs, symbols, and terms used to represent concepts; and can interpret the
assumptions and relations involving concepts in mathematical settings. Such understandings are essential
to performing procedures in a meaningful way and applying them in problem-solvingsituations.
Procedural Knowledge
Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to
select and apply appropriate procedures correctly, verify and justify tha correctness of a procedure using
concrete models or symbolic methods, and extend or modify procedures to deal with factors inherent in
problem settings.
Procedural knowledge includes the various numerical algorithms in mathematics that
have been created as tools to meet specific needs in an efficient manner.
It also encompasses the abilities
to read and produce graphs and tables, execute geometric constructions, and perform noncomputationai
skills such as rounding and ordering,
LProblem Solving
1111.1.MIMIM.1111
In problem solving, students are required to usa their reasoning and analytic sbilit
when they encounter
new situations.
Problem solving includes the ability to recognize and formulate problems: determine the
sufficiency and consistency of data: use strategies, data, models, and relevant mathematics: generate,
extend, and modify procedures: use reasoning (Le.,
spatial,
inductive, deductive,
statistical, and
proportional): and judge the reasonableness and correctness of solutions.
t3;
84
THE 1990 NAEP TRIAL. STATE ASSESSMENT
Minnesota
A scale ranging from 0 to 500 was created to report perfonnance for each content area.
Each content-arm scale was based on the distribution of student perfomiance across all
three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean
of 250 and a standard deviation of 50.
A composite scale was created as an overall measure of students' mathematics proficiency.
The composite scale was a weighted average of the five content area scales, where the
weight for each content area was proportional to the relative importance assigned to the
content area in the specifications developed by the Mathematics Objectives Panel.
Scale Anchoring
Scale anchoring is a method for defining performance along a scale. Traditionally,
performance on educational scales has been defined by norm-referencing -- that is, by
comparing students at a particular scale level to other students. In contrast, the NAEP
scale anchoring is accomplished by describing what students at selected levels know and
can do.
The scale anchoring process for the 1990 Trial State Assessment began with the selection
of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels
below 200 and above 350 could theoretically have been defined, they were not because so
few students performed at the extreme ends of the scale. Any attempts to define levels at
the extremes would therefore have been highly speculative.
To define performance at each of the four levels on the scale, NAEP analyzed sets of
mathematics iter s from the 1990 assessment that discriminated well between adjacent
levels. The critei a for selecting these "benchmark" items were as follows:
1 3 de :Inc performance at level 200, items were chosen that were answered
cor-ectly by at least 65 percent of the students whose proficiency was at or
eal 200 on the scale.
To defme performance at each of the higher levels on the scale, items were
chosen that were: a) answered correctly by at least 65 percent of students
whose proficiency was at or near that level; and b) answered incorrectly by
a majoeity (at least 50 percent) of the students performing at or near the
next lower level.
The percentage of students at a level who answered the item correctly had
to be at least 30 points Mgher than the percentage of students at the next
lower level who answered it correctly.
DO
THE 1990 NAEP TRIAL STATE ASSESSMENT
85
Minnesota
Once these empirically selected sets of questions had bevn identified, mathematics educators
analyzed the questions and used their expert judgment to characterize the knowledge, skills,
and understandings of students performing at each level. Each of the four proficiency levels
was defined by describing the types of mathematics questions that most students attaining
that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides
a summary of the levels and their characteristic skills. Example questions for each level are
provided in Figure A3, together with data on the estimated proportion of students at or
above each of the four proficiency levels who correctly answered each question.'
Questionnaires for Teachers and Schools
As part of the Trial State Assessment, questionnaires were given to the mathematics
teachers of assessed students and to the principal or other administrator in each
participating school.
A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made
recommendations concerning the design of these questionnaires. For the 1990 assessment,
the teacher and school questionnaires focused on six educational areas: curriculum,
instructional practices, teacher qualifications, educational standards and reform, school
conditions, and conditions outside of the school that facilitate learning and instruction.
Similar to the development of the materials given to students, the policy guidelines and the
teacher and school questionnaires were prepared through an iterative process that involved
extensive development, field testing, and review by external advisory groups.
MATHEMATICS TEACHER QUESTIONNAIRE
The questionnaire for eighth-gade mathematics teachers consisted of two parts. The first
requested information about the teacher, such as raceiethnicity and gender, as well as
academic depees held, teaching certification, training in mathematics, and ability to get
instructional resources. In the second part, teachers were asked to provide information on
each class they taught that included one or more students who participated in the Trial
State Assessment Program. The information included, among other things, the amount
of time spent on mathematics instruction and homework, the extent to which textbooks
or worksheets were used, the instructional emphasis placed on different mathematical
topics, and the use of various instructional approaches. Because of the nature of the
sampling for the Trial State Assessment, the responses to the mathematics teacher
questionnaire do not necessarily represent all eighth-pude mathematics teachers in a state
or tenitory. Rather, they represent the teachers of the particular students being assessed.
Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions
exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the
twelfth-grade national assessment.
n. I
86
THE 1V90 NAEP TRIAL STATE ASSESSMENT
Minnesota
FIGURE A3
I
Example Items for Mathematics Proficiency Levels
Level 200:
Simple Additive Reasoning and Problem Solving with Whole
Numbers
EXAMPLE
Cor
0
SAW
7. la& MO dow kw Wow a bbo swab ma owl slaw albums bah of
bona w ion arm I the Ms owe box wiab sbo Mod a( balls dorm
wimb boa WI bow dm fellow
lo kV
Ths boa v041 tho mode bob
Tho boa owit tho
lab
00 Ma boo wbb tho Mbar bolo
0 %a coo's wai.
EXAMPLE 2
011 *UT MI=
AT FARAWAY MAW
000016
UMW
&woo*
L. How awry boono of wooips woo Sang os Thwidayi
CD SS
O 60
O 70
0 so
a) to
CD I deal know.
VIE 1990 MEP TRIAL STATE ASSESSMENT
9 2
Grads 4
Oman Paroardag CArrect 73%
Percontag Correct for Anohor Lvela
Mg
MI
344
114
55
91
100
Grade 4
Ovarall Paroontaga
Paroantaga Correct
SG
CIO
75
91
Grad. 8
Nara Percentage
Percentage Caract
VA
57
:yak,n.
80%
for
.ocr Levels:
2Q2
100
Correct: 89%
for Anchor tavola:
Si?
96
100
Sknple Mull !Okays Reasoning end Two-Step Problem Solving
1
Minnesota
FIGURE A3
I
Example Items for Mathematics Proficiency Levels
(continued)
ILin"! 250:
EXAMPLE 1
1. What is the value of n +
whez n a.. 3
Answer:
EXAMPLE 2
The es* slows thews Ihe NO* el a serm d Irk Wee. On Ai Weis
West, asks s tie* psalm Amen she dos la die al& Label aw1
iss al the chile ipapb with lie amen bar NW.
Da Tv,
ebe cabooses ea this Iterselese?
0 lb*
0 Hs
EXAMPLE 3
6. Ilashkes I psalms bessIall Ws bons lad bee Web 6 baseballs. Obe
hos 24 hak Which eassabse reeteeme iU help ha fled eel how we?
hews aloe wit smog
CD34
me 24 +4.0
024 +6-0
14 6 ee
cp I deal bow.
138
Grade 8
Overall PINVINT11041 COM& 76%
Percentage coma for Anchor Levels:
222
MN
202
MI)
a
ee
95
96
Grade 8
Overall Percentage Contact 73%
Percentage Coma for Anchor Levels:
222
2111
MQ
21
119
92
92
Grade 8
Omit Pementag Correct 77%
Percentage Correct for Anchor LavIs:
222
Mg
22/
37
71
95
100
f? 3
ME 1990 NAM TRIAL STATE ASSIZE..4BM
Minnesota
FIGURE A3
I
Example Items for Mathematics Proficiency Levels
(continued)
L
Level 300:
Reasoning and Problem Solving involving Fractions, Decimal%
Percent% Elementary Geometric Properties, and Simple
Alpbralc Manipulations
EXAMPLE 1
IL Width el the fedeeriee show as mob et Aimee ths almsra usaaglo woe
shs Vas it
EXAMPLE 2
tV
d sews dos a dos io bad*. e eat IS la loVuiriatia
by a *de wail lead Jew V the seem ode i mak a
3.1 len
Web weal be terremesod ei
me)* mead hew dal Wes W#0
rod yea we abc aelehdeter ea dds 'wade?
0 Vie
0 Se
Grade
OveraN Percentage Correct OM
Peroentege Corned for Moho( Levels:
2121
i22
33
40
77
90
Grade 12
Overall Percentage Correct: 75%
Percentage Correct for Anchor Levels:
2411
210
222
---
46
79
05
Grade 11
Overall Percentage Correct 50%
Percentage Correct for Moho; Levels:
ag,
2Q5/
1,112
17
46
BB
90
BEST COPY AVAILABLE'
Minnesota
FIGURE A3
I
Example Items for Mathematics Proficiency Levels
(continued)
1
Level 350:
Reasoning and Problem Solving involving Geometric
Relationships, Algebraic Equations; and Beginning Statistics and
Probability
EXAMPLE
Qwwitiono 16-17mint to th øi1a os sum do4-14ur.m
1
2
1
16. It &Ms dams al den-ligures ia eattnaood. bate may does wiI b 4i au
10474 figural
CD 100
CID 101
CD 199
CD 200
CP 201
EXAMPLE 2
17. tipliin Mow you ;wind you, anon: ***gains 16.
Mawr
Grade 8
Overall Percentage Correct 34%
Percentage Oxrect for Moho( Levels:
Mg
22:1
gria
13
19
53
ea
Grade 12
Overall Percentage Correct 49%
Percentage Correct for Anchor 1.11V*11:
221
alg
292
222
---
22
48
90
Grade 8
Overall Percentage Correct: 15%
Percentage Correct for Anchor Levels:
2124
222
1
4
26
74
Grade 12
Overall Percentage Correct 27%
Percentage Correct for Mchor Levels:
ZSE
21§2
Ng
MO
3
22
74
90
TIM 1990 NAB? TRIAL STA1E ASSESSMENT
Minnesota
SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE
An extensive school questionnaire was completed by principals or other administrators in
the schools participating in the Trial State Assessment. In addition to questions about the
individuals who completed the questionnaires, there were questions about school policies,
coursc offerings, and speciai priority areas, among other topics.
It is important to note that in this report, as in all NAEP reports, the student is always the
unit of analysis, even when information from the teacher or school questionnaire is being
reported. Ilaving the student as the unit of analysis makes it possible to describe the
instruction received by representative samples of eighth-grade students in public schools.
Although this approach may provide a different perspective from that which would be
obtained by simply collecting information from a sample of eighth-grade mathematics
teachers or from a sample of schools, it is consistent with NAFP's goal of providing
information about the educational context and performance of students.
Estimating Variability
The statistics xported by NAEP (average proficiencies, percentages of students at or above
particular scale-score levels, and percentages of students responding in certain ways to
background questions) are estimates of the corresponding information for the population
of eighth-grade students in public schools in a state. These estimates are based on the
performance of a carefully selected, representative sample of eighth-grade public-school
students from the state or territory.
If a different representative sample of students were selected and the assessment repeated,
it is likely that the estimates might vary somewhat, and both of these sample estimates
might differ somewhat from the value of the mean or percentage that would be obtained
if every eighth-grade public-school student in the state or territory were assessed. Virtually
all statistics that are based on samples (including those in NAFP) are subject to a certain
degee of uncertainty, The uncertainty attributable to using samples of students is referred
to as sampling error.
like almost all estimates based on assessment measurc;, NAFP's total group and subgoup
proficiency estimates are subject to a second source of .mcertainty, in addition to sampling
error. As previously noted, each stucient who participraed in the Trial State Assessment
was administered a subset of questions from the total set of questions. If each student had
been administered a different, but equally appropriate, set of the assessment questions
or the entire set of questions -- somovhat different estimates oi' total group and subgroup
proficiency might have been obtained. Thus, a second source of uncertainty arises because
each student was administered a subset of the total pool of questions.
n 6
THE 1990 NAEP TRIAL STATE ASSESSMENT
91
Minnesota
In addition to reporting estimates of avenge proficiencies, proportions of students at or
above particular scale-score levels, and proportions of students giving various responses to
background questions, this report also provides estimates of the magnitude of the
uncertainty associated with these statistics. These measures of the uncertainty are called
standard errors and are given in parentheses in each of the tables in the report. The
standard errors of the estimates of mathematics proficiency statistics reflect both sources
of uncertainty discussed above. The standard errors of the other statistics (such as the
proportion of students answering a background question in a certain way or the proportion
of students in certain racial/ethnic groups) reflect only sampling error. NAEP uses a
methodolou called the jackknife procedure to estimate these standard errors.
D-awing Inferences from the Results
One of the goals of the Trial State As:essment Program is to make inferences about the
overall population of eighth-grade students in public schools in each participating state and
territory based on the particular sample of students assessed. One uses the results from the
sample -- taking into account the uncertainty associated with all samples -- to make
inferences about the population.
The use of confidence intepvals,bAscd on the standard errors, provides a way to make
inferences about the population nans and proportions in a manner that reflects the
uncertainty associated with the sample estimates. An estimated sample mean proficiency
2 standard errors represents a 95 percent confidence interval for the corresponding
population quantity. This means that with approximately 95 percent certainty, the average
performance of the entire population of interest (e.g., all eighth-grade students in public
schools in a state or territory) is within ± 2 standard errors of the sample mean.
As an example, suppose that the average mathematics proficiency of the students in a
particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence
interval for the population quantity would be as follows:
Mean ± 2 standard errors = 256 ± 2
(1.2)
256 ± 2.4 =
256 - 2.4 and 256 + 2.4 = 253.6, 258.4
Thus, one can conclude with 95 percent certainty that the average proficiency for the entire
population of eighth-grade students in public schools in that state is between 253.6 and
258.4.
Similar confidence intervals can be constructed for percentages, provided that the
percentages are not extremely large (greater than 90 percent) or extremely small (less than
10 percent ). For extreme percentages, confidence intervals constructed in the above
manner may not be appropriate and procedures for obtaining accurate confidence intervals
are quite complicated.
S 7
92
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
Analyzing Subgroup Differences in Proficiencies and Proportions
In addition to the overall results, this report presents outcomes separately for a variety of
important subgroups. Many of these subgroups are defined by shared characteristics of
students, such as their gender, race/ethnicity, and the type of community in which their
school is located. Other subgroups are defined by students' responses to background
questions such as About how much time do you usually spend each day on mathematics
homework? Still other subgroups are defined by the responses of the assessed students'
mathematics teachers to questions in the mathematics teacher questionnaire.
As an example, one might be interested in answering the question: Do students who
reported spending 45 minutes or more doing mathematics homework each day exhibit higher
average nulhematics proficiency than students who reported spending 15 minutes or less?
To answer the question posed above, one begins by comparing the average mathematics
proficiency for the two groups being analyzed. If the mean for the group who reported
spending 45 minutes or more on mathematics homework is higher, one may be tempted
to conclude that that group does have higher achievement than the group who reported
spending 15 minutes or less on homework. However, even though the means differ, there
may be no real difference in performance between the two groups in the population because
of the uncertainty associated with the estimated average proficiency of the groups in the
sample. Remember that the intent is to make ;, statement about the entire population, not
about the particular sample that was assessed, The data from the sample are used to make
inferences about the population as a whole.
As discussed in the previous section, each estimated sample mean proficiency (or
proportion) has a degree of uncertainty associated with it. It is therefore possible that if
all students in the populatiun had been assessed, rather than a sample of students, or if the
assessment had been repeated with a different sample of students or a different, but
equivalent, set of questions, the performances of various groups would have been different.
Thus, to determine whether there is a real difference between the mean proficiency (or
proportion of a certain attribute) for two groups in the population, one must obtain an
estimate of the degree of uncertainty associated with the Jifference between the proficiency
means or proportions of those groups for the sample. This estimate of the degree of
uncertainty -- called the standard erroP of the difference between the groups -- is obtained
by taking the square of each group's standard error, summing these squared standard errors,
and then taking the square root of this sum.
Similar to the manner in which the standard error for an individual group mean or
proportion is used, the standard error of the difference can be used to help determine
whether differences between groups in the population are real. The difference between the
mean proficiency or proportion of the two groups ± 2 standard errors of the difference
repreients an approximate 95 percent confidence interval. If the resulting interval includes
zero, one should conclude that there is insufficient evidence to claim a real difference
between groups in the population. If the interval does not contain zero, the difference
between groups is statistically significant (different) at the .05 level.
THE 1990 NAEP TRIAL STATE ASSESSMENT
93
Minnesota
As an example, suppose that one welt interested in determining whether the average
mathematics proficiency of eighth-grade females is higher than that of eighth-grade males
in a partirular state's public schools. Suppose that the sample estimates of the meaal
proficiencies and standard errors for females and males were as follows:
Group
Average
Proficiency
Standard
Error
Female
259
I..
2.0
Male
255
2.1
The 4ifference between the estimates of the mean proficiencies of females and males is four
points (259 - 255). The standard error of this difference is
Ni2.02 + 2.12 = 2.9
Thus, an approximate 95 percent confidence interval for this difference is
Mean difference ± 2 standard errors of the difference =
4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8
The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero
is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to
claim a difference in average mathematics proficiency between the population of
eighth-grade females and males in public schools in the state.'
Throughout this report, when the mean proficiency or proportions for two groups were
compared, procedures like the one described above were used to draw the conclusions that
are presented. If a statement appears in the report indicating that a particular group had
higher (or lower) average proficiency than a second group, the 95 percent confidence
interval for the difference between groups did not contain zero. When a statement indicates
that the average proficiency or proportion of some attribute was about the same for two
groups, the confidence interval included zero, and thus no difference could be assumed
between the groups. The reader is cautioned to avoid drawing conclusions solely on the
basis of the magnitude of the differences. A difference between two groups in the sample
that appears to be slight may represent a statistically significant difference in the population
because of the magnitude of the standard errors. Conversely, a difference that appears to
be large may not be statistically significant,
3 The procedure described above (especially the estimation of the standard error of the difference) is, in a strict
sense, only appi opriate when the statistics being compared come from independent samples. For certain
comparisons in the report, the groups were not independent. In those cases, a different (and more
appropriate) estimate of the standard error of the difference was used.
C
7
94
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95
percent confidence interval), are based on statistical theory that assumes that only one
confidence interval or test of statistical significance is being performed. However, in each
chapter of this report, many different groups are being compared (i.e., multiple sets of
confidence intervals are being analyzed). When one considers sets of confidence intervals,
statistical theory indicates that the certainty associated with the entire set of intervals is less
than that attributable to each individual comparison from the set. lf one wants to hold the
certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called
multiple comparison procedures) must be made: to the methods described in the previous
section. One such procedure -- the Bonferroni method -- was used in the analyses described
in this report to form confidence intervals for the differences between groups whenever sets
of comparisons were considered. Thus, the confidence intervals in the text that are based
on sets of comparisons are more conservative than those descri)-...: on the previous pages.
A more detailed description of the use of the Bonferroni procedure appears in the Trial
State Assessment technical report.
Statistics with Poorly Determined Standard Er7ors
The standard errors for means and proportions reported by NAEP are statistics and
therefore are subject to a certain degree of uncertainty. In certain cases, typically when the
standard error is based on a small number of students, or when the group of students is
enrolled in a small number of schools, the amount of uncertainty associated with the
standard errors may be quite large. Throughout this report, estimates of standard errors
subject to a large degree of uncertainty are followed by the symbol "!".
In such cases, the
standard errors -- and any confidence intervals or significance tests involving these standard
errors -- should be interpreted cautiously. Further details concerning procedures for
identifying such standard errors are discussed in the Trial State Assessment technical report.
Minimum Subgroup Sample Sizes
Results for mathematics proficiency and background variables were tabulated and reported
for groups defmed by race/ethnicity and type of school community, as well as by gender
and parents' education level. NAEP collects data for five racial/ethnic subgroups (White,
Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) and four
types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and
Other Communities). However, in many states or territories, and for some regions of the
country, the number of students in some of these groups was not sufficiently high to permit
accurate estimation of proficiency and/or background variable results. As a result, data are
not provided for the subgroups with very small sample sizes. For results to be reported for
any subgroup, a minimum sample size of 62 students was required. This number was
determined by computing the sample size required to detect an effect size of .2 with a
probability of .8 or greater.
1
o
THE 199(1 NAEP TRIAL STATE ASSESSMENT
95
Minnesota
The effect size of .2 pertains to the true difference between the average proficiency of the
subgroup in question and the average proficiency for the total eighth-grade public-school
population in the state or tenitory, dividal by the standard deviation of the proficiency in
the total population. If the oue difference between subgroup and total group mean is .2
tot& group standard deviation units, then a sample size ef at least 62 is required to detect
such a difference with a probability of .8. Further details about the procedure for
determining minimum sample size appear in the Trial State Assessment technical report.
Describing the Size of Percentages
Some of the percentages reported in the text of the report are given quantitative
descriptions. For example, the number of students being taught by teachers with master's
degrees in mathematics might be described as "relatively few" or "almost all," depending
on the size of the percentage in question Any convention for choosing descriptive temis
for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used
in the report and the rules used to select them are shown below.
Percentage
,
Descripdon of Text in Report
...
.
.,
p --:-- 0
None
0 < p
.5_ 10
Relatively few
10 < p 5 20
Some
20 < p 5 30
About one-quarter
30 < p 5 44
Less than half
44 < p 5 55
About half
55 < p 5 69
More than half
69 < p 5 79
About three-quarters
79 < p 5 8g
Many
89 < p < 100
Almost all
p = 100
All
.
_i
96
THE 1990 NAEP TRIAL STATE ASSESSMENT
THE NATION'S
REPORT
CARD
DATA APPENDIX
For each of the tables in the main body of the report that presents mathematics proficiency
results, this appendix contains corresponding data for each level of the four reporting
subpopulations -- race/ethnicity, type of community, parents' education level, and gender.
102
THE 1990 NAEP TRIAL STATE ASSESSMENT
97
Minnesota
TABLE AS
1 Students' Reports on the Mathematics Class
I They Are Taking
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1
191113 NAEP TRIAL
Eighth-grede
STATE ASSESSMENT
Mathematics
Pre-Sigleri
Algebra
TOTAL
Pactentapo
and
Pro Wow
Ponmadage
and
fondialkanot
Rintentaga
and
Prallohancy
State
54 ( 3.0)
25 ( 24)
17 ( 1,4)
268( 1.3)
261 ( 1.1)
3C3 ( 1.6)
Nation
621 2.1)
10( 14)
15 ( 1.2)
251 ( 14)
272 ( 2.4)
296 ( 2.4)
NACE/ETHNICITY
Milts
State
53 ( 3.1)
25 ( 2.4)
18 ( 1.5)
269 ( 1.3)
262 ( 1.2)
308 ( 1.5)
Nation
59 ( 2.5)
21 ( 2.4)
17 ( 1.5)
259 ( 1.6)
277 ( 2,2)
300 ( 2.3)
Black
State
71 (
004 ( 6.2)
21 ( 4.4)
.41
8 (
(
3.2)
***)
Nation
72 ( 4.7)
18 ( 3.0)
9 ( 22)
232 ( 3.4)
248 ( 6.4)
( ***)
Hispanic
State
65 ( 6.2)
23 ( 5 .5)
( 2.7)
01/
Me*
Nation
75 ( 4.4)
13 ( 3.9)
6 ( 1.5)
240 ( 2.4)
( "*)
Asian
State
4,5 ( 6.1)
17 ( 3.4)
29 ( 4.7)
(
Nation
32 ( 6.5)
21 ( 63)
**..)
41 ( 7.4)
TYPE OF COMMUNITY
Advantaged urban
State
58 ( 4.9)
27 ( 4.4)
13 ( 1.7)
267 ( 2.0)
286 ( 2.3)1
314 ( 3.7)
Nation
55 ( 9.4)
22 ( 7.9)
21 ( 4.4)
269 ( 2.5)1
Extreme rural
State
58 ( 6.8)
24 ( 4.9)
18 ( 3.2)
270 (
2.0)1
280 ( 2.3)1
295 ( 45)1
Nation
74 (
249 (
4.5)
3.1)1
14 ( 5.0)
.04.*)
7 ( 2.2)
Other
State
55 ( 5.0)
25 ( 4.2)
17 ( 2.3)
269 ( 23)
283 (
1.7)1
308 ( 2.3)
Nation
61 ( 2.2)
20 ( 2.1)
10 ( 1.4)
251 ( 2.0)
272 ( 2.8)
294 ( 2.7)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because a small number of students
reported taking other mathematics courses. I Interpret with caution -- the nature of the sample does not allow
accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to
permit a reliable estimate (fewer than 62 students).
98
THE 1990 NAEP TRIAL. STATE ASSESSMENT
Minnesota
TABLE AS
I Students' Reports on the Mathematics Class
(continued)
They Are Taking
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAEP TRIAL
Eighth-grade
STATE ASSESSMENT
Mathematics
Pre-algebra
TOTAL
Pereentage
anti
Proficiency
Peroentlles
and
Prelkiency
Percents.
and
Proficiency
State
54 ( 3.0)
25 ( 2.4)
17 ( 1.4)
2ee ( 1.3)
281 ( 1.1)
303 ( 1.6)
Nation
62 ( 2.1)
19 ( 1.9)
16 ( 1.2)
251 ( 1.4)
272 ( 2.4)
293 ( 2.4)
PARENTS' EDUCATION
HS non-graduate
State
70 (
253 (
5.2)
4.0)
17 (
4 ( 42)
**)
11 (
*iv
( 3.4)
Nation
77 ( 3.7)
13 ( 3A)
3 ( 1.1)
241 ( 2.1)
ra.
trirl
$43 gracluate
State
64 ( 3.7)
29 ( 3.1,
9 ( 1.4)
259 ( 1.8)
275 ( 1.9)
288 ( 4.3)
Nation
70 ( 2.6)
18 ( 2.4)
$ ( 1.1)
249 ( 1.9)
266 ( 3$)
277 ( 5.2)
Soma coliorga
State
52 ( 3,5)
26 ( 2.7)
1: ( 2.2)
274 ( 1.7)
284 ( 2.0)
306 ( 2.3)
Nation
80 ( 3.1)
21 ( 2.9)
15 ( 1.9)
257 ( 2.1)
276 ( 2.8)
295 ( 3.2)
Co Nage graduate
State
48 ( 3.n!
27 ( 2.9)
23 ( 2.0)
273 (
284 ( 1.3)
310 ( 1.5)
Nation
53 ( 2.7j
21 ( 2.3)
24 ( 1.7)
259 (
1.5)
278 ( 2.8)
303 ( 2.3)
GENDER
Male
State
54 ( 3.2)
24 ( 2.5)
18 ( 1.8)
266 ( 1.7)
281 ( 1.4)
305 ( 2.2)
Nation
63 ( 2.1)
18 ( 1.8)
15 ( 1.2)
252 ( 1.8)
275 ( 2.9)
299 ( 2.5)
Female
State
54 ( 3.2)
25 ( 2.5)
17 ( 1.6)
266 (
1.4)
281 ( 1.4)
301 ( 2.1)
Nation
61 ( 2.6)
20 ( 2.3)
15 ( 1.7)
251 ( 1.5)
269 ( 3.0)
293 ( 2.8)
The standard errors of the estimated statistics appear in i.,..rentheses.
It can be said wnh about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample. The percentages ray not total 100 percent because a small number of students
reported taking other mathematics courses. *** Sample stze is insufficient to permit a reliable estimate (fewer
than 62 students).
104
THE 1990 NAEP TRIAL STATE ASSESSMENT
99
Minnesota
TABLE A6
Teachers' Reports on the Amount of Time
Students Spent on Mathematics Homework
Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 MEP TRIAL
STATE ASSESSMENT
None
15 linen
30 Mkiutn
46 Minutes
,
An liar or
Mors
TOTAL
Penntage
and
Praticisnty
2 ( 0.5)
*44,)
( 0.3)
*141 ( Van
2 ( 0.4)
1 ( 0.3)
*44(4*4 )
2 ( 1.8)
(
( 0.7)
.44 ( *41
( 3.1)
.4* ( `44)
( 0.8)
( **4)
6 ( 3.0)
*4-1
0 ( 0.0)
2 ( 0.7)
444 ( "*)
( 0.9)
0 ( 0.0)
2 ( 0.9)
*IN (
*HP )
( 04)
444 ( 414)
Percentage
and
Praia Amy
a ( 3.4)
273 ( 1.5)
43 ( 4,2)
251 ( 2.3)
46 ( 3.8)
27$ ( 14)
39 ( 4.5)
286 ( 2.2)
58 ( 6.9)
*44(44*)
55 ( 7.8)
232 ( 3.1)
41 ( 7.6)
46 ( 7.8)
245 (
3.0)1
30 ( 5.7)
IP** (
29 ( 7.8)
48 ( 5.2)
274 ( 3.1)1
61 (11.3)
273 ( 3.1)1
49 ( 8.5)
275 ( 2.5)1
68 (14.9)
253 ( 5.4)1
48 ( 4.5)
279 ( 1.9)
37 ( 4.3)
256 ( 3.1)
State
Nation
RACE/ETHNICITY
White
State
Nation
Black
State
Nation
Hispanic
State
Nation
Asian
State
Nation
TYPE OF COMMUNITY
Advantaged urban
State
Nation
Extrema nral
State
Nation
Other
State
Nation
Peroseiage
and
Pre Many
42 ( $.3)
2.6)
276
1.6)
43
4.3
200
)
42 ( 3,4)
278 ( 1.6)
45 ( 5.1)
270 ( 2.7)
34 ( 7.2)
.641
40 ( 8.7)
24$ ( 5.3)
47 ( 7.1)
.04* ( 441
34 ( 6.8)
251 ( 4.2)1
1144 (
37 ( 8.8)
42 ( 4.7)
278 ( 2.8)
32 ( 8.8)
444 ( ***)
40 (
8.0)
275 (
3.8)1
14 (10.9)
4,4.)
44 ( 4.9)
277 ( 2.8)
48 ( 5.1)
265 ( 2.5)
ihwasrata.
and
and
libralkinagi
Peak* lacY
7 ( 11)
2 ( 1.1)
290 ( 4.0$
267
6.3)I
10 ( IA)
4
0.9)
272 ( 5.7)I
27$
5.1)1
( 1.6
2 (1.1)
292 ( 4,0)4
eel
11 ( 2.4)
4 ( 01)
277 ( 74)1
279 ( 5.9)4
7 ( 3.9)
1 ( 1.2)
es.)
3 ( 1.2)
21 0.0
1141.
IMO )
44* ( (HI
2.6)
( 1.1)
.44)
INr
13 ( 2.9)
7 ( 2.1)
414 (
( 4.3)
( 52)
44' ( 4441
10 ( 5.4)
24 (10.2)
.44 (
-.*
3 (
1.6)
( 0.9)
"4 (
444)
5 ( 3.4)
0 ( 0.0)
mod, (
a** (
( 4.2)
1 ( 1.1)
(
8 ( 5.8)
10 ( 7.3)
*44(44*)
+al
5 (
1.3)
4 ( 2.7)
*-4/4
41
." ( 4")
10 ( 2.4)
4 ( 1.1)
276 ( 8.6)1
282 (11.6)1
The standard errors of the estimated statistics appear in parentheses.
It can be said with about cs percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
100
1 15
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A6
Teachers' Reports on the Amount of Time
(cmtinued)
Students Spent on Mathematics Homework
Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
_
Vane
16 Minutes
30 Minutes
45 Minutes
An Hour or
More
TOTAL
State
Nation
PARENTS' EDUCATION
aid
Preaching
2 ( 0.5)
( *01
1 ( 0.3)
( ***)
6
3.1)
1 ( 0.8)
«it
49)
1 ( 0.6)
**it
( 0.5)
(
1 ( 0.6)
444 ( 444)
1 ( 0.9)
"4 ( 4")
2 ( 0.7)
( 0.3)
grfr,
(
1 ( 0.3)
2 ( 0.5)
*** (*")
1 ( 0.4)
*** ( * )
Perceniage
and
Proldency
46 ( 3.4)
273 ( 1.5)
43 ( 4.2)
250 ( 2.3)
45 ( 5.3)
*el
Aq ( 8.3)
240 ( 2.8)
50 ( 4.7)
263 ( 2.2)
43 ( 5.2)
249 ( 3.1)
44 ( 4.2)
281 ( 2.0)
44 ( 5.4)
265 ( 2.8)
45 ( 3$)
282 ( 1.7)
40 ( 4.7)
285 ( 2.5)
47 ( 3.8)
275 ( 1.8)
44 ( 4.4)
257 ( 2.9)
45 ( 3.5)
272 ( 1.7)
41 ( 4.4)
255 I 2.3)
Perienteso
and
Proficiency
42 ( 3.3)
270 ( /11)
43 ( 4.3)
200 ( 2.6)
40 ( 54)
1141.
NIP1
40 ( 6.1)
246 ( 3.7)
42 ( 4.7)
265 ( 1.9)
44 ( 5.8)
258 ( 2.7)
42 ( 3.8)
282 ( 2.1)
43 ( 5.8)
270 ( 3.6)
42 ( 3.1)
254 ( 2.2)
44 ( 4.1)
277 ( 3.0)
42 ( 35)
278 ( 2.1)
43 ( 4.3)
288 ( 2.9)
42 ( 3.3)
276 ( 1.8)
43 ( 4.7)
284 ( 2.8)
Porcenialle
and
Proidensi
7 ( LS)
290 ( 4.0)I
10 (
1.51)
272 ( 51),
6 ( 3.1)
6 ( 1.7)
**4 ( "4)
4 ( 1.4)
9 ( 3.1)
11 ( 2.7)
7 ( 2.1)
*** ( ***)
8 ( 1.8)
300 ( 3.9)1
11 ( 2.3)
207 ( 8.1)1
7 ( 1.6)
293 ( 5.1)1
9 ( 1.9)
273 ( 7.3)1
8 ( 1.8)
288 ( 5.0)1
11 ( 2.0)
272 ( 5.7)1
Paved..
and
Prodding,
2 ( 1.1)
207 ( 03)f
2748
5a9.4
3 ( 2.4)
gvn
4 ( 1.3)
2 ( 1.3)
3 ( 1.0)
04+ (
3 ( 1.4)
4 ( 1.0)
444 ( 444)
3 ( 1.0)
5 ( 1.3)
(
5 ( 1.3)
279 ( 7.7)1
3 ( 1.2)
4,4)
IM non-graduate
State
Nation
NS graduate
State
Nation
Some college
State
Nation
College graduat
State
Nation
GENDER
Male
State
Nation
Female
State
Nation
The standard errors of the estimated statistics apoear in parentheses.
It can be said with
certainty that, for each population of interest, the value for the entire population is within ±
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does n
determination of the variability of this estimated mean proficiency. *** Sample size is insulT
reliable estimate (fewer than 62 students).
about 95 percent
2 standard errors
ot allow accurate
icient to permit a
THE 1990 NAEP TRIAL STATE ASSESSMENT
101
Minnesota
TABLE A7
I Students' Reports on the Amount of Time They
Spent on Mathematics Homework Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL
STATE ASSESSMENT
None
16 Minutes
-
30 Itkuttes
46 Minutes i An Hoar or
1
Mere
TOTAL
Percentege
and
Proficiency
Percentene
and
Proficiency
Peroentegs
and
Proliciency
Percentage
and
Prelicioacy
Percentage
and
Proficiency
State
10 ( 0.7)
S3 ( 1.3)
30 ( 1.0)
1.0)
12 ( 1.0)
271 ( 24)
278 ( 1.2)
276 ( 1.3)
276
1.6)
274 ( 1.8)
Nation
( 0.3)
31 ( 2.0)
32 ( 1.2)
10
1.0)
12 ( 1.1)
251 ( 24)
254 ( 1.13)
263 ( 12)
266 ( 1.9)
256 ( 3.1)
RACE/ETHNICITY
*Hite
State
10 ( 0.8)
34 ( 1.4)
30 ( 1.1)
15( 1.1)
11 ( 0.9)
273 ( 22)
230 ( 1.1)
279 ( 1.3)
278 ( 1.7)
279 ( 1.9)
Nation
10 ( 1.0)
33 ( 2.4)
32 ( 1.3)
15 ( 0.11)
11 ( 1.3)
sack
293 ( 3.4)
270 ( 1.9)
270 ( 2.1)
277 ( 2.2)
268 ( 9.9)
State
10 ; 3.4)
22 ( 5.3)
hi* (
«pi
13 ( 4.0)
*Mt
14 ( 5.7)
«NI
(
(
(
(
Nation
26 ( 2.5)
33 ( 2.7)
18 ( 2.3)
18 ( 1.9)
241 ( 3.6)
237 ( 3.5)
240 ( 16)
232 ( 3.7)
Hispanic
State
7 ( 3.4)
32 ( 4.9)
31 ( 3.9)
10 ( 3.9)
15 ( 3.4)
1,44
-** )
Ir*
MIN)
*44 ( *Of )
Nation
12 ( 1.5)
27 ( 3.0)
30 ( 2.6)
17 ( 2.1)
44 ( 1.7)
( eee)
246 ( 3.6)
248 ( 3A)
241 ( 4.3)
Asian
State
4 ( 2.2)
20 ( 4.7)
30 ( 5.9)
22 ( 4.6)
Nation
4 ( 2.0)
***)
22 ( 4.6)
31 ( 5.6)
18 ( 3.9)
25 ( 6.2)
TYPE OF COMMUNITY
Advantaged urban
State
9 ( 1.6)
«N.)
36 ( 2.6)
281 ( 2.4)
32 ( 1.8)
277 ( 3.2)
11 ( 1.7)
Nation
(
41 (124)
27$ ( 3.0)1
31 ( 6.6)
230 ( 4.5)1
12 ( 3.3)
eee (
)
7 ( 3.4)-)
Extreme nral
State
9 ( 1.6)
31 ( 2.8)
28 ( 2.1)
18 ( 2.6)
14 ( 2.0)
278 ( 2.4)1
273 ( 2.8)1
274 ( 2.2)
271 ( 2.5)1
Nation
8 ( 2.3)
*iv
41.11
38 ( 4.6;
260 ( 3.5)1
31 ( 2.9)
255 ( 5.1)!
1$ ( 3.8)
( 2.7)
*4.
Other
State
11 ( 1.2)
34 ( 2.4)
31 ( 1.7)
14 ( 1.5)
10 ( 1.4)
276 ( 3.4)
280 ( 1.9)
278 ( 1.3)
278 ( 2.7)
279 ( 3.5)
Nation
9 ( 1.0)
30 ( 16)
32 ( 1.3)
15 ( 1.1)
13 ( 1.1)
250 ( 3.3)
283 ( 2.3)
264 ( 2.3)
267 ( 2.1)
258 ( 3.6)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
1 Interpret with caution - the nature of the sample does not allow accarate
determination of the variability of this estimated mean proficiency.
**6 Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
102
1
7
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A7
Students' Reports on the Amount of Time They
(mitinued)
I Spent on Mathematics Homework Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1910 NAEP TRIAL
STATE ASSESSMENT
None
I
15 Minutes
30 Minutes
45 Minutes
An Kew or
Mere
TOTAL
Pementa.
and
Prailitisty
Permits.
and
Prelideney
Permits.
and
Prenaiony
Percentage
and
tree:ken
Poivaidage
and
Prolkiency
State
10 ( 0.7)
33 ( 1.3)
30 ( 1.0)
15 ( 1.0)
12 ( 1.0)
271 ( 2.4)
278 ( 1.2)
276 ( 1.3)
278 ( 1.8)
274 ( 1.6)
Nation
( 0.6)
31 ( 2.0)
aa ( 12)
le ( 1.0)
12 ( 1.1)
251 ( 21)
264 ( 1.9)
263 ( 1.9)
206 ( 1.9)
256 ( 3.1)
PARENTS' EDUCATION
NS nen-graduato
State
11
044 ( 3.5)
( *01
30 ( 5.0)
23 ( 5.1)
14 ( 3.6)
22 (
044.
5.5)
Nation
17 ( 3.0)
26 ( 3.3)
34 ( 4.4)
12 ( 2.5)
10 ( 2.2)
(
2445 ( 4.0)
246 ( 2.6)
*IN ( 641
(
NI graduate
State
12 ( 1.1)
33 ( 2.1)
23 ( 1.9)
14 ( 1.5)
13 ( 1.5)
267 ( 3,6)
296 ( 2.0)
203 ( 2.4)
262 ( 2.9)
262 ( 3.3)
Nation
10 ( 1.7)
33 ( 22)
31 ( 1.9)
16 ( 1.4)
11 ( 1.5)
24$ ( 4.2)
250 ( 32)
254 ( 2.4)
256 ( 2.8)
244 ( 3.4)
Sane ceflege
State
8
we. ( 12)
36 (
285 (
2.1)
1.9)
31 (
282 (
1.6)
2.2)
16 (
282 (
1.8)
2.5)
(
( 1.3)
«64)
Nation
9 ( 1.2)
30 ( 2.7)
36 ( 2.1)
14 ( 1.8)
11 ( 1.5)
(
266 ( 3.0)
266 ( 2.6)
274 ( 3.5)-
11-4-0
**111
While graduate
State
9 ( 1.0)
33 ( 1.9)
32 ( 1.7)
15 ( 1.3)
12 ( 1.2)
278 ( 3.0)
285 ( 1.5)
285 ( 1.7)
286 ( 2.8)
286 ( 2.8)
Nation
7 ( 0.9)
31 ( 3.4)
31 ( 2.0)
18 ( 1.2)
14 ( 1.9)
265 ( 3.6)
275 ( 2.0)
275 ( 2.5)
278 ( 3.2)
271 ( 2.8)
GENDER
M.
State
14 ( 1.2)
33 ( 1.5)
27 ( 1.4)
15 ( 1.1)
11 ( 1.2)
273 ( 2.2)
279 ( 1.8)
277 ( 1.7)
276 ( 2.5)
273 ( 2.6)
Nation
11 ( 1.1)
34 ( 2.4)
29 (
1.3)
15 ( 1.2)
11 ( 1.4)
255 ( 3.9)
264 ( 2.8)
256 ( 2.4)
265 ( 3.0)
255 ( 4.1)
Female
State
( 0.6)
34 ( 1.6)
33 ( 1.3)
15 ( 1.3)
12 ( 1.1)
266 ( 4.3)
277 ( 1.5)
276 ( 1.6)
275 ( 2.1)
276 ( 2.5)
Nation
7 ( 0.9)
28 ( 2.0)
35( 1.7)
17 ( 1.0)
13 ( 1.3)
246 ( 4.1)
263 ( 1.5)
260 ( 2.0)
267 ( 2.4)
258 ( 3.3)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each populittion of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
*** Sample size is insufficient to permit a reliable estimate (fewer than 62
students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
103
Minnesota
TABLE AS
I Teachers' Reports on the Emphasis Given To
1 Specific Mathematics Content Areas
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
116.11M
1990 NAEP TRIAL
STATE ASSESSMENT
Numbers and Oplrations
Measurement
Geometry
Heavy
Emphasis
Little or No
Emphasis
Heavy
Emphasis
Little or No
Emphasis
Heavy
Emphasis
Little or No
Emphasis
TOTAL
State
Nation
RACE/ETHNICITY
Percents.
and
Proficiency
36 ( 3.3)
275 ( 1.8)
49 ( 3.8)
26) ( 1.8)
36 ( 3.4)
276 ( 1.8)
48 ( 3.7)
267 ( 2.2)
29 ( 7.0)
oN)* (
54 ( 7.9)
2434 4.3)
48 ( 6.8)
(
47 ( 8.7)
246 ( 4.8)
27 ( 7.7)
***)
32 ( 0.8)
(
)
40 ( 6.2)
273 ( 3.2)1
28 (13.0)
45 ( 9.8)
277 ( 4.0)1
53 (12.4)
257 ( 7.1)1
32 ( 4.1)
280 ( 2.9)
52 ( 4.1)
260 ( 2.3)
Poreentene
and
Proficiency
13 ( 1.7
901 ( 2.7
15 ( 2.1
237 ( 3.4)
13 ( 1.8)
902 ( 2.7)
18 ( 2.4)
2as ( 3.5)
14 ( 4.8)
11 ( 3.3)
( 4.1
5 ( 2.5)
«H. (
8 ( 2.2)
27 ( 5.2)
0*
41** )
22 ( XS)
302 ( 5.3)1
16 ( 42)
5 ( 2.5)
6 ( 3.6)
.1.4,
9 ( 1.5)
304 ( 5.3)1
16 ( 2.7)
286 ( 3.8)
Perventage
and
Proficiency
12
2.2)
206
4.1
17
as
250 ( 5.8 )
13 ( 2.3)
268 ( 4.3)
14 ( 3.4)
259 ( 8.9)1
8 ( 3.4)
*gm
*41
25 ( 7)
228 ( 2.6)1
11 ( 4.8)
*4* (
4.414)
23 ( 4.1)
11 ( 5.2)
441
23 ( 5.6)
',h.)
11 ( 4.2)
9 (
7.0)
**.
***)
14 ( 5.1)
( "e)
6 ( 4.9)
12 ( 3.5)
27a
7.2)1
16 ( 3.9)
253 (
7.1)1
Tercentage
and
Treadway
47 ( 3.1
277 ( 1.3
33 ( 4!:#)
272 ( 4.0)
47 ( 3.7)
280 ( 1.7)
96 ( 4.71
277 ( 4.3)
34 ( 6.4)
*11(141
23 4 5.7)
238 ( 8.1)i
52 ( 7.9)
34 (5.8)
255 ( 4.4)1
48 ( 8.9)
4..
44 ( 8.9)
45 ( 4.2)
276 ( 3.5)
40 ( 8$)
m
40 ( 9.4)
280 ( 4.6)1
32 (11.7)
265 ( 9.1)1
52 ( 5.6)
278 ( 2.8)
34 ( 5.3)
270 ( 4.6)
Percentage
end
Proficiency
19 ( 3.0
270 ( 2.5
28 ( 3.8
260 ( 3.2
19 ( 3.1)
273 ( 2.4)
27 ( 4.4)
265 ( 3.3)
24 ( 6.5)
***
4441
93 ( 7.9)
242 ( asp
20 ( 6.9)
***
27 ( 0.5)
*44)
19 ( 5.9)
***
.41
34 ( 9.2)
25 ( 5.0)
276 (
3.8)1
38 ( 9.4)
207 ( 4.9)1
23 ( 9.0)
270 (
3.0)1
9 ( 61)
*44 (
11.4 *)
14 ( 3.8)
272 ( 4.2)1
28 ( 4.6)
260 ( 3.9)
White
State
Nation
Black
State
Nation
Hispanic
State
Nation
Asian
State
Nation
TYPE OF COMMUNITY
Advantaged urban
State
Nation
Extrema rural
State
Nation
Other
State
Nation
Perosnlais
and
Proficiency
27
2.9)
275
2.11
21
3.3)
264 ( 5.4)
27 ( 3.0)
277 ( 2.0)
22 ( 3.4)
273 ( 5.8)
17 ( 8.4)
24 ( 7.3)
233 ( 4.7)4
29 ( 6.5)
***
***)
16 ( 5.5)
32 ( 7.9)
14 4 6.8)
(+0440*)
30 4 3.4)
275 ( 4.5)
13 ( 3.2)
04,-..)
21 ( 5.5)
272 ( 3.2)1
16 ( 7.9)
..**
.00.)
29 ( 5.8)
278 4 3.41i
24 ( 4.3)
265 ( 5.7)
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within
2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis"
category is not included.
1 Interpret with caution - the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
()
t
104
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE AS
I Teachers' Reports on the Emphasis Given to
("'Itinued)
1 Specific Mathematics Content Areas
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1980 NAEP TRIAL.
STATE ASSESSMENT
Numbers and Operations
Measurement
Geometry
-
-
Heavy
Emphasis
,
Little or No
Emphasis
Heavy
Emphasis
-
Utile or No
Emphasis
Heavy
Emphasis
,
Uttle or N.)
Emphasis
TOTAl.
State
Nation
PARENTS' EDUCATION
NS non.grackiate
State
Nation
HI graduate
State
Nation
Some cottage
State
Nation
College graduate
State
Nation
GENDER
Male
State
Nation
Female
State
Nation
Percentage Percenfage Percentage Peon*. Pernotage Poraeillage
and
and
aid
and
and
and
Prolliciency
Praficiency
Proficienay Prfaciancy Pripeciancy
2g
3:4
1771
12
288
4.1
49 ( 3.8
15
2.1
17
3.0
280 ( 1.8)
237 ( 3.4)
250
5.0
38 ( 8.5)
5 ( 2.4)
11 ( 4.0)
***)
c.a.)
so ( 63)
7 ( 2.3)
22 ( 5.3)
251 ( 3.4)
(
*** ( )
39 ( 4.3)
9 ( 1.9)
18 ( 3.3)
265 ( 3.2)
*" ( ***)
248 ( 8.0)i
55 ( 4.8)
11 ( 2.8)
17 ( 3.9)
259 ( 23)
( ")
251 ( 6.1)1
36 ( 33)
12 ( 2.1)
8 ( 2.1)
282 ( 2.4)
296 ( 5.4)
*** ( it")
47 ( 4.4)
17 ( 3.3)
12 ( 2.7)
265 ( 2.8)
284 ( 4.1)1
*** (
32 ( 3.4)
18 1 2.1)
12 ( 2.5)
283 ( 2.2)
308 ( 3.0)
279 ( 5.0)I
44 ( 4.1)
19 ( 2.4)
16 ( 3.3)
289 ( 2.8)
298 ( 3.4)
264 ( 7.2)1
36 ( 3.5)
13 ( 2.0)
14 ( 2.8)
274 ( 2.4)
304 ( 33)
272 ( 42y
48 ( 4.1)
14 ( 2.1)
17 ( 3.3)
261 ( 2.5)
287 ( 4.4)
258 ( 0.7)
35 ( 3.5)
13 ( 1.7)
11 ( 1.9)
276 ( 2.2)
299 ( 3.0)
2e0 ( 6.1)
51 ( 3.9)
15 ( 2.4)
17 ( 32)
260 ( 2.0)
286 ( 3.3)
241 ( SA)
,ft.
47 (
277 ( 1.8
191 2311
2r5
33 (
272 (
4.0
4.0
25
3.81
21
143
48 (
*44, ( 5.7)
***)
20 ( 51)
29 I 5.4)
25
5.31
32 (
«14 ( 8.3)
20 (
ibmt
48 ( 4.8)
21 ( 4.5)
25 ( 3.4)
262 ( 34.2)
261 ( 4.1 $
( 3.1)
27 ( 5.0)
21 ( 4.5)
24 ( 5.1)
253 ( 4.7)4
255 ( 4.2)
248 ( 4.3)4
47 ( 3.8)
19 ( 3.4)
26 ( 3.3)
218 ( 23)
276 ( 2.5)4
279 ( 23)
30 ( 5.5)
27 ( 5.0)
23 ( 4.1)
279 ( 4.5)
262 ( 4.8)1
270 ( 4.7)
48 ( 3.7)
18 ( 23)
2$ ( 3.3)
287 ( 2.0)
277 ( 3.5)
286 ( 2.7)
37 ( 3.8)
26 ( 3.4)
21 ( 2.9)
383 ( 3.8)
270 ( 3.8)
280 ( 84)
47 ( 3.7)
19 ( 3.0)
27 ( 23)
282 ( 2.4)
269 ( 3.7)
275 ( 2.7
32 ( 33)
29 ( 4.1)
20 ( 3.3)
275 ( 41)
263 ( 3.8?
266 ( ILO
47 ( 3.8)
20 ( 3.3)
27 ( 3,2
272 ( 2.1)
271 ( 2.5)4
275 ( 2.4
35 ( 4.3)
27 ( 3.9)
23 ( 3.5
268 ( 4.1)
256 ( 3.3)
263 ( 5.0
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis"
category is not included.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. " Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
105
Minnesota
TABLE A8
I Teachers' Reports on the Emphasis Given To
(mntinued)
I Specific Mathematics Content Areas
r ERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
Analysis, Statistics, and
Probability
Algebra and Functions
Heavy Empnasis
Little or No
Emphasis
Heavy Emphasis
_
Little or No
Emphasis
TOTAL
Pooantage
and
Pralksidacy
Percentage
and
Prilicioncy
Pamintsige
arid
Proficiency
Percoodip.
and
Pralkidney
State
( 18)
69 ( 2.8)
SO ( 3-2)
( 1.3)
207 ( 3.3)i
279 ( 1.3)
285 ( 1.5)
248 ( SA)
Nation
14 ( 2.2)
53 ( 4.4)
4$ ( 3.8)
20 ( 3.0)
280 ( 4.3)
261 ( 2.9)
275 ( 2$)
243 ( 3.0)
RACE/ETHNICITY
Milts
State
9 ( 1.8)
09 ( 2.7)
51 ( 3.2)
8 ( 1.3)
288 ( 3.1)1
282 ( 1.2)
287 ( 1.5)
252 ( 3.5)
Nation
14 ( 2.4)
53 ( 5.0)
48 ( 4.2)
1$ ( 2.8)
270 ( 4.1)
271 ( 3.1)
281 ( 3.0)
251 ( 3.3)
Slack
State
( 4.2)
OS (11.0)
49 ( 8.2)
14 ( 7.6)
( ***)
dire.
( 'imp)
Nation
14 ( 3.4)
53 ( 82)
39 ( 7.1)
27 ( 6.9)
22.5 ( 43)
253 ( 6.3)
226 ( 2.2)1
Hispanic
State
5 ( 2.9)
801 4.8)
35 ( SI)
23 ( 5.7)
(
( ear )
Nation
15 ( 4.1)
56 ( 6.3)
4$ ( 5.9)
18 ( 4.2)
*** ( "")
246 ( 4.4)
257 ( 4.0)1
Asian
State
4 ( 2.0)
SO ( 7,$)
14 ( 4.9)
( "")
***
IP**)
( ***)
Nation
34 ( 8.7)
*** ( "`)
35 ( 7.1)
0.*)
61 ( 8.1)
( "HI
9 ( 4.9)
TYPE OF COMMUNITY
Advantaged urban
State
81 ( 5.4)
58 ( 3.9)
12 ( 3.4)
( ***)
281 ( 3.0)
288 ( 3.3)
Nation
11 ( 6.6)
65 (19.4)
41 ( L9)
18 ( 5.3)
284 ( 7.4)1
298 ( 7.9)1
Extreme rout
State
4..4)
83 ( 5.6)
278 ( 2.2)
37 ( 8.3)
280 ( 4.2)1
Nation
BS (16.9)
42 (16.0)
254 ( 6.7)1
241 ( 5.9)1
Other
State
11 ( 2.8)
8T( 5.0)
51 ( 4.7)
10 ( 2.1)
291 (
7.1)1
281 ( 2.2)
286 ( 2$)
254 ( 4.0)1
Nation
15 ( 2.9)
53 ( 5.2)
47 ( 4.3)
17 ( 3.3)
267 ( 4.7)
260 ( 3.4)
276 ( 2.8)
24$ ( 4.4)1
4111=M111
The standard errors of the estimated statistics appear in parentheses,
lt can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within
2 ciandard errors
of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis"
category is not included.
1 Interpret with caution - the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
106
THE 1990 NAEP TRIAL STATE 1,ES:21SSMENT
Minnesota
TABLE A8
I Teachers' Reports on the Emphasis Given To
(continued)
I Specific Mathematics Content Areas
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
Data Analysis, Statistics, and
ProbabilNy
Algebra and Functions
Heavy Emphasis
Little or No
Emphasis
Heavy Emphasis
Little or No
Emphasis
TOTAL
Parcantd0
and
Pralkievay
Poreantage
and
Profit:tang/
PoradINN
and
Praalency
Parcsolage
and
kWh:Wm
State
8 ( 1.8)
69 ( 2.6)
50 ( 3.2)
( 1.3)
207 ( 3.3)1
279 ( 1.3)
215 ( 1$)
249 ( 3.4)
Nation
14 ( 2.2)
53 ( 4.4)
4e ( 3.8)
20 ( 3.0)
259 ( 4.3)
261 ( 2.9)
275 ( 2$)
243 ( 3.0)
PARENTS EDUCATION
fiS non-graduate
State
5 (
Mit
( 3.5)
11441
72 (
257 (
5.8)
5.2)
36 (
*0* ( 5.0)
*41
15 ( 4.3)
( roe)
Nation
9 (
( 3.0)
53 (
240 (
7.7)
6.2)
25 (
..
5.2)
29 ( 8.9)
.44,)
HS graduate
State
S ( 2.5)
72 ( 3.2)
41 ( 4.0)
11 ( 2.0)
*44 ( 441
267 ( 1.7)
272 ( 2.5)
243 ( 4.8)
Nation
17 ( 3.7)
54 ( 5.4)
44 ( 4.8)
23 ( 3.9)
261 ( 6.0)1
247 ( 2.9)
265 ( 3.5)
239 ( 3.4)
Sonia college
State
7 ( 1.9)
72 (
286 (
3.0)
1.9)
53 (
288 (
3.8)
22)
8 ( 1.4)
1114")
Nation
13 ( 2.5)
.41
57 (
270 (
5.8)
3.7)
48 (
278 (
4.8)
3.0)
17 ( 3.1)
Whigs graduate
State
9 ( 2.2)
65 ( 3.4)
58 ( 3.2)
6 ( 1.3)
298 ( 4.8)1
289 ( 1.5)
292 ( 1.8)
(
Nation
15 ( 2.4)
53 ( 4.4)
50 ( 3.9)
18 ( 2.4)
282 ( 4.5)
275 ( 3.6)
Via ( 3.0)
249 ( 4.0)
GENDER
Male
State
( 1.9)
71 ( 2.6)
49 ( 3.1)
10 ( 1.6)
288 ( 4.1)1
278 ( 1.9)
284 ( 1.8)
246 ( 3.9)
Nation
13 ( 2.2)
54 ( 4.7)
44 ( 4.1)
22 ( 3.6)
275 ( 5.8)
2e0
35)
27$ ( 3.2)
243 ( 3.0)
FIKMI111
State
8 ( 1.8)
65 ( 2.9)
52
3.5)
7 ( 1.3)
285 ( 4.3)1
279 (
1.6)
295 ( 1.6)
248 ( 4.9)
Nation
16 ( 2.4)
53 ( 45)
48 ( 3.6)
18 ( 2.9)
263 ( 4.4)
282 ( 2.8)
274 ( 2.7)
244 ( 3.9)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within + 2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis"
category is not included.
! Interpret with caution - the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
107
Minnesota
TABLE A9
I Teachers' Reports oil the Availability of
Resources
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAY TRIAL
I Get AM the Resources I
I Get Most of the
I Get Same or Mom of
STATE ASSESSMENT
hood
Resources I Need
the Resources I Need
Pmentase
and
Proliaistcy
12 ( 2,1)
281 ( 2.8)
13 (
285 ( 42)
Panagabor
IM
69(3.7
27$ ( 12)
5$ ( 4.0)
285 ( 2.0)
PereeNtese
an6
Pnalliciancy
23
273
31
201
( 3.01)
( 1.9)
( 4.2)
( 2.9)
State
Nation
RACE/ETHNICITY
State
12 ( 2.1)
135 ( 3.7)
23 ( 3.8)
263 ( 2.8)
278 ( 1.0)
277 ( 1.8)
Nation
11 ( 2.5)
58 ( 4.8)
30 ( 4.5)
275 ( 3.5)1
270 ( 2.3)
207 ( 3.3)
Mark
State
1 (
IS* ( 1.8)
89 (167)
29 (10.4)
.44)
Nation
15 ( 4.2)
52 ( 8.8)
33 ( 7 2)
ttlivente
241 ( 53)1
242 ( 2.4)
236 ( 4 .11)
State
19 ( 5.9)
***)
59 ( 8.1)
21 ( 5.8)
*4*
0.041
Nation
23
7.8)
44 ( 4.9)
34 ( 7.7)
248 ( 7.7)1
250 ( 2.9)
244 ( 3.0)!
Asian
State
14 (
04* ( 5.0)
44)
et* ( hal
32 ( 7.8)
11.414'
Mgr)
Nation
19 (
*fr.
8.8)
37 ( 7.7)
44 (12.7)
( *41
TYPE OF COP' /AUNITY
Adventn..4 titan
State
13 ( 4.1)
76 ( 4.7)
0 ( 3.7)
281 ( 8.1)1
277 ( 2.1)
Nation
36 ( 9.2)
50 ( 8.9)
3 ( 3.1)
lbdreme nrel
272 ( 8.5)1
26a ( 13)1
State
18 ( 4.7)
81 ( 5.4)
23 ( 8.3)
278 ( 4.2)1
275 (
2.5)1
273 ( 2.7)1
Nation
2 (
( 2.8)
.41
54 (10.4)
200 ( 6.8)1
43 (10.3)
257 ( 5.0)4
Other
State
10 ( 3.1)
84 ( 8.0)
26 ( OA)
250 ( 5.4)1
270 ( 14)
279 ( 2.7)1
Nation
11 ( 2.9)
56 ( 5.4)
31 ( 5.8)
265 (
3.9)1
264 ( 21)
283 ( 4.2)
The standard errors of the estimaied statistics appear in parentheses. It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the ?stimate for the sample,
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this 7.itimated mean proficiency. *" Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
108
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A9
I Teachers' Reports on the Availability of
(continuee
I
Resources
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1960 MEP TRIAL
I Got All the Resotrces I
I Got Most of the
I G( Some or None of
STATE ASSESSMENT
Need
Resotrces 1 hood
the Resources I Need
TOTAL
Percentage
and
Proficiency
Portentage
and
Proficiency
Percentage
and
Proficiency
State
12 ( 2.1)
65
3.7)
23 ( 3.8)
281 ( 2.8)
278 ( 1.2)
273 ( 1.9)
Nation
13 ( 2.4)
58 ( 4.0)
31 ( 4.2)
265 ( 4.2)
265 ( 2.0)
261 ( 2.9)
PARENTS EDUCATION
HS non-graduate
State
10 ( 3.0)
57 ( 6.7)
33 ( 7.0)
Nation
B ( 2.8)
...)
54 (
244 (
5.7)
2.7)
38 (
243 (
8.3)
3.5)1
HS graduate
State
io ( 2.2)
67 ( 4.7)
24 ( 4.7)
264 (
1.8)
262 ( 2.9)1
Nation
10 ( 2.5)
54 (
4.9)
35 ( 4.2)
253 ( 4.8)1
256 (
1.9)
256 ( 2.8)
Some college
State
12 (
.44 ( 2.2)
65 (
283 (
4.1)
1.6)
23 (
281 (
4.3)
2.4)1
Nation
13 (
'hp*
3.3)
62 (
269 (
4,3)
23)
25 (
267 (
4.1)
3.8)
College gradmte
State
14 ( 2.5)
es
3.4)
21 ( 3.6)
288 ( 3.3)
284 (
1.5)
284 ( 2.1)
Nation
15 ( 2.9)
56 ( 4.9)
30 ( Si)
276 ( 5.4)1
276 (
2.2)
273 ( 3,7)
GENDER
Male
State
11 ( 1.9)
68 ( 3.7)
21 ( 3.6)
284 ( 3,7)
277 (
1.4)
272 ( 3,0)
Nation
13 ( 2.6)
57 ( 4.0)
30 ( 4,0)
264 ( 5.0)1
265 (
2.6)
264 ( 3.3)
Female
State
13 ( 2.4)
62 ( 4.0)
25 ( 4.3)
279 ( 2.8)
275 (
1.3)
274 ( 2.1)
Nation
13 ( 2.4)
55 ( 4.4)
32 ( 4.7)
2r; ( 3.9)
264 (
2.0)
257 ( 3.0)
The standard errors of the esumated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within
2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
174
THE 1990 NAEP TRIAL STATE ASSESSMENT
109
ilinv
Minnesota
TABLE AlOa I Teachers' Reports on the Frequency of Small
Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
At Least Once a Week
Less Than Once a Week
Now
TOTAL
and
Praidency
poresodage
and
Proficiency
Peroonfage
and
Proficiency
State
43 ( 10)
50 ( 3.1)
( 1.9)
279 ( 1.8)
213 ( 1.4)
279 ( 3.8)1
Nation
50 ( 4.4)
43 ( 4.1)
8 ( 2.0)
260 ( 2.2)
264 ( 2.3)
277 ( 5.4)1
RACE/ETHNICITY
White
State
43 ( 3.0)
50 ( 3.2)
8 ( 1.9)
281 ( 1.8)
275 ( 1.2)
281 ( 3.6)1
Nation
49 t 4.6)
43 ( 4$)
8 ( 2.3)
265 ( 2.7)
271 ( 2.2)
285 ( 4.9)1
Black
State
45 ( 6.6)
***)
49 ( 6.7)
(
S ( 3.1)
)
Nation
47 ( 8.1)
240 ( 3.4)
45 ( 7.0)
238 ( 4.0)
9 ( 4.1)
( ***)
Hispanic
State
43 ( 7.2)
56 ( 73)
2 (
1.6)
*** ( *44)
Nation
64 ( 72)
32 ( 6.9)
4 (
1.4)
246 ( 2.5)
247 ( 6.3)1
( *1")
Asian
State
51 ( 7.2)
10 ( 4.7)
*411
(
ViHt
Nation
60 ( 6.2)
***
( ***)
37 ( 7.9)
4 ( 2.7)
( ***)
TYPE OF COMMUNITY
Advantaged titan
State
38 ( 2.8)
5.S ( 4.7)
9 ( 3.3)
284 ( 5.0)
274 ( 2.4)
( ".)
Nation
39 (22.9)
41 (17.9)
20 (12.2)
273 ( 6.0)1
( *4")
Extreme rural
State
38 ( 8.2)
53 ( 8.3)
9 ( 5.0)
279 ( 3.8)!
271 ( 14)1
4HIN
Nation
35 (14.6)
255 ( 5.5)!
50 (17.1)
258 ( 5.9)1
9 ( 9.6)
4.4" ( ***)
Other
5tate
48 ( 5.3)
46 ( 4.8)
( 2.3)
280 ( 2.7)
277 ( 2.6)
Nation
50 ( 4.4)
44 ( 4$)
( 1.8)
260 ( 2.4)
264 ( 2.8)
277 ( 8.3)1
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
110
THE 1990 NAEP TRIAL ST1TE ASSESSMENT
Minnesota
TABLE AI Oa
Teachers' Reports on the Frequency of Small
(c°ntinued)
I Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL
STATE ASSESSMENT
-
At Least Once a Week
Less Than Once a Week
Never
emInmplow
TOTAL
Percentage
and
Proficiency
Percentage
and
Preficiertcy
Percentage
and
Proficiency
State
43 ( 3.0)
50 ( 3.1)
( 1.9)
279 ( 14)
273 ( 1.4)
279 ( 34)1
Nation
50 ( 44)
43 ( 4.1)
8 ( 2.0)
200 ( 2.2)
264 ( 2.3)
277 ( 5,4)1
PARENTS' EDUCATION
NS non-graduate
State
39 ( 5.3)
54 ( 5.4)
7 ( 3.3)
4
Nation
60 ( 8.4)
36 ( as)
1
( 1.4)
244 ( 3.2)
244 ( 3.2)1
NS graduate
State
42 ( 3.9)
51 ( 4.3)
7 ( 2.0)
267 ( 2.1)
263 ( 2.3)
11.**
Nation
49 ( 4.8)
45 ( 5.1)
( 2.5)
252 ( 2.8)
257 ( 2.7)
Some cottage
State
44 (
285 (
3.9)
1.9)
50 (
279 (
3.9)
1.7)
.4*
Nation
51 (
266 (
5.2)
3.1)
42 (
268 (
5.1)
3.2)
7 (
**,
( 2.3)
*44. )
College graduate
State
43 ( 3.1)
48 ( 3.2)
9 ( 22)
289 ( 2.3)
281 ( 1.8)
289 ( 3.7)1
Nation
46 ( 5.2)
43 ( 4.4)
11 ( 2.7)
271 ( 2.6)
276 ( 3.0)
285 ( 4.9)1
GENDER
Male
State
44 ( 3.2)
48 ( 3.1)
8 ( 1.9)
280 ( 2.1)
273 ( 1.8)
279 ( 5.4)1
Nation
50 ( 4.5)
42 ( 4.0)
8 ( 2.1)
201 ( 3.0)
265 ( 3.1)
278 1 5.3)1
Female
State
41 ( 3.1)
52 ( 3.5)
7 ( 2.0)
278 ( 1.9)
273 ( 1.5)
278 ( 4.9)!
Nation
50 ( 4.7)
43 ( 4.7)
( 2.1)
259 ( 2.2)
263 ( 2.1)
275 ( 6.6)1
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
6
THE 1990 NAEP TRIAL STATE ASSESSMENT
111
Minnesota
TABLE AlOb I Teachers' Reports on the Use of Mathematical
Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
At Least Once a Week
Less Than Once a Week
Never
L_
TOTAL
Percentage
and
Proaciency
Percentage
and
Preticiency
Percentage
and
Prcadency
State
19 ( 3.3)
72 ( 3.4)
9 ( 1.8)
271 ( 2,1)
276 ( 0.9)
290 ( 41.;)
Nation
22 ( 3.7)
3.9)
9 ( 2.6)
254 ( 32)
2.3 ( 1.9)
282 ( 5.9))
RACE/ETHNICITY
White
State
19 ( 3.4)
71
( 3.5)
10 ( 1.9)
274 (
1.9)1
278 ( 0.9)
292 ( 4.5)
Nation
17 ( 4.0)
72 ( 4.2)
10 ( 2.7)
261 (
3.8)1
269 ( 2.1)
288 ( 6.2)'
Slack
State
20 ( 9,3)
70 ( 1 0
4 ( 2.9)
*4*
(
Nation
22 ( 5.9)
70 ( 6.3)
8 ( 3.9)
233 ( 5.9)1
241 ( 2.9)
Hispanic
State
17 ( 5.4)
Nation
39 (
247 (
7.5)
3,8)
55
245
( 7.3)
(
3,8)1
***)
Asian
State
16 (
Or*
5.5)
.-**)
5 (
( 3.2)
*0.)
Nation
52 ( 5.7)
6 ( 4.2)
*.)
TYPE OF COMMUNITY
Advantaged whin
State
9 ( 4.5)
84 ( 4.7)
"`)
277 ( 2,0)
Nation
23 (14A)
63 (11,5)
15 ( 9.3)
278 ( 5.6)1
Extreme rural
State
38 ( 9.3)
54
( 9.2)
8 ( 2.8)
270 (
1.3)1
276 (
1.9))
Nation
27 (14.9)
65 (14.6)
8 ( 3.9)
262
(
2.8)1
Other
Stat
15 ( 4.0)
73 ( 4.7)
11 ( 3.6)
272 ( 4.0)I
278 (
1.6)
285 ( 52)1
Nation
19 ( 4.3)
72 ( 5.0)
( 3.3)
253 (
3.9)1
263 ( 22)
281 ( 7,1)1
Im
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
' Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
1
,
r
112
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE AlOb I Teachers' Reports on the Use of Mathematical
(c°ntinued)
Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
Al Least Once a Week
Less Than Once a Week
Never
_
TOTAL
Peroentage
mid
Proficiency
Percentage
and
Proficiency
Percentate
aid
Praiidancy
State
19 ( 3.3)
72 ( 3.4)
9 ( 1.6)
271 ( 2.1)
276 ( 0.9)
290 ( 4$)
Nation
22 ( 3.7)
69 ( 3.9)
9 ( 2,6)
264 ( 3.2)
263 ( 1.9)
262 ( 5.9)1
PARENTS' EDUCATION
HS non-graduate
State
23 ( 5.1)
71 ( 5.2)
6 ( 2.7)
.
alt
(
044
Hrlt )
4*-41 )
Nation
25 ( 5.6)
irk,
(
I4r11)
66 (
243 (
7.2)
2.2)
9 ( 8$)
-e)
HS graduate
State
22 ( 4.5)
69 ( 4.5)
8 ( 1.9)
262 ( 3.0)1
265 ( 1.5)
(
Nation
23 ( 4.8)
246 ( 4.0)1
70 (
255 (
5.3)
22)
7 ( 2.8)
,H.4)
Some college
State
18 ( 3.r)
280 ( 2.8)1
73 (
281 (
4.1)
1.5)
.44
Nation
18 ( 4.0)
261 ( 4.4)i
73 (
269 (
4.3)
2.3)
9 ( 2.4))
College graduate
State
16 ( 3.0)
73 ( 3.3)
11 '( 2.3)
281 ( 2.9)1
284 ( 1,3)
297 (
4.5)1
Nat on
20 ( 3.9)
89 ( 3.7)
11 ( 2.5)
266 ( 3.5)1
274 ( 2.2)
297 (
4.2)1
OENDER
Male
State
18 ( 3.2)
72 ( 3.4)
9 (
1.8)
270 ( 3.1)
276 ( 1.2)
294 ( 4.7)
Nation
22 ( 4.1)
69 ( 4.1)
8 (
2.0)
255 ( 4.1)
265 ( 2,1)
287 ( 7.2)1
Female
State
19 ( 3.6)
71 ( 3.7)
9 ( 2.0)
273 ( 2.5)
275 (
1.3)
285 ( 4.6)1
Nation
21 ( 3.6)
69 ( 4.2)
10 ( 3.3)
254 ( 3.3)
262 (
1.9)
278 (
6.0)1
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each populauon of interest, the value for the entire population is within I 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficie.lcy. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
113
Minnesota
TABLE Alla I Teachers' Reports on the Frequency of
Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
UM NAEP TRIAL
STATE ASSESSMENT
Almost Every Day
Several Times a Week
-
About Once a Wook or
Less
TOTAL
Percentage
and
Proficiency
Percentage
and
Proficiency
Percentile
and
ProgicioncY
State
73 ( 3.9)
29 ( 3.9)
4 ( 1.3)
279 ( 1.2)
271 ( 1.8)
259 ( 6.1)1
Nation
82 ( 3.4)
31 ( 3.1)
7 ( 1.8)
287
( 1.8)
254 ( 2.9)
280 ( 5.1)1
RACE/ETHNICITY
White
State
73 ( 4.0)
23 ( 4.0)
4 (
1
)
281 ( 1.1)
273 ( 1$)
262 ( 5.6)1
Nation
84 ( 3.7)
28 ( 3.2)
8 ( 2.3)
272 ( 1.9)
284 ( 3.4)
264 ( 5.4)!
Black
State
84 (13.9)
...)
26 (11.7)
Vi
10 (
444 (
63)
444)
Nation
50 ( 7.7)
41 (
7.9)
2 ( 1.4)
244 ( 4.0)
233 (
3,9)1
"4 ( 4")
Hispanic
State
...)
24 ( 5.5)
14 ( 5.2)
Nation
81 ( 8.8)
32 ( 5,3)
8 ( 2.3)
251 ( 3.1)
240 ( 4.3)1
4" ( 44)
Asian
State
*Mir
24 ( 8.8)
2 (
444 (
2.3)
444)
Nation
83
284
( 8.9)
(
7.0)1
1 0 ( 31)
...)
(
(
5.1)
444)
TYPE OF COMMUNITY
Advantaged urban
State
81
280
( 5.6)
( 2.3)
...)
7
Nation
83
283
(15.9)
( 7.3)t
23 ( 52)
14 (14.6)
. )
Extreme twat
State
67 (10 3)
30 (10.5)
2 (
2.5)
277 ( 2.4)1
271
(
2,7)1
Nation
50
268
(10.6)
(
4.0)1
40
247
(10.0)
(
7,6)1
10 (
7.3)
.4.)
Other
State
73 ( 5.5)
23 ( 5.5)
4 ( 2.3)
282 ( 1.9)
278 (
1.7)1
)
Nation
63 ( 3.9)
31 ( 3.5)
6 (
1.9)
267 ( 2.3)
255 ( 3.1)
257 (
5.8)1
The standard errors of the esOmated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within
2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
1
114
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE Al la I Teachers' Reports on the Frequency of
(continued)
Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
-
1990 NAEP TRIAL
Day
Several Times
Week
About Once a Week or
STATE ASSESSMENT
Almost Every
a
Lass
_
TOTAL
Percentage
awl
Proficiency
Pereentage
and
'Drachm/
ParaNdapo
and
PrOdency
State
73 ( 3,9)
23 ( 3.9)
( 1.3)
279 ( 1.2)
271 ( 1.6)
259 ( 0.1)1
Nation
62 ( 3.4)
31 ( 3.1)
7 ( 1.8)
267 ( 1.8)
254 ( 2.9)
200 (
PARENTS EDUCATION
HS non-graduate
State
62 ( 7.3)
34 ( 72)
.44)
4 ( 2.7)
( del
Nation
67 ( 5.5)
27 ( 5.2)
( 2.1)
245 ( 32)
4911
HS graduate
State
71
( 4.7)
24 ( 4.4)
5 ( 1.6)
269 ( 1.4)
258 ( 3.5)1
Nation
61 ( 4.4)
34 ( 3.7)
6 ( 1.5)
257 ( 2.5)
250 ( 2.9)
Some college
State
74 (
284 (
4.3)
1.3)
22 (
280 (
4.2)
2.1)1
4 (
.44
1.4)
Nation
68 ( 4.2)
26 ( 3.7)
6 ( 1.9)
272 ( 2.7)
258 ( 52)
College graduate
State
75 ( 3.7)
21 ( 3.6)
4 ( 1.5)
288 (
1.5)
280 ( 2,3)
Nation
81 ( 4.0)
31 ( 3.9)
( 3.4)
281 ( .2.2)
285 ( 3.1)
GENDER
Male
State
72 ( 3.9)
23 ( 3.8)
280 (
1.3)
289 ( 2.1)
( ".)
Nation
60 (
3.7)
33 ( 3.4)
7 ( 1.9)
269 ( 2.1)
258 ( 3.8)
281 ( 8.7)1
Female
State
73 ( 4.3)
23 ( 42)
3 ( 1.1)
278 (
1.5)
272 (
1.7)1
( ***)
Nation
65 ( 3.6)
28 ( 3.3)
268 ( 1.8)
253 ( 2.5)
...M1=1
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the enure population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency.
*** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
115
Minnesota
TABLE Al lb I Teachers' Reports On the Frequency of
Mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 MEP TRIAL
STATE ASSESSMENT
At Least Several Times
a Week
About Onca a Week
Less than Weeidy
TOTAL
Peroaddp
atd
Prof/Ana
Porountage
And
Prolickacy
Pitramta.
and
Proitolency
State
39 ( 33)
32 ( 3.5)
29 ( 3.6)
271 ( 1.5)
275 ( 1.9)
284 ( 2.2)
Nation
34 ( 3.6)
33 ( 3.4)
32 ( 3.6)
256 ( 23)
260 ( 2.3)
274 ( 2.7)
RACE/ETHNICITY
Whit
State
39 ( 3,5)
32 ( 3.6)
30 ( 3.7)
273 ( 1.5)
278 (
1.7)
266 ( 2.2)
Nation
32 (
264 (
4.1)
2.7)
33 (
264 (
35)
2.7)
35
279
( 3.8)
( 2.9)
Mack
State
42 ( 79)
20 ( 4.5)
444 ( 441
Nation
( 7.5)
31 ( 7.6)
23 ( 6.3)
232 ( 3.1)1
243 ( 2.3)1
246 ( 7.0)1
Hispanic
State
62 ( 7.6)
29 ( 6.6)
20 ( 7.2)
(
Nation
41 (
7.7)
26 ( 5,3)
3$ ( 7.61
242 ( 32))
244 ( 5.1)1
257 ( 23)1
Asian
State
35 ( 7.0)
**4
( ***)
22
.4*
( 5.3)
(
Nation
37 ( 6.3)
35 ( 9.7)
27 (10.4)
TYPE OF COMMUNITY
Advantaged urban
State
39 ( 6.5)
31 ( 4.5)
30 ( 5.3)
270 ( 4.5)1
275 ( 3.6)
288 ( 4,2)1
Nation
59 (1;,.9)
20 ( 6,0)
21
( 8.2)
273
t
Extrema rural
State
32 ( 8.5)
45 ( 7.4)
23 (
7.7)
269 (
1,5)1
275 (
2.4)1
283 ( 4,6)1
Nation
27 (14.3)
49 (12,7)
24 (10.1)
re (
)
258 (
6.7)1
Other
State
42 ( 5.4)
24 ( $.6)
34 ( 6.0)
275 ( 1$)
280 ( 4.1)!
283 (
3.3)1
Nation
30 ( 4.4.)
3.5 ( 4.3)
36 ( 4.2)
256 ( 3.3)
259 ( 2.8)
272 ( 2.9)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within
r 2 standard errors
of the estimate for the sample.
! Interpret with caution
the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
116
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE Al lb 1 Teachers' Reports on the Frequency of
(continued)
mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL
STATE ASSESSMENT
At Least Sews] Times
a Week
About Once a West
Less than WIdy
TOTAL
Percentage
and
ProRdency
Percentage
and
Proecietioy
Percentage
and
Pronclency
State
39 ( 3.5)
32 ( 3.5)
29 ( 3.6)
271 ( 1.5)
275 ( 1.9)
264 ( 2.2)
Nation
34 ( 3.8)
33 ( 3.4)
32 ( 3.6)
256 ( 2.3)
260 ( 2.3)
274 ( 2.7)
PARENTS EDUCATION
HS non-graduate
State
48 ( 5.2)
19 ( 4.6)
.44)
Nation
35 ( 6.0)
29 ( 6.3)
36 ( 69)
239 ( 3.5)
250 ( 43)1
NS graduate
State
45 ( 4.7)
30 ( 4.3)
25 ( 4.2)
262 ( 23)
263 ( 2.5)
272 ( 2.4)
Nation
35 ( 5.3)
36 ( 4.5)
30 ( 4.6)
250 ( 3.8)
250 ( 2.7)
263 ( 3.4)
Some college
State
35 ( 4.0)
37 ( 4.6)
28 ( 3.4)
276 ( 2.3)
293 ( 1.9)
290 ( 2.5)
Nation
33 ( 4.7)
32 ( 4.0)
35 ( 4.1)
260 ( 2.8)
266 ( 4,2)
278 ( 2.6)
College graduate
State
36 ( 3.6)
31 ( 3.4)
33 ( 3.9)
279 ( 1.9)
285 ( 2.3)
292 ( 2.4)
Nation
35 ( 3.6)
32 ( 3.4)
33 ( 3.5)
264 ( 2.6)
271 ( 2.4)
289 ( 2.9)
GENDER
Male
Esate
41 ( 3.6)
31 ( 3.5)
28 ( 3.4)
271 ( 2.0)
275 ( 2.3)
265 ( 2.4)
Nation
35 ( 4.1)
35 ( 3.6)
31 ( 3.5)
257 ( 3.2)
261
( 2.6)
275 ( 3.2)
Female
State
37 ( 3.6)
33 ( 3.7)
30 ( 3.9)
270 ( 1.8)
275 ( 2.2)
284 ( 2.5)
Nation
34 ( 4.1)
32 ( 3.7)
34 ( 4.1)
254 ( 2.1)
258 ( 2.3)
273 ( 2.8)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. 6** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
117
Minnesota
TABLE A 12
I Students' Reports on the Frequency of Small
I Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAEP TRIAL
STATE ASSESSMENT
At Least Oncoa Weak 'Loss Than Once a Walk
Now
TOTAL
State
Nation
RACEiETNNICITY
White
State
Nation
Mack
State
Nation
Hispanic
State
Nation
Asian
State
Nation
TYPE OF COMMUNITY
Advantaged urban
State
Nation
Extrema rural
State
Nation
Other
State
Nation
Ponandage
Peroatitaga
Percentage
ind
and
and
PraIdency
Proldercy
Prolicioncy
2e( 2.0)
28 ( 1.7)
45 ( 2.3)
277 ( 1.7)
279 ( 1.2)
273 ( 1.3)
28 ( 24)
28 ( 1.4)
44 ( 2.9)
25$ ( 2.7)
267 ( 2.0)
261 ( 1.6)
26 ( 1.9)
28 ( 1.9)
46 ( 2.4)
280 ( 1.9)
281 ( 1.2)
276 ( 1.1)
27 ( 2.9)
29 ( 1.7)
44 ( 3.5)
268 ( 3.1)
272 ( 1.9)
270 ( 1.7)
39 ( 53)
24 ( 5.0)
37 ( 7.0)
11-41,
)
11. ft*
(
)
4.441
28 ( 3.0)
24 ( 34)
48 ( 4.7)
234 ( 3.0)
245 ( 4.6)
234 ( 3.1)
23 ( 4.7)
29 ( 5.0)
43 ( 5.4)
(
4** ( 0+1
11.
*** )
37 ( 5.2)
22 ( 3.6)
41 ( 5.0)
242 ( 3.9)
250 ( 3.4)
240 ( 2.8)
25 ( 8.9)
27 ( 6.8)
4.8 ( 7.4)
*IV ( GI )
Rt.
*** )
(
)
28 ( 6.4)
32 ( 4.0)
40 ( 6.2)
441 ( !WO )
4* ( MI* )
4*14
( SIM )
19 ( 2.7)
29 ( 2.9)
51 ( 3.5)
277 ( 44)
279 ( 2.2)
276 ( 1.8)
27 (13.9)
33 ( 44)
4° (13.4)
28e
5.4)1
279 ( 3.5)1
26 ( 3.9)
24 ( 3.9)
SO ( 5.1)
281 ( 4.6)
278 ( 2.9)1
272 ( 1.8)1
34 (10.8!
27 1 3.8)
39 (11.6)
249 ( 52)1
264 ( 34)1
256 ( 6.2)4
27 ( 3.0)
31 ( 2.8)
42 ( 3.8)
278 ( 2.3)
283 ( 1.7)
277 ( 2.3)
27 1 2.6)
28 ( 1.7)
45 ( 3.3)
260 ( 3.3)
254 ( 2.1)
262 ( 2.2)
The standard errors of the estimated statistics appear in parentheses.
It c.
be said with about 95 percent
certamty that, for each population of interest, the value for the entire population is within -; 2 standard errors
of the estimate for the sample,
! Interpret with caution
the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency.
*** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
I
4 r
,
IS
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A 12
I Students' Reports on the Frequency of Small
(continued)
I Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAEP TRIAL
STATE ASSESSMENT
At Least Once a Weak
Less Than Once a Week
Never
TOTAL
Percentage
mid
PrOdckenty
Parentage
and
Proficiency
Percentage
and
Mildewy
State
26 ( 2.0)
28 (
1.7)
45 ( 2.3)
277 ( 1.7)
279 ( 1.2)
273 ( 1.3)
Nation
2$ ( 2.5)
28 ( 1.4)
44 ( 2.9)
258 ( 2.7)
267 ( 2.0)
261 ( 1.6)
PARENTS' EDUCATION
HS non-graduate
State
24 (
04*
( 5.0)
111111
21 ( 3.9)
55 ( 6.3)
...)
Nation
29 ( 4.5)
29 ( 3.0)
42 ( 4$)
242 ( 3.4)
244 ( 3.0)
242 ( 2.7)
HS graduate
State
25 ( 2.3)
26 ( 2$)
49 ( 3.0)
263 ( 2.6)
269 ( 2.1)
262 ( 22)
Nation
28 ( 3.0)
2$ ( 1.8)
43 ( 3.4)
251 ( 3.7)
261 ( 2.6)
252 (
1.7)
Some college
State
25 ( 2.7)
31 (
2.51
44 (
3.1)
285 ( 3.1)
285 (
1.9)
280 ( 1$)
Nation
27 ( 3.9)
27 ( 2.4)
48 ( 3.8)
265 ( 3.6)
268 ( 3.3)
266 ( 2.1)
College graduate
State
28 ( 2,3)
30 ( 2.0)
4.. ( 2.3)
287 ( 2.0)
285 (
1.6)
283 (
1.7)
Nation
28 ( 3,0)
28 (
1.8)
44 ( 3.6)
270 ( 2.7)
278 ( 2.8)
275 ( 2.2)
GENDER
Male
State
28 ( 2.2)
29 (
2.1)
43 ( 2.5)
277 (
2,0)
280 ( 1.6)
274 (
1.6)
Nation
31 ( 2.9)
28
1.7)
41 ( 2.9)
259 ( 3.3)
268 (
2.6)
282 ( 1.8)
Female
State
25 ( 2.0)
28 (
1,9)
47 ( 2.6)
277 ( 2.2)
279 (
1.6)
272 (
1.5)
Nation
26 ( 2.4)
27 (
1.8)
47 ( 3.2)
257 ( 2.8)
266 (
1.7)
260 (
1.8)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within
2 standard errors
of the estimate for the sample,
*** Sample We is insufficient to permit a reliable estimate (fewer than 62
students).
1 4. 4
THE 1990 NAEP TRIAL STATE ASSESSMENT
119
Minnesota
TABLE A13
I Students' Reports on the Use of Mathematics
Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAEP TRIAL
STATE ASSESSMENT
At Least Once a Week
Less Than Once a We*
Never
TOTAL
Percentage
and
Proficiency
Perventege
and
Proltdency
Perteldip
State
23 ( 2.1)
38 ( 14)
39 ( 22)
270 ( 1.5)
280 ( 1.1)
275 ( 1.3)
Nation
28 ( 1.8)
31 ( 1.2)
41 ( 2.2)
256 ( 2.8)
209 ( 1.5)
259 ( 1.8)
RACE/ETHNICITY
Who
State
23 ( 2.2)
39 ( 1.7)
38 ( 2.3)
273 ( 1.5)
282 ( 1.1)
278 ( 1.3)
Nation
27 ( 1.9)
33 ( 1.8)
40 ( 2.5)
208 ( 2.8)
275 ( 1.6)
2e$ ( 1.8)
Black
State
28 ( 8.8)
( «al
29 ( 54)
..«*)
43 (
11111
7.1)
***)
Nation
27 ( 3.3)
27 ( 3.2)
48 ( 4.5)
234 ( 3.7)
24.8 ( 43)
232 ( 2.6)
Hispanic
State
22 ( 4.7)
( *al
38 ( 4.6)
42 ( 5.7)
$4,41
38 ( 42)
23 ( 2.0)
40 ( 4.0)
241 ( 4.8)
253 ( 4.3)
240 ( 1.9)
Asian
State
27 (10.1)
(
25 (
***
5.8)
(
Nation
32 ( 3.7)
*v.)
30 ( 3.2)
38 (
4.04,
4.7)
TYPE OF COMMUNITY
Advantaged urban
State
21 ( 3.4)
41 ( 2.4)
:119 ( 3.8)
271 ( 3.8)1
260 ( 2.7)
2/8 ( 2.1)
Nation
36 (10.3)
33 ( 4.8)
32 (11.1)
278 ( 6.1)1
264 ( 3.2)1
281 ( 5.9)3
Extreme rtral
State
29 ( 5.6)
( 3.9)
31 ( 4.3)
289 ( 1.9)1
280 ( 1.8)
277 ( 2.8)
Nation
37 ( 4.7)
43 ( 5.0)
ilhb
( *YIP)
262 ( 4.7)1
251 ( 5.2)I
Other
State
20 ( 3.0)
37 ( 2.6)
43 ( 4.2)
278 ( 2.7)
282 ( 1.8)
27'6 ( 1.9)
Nation
27 ( 2.0)
31 ( 1.4)
41 ( 2.4)
256
2.9)
270 ( 1.8)
260 ( 2.2)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. "* Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
120
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A 13
I Students' Reports on the Use of Mathematics
("mtinued)
I Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAV TRIAL
STATE ASSESSMENT
At Least Once a Week
Loss Than Once a Wook
New
TOTAL
Peivantage
and
Prolicioncy
Percentage
and
Proficiency
Rorcontace
and
Proficiency
State
23 ( 2.1)
38 ( 1.5)
38 ( 2.2)
270 ( 1.5)
260 ( 1.1)
275 ( 1,3)
Nation
28 (
1.8)
31 ( 1.2)
41 ( 2.2)
25$ ( 2.8)
289
1.5)
259 ( 1.8)
PARENTS EDUCATION
HS non-graduate
State
23 ( 4.1)
33 ( 5.6)
44 ( 4.7)
)
Nation
27 ( 4.2)
26 ( 2.7)
47 ( 5.0)
237 ( 3.0)
253 ( 3.5)
240 ( 2.3)
HS graduate
State
24 ( 3.2)
38 ( 2.2)
40 ( 2.9)
258 ( 3.0)
271 (
1.8)
282 ( 1.7)
Nation
27 ( 2.7)
31 ( 2.4)
43 ( 3.3)
250 ( 2.4)
259
( 2.7)
253 ( 2.1)
Some college
State
21 ( 2.0)
40 ( 2.4)
39 ( 2.9)
277 ( 3.0)
285 ( 1.3)
283 ( 2.2)
Nation
29 ( 2.8)
36 ( 2.3)
35 ( 2.6)
261 ( 3.5)
274 ( 2.2)
263 ( 2.1)
College graduate
State
23 ( 2.4)
39 ( 1.9)
38 ( 2.8)
281 ( 1.9)
287 ( 1.8)
285 (
1.7)
Nation
30 ( 2$)
32 ( 2.0)
38 ( 2.6)
269 ( 3.0)
278 ( 2.0)
275 ( 2.0)
GENDER
Male
State
26 ( 2.3)
38 ( 1.7)
38 ( 2$)
271 ( 2.0)
280 ( 1.3)
276 (
1.8)
Nation
32 ( 2.0)
30 ( 1.5)
38 ( 2.2)
25$ ( 2.9)
271 ( 2.1)
260 ( 1.8)
Female
State
20 ( 2.4)
40 ( 2.1)
40 ( 2$)
269 ( 2,5)
280 ( 1.5)
274 ( 1.4)
Nation
25 ( 2.0)
31
( 1.9)
44 ( 2.6)
257 ( 10)
268 ( 1.5)
257 (
1.9)
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
*** Sample size is msufficient to permit a reliable estimate (fewer than 62
students).
126
THE 2990 NAEP TRIAL STATE ASSESSMENT
221
Minnesota
TABLE A14
I Students' Reports on the Frequency of
Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 /MEP TRIAL
STATE ASSESSMENT
Almost Every Day
Several Tknes a Week
About Once a Week or
Less
TOTAL
and
Proficiency
Percentage
and
PnatIciency
Peramtage
and
Proficiency
State
81 ( 1.5)
12 ( 1-2)
7 ( 1.2)
279 ( ('.9)
206 ( 1.8)
257 ( 4.4)
Nation
74 ( 1-9)
14 ( 0.8)
12 ( 1.8)
267 ( 1.2)
252
1.7)
242 ( 4.5)
RACE/ETHNICITY
White
State
82 ( 1.4)
12 ( 1.2)
6 ( 1.0)
281 ( 0.9)
268 ( 1.8)
264 ( 3.8)
Nation
76 ( 2.5)
13 ( 0.8)
11 ( 2.2)
274 ( 1.3)
258 ( 2.2)
252 ( 5.1)1
Black
State
76 (12.8)
3 ( 2.1)
21 (14.4)
.4*
4Nri
Nation
71 ( 2.8)
15 ( 1.7)
14 ( 32)
240 ( 2.9)
232 ( 3.1)
223 ( 6.1)1
Hispanic
State
69 ( 5.8)
Vi
12 (
( 3.7)
18 (
frS
Nation
61 ( 3.7)
21 ( 2.9)
17 ( 2.7)
249 ( 2.3)
242
51)
224 ( 3.4)
Asian
State
73 ( 5.0)
9 ( 3.4)
*4.
(
)
( ***)
(
Nation
79 (
289 (
4.9)
5.0)1
13 (
***
(
3.4)
***)
8 (
***
(
2.6)
***)
TYPE OF COMMUNITY
Advantaged urban
State
81 ( 3.4)
12 ( 2.5)
280 ( 1.6)
Nation
73 (11.1)
13 ( 1.7)
14 (10.4)
286 1. 4.6)1
*4-Ir
Extreme rural
State
81 ( 3.8)
14 ( 3.0)
277 ( 1.9)
270 ( 2.8)1
Nation
68 (11.3)
15 ( 3.6)
17 ( 8.2)
263 ( 4.2)1
(
Other
State
84 ( 1.4)
9 ( 1.5)
7 ( 2.0)
282 ( 1.5)
269 ( 2.8)
257 ( 5.2)1
Nation
75 ( 2.2)
14 ( 1.0)
10 ( 1.9)
207 ( 1,5)
252 ( 2.6)
( 4.3)1
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency,
*I's Sample Sin is insufficient to permit a
reliable estimate (fewer than 62 students).
'I
122
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A14
I Students' Reports on the Frequency of
(continued)
Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAEP TRIAL
STATE ASSESSMENT
Almost Every Day
Several Times a Week
About Once a Win* or
Loss
TOTAL
Poreordago
and
Pso Scion
Percentage
and
ProMoney
Peiventage
and
Modality
State
81 ( 1.5)
12 ( 12)
7 (
1.2)
279 ( 0.9)
200 ( 1.8)
257 ( 4.4)
Nation
74 ( 1.9)
14 ( 0.8)
12 (
1.8)
267 ( 1.2)
252 ( 1.7)
242 ( 4.5)
PARENTS' EDUCATION
non-gracksate
State
60 ( 3.7)
11 ( 2.7)
9 ( 3.0)
256 ( 3.6)
(
*44 (
Nation
64 (
245 (
3.4)
2.3)
18 (
ow.
2.0)
18 (
*44 (
3.1)
.")
HS graduate
State
78 (
267 (
2.2)
1.5)
13 (
257 (
1.5)
2.7)
9 (
1.4)
Nation
71 ( 3.6)
16 ( 1.8)
13 ( 2.8)
25$ ( 1.6)
249 ( 3.2)
239 (
3.4)1
Some cottage
State
81 ( 2.2)
13 ( 1.9)
6
285 ( 1.3)
276 ( 3.8)
(
Nation
80 (
270 (
2.0)
1.9)
"* (
)
***)
Co liege graduate
State
85 ( 1.7)
10 ( 1.3)
5.(
1.3)
287 ( 1.1 )
275 ( 3.1)
Nation
77 ( 2.7)
13 ( 0.9)
10 (
2.3)
279 ( 1.6)
260 ( 2.8)
257 (
6.4)1
GENDER
Male
State
79 ( 1.8)
13 (
1.3)
8 (
1.5)
280 ( 1.2)
265 ( 2.8)
258 ( 4.7)
Nation
72 ( 2.4)
16 ( 1.2)
12 ( 2.1)
268 (
1.6)
252 ( 2.5)
242 ( 6.1)
Female
State
84 ( 1.5)
11 (
1.4)
5 ( 0.9)
278 ( 1.1)
267 ( 2.4)
255 ( 5.1)
Nation
76 ( 1.8)
13 ( 1.0)
11 ( 1.6)
265 ( 1.3)
250 (
2.5)
242 ( 3.8)
The standard errors of the estimated statistics appear in parentheses.
It can bc said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
Interpret with caution -- the nature of the sample does not allow accurate
de.?rmination of the variability of this estimated mean proficiency. ** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
123
Minnesota
TABLE Al5
1 Students' Reports on the Frequency of
I Mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
At Least Several Times
STATE ASSESSMENT
Week
About Once a Week
Liss Than Weekly
-
TOTAL
ond
Proficiency
and
Proficiency
Percentage
and
Proficiency
State
33 ( 2.2)
29 ( 1.6)
37 ( 2.4)
269 ( 1$)
275 ( 1.3)
282 ( 1.5)
Nation
38 ( 2.4)
25
1.2)
37 ( 2.5)
253 ( 2.2)
261 ( 1.4)
272 ( 1.9)
RACE/ETHNICITY
White
State
32 ( 2.2)
30 ( 1.7)
38 ( 2.6)
273 ( 1.3)
277 ( 12)
284 ( 1.5)
Nation
35 ( 2.9)
24 ( 1.3)
41 ( 3.0)
282 ( 2.5)
269 ( 1.5)
277 ( 2.0)
Mack
State
46 (11.2)
31 ( 7.9)
23 ( 8.8)
41,*4
.414
Nation
413 ( 3.8)
32 ( 2.7)
20) 3.1)
232 ( 4.3)
241 ( 2.9)
241 ( 4.4)
Hispanic
State
50 ( 5.8)
27 ( 5.5)
24 ( 5.1)
..*)
Nation
44 ( 4.1)
25 ( 3.4)
32 ( 4.3)
238 ( 3.9)
247 ( 3.3)
248 ( 3.3)
Asian
State
26 ( 5.2)
22 ( 5.8)
52
( ***)
(
4- )
Nation
32 ( 5.1)
*** ( e")
51 ( 5.9)
***)
TYPE OF COMMUNITY
Advantaged urban
State
35 ( 3.8)
28 ( 2.4)
37 ( 3.9)
269 ( 3.6)
277 ( 2.7)
285 ( 2.8)
Nation
50 t 9.0)
31 ( 9.3)
271 ( 3.3)1
(
299 ( 5.3)1
Extreme nes!
State
33 ( 5.8)
35 ( 3.8)
31 ( 5.1)
271 ( 2.0)1
275 (
2.0)1
281 ( 3.5)
Nation
42 (10.1)
30 ( 4.4)
28 ( 7.5)
249 ( 4.0)1
256 ( 3.4)1
267 (
7.3)1
Other
State
33 ( 3.2)
27 ( 2.3)
41 ( 3.7)
274 ( 2.3)
279 ( 2.2)
283 (
1.9)
Nation
36 ( 2,9)
26 ( 1.2)
38 ( 2.9)
252 ( 3.0)
261 ( 2.1)
272 (
1.8)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency.
*** Sample size Is insufficient to permit a
reliable estimate (fewer than 62 students).
1
124
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A1S
I Students' Reports on the Frequency of
(continued)
I Mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAEP TRIAL
STATE ASSESSMENT
At Least Several Times
a W eek
About Once a Week
Lass Than %moldy
TOTAL
Poventage
and
Proeciency
Pawls,
&id
Proliclancy
Paraanlaga
and
Pndidency
state
33 ( 2.2)
29 ( 1$)
$7 ( 2.4)
269 ( 1.5)
275 ( 1.3)
282 ( 1.5)
Nation
3$ ( 2.4'
25 ( 1.2)
37 ( 2.5)
253 (
261 ( 1.4)
272 ( 1.9)
PARENTS EDUCATION
HS non-gr*duate
State
41 ( 5.1)
11.11.11
39 (
*4* ( 4.8)
20 ( 4.7)
Nation
41 ( 4.5)
30 ( 2.7)
29 ( 4.0)
235 ( 3.1)
243 ( 2.7)
253 ( 2.8)
HS gi'aduate
state
35 ( 3.2)
29 ( 2.4)
37 ( 3.0)
257 ( 2.0)
285 ( 1.7)
270 ( 2.0)
Nation
40 ( 3.2)
29 ( 22)
32 ( 3.8)
247 ( 2.7)
258 ( 24)
262 ( 2.2)
Some college
State
33 ( 2.5)
30 ( 2.0)
37 ( 2.7)
278 ( 2.1)
284 ( 2.2)
28a ( 2.1)
Nation
34 ( 3.4)
28 ( 2.2)
40 ( 3.6)
259 ( 2.3)
269 ( 2.8)
271 ( 2.8)
College graduate
State
32 ( 2.1)
29 ( 1.8)
39 ( 2.4)
279 ( 2.1)
282 ( 2.1)
291 (
1.7)
Nation
33 ( 2.8)
22 ( 1.8)
41 ( 2.6)
284 ( 2.8)
273 ( 2.5)
285 ( 2.3)
GENDER
MmIe
State
34 ( 2.3)
31 ( 1.8)
36 ( 2.4)
288 ( 2.1)
277 ( 1.6)
283 (
1.9)
Nation
39 ( 2.7)
25 ( 1.6)
35 ( 2.7)
253 ( 2.7)
263 ( 2.3)
274 ( 2.4)
Female
State
33 ( 2.5)
28 ( 1.7)
39 ( 2.8)
271 ( 1.7)
273 ( 1.8)
281 ( 1.8)
Nation
37 ( 2.5)
25 ( 15)
38 ( 2.8)
253 I. 2.1)
259 ( 1.8)
280 ( 2.2)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
*** Sample size is insufficient to permit a reliable estimate (fewer than 62
students),
130
THE 1990 NAEP TRIAL STATE ASSESSMENT
125
Minnesota
TABLE Al8
Students' Reports on Whether They Own a
Calculator and Whether Their Teacher Explains
How to Use One
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1000 NAEP TRIAL
STATE ASSESSMENT
Oen a Calcdator
Teacher Expia Ins Calculator Use
Yes
No
Yes
No
TOTAL
Parcentege
and
Proficiency
ad ( 02)
276 ( 0.6)
97 ( OA)
263 ( 1.3)
99 ( 02)
279 ( 0.8)
96 ( 0.3)
270 ( 1.5)
93 ( 2$)
11,011,
11.1
1113 (
1
)
237 ( 2.8)
96 ( 1.9)
241 ( 3.7)
92 ( 1.2)
245 ( 2.7)
100 ( 0.0)
267 ( 4.6)
99 ( 0.9)
282 ( 5.3)1
99 ( 0.4)
277 ( 1.7)
99 (
1.0)
281 (
3.8)s
98 ( 0.5)
276 ( 1.6)
96 (
1.3)
257 (
3.9)1
99 ( 0.4)
279 ( 1.3)
97 ( 0.5)
263 (
1.7)
Percentage
and
Proficiency
1 ( 0.2)
3 ( 0.4)
234 ( 3.8)
1 ( 0.2)
2 ( 0.3)
7 ( 2,5)
( .41
7 (
1
(
4 ( 1.9)
8 ( 1.2)
( «4)
0 ( 0.0)
1 ( 0.9)
1 (
1,0)
2 ( OS)
4 (
1.3)
(
1 ( OA)
(
***)
3 ( 03)
233 (
5.4)
Percenteoe
and
Proficiency
51 ( 2.1)
274
1.3)
49 (2.3)
258 ( 1.7)
50 ( 2.1)
277 ( 1,1)
48 ( 2.6)
268 ( 1.5)
87 ( 9.6)
Mr* (
114111
53 ( 4.9)
235 ( 3.8)
58 ( 8.0)
***
63 ( 4.3)
243 ( 3,4)
48 ( 8.4)
.41
52 ( 4.8)
***)
62 ( 3.2)
273 ( 2.5)
45 (12.2)
278 (
2.5)1
48 ( to)
274 (
2.4)1
42 ( 8.7)
251 ( 4,8)1
52 ( 3.3)
277 (
1.7)
50 ( 2.7)
258 ( 2.1)
Percenteoa
and
Proficiency
40 ( 2.1)
276 ( 1.1)
51 ( 2.3)
208 ( 1$)
50 ( 2.1)
280 ( 1.1)
54 ( 2.6)
273 ( 1.8)
33 (
9.15)
***)
47 ( 4.9)
239 ( 2.7)
42 ( 0.0)
a4,1
37 ( 4.3)
245 ( 2.9)
52 ( 6.4)
4,41
46 ( 4.8)
(
48 (
3.2)
282 ( 2.2)
55 (12.2)
285 ( 8.4)1
54 ( 6.0)
277 ( 2.0)1
58 ( 8.7)
261 ( 4.4)1
46 ( 3.3)
280 (
1.8)
50 ( 2.7)
268 ( 2.0)
State
Nation
RACE/ETHNICITY
Mgt*
State
Nation
Black
State
Nation
Hispanic
State
Nation
Asian
State
Nation
TYPE OF COMMUNITY
Advartaged urban
State
Nation
Extreme rural
State
Nation
Mar
State
Nation
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within
2 standard errors
of the estimate for the sample.
Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency.
Sample sin is insufficient to permit a
reliable estimate (fewer than 62 students).
126
1HE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE Al8
(continued)
Students' Reports on Whether They Own a
Calculator and Whether Their Teacher Explains
How To Use One
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL.
STATE ASSESSMENT
-
Own a Calculator
.
Teacher E.xplakts Calculator Use
Yes
,
,
No
YeS
No
TOTAL
State
Nation
PARENTS' EDUCATION
NS non-graduate
State
Nation
HS graduate
State
Nation
Sono college
State
Nation
College graduate
State
Nation
GENDER
Male
State
Nation
Female
State
Nation
Percentage
and
Proadency
99 ( 0.2)
276 ( 0.8)
97 ( 0.4)
263 ( 1.3)
93 ( 2.0)
256 ( 3.2)
92 ( 1.6)
243 ( 2.0)
98 ( 0.5)
264 (
1.4)
97 ( 0.6)
255 ( 1.5)
99 ( 0.4)
283 ( 1.2)
98 ( 0.9)
268 ( 1.8)
99 ( 0.3)
285 ( 1.1)
99 ( 0.2)
275 ( 1.6)
98 ( 0.3)
277 ( 1.1)
07 ( 0.5)
264 ( 1.7)
99 ( 03)
178 ( 1.0)
97 ( 0.5)
282 ( 1.3)
Permits..
PeresKaga
and
and
and
Preaching.
Protkiancy
Prolkkoncy
( 0.2)
( ***)
3 ( 0.4)
234 ( 31)
7 ( 2.0)
444 ( 444)
8 (
1.8)
( *)
2 ( 0.5)
3 ( 0.6)
444 (
444)
( 0.4)
444 ( 4")
4 ( 0,9)
4"
444)
1 ( 0.3)
444 ( 4")
1 ( 02)
444 ( )
2 ( 0.3)
1
( 0.3)
444 ( 4")
3 ( 0.5)
51 ( 2.1)
274 ( 1.3)
49 ( 2.3)
258 ( 1.7)
51 ( 4.9)
53 ( 4.8)
242 ( 2.9)
53 ( 3.1)
262 ( 2.0)
54 ( 3.0)
252 ( 1.9)
52 ( 2.8)
280 (
1.5)
48 ( 3.2)
265 ( 2.4)
49 ( 2.2)
283 ( 1.6)
46 ( 2.6)
268 ( 2.2)
54 ( 2.3)
274 (
1.7)
51 ( 2.6)
258 ( 2.1)
( 2.3)
273 ( 1,4)
47 ( 2,5)
258 (
1.7)
49 ( 2.1)
278 ( 1.1)
51 ( 2.3)
266 ( 1.5)
49 ( 4.9)
-
47 ( 4.6)
243 ( 2.5)
47 ( 3.1)
266 ( 1.9)
46 ( 3.0)
258 ( 2.0)
48 ( 2.8)
288 ( 1.7)
52 ( 3.2)
268 ( 22)
51 ( 2.2)
287 ( 1.5)
54 ( 2.8)
280 ( 1.9)
46 ( 2.3)
279 ( 1.6)
49 ( 2.6)
269 ( 2.1)
52 ( 2-3)
27$ ( 1.3)
53 ( 2.5)
263 ( 1.8)
The standard errors of the estimated statistics appear in parentheses.
lt can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
*** Sample size is insufficient to permit a reliable estimate (fewer than 62
students).
132
THE 1990 NAEP TRIAL STATE ASSESSMENT
127
Minnesota
TABLE A19
I Students' Reports on the Use of a Calculator
I for Problem Solving or Tests
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAEP TRIAL
STATE ASSESSMENT
Worthig Problems
Class
Doing Problems at Horne
Taking Quizzes or Tests
Almost
Always
Never
Almost
Always
NeVer
Almost
Always
,
Never
TOTAL
Percintep
and
Proliciency
Pereentso
and
Proficiency
Patentee,
and
Proficiency
Patents',
and
Preticiency
Percents.
and
Proficiency
Percentsgs
and
Proficiency
State
46 ( 1.5)
20 ( 1.6)
( 1.3)
15 ( 0.8)
21 ( 1.5)
31 ( 1.6)
269 ( 1.2)
286 ( 1.2)
275 ( 1.3)
277 ( 1.7)
272 ( 2.1)
286 ( 1.2)
Nation
43 ( 1.5)
23 ( 1.9)
90 (
1.3)
19 ( 0.9)
27 ( 1.4)
30 ( 2.0)
254 ( 1.5)
272 ( 1.4)
261 (
1.8)
263 ( 1.8)
253 ( 2.4)
274 ( 1.3)
RACE/ETHNICITY
WM.
State
44 ( 1.6)
21 ( 1.6)
29 ( 1.4)
15 ( 0.9)
21 (1.6)
33 ( 1.7)
272 ( 1.1)
286 ( 1.3)
277 ( 12)
279 ( 1.8)
275 (
1.8)
287 ( 1.2)
Nation
4$ ( 1.7)
24 ( 2.2)
31 ( 1.5)
18 ( 1.2)
25 ( 1.6)
32 ( 2.3)
262 ( 1.7)
278 ( 1.3)
270 ( 1.7)
269 ( 2.3)
263 ( 2.6)
279 ( 1.2)
Slack
State
65 ( 6.8)
17 ( 5.4)
19 (
It*
( 3.5)
11+1)
41 (10.1)
**.)
16 (
( 4.3)
Nation
57 ( 3.2)
20 ( 3.9)
31 ( 2.0)
18 ( 1.9)
38 ( 3.3)
24 ( 3.1)
232 ( 2.4)
249 ( 4.0)
233 ( 3.3)
248 ( 5.5)
230 ( 3.6)
251 ( 4.1)
Hispank
State
52 ( 4.8)
4*4(444)
4 ( 1.3)
44t4 )
31 ( 4.4)
20
*** ( 4.2)
**4)
Nation
51 ( 2.9)
16 ( 3.5)
26 ( 32)
21 ( 2.1)
2$ ( 2.7)
22 ( 3.1)
239 ( 2.8)
252 ( 3.3)1
238 ( 4.8)
244 ( 3.1)
237 ( 3.2y
256 ( 4.2)
Asian
State
49 ( 5.0)
19 (
INN
5.0)
ief )
27
4.6)
( *es)
10 ( 3.6)
15 ( 5.2)
21 (
(
5.3)
***)
Nation
35 ( 6.3)
***)
29 ( 5.8)
30 ( 8.3)
***)
23 (
*4.
4.4)
23 ( 5.8)
48 (
444
8,4)
*44)
TYPE Of COMMUNITY
Advantaged urran
State
46 (
269 (
3.1)
3.0)
17 (
289 (
2.8)
2.7)1
33 (
272 (
2.9)
2.6)
11 (
*4.
1.2)
23
272
( 3.0)
( 4.8)
28 (
292 (
3.0)
2.1)
Nation
51 ( 5.4)
23 (10.7)
32 ( 6.1)
15 ( 2.4)
31 ( 3.8)
28 ( 91)
270 ( 4.7)1
274 ( 4.9)f
281 ( 7.8)1
285 ( 4.2)1
Extreme nral
State
42 ( 3.1)
22 ( 3.6)
27 (
1.5)
14 ( 1.8)
14 ( 1 .8)'
34 1 2.5)
271 ( 1.8)
285 ( 2.2)1
271 ( 2.3)
275 ( 3.5)1
271
1
2.6)1
287 (
2.7)1
Nation
46 (
246
7.4)
4,3)1
29 ( OS)
268 ( 6.1)1
20 ( 2.5)
23 (
263 (
3.9)
4,4)1
24.. ( 6.6)
37 (
270 (
8.3)
4.0)1
00w
State
45 ( 2,4)
19 ( 2.9)
( 2.3)
16 ( 1.6)
22 ( 2.7)
32 ( 3.1)
273 ( 2.0)
286 ( 2.0)
279 (
1.9)
283 ( 2.0)
277
( 2.2)
286 ( 1.7)
Nation
48 ( 1.9)
22 ( 2.0)
32 ( 1.7)
18 ( 1.1)
27 (
1.8)
29 ( 2.1)
254 ( 2.1)
272 ( 1.8)
263 ( 2.3)
263 ( 2.8)
253 ( 2.7)
275 (
1.9)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within t 2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category
is not included.
1 Interpret with caution
the nature of the sample does not allow accurate determination of
the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate
(fewer than 62 students).
128
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A19
I Students' Reports on the Use of a Calculator
(continued)
1 for Problem Solving or Tests
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1000 NAEP TRLAL
STATE ASSESSMENT
taticleldng Pr°134ms
6-
Class
Doing Problems at Nome
..
Taidng Quiztes or Toots
Almost
Always
-
Never
Almost
Always
Never
Almost
Always
Never
TOTAL
Percentage
and
Proficiency
Palmtop'
end
Proaciency
Percentage
and
ProNciancy
Percentage
and
Proficiency
Percentage
and
Proficiency
Percentage
and
Profit Norm
State
45 (
1.5)
20 (
1.13)
29 ( 1.3)
15 ( 0.8)
21 ( 15)
31 ( 1.6)
2e9( 1.2)
285 ( 1.2)
275 (
1.3)
277 ( 1.7)
272 ( 2.1)
236 ( 1.2)
Nation
48 ( 1.5)
23 ( 1.9)
30 (
1.3)
19 ( 0.9)
27 (
1.4)
30 ( 2.0)
254 ( 1.5)
272 ( 1.4)
261 ( 1.5i
263 ( 1.8)
253 ( 2.4)
274 ( 1.3)
PARENTS EDUCATION
NS non-graduate
State
51 ( 6.0)
19 ( 3.6)
38 ( 5.5)
16 ( 41.5)
24 ( 5.8)
25 ( 4.3)
(
(
(
(
(
(
Nation
54 ( 3.3)
19 ( 3.8)
26 ( 3.1)
22 ( 2.6)
32 ( 3.8)
24 ( 3.2)
240 ( 2.3)
244 ( 3.8)
244 ( 4.2)
237 ( 2.3)
251 ( 4.6)
NS gradual.
State
49 ( 2.0)
16 ( 1.7)
23 (
1.9)
16 ( 1.4)
22 ( 2.2)
26 ( 2.1)
293 ( 2.0)
273 ( 2.3)
261 ( 2.4)
270 ( 3.5)
260 ( 2.7)
275 ( 1.8)
Nation
52 ( 2.5)
20 ( 2.4)
29 (
1.9)
18 ( 1.5)
20 ( 1.8)
27 ( 2.2)
249 ( 1.4)
265 ( 2.7)
250 ( 2.4)
258 ( 2.4)
24$ ( 2.8)
265 ( 2.0)
Som. college
State
42 ( 2.2)
24 ( 1.9)
27 ( 2.2)
12 ( 1.3)
1$ (
2,0)
39 ( 25)
276 ( 1.7)
280 ( 2.4)
280 ( 2.0)
282 ( 3.5)
277 ( 3.0)
290 ( 2.0)
Nation
46 ( 2.8)
26 ( 2.8)
28 ( 2,0)
20 ( 1.9)
26 ( 2.4)
35 ( 2.5)
258 ( 2.1)
272 ( 2.5)
287 ( 3.0)
260 ( 3.2)
255 ( 3.6)
275 ( 2.0)
Co neg. graduate
State
43(
1.9)
22 ( 2.3)
33 ( 2.0)
14 ( 1.0)
22 (
1.9)
33 ( 2.1)
278 (
1.7)
291 ( 1.7)
283
1.8)
287 ( 2.1)
282 ( 3.0)
293 ( 1.5)
Nation
45( 1.9)
25 ( 2.4)
33 ( 2.0)
16 ( 1.4)
26 (
1.6)
33 ( 2.7)
265( 1.7)
284 ( 1.8)
274 ( 2.2)
278 ( 2.8)
266 ( 2.6)
285 ( 2.0)
GENDER
Male
State
48 (
1.8)
17 ( 1.4)
28 ( 1.7)
17 ( 1.2)
20 (
1.6)
28 ( 1.8)
Zr0 ( 1.5)
287 ( 2.2)
275 ( 1.8)
276 ( 2.7)
272 ( 2.6)
238 ( 1.8)
Nation
50(
1.7)
20 ( 2.0)
29 (
1.6)
19 (
1.3)
27 ( 1$)
26 ( 2.1)
255( 1.9)
275 ( 2.2)
264 ( 2.8)
263 ( 2.5)
256 ( 3.0)
277 ( 1.9)
Female
State
42 ( 2.1)
23 ( 2.1)
29 (
1.5)
12 ( 1.2)
23 ( 2.0)
35 ( 2.1)
268 (
1.5)
283 ( 1.4)
275 ( 1.6)
279 ( 2.0)
271 (
2.3)
284 ( 1.5)
Nation
46 (
2,0)
26 ( 2.1)
32 (
1.6)
18 ( 1.2)
27 (
1.8)
33 ( 2.1)
252 (
1.7)
209 ( 1.8)
259 (
1.7)
263 ( 2.4)
251 ( 2.4)
271 ( 1.5)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category
is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students).
,? 4
THE 1990 NAEP TRIAL STATE ASSESSMENT
129
Minnesota
TABLE A20
I
Students' Knowledge of Using Calculators
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
_
1990 NAEP TRIAL
"Calculator-Use"
"Calculator-Use"
STATE ASSESSMENT
High
Group
Other
Group
TOTAL
Panantafe
and
Pnatiancy
Paraantaga
and
Proficlincy
State
50 ( 1.0)
50 ( 1.0)
252 ( 1.0)
200 ) 1.2)
Nation
42 ( 1.3)
56 ( 1.3)
272 ( 1,8)
255 ( 1.5)
RACE/ETHNICITY
White
State
SOf 1.0)
50 ( 1.0)
284 ( 1.0)
273 ( 1.2)
Nation
44 ( 1.4)
56 ( 1.4)
277 ( 1.7)
263 ( 1.7)
Black
State
40 ( 5.1)
( *1.1
ft** (
N ation
37 ( 3.4)
63 ( 3.4)
246 ( 3.9)
231 ( 3.0)
Hispanic
State
60 ( 6.2)
Nation
36 ( 4.2)
54 ( 4.2)
254 ( 4.6)
238 ( 10)
Asian
State
45 ( 7.4)
41,141.
4+1
Nation
50 ( 4.5)
SO ( 4.8)
0* (
TYPE OF COMMUNITY
Advantaged urban
State
51 ( 2.3)
49 ( 2.3)
280 ( 1.9)
270 ( 2.8)
Nation
50 ( 3.8)
50 ( 3.8)
288 ( 4.9)!
275 ( 4.4)!
Extreme rural
State
51 ( 2.6)
49 ( 2.6)
282 (
1.7)
270 ( 2.3)1
Nation
39 ( 5.6)
81 ( 5.6)
269 ( 4.4)!
248 ( 4.3)1
Other
State
50 (
1.7)
50 ( 1.7)
285 (
1.5)
273 ( 1.7)
Nation
42 ( 1.4)
58 ( 1.4)
271 (
1.9)
255 ( 2.0)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value fur the entire populauon is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample sue is insufficient to permit a
reliable estimate (fewer than 62 students).
130
1 f'
77.1
.-
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A20
I Students' Knowledge of Using Calculators
(continued)
I
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO INAEP TRIAL
STATE ASSESSMENT
High "Ca lculator-Usa" Group
Other "Calculator-Use Grow
TOTAL.
Percentage
and
Proficiency
Percentage
and
Proficiency
State
50 ( 1.0)
50 ( 1.0)
262 ( 1.0)
249 ( 12)
Nation
42 ( 1.3)
58 ( 1.3)
272 ( 1.8)
255 ( 15)
PARENTS EDUCATION
HS non-graduate
State
48 ( 5.8)
54 ( 5.8)
.44 )
Nation
34 ( 3.3)
68 ( 3.3)
248 ( 4.4)
242 ( 2.4)
HS graduate
State
48 ( 2.0)
54 ( 2.0)
270 ( 1.6)
259 ( 2.0)
Nation
40 ( 22)
00 ( 2.2)
283 ( 2.0)
249 ( 1.8)
Some collage
State
54 ( 2.8)
46 ( 2.6)
289 ( 1.5)
277 ( 2.1)
Nation
4$ ( 2.2)
52 ( 2.2)
277 ( 2.6)
258 ( 2.5)
College graduate
State
53 ( 1.8)
47 ( 1.8)
290 ( 1.3)
279 ( 1.9)
Nation
46 ( 2.0)
54 ( 2.0)
282 ( 2.1)
268 ( 1.9)
GENDER
Male
State
46 ( 1.5)
54 ( 1.5)
284 ( 1.6)
269 ( 1.3)
Nation
39 ( 2.0)
61 ( 2.0)
274 ( 2.0)
255 ( 2.3)
Female
State
53 ( 1.4)
47 ( 1.4)
280 ( 1.1)
269 ( 1.7)
Nation
45 ( 1.8)
55 ( 1.8)
289 ( 1,7)
254 ( 1.3)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within t 2 standard errors
of the estimate for the sample.
*** Sample size is insufficient to permit a reliable estimate (fewer than 62
students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
131
Minnesota
TABLE A24 I Students' Reports on lyp cb of Reading
Materials in the Home
PERCENTAGE OF STUDENTS AND
AVERAGE P4.4ATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
Zero to Two Types
Three Types
Four Types
I
TOTAL
Percentage
and
Proficiency
Percentage
and
Proficiency
Percentage
seW
!cadency
State
12 ( 0.7)
31 ( 0.7)
57 ( 1.0)
258 ( 1.9)
274 ( 1.3)
281 ( 0.9)
Nation
21 ( 1.0)
30 ( 1.0)
48 ( 1 3)
244 ( 2.0)
258 ( 1.7)
272 ( 1.5)
RACE/ETHMICITY
white
State
10 ( 0.6)
31 ( 0.8)
59 ( 1.0)
282 ( 2.2)
278 ( 1.1)
282 ( 0.9)
Nation
18 ( 1.1)
29 ( 1.3)
56 ( 1.5)
251 ( 2.2)
288 ( 1.5)
276 ( 1.7)
Slack
State
26 ( 8.8)
.4.
....)
( .41
39 ( 6.6)
Nation
31 ( 1.9)
38 ( 2.2)
33 ( 2.4)
232 ( 3.2)
233 ( 32)
24.5 ( 3.3)
Hispanic
State
20 ( 4.1)
35 ( 5.8)
45 ( 8.1)
( .")
Nation
44 ( 3.0)
30 ( 2.4)
28 ( 2.3)
237 ( 3.4)
244 ( 4.3)
253 ( 2.4)
Asian
State
38 ( 8.5)
firir
--*)
28 ( 5.3)
)
34 ( 7.2)
ree
(
eee)
Nation
28 ( 6.0)
.44 ( .4.)
33 ( 5.8)
ree ( ere)
38 ( 4.2)
ree ( ere)
TYPE OF COMMUNITY
Advantaged Winn
State
34 ( 2.2)
50 ( 2.8)
276 ( 2.3)
281 ( 2.0)
Nation
13 ( 3.8)
26 ( 2.1)
61 ( 4.9)
4-9 ( *44
287 ( 3.6)1
Extreme nral
State
27 ( 1.6)
63 (
1.8)
274
2.4)
281
1.9)
Nation
17 ( 4.9)
33 ( 3.2)
50 ( 5.1)
(
253 ( 4.3)!
263 ( 5.6))
Other
State
10 ( 0.9)
31 ( 1.3)
60 ( 1.6)
285 ( 3.2)
277 (
1.9)
282 (
1.4)
Nation
22 ( 1.5)
30 ( 1.3)
48 (
1.5)
244 ( 2.8)
252 ( 2.2)
272 ( 1.7)
11111MIIMMINIMIlinm.MMEMIIM.MFlp.lk
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of inter...st 'he value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Ti.:erpLL with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit
a
reliable estimate (fewer than 62 students).
1 e .
132
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A24
I Students' Reports on Types of Reading
(c°ntinued)
Materials in the Home
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
IWO NAEP TRIAL
1
STATE ASSESSMENT
Zero to TWo Typos
Thre Types
Four Typos
TOTAL
Pereentage
and
Praciency
Percentage
and
Proactency
Percentage
and
Proectency
State
12 ( 0.7)
31 ( 0.7)
57 ( 1.0)
258 ( 1.9)
274 ( 1.3)
281 ( 0.9)
Nation
21 ( 1,0)
30 ( 1.0)
48 ( 1.3)
244 ( 2.0)
258 ( 1.7)
272 ( 1.5)
PARENTS' EVOCATION
NS non-gradua
State
36 ( 4.7)
( 5.1
36 ( 4.6)
Off
(
*RR )
( *Olt )
*4-
Nation
47 ( 4.0)
28 ( 3.0)
25 ( 2.8)
240 ( 3.4)
243 ( 3.3)
246 ( 3.3)
KS gradtato
State
14 ( 1.4)
37 ( 1.7)
49 ( 1.8)
253 ( 3.4)
263 ( 1.7)
269 ( 1.7)
Nation
26 ( 2.2)
33 ( 1.9)
40 ( 1.7)
246 ( 2.2)
253 ( 2.7)
260 ( 2.1)
Some cotlogo
State
9 ( 1.2)
27 ( 1.7)
64 ( 1.9)
(433 ( 2.2)
284 ( 1.4)
Nation
17 ( 1.5)
32 ( 1.7)
51 ( 2.0)
251 ( 4.0)
262 ( 2.6)
274 ( 1.9)
College graduate
State
6 ( 0.9)
30 ( 1 2)
64( 1.4)
272 ( 3.7)
280 ( 1.9)
288 ( 1.2)
Nation
10 ( 0.8)
28 ( 1.8)
62 ( 2.0)
254 ( 2.8)
269 ( 2.5)
280 ( 1.8)
GENDER
State
12 ( 1.0)
.
,
2)
56 ( 1.3)
258 ( 2.8)
274 t t.6)
282 ( 1.3)
Nation
21 ( 1.5)
31 ( 1.5)
48 ( 1.4)
244 ( 2.3)
259 ( 2.1)
273 ( 2.0)
Femal
State
12 ( 1.0)
30 ( 1.3)
59 ( 1.5)
258 ( 2.9)
273 ( 1.6)
280 ( 1.1)
Nation
22 ( 1.2)
29 ( 1.4)
49 ( 1.9)
244 ( 2.2)
258 ( 1.9)
270 ( 1.7)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within -I-. 2 standard errors
of the estimate for the sample.
*** Sample size is insufficient to permit a reliable estimate (fewer than 62
students).
1
8
THE 1990 NAEP TRIAL STATE ASSESSMENT
133
Minnesota
TABLE A25
I Students' Reports on the Amount of Time Spent
Watching Television Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 NAEP TRIAL
STATE ASSESSMENT
One Hour or
Less
Two Hours
Three Hours
Four to Five
Hours
Six Hours or
Moro
TOTAL
Parcentage
and
Proficiency
Percentage
and
ft:Adam
Percentage
and
Proficiency
Percentage
and
Proficiency
Percentage
and
Proficiency
State
15 ( 0.8)
27 ( 0.8)
26 ( 0.9)
25 ( 0.7)
( 05)
281 ( 1.7)
281 ( 1.5)
277 ( 1.1)
271 ( 1.4)
260 ( 2.3)
Nation
12 ( 0.8)
21 ( 0.9)
22 ( 0.8)
28 ( 1.1)
18 (
1.0)
209 ( 2.2)
268 ( 1.8)
265 ( 1.7)
280 ( 1.7)
245 ( 1.7)
1ETHNICITY
we
State
15 ( 0.9)
27 ( 0.8)
27 ( 0.9)
25 ( 01)
( 0.5)
283 ( 1.5)
283 ( 1.4)
279 ( 1.2)
274 ( 1.4)
264 ( 2$)
Nation
13 ( 1.0)
23 ( 1.2)
24 ( 1.1)
27 ( 1.4)
12 ( 1.2)
276 ( 2.5)
275 ( 2.2)
272 ( 1.9)
287 ( 1.7)
253 ( 2.6)
Black
State
3 (
1.9)
***)
18 ( 3.8)
54 ( 5.4)
( ...)
Nation
6 ( 0.8)
13 ( 1.7)
17 ( 2.1)
32 ( 1.8)
32 ( 22)
239 ( 7.0)
239 ( 5.0)
239 ( 4.0)
233 ( 2$)
Hispanic
State
16 ( 4.1)
22 ( 4.5)
...)
29 ( 4.8)
**)
23 (-
4.3)
441
10 ( 3.4)
Nation
14 ( 2.4)
20 ( 2.5)
19 ( 2.1)
31 ( 3.1)
17 (
1.7)
( ".)
245 ( 3.2)
242 ( 5.6)
247 ( 3.5)
236 ( 3.8)
Asian
State
12
( ***)
20 (
5*.
( 3.7)
04-5)
22 ( 4.5)
(
Nation
18 ( 5.0)
24 (
"e (
4.2)
"*)
22 (
.0. ( 3.1)
...)
23 ( 4.7)
43 (
( 4.0)
IN* )
TYPE OF COMMUNITY
Advantaged urban
State
19 (
279 (
1.7)
2.4)
29 (
282 (
1.1)
2.6)
23 (
277 (
1.5)
2.2)
22 (
274 (
1.5)
2.5)
8 (
***
1.1)
***)
Nation
18 ( 1.4)
21 ( 1.8)
...)
30 ( 4.3)
6 (
*** (
2.0)
***)
Extreme rural
State
13 ( 1.4)
25 ( 1.8)
291 2.3)
27 ( 1.9)
7 ( 1.0)
282 ( 4.0)1
281 ( 2.5)
274 (
1.9)1
272 ( 2.8)
Nation
14 ( 3.3)
19 ( 2.6)
26 ( 2.7)
19 ( 3.8)
256 ( 3.6)1
Other
State
15 (
1.4)
28 ( 1.4)
27 ( 1.2)
24 ( 1.1)
2as
1.7)
282 ( 2.5)
279 ( 2.0)
273 ( 1.9)
Nation
12 (
1.0)
21 ( 1.0)
23 ( 1.2)
27 ( 1.2)
17 ( 1.4)
268 ( 2.6)
269 ( 2.3)
265 ( 2.1)
259 ( 2.2)
246 ( 2.5)
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
1
I
134
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A25
1 Students' Reports on the Amount of Time Spent
(continued)
Watching Television Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
One Hour or
Four to Five
Six Hours or
STATE ASSESSMENT
Lass
Two IRA's
Throe Hours
Hours
Mon
-
-
TOTAL
Pen:~
and
Proficiency
Peroenlass
and
Proficiency
Parcentage
and
Proficiency
Penalise
and
Proficiency
Pereentsp
and
Prefidency
State
16 ( 0.6)
27 ( 0.8)
26 ( 0.9)
25 ( 0.7)
7 ( 04)
281 ( 1.7)
201 ( 1.5)
277 ( 1.1)
271 ( 1.4)
200 ( 2.3)
Nation
12 ( 0.8)
21 ( 0.9)
22 ( 0.8)
28 ( 1.1)
18 ( tO)
209 ( 22)
286 ( 1.8)
265 ( 1.7)
200 ( 13)
245 ( 13)
PARENTS' EDUCATION
HS non-graduate
State
11 ( 3.2)
( **lb )
19 ( 4.7)
*4.1
22 ( 4.3)
41 ( 4.7)
8 ( 3.2)
4.01
Nation
12 ( 2.2)
e.*)
20 ( 3.1)
21 ( 2.8)
28 (
244 (
2.9)
3.2)
20 ( 2.4)
444)
HS graduate
State
13 ( 1.3)
24 ( 14)
25 ( 1.9)
31 ( 1.8)
8 ( 1.1)
263 ( 3.4)
268 ( 2.0)
265 ( 2.5)
262 ( 2.3)
41411
(
Nation
8 ( 1.0)
17 ( 1.4)
23 ( 2.0)
32 ( 2.3)
1 9 ( 1.6)
249 ( 4.7)
257 ( 2.8)
259 ( 3.2)
253 ( 2.5)
248 ( 3.0)
Some college
State
15 ( 1.9)
30 ( 1.6)
2$ ( 1.7)
21 ( 1.7)
8 ( 1.2)
288 ( 2.4)
282 ( 2.1)
285 ( 2.0)
279 ( 2.1)
044 ( ***
Nation
25 ( 2.4)
23 ( 2.6)
28 ( 2.2)
14 ( 1.5)
27$ ( 2.7)
269 ( 3.5)
267 ( 2.5)
242 ( 3.4)
College graduate
State
17 ( 1.4)
29 ( 1.3)
20 ( 1.3)
23 ( 1.6)
5 ( 0.6)
290 ( 1.8)
292 ( 1.5)
283 ( 1.7)
277 ( 2.0)
Nation
17 ( 1.3)
22 ( 1.6)
23 ( 1.1)
25 (
1.5)
12 ( 1.1)
282 ( 2.6)
280 ( 2.5)
277 ( 2.2)
270 ( 2.4)
255 ( 3.2)
GENDER
Male
State
12 ( 1.1)
25 ( 1.1)
26 ( 1.4)
28 ( 1.3)
8 ( 0.9)
280 ( 2.3)
282 ( 1.8)
277 ( 1.8)
273 ( 1.8)
260 ( 3.1)
Nation
11 ( 0.9)
22 ( 1.2)
22 ( 1.0)
2. ( 1.3)
17 ( 1.5)
269 ( 3.3)
267 ( 2.6)
267 ( 2.2)
262 ( 21)
248 ( 24)
Female
State
18 ( 1.3)
28 ( 1.2)
27 ( 14)
23 ( 1.1)
5 ( 0.7)
282 ( 2.2)
279 ( 2.0)
277 ( 1.3)
267 ( 12)
**.
***
Nation
14 ( 1.1)
20 ( 1.3)
23 ( 1.4)
28 ( 1.6)
15 ( 1.2)
269 ( 2.8)
269 ( 2.2)
264 ( 1.8)
258 ( 1.9)
241 ( 2.2)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
*** Sample size is insufficient to permit a reliable estimate (fewer than 62
students).
I Liu
THE 1990 NAEP TRIAL STATE ASSESSMENT
135
Minnesota
TABLE A26
I Students' Reports on the Number of Days of
i School Missed
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL.
STATE ASSESSMENT
None
One or Two Days
Three Days or More
TOTAL
Porcantiga
and
Prodidancy
Percentage
and
Proficiency
Ravening,
and
Prolidency
State
44 ( 1.0)
38 ( 1.0)
20 ( 0.9)
230 ( 1.0)
278 ( 1.3)
285 ( 1A)
Nation
45 ( 1.1)
32 ( 0.9)
23 ( 1.1)
265 ( 1.8)
286 ( 1.5)
250 ( 1.9)
RACE/ETHNICITY
White
State
44 ( 1.0)
38 ( 1.1)
20 ( 0.9)
282 ( 1.0)
280 ( 1.3)
269 ( 1.2)
Nation
43 ( 12)
34 ( 1.2)
23 ( 12)
273 ( 1.8)
272 ( 1.7,
258 ( 2.1)
Black
Sta te
32 ( 8.0)
0-0.
34 ( 4.4)
33 ( 7.2)
Nation
58 ( 3.1)
21 ( 1.8)
23 ( 2.5)
240 ( 3.2)
240 ( 4.1)
224 ( 3.5)
Hispanic
State
27 ( 5.2)
29 ( 8.1)
(
*44(44*)
Nation
41 ( 3.3)
32 ( 2.2)
27 ( 2.6)
245 ( 4.6)
250 ( 3.3)
235 ( 3.1)
Asian
State
49 ( 4.7)
39 ( 5.0)
*** ( "*)
11 ( 3.6)
*** ( *44)
Nation
62 ( 5.6)
287 ( 4.7)1
27 ( 5.3)
***
(
11 ( 4.9)
TYPE OF COMMUNITY
Advantaged urban
State
37 ( 2.5)
41 ( 2.2)
22 ( 1.3)
280 ( 2.4)
280 ( 3.2)
26a ( 2.1)
Nation
47 ( 2.3)
284 ( 4.4)1
38 ( 2.8)
279 ( 4.5)1
15 ( 3.7)
***)
Extrema rural
State
43 ( 1.8)
38 ( 1.8)
19 ( 2.1)
278 ( 1.8)
279 ( 2.5)
263 ( 2.4)1
Nation
43 ( 4.4)
32 ( 4.2)
25 ( 3.9)
257 ( 4.1)1
284 ( 5.8)1
Otfiar
State
48 ( 1.8)
33 ( 1.5)
19 ( 1.5)
282 ( 1.5)
279 ( 1.7)
270 ( 2.4)
Nation
45 ( 1.3)
32 ( 1.1)
23 (
1.1)
285 ( 2.2)
266 ( 1.9)
251 ( 2.4)
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
txrtainty that, for each population of interest, the value for the entire population is within t 2 standard errors
of the estimate for the sample.
I Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permlt
reliable estimate (fewer than 62 students).
136
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A26 I Students' Reports on the Number of Days of
(continued)
1 School Missed
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
[STATE
ASSESSMENT
1990 NAEP TRIAL
None
One or Two Days
Three Days or More
TOTAL
Percentage
and
Proficiency
Percentage
and
ProlIdency
Pstrantage
and
Praficioney
State
44 ( 1.0)
30 ( 1.0)
20 ( 0.9)
280 ( 1.0)
278 ( 1.3)
265 ( 1.4)
Nation
45 ( 1.1)
32 ( 0.9)
23 ( 1.1)
265 ( 1.8)
266 ( 1$)
250 ( 1.9)
PARENTS EDUCATION
HS non-graduate
State
28 ( 5.0)
...)
33 ( 5.2)
...)
38 ( 4.3)
Nation
36 ( 3.2)
26 ( 3.1)
38 ( 3.5)
245 ( 3.0)
249 ( 3.3)
237 ( 3.1)
HS graduate
State
40 ( 1.8)
36 ( 1.8)
24 ( 1.8)
266 ( 1.5)
267 ( 1.9)
257 ( 2.7)
Nation
43 ( 2.1)
31 ( 1.9)
27 ( 1.9)
255
2.0)
257 ( 2.8)
249
2.4)
Some college
State
46 ( 2.2)
35 ( 2.3)
18 ( 1.6)
286 ( 1.3)
283 ( 22)
273 ( 2.4)
Nation
1.8)
37 ( 1.6)
23 ( 1.6)
270 ( 3.0)
271 ( 2.5)
253 ( 3.1)
College graduate
State
47 ( 1.6)
37 ( 13)
17 ( 1.0)
288 ( 1.2)
286 ( 1.5)
275 ( 23)
Nation
51 ( 1.6)
33 ( 1.2)
16 ( 1.3)
275 ( 2.1)
277 ( 1.7)
265 ( 3.1)
GENDER
Male
State
44 ( 1$)
36 ( 1$)
20 ( 1.1)
280 ( 1.4)
280 ( 1.6)
264 ( 2.3)
Nation
47 ( 1.6)
31 ( 1.4)
22 ( 1.4)
266 ( 2.0)
267 ( 2.1)
250 ( 2.6)
Female
State
43 (
1.5)
36 ( 1.3)
20 ( 1.2)
280 ( 1.1)
276 ( 1.6)
268 ( 1 6)
Nation
43 ( 1.4)
32 ( 1.1)
25 ( 1.3)
264 ( 2.3)
266 ( 1.7)
250 ( 1.8)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
'1" Sample size is insufficient to permit a reliable estimate (fewer than 62
students).
142
THE 1990 NAEP TRIAL STATE ASSESSMENT
137
Minnesota
TABLE A27
I Students' Perceptions of Mathematics
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1000 NAEP TRIAL
STATE MSESSMENT
Strongly Agree
Aare.
Undecided, Disagree,
Sirongiy Disagree
_
TOTAL
Pavan lags
NW
Pro &dem
Pernentar
and
Prolkdanqt
Panwdapo
and
Madam
State
20 ( 1.3)
51 ( 1.3)
23 ( 1.2)
269 ( 1.3)
276 ( 1.1)
263 ( 1.3)
Nation
27 ( 4.3)
49 ( 1.0)
24 ( 1.2)
271 ( 1.9)
262 ( 1.7)
251 ( 1.8)
RACE/ETHNICITY
White
State
26 ( 1.4)
SO ( 1.3)
24 ( 1.3)
291 ( 1.3)
278 ( 1.1)
265 ( 1.1)
Nation
20 ( 1,6)
48 ( 1.3)
26 ( 1$)
279 ( 2.0)
272 ( 1.8)
257 ( 2.0)
Black
State
26 ( 3.7)
46 (
.44 ( 5.3)
444)
26 ( 5.2)
Nation
32 ( 2.5)
52 ( 2.3)
16 ( 1.9)
247 ( 4.1)
233 ( 3.3)
227 ( 4.2)
Hispanic
State
20 ( 3.8)
SO ( 5.6)
.44 (
20
1-dr ( 5.3)
***)
Nation
24 ( 2,5)
46 ( 2.6)
28 ( 2.1)
257 ( 5.5)
244 ( 2.2)
236 ( 3.8)
Asian
State
23 ( 4.9)
441
55 ( sa)
17
iHr
( 4.8)
( 0+1
Nation
29 ( 5.5)
53 ( 5.6)
17
444 ( 4.9)
( .441
TYPE OF COMMUNITY
Advantaged urban
State
24 (,1.9)
54 (
1.8)
23
( 1.4)
292 ( 2.2)
27$ ( 2.5)
261 ( 2.5)
Nation
17 ( 3.2)
55 (
280 (
2.4)
4.1)1
23
.4* ( 4.2)
Extreme rural
State
24 ( 2.8)
52 ( 3.1)
25 ( 2.8)
292 ( 3.0)/
274 ( 1.5)
203 ( 2$)1
Nation
34 (
270 (
2.8)
3.9)1
49 (
252 (
2.2)
4.1)1
17
1,44
( 1.4)
(
Odor
State
28 ( 2,5)
50 ( 1.9)
21
( 1.9)
290 ( 2.2)
278 ( 1.9)
267 ( 1.7)
Nation
27 ( 1.4)
48 ( 1.2)
25 ( 1.4)
271 ( 2.4)
263 ( 2.2)
250 ( 1.9)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution
the nature of the sample does not allow accurate
deterrnMation of the variability of this estimated mean proficiency.
*** Sample size is insufricient to permit a
reliable estimate (fewer than 62 students).
138
THE 1990 NAEP TRIAL STATE ASSESSMENT
Minnesota
TABLE A27
I Students' Perceptions of Mathematics
(continued)
I
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
19.0 NAEP TRIAL
STATE ASSESSMENT
Strongly Agree
,
Agree
_
Undecided, Disagree,
Strongly Disagree
TOTAL
Peroentage
and
Prolidency
Percentage
and
Proficiency
Percentage
and
Proficiency
State
26 ( 1.3)
51 ( 1.3)
23 ( 1.2)
289 ( 1.3)
276 ( 1.1)
263 ( 1.3)
Nation
27 ( 1.3)
49 ( 1.0)
24 ( 1.2)
271 ( 1.9)
262 ( 1.7)
251 ( 1.8)
PARENTS' EDUCATION
HS non-graduate
State
16 ( 4.2)
43 ( 5.0)
4.2 ( 5.6)
*4r*
e*)
*It
( Mt)
di
4.14)
Nation
20 ( 2.6)
50 ( 3.3)
30 ( 3.6)
,i,-4-
( ii...)
243 ( 2.6)
238 ( 4.3)
HS graduate
State
21 ( 1.7)
51 ( 1.8)
2$ ( 2.1)
275 ( 2.1)
265 ( 1$)
255 ( 2.2)
Nation
27 ( 2.1)
47 ( 2.3)
26 ( 2.0)
262 ( 2.7)
255 ( 2.3)
245 ( 2.4)
Some college
State
27 ( 2.3)
51 ( 2.2)
22 ( 2.0)
296 ( 2.3)
280 ( 1.5)
274 ( 1.8)
Nation
28 ( 2.5)
47 ( 2.4)
25 ( 1.8)
274 ( 3.1)
287 ( 1.9)
258 ( 3.2)
College graduate
State
30 ( 1.7)
52 ( 2.1)
18 ( 1.4)
295 ( 1.5)
284 ( 1.41
288 ( 2.1)
Nation
30 ( 2.3)
51 ( 1.6'
19 ( 1.8)
280 ( 2.41
274 ( 2.2)
266 ( 2.5)
()ENDER
Male
State
29 (
1.3)
48 (
1.5)
23 (
1.4)
289 ( 1.7)
276 ( 1.6)
262 ( 2.0)
Nation
28 ( 1.5)
48 ( 1.2)
24 (
1.4)
273 ( 2.3)
263 ( 2.0)
251 ( 2.4)
Female
State
23 ( 1.8)
53 ( 1.7)
24 ( 1.5)
288 ( 1.5)
275 (
1.3)
263 (
1.6)
Nation
26 ( 1.7)
50 ( 1.7)
25 ( 1.9)
289 ( 2.1)
262 ( 1.8)
252 ( 1.9)
The stanciard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ±. 2 standard errors
of the estimate for the sample.
*** Sample size is insufficient to permit a reliable estimate (fewer than 62
students).
144
THE 1990 NAEP TRIAL STATE ASSESSMENT
139
Acknowledgments
The design, development, analysis, and reporting of the first Trial State Assessment was truly a
collaborative effort among staff from State Education Agencies, the National Center for Education Statistics
(NCES), Educational Testing Service (En), Westat, and National Computer Systems (NCS). The program
benefitted from the contributions of hundreds of individuals at the state and local levels
Governors, Chief
State School Officers, State and District Test Directors, State Coordinators, and district administrators
who
tirelessly provided their wisdom, experience, and hard work. Finally, and most importantly, NAEP is grateful
to the students and school staff who participated in the Trial State Assessment.
Special recognition is due the Council of Chief State School Officers (CCSSO) for its considesable
contributions to the program, especially its management of the National Assessment Planning Project. That
project resulted in the mathematics framework and objectives for the asseument and recommendations
about reporting the results of the program. In particular, we note the significant contributions of Ramsay
Se Idea, Director of the State Education Assessment Center for the CCSSO and the members of the Steering,
Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project.
The Trial State Assessment was funded through NCES, in the Office of Educational Research and
Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided
consistent support and guidance. The staff
particularly Gary Phillips, Eugene Owen, Stephen Gorman,
Maureen Treacy, and Raul Garza
worked closely and collegially with ETS, Westat, and NCS staff and
played a crucial role in all aspects of the program.
The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve
credit for their advice and guidance.
We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring
Panels. These people
from school districts, colleges and universities, and State Education Agencies
worked tirelessly to help ETS staff develop the assessment and a framework for interprefing the results.
Under the NAEP contract to Ers, Archie Lapointe sesved as the project director and Ina Mullis as
the deputy director. Statistical and psychometric activities were led by John Mazzeo, with consultation from
Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the
operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal
aspects; and Stephen Koffler, state smices. Sampling and data collection activities were carried out by
Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen.
The printing, distribution, and proeff.sing of the materials were the responsibility of NCS, under the direction
of John O'Neill and Lynn Zabac.k.
The large number of states and territories participating in the first Trial State Assessment introduced
many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction
based on its characteristics and the results of its assessed students. To meet this challenge, a computerized
report generatical system was built, combining the speed and accuracy of computer-generated data with high
resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the
system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this
report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate
the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti.
Debra Kline coordinated the efforts of the data analysis staff. Stephen Korner wrote the text for the report.
Kent Ashworth was responsiNe for coordinating the cover design and final printing of this report.
Special thanks are also due to many individuals for their invaluable assistance in reviewing the
reports, especially the editors who improved the text and the analysts who checked the data.
1
'5
U.S. GOVERNMENT PRINTING OFFICE : 1991 0 - 293-276 QL 8 (BIL 211
146