DOCUMENT RESUME
ED 330 567
SE 052 077
TITLE
The State of Mathematics Achievement in Montana:
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; I53N-0-88685-14-9
PUB DATE
Jun 91
NOTE
146p.; The entire Report consists of a cc.:mposite
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;
Mathematics Tests; National Proc.:rams; Problem
E lying; Public Schools; *State Prylrams; Student
Attitudes; Teacher Attitudes; 2glachel: Qualifications;
Television Viewing
IDENTIFIERS
*Montana; National Assessment of EducAttonal
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-stite
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 Montana, 2,488 students in 100 public
schools were assessed. This report describes the mathematics
proficiency of Montana eighth-graders, compares their overall
performance to students in the West 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
televisioa
watched, absenteeism). On the NAEP math scale, Montana students
had
an average proficiency of 280 compared to 261 nationwide. Many.fewer
students (Montana-23%; U.S.-12%) appear to have acquired reasoning
and problem solvIng skills. (JJVCRW)
NATIONAL CENTER FOR EDUCATION STATISTICS
The STATE of
_kg!
A le.
in MONIUNA
The Trial. State Aotsessinent at Grade Eight
THE NATION'S
REPORT
CARD
r17'iZT PAn AVMLJLE
U S DEPARTMENT OF EDUCATION
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Prepared by Educational Tesfing Service under Contract with the National Center for Education Statistics
Office of Edu.-,ational Research and Improvement US. Department of Education
2
What is The Nation's Report Card?
THE NATION'S REPORT CARD, the NatMnal Assessment of Educational Progress tNIAEP). is the only nationally representative and
continuing assessment of what America's students know and can do in various subject areas. Since 19(19. assessments have been conducted
periodically in reading. mathematics, science, writing, history/geography. and other fields. By making obje:tive 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 guarantet!s
the privacy of individual students and their families.
NAEP is a congressionally inundated project of the National Center for Edueation Statistics. the U.S. Department of Education. The
Commissioner of Education Statistics is responsible. by law, for carrying out the NAEP project through competitive awards to qualified
organizations. NAEP reports 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
responsible for selecting the subjixt 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
Exeeluive Director
Martha Holden Jennings Foundation
Cleveland, Ohio
Phyllis Williamson Aldrich
Curriculum Coordinator
Saratoga-Warren B.O.C.E.S.
Saratoga Springs. New York
Franck Aksander
Associate Superintendent
California Department of Education
Sacramento, California
David P. Battini
High School History Teacher
Cairo-Durham High School
Cairo, New York
Parris C. Battle
Teacher
Horace Mann Elementary School
Miami. Florida
Mary R. Blanton
Attorney
Cromwell, Porter, Blanton & Blanton
Salisbury. North Carolina
Boyd W. Boehije
Attorney
Gaass, Klyn. & Boehlje
Pella, Iowa
Linda R. Bryant
Teacher
Cireenway Middle School Teacher Center
Pittsburgh. Pennsylvania
Honorable Michael N. Castk
Governor of Delaware
Cartel State Office Building
Wilmington, Delaware
Honorabk Naomi K. Cohen
State of Connecticut
House of Representatives
Legislative Office Building
Hartford, Connecticut
Chesier E. Finn, Jr.
Professor of Education and Public Policy
Vanderbilt University
Washington. D.C.
Michael S. Glade
Wyoming State Board of Education
Saratoga, Wyoming
Christine Johnson
Principal
Abraham Lincoln High School
knver. Colorado
John Lindley
Principal
South Colby Elementary School
Port Or0 -ad. Washington
Carl J. Maser
Director of Schools
The Lutheran Church -- Missouri Synod
International Center
St. Louis, Missouri
Mark D. Musick
President
Southern Regional Education Board
Atlanta. Georgia
Honorabk Carolyn Pollan
Arkansas House of Representatives
Fort Smith, Arkansas
Matthew W. Prophet, Jr.
Superintendent
Portland Oregon School District
Portland, Oregon
Honorabk William T. Randall
Commis.sioner of Education
State Department of Education
Denver. Colorado
Dorothy K. Rich
President
Home and School Institute
Special Projects Office
Washington. D.C.
Honorable Richard W. Riky
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. Illino;s
Assistant Secretary for
Educational Research and
Improvement (Ex-Officio)
U.S. Department of Education
Washington. D.C.
Roy Truhy
Executive Directin. NAGB
Washington. D.C.
3
NATIONAL CENTER FOR EDUCATION STATISTICS
The STATE of
Mathematics
Achievement
in MONTANA
The Trial State Assessment at Grade Eight
THE NATION'S
REPORT
CARD
Report No: 21-ST-02
June 1991
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
4
U.S. Department of Education
Lamar Alexander
Secretary
Office of Educational Research and Improvement
Bruno V. Manno
Acting Assistant Secretary
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 availabledirectly from the participating
States. For ordering information, please contact the assessment division of yourSuite Department of Education. For
oraering 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).
Libnuy of Ccargrcss, Catalog Card Number: 91-61478
ISBN: 048685-14-9
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 Saviee is an equal opporumity/affirmative action employer.
Educalional Taiing Service, ETS, and
arc tegistered trademarks of Educational Testing Service.
Table of Contents
EXECUTIVE SUMMARY
INTRODUCTION
7
Overview of the 1990 Trial State Assessment
This Report
9
Guidelines for Analysis
12
Profile of Montana
14
Eighth-Grade School and Student Characteristics
14
Schools and Students Assessed
15
PART ONE
How Proficient in Mathematics Are Eighth-Grade Students
in Montana Public Schools/
17
Chapter 1.
Students' Mathematics Performance
1 8
Levels of Mathematics Proficiency
19
Content Area Performance
19
Chapter 2.
Mathematics Performance by Subpopulations
24
Race/Ethnicity
24
Type of Community
'7
Parents' Education I. vel
29
Gender
Content Area Performance
33
THE 1990 NAEP TRIAL STAI.E ASSESSMENT
0
In
PART TWO
Finding a Context for Understanding
Students' Mathematics Proficiency
37
Chapter 3.
What Are Students Taught in Mathematics"
39
Curriculum 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 Eighth-Grade Mathematics'
67
Educational Background
68
Summary
71
Chapter 7.
The Conditions Beyond School that Facilitate Mathematics Learnmg 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
81
DATA APPENDIX
...97
THE 1990 NAEP TRIAL STATE ASSESSMENT
NE NATION'S
REPORT
CARD
EXECUTIVE SUMMARY
In 1988, Congress passed new legislation for the National Assessment of FAlucational
Progress (NAEP), which included -- for the first time in the projeet'slUstory -- a provision
authorizing voluntary state-by-state assessments on a trial hasis, in addition to continuing
its primary mission, the nation41 .issessments that NAEP has conducted since its inception.
As a result of the legislation the 1990 NAEP program included a Trial State Assessrmnt
Program in eighth-grade mithematics. National assessments in mathematics, readmg,
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 carefuliy 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
program. Local school district personnel administered all assessment sessions, and the
contractjes staff monitored 50 percent of the sessions as part of the quality assurance
progam 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
Montana
In Montana, 100 public schools participated in the assessment. The weighted school
participation inte was 90 percent, which means that all of the eighth-grade students in this
sample of schools were representative of 90 percent of the eighth-grade public .school
students in Montana.
In each school, a random sample of students was selected to participate in the assessment.
As estimated by the sample, 0 percent of the eighth-grade public-school population was
claskfied as limited English Proficient (LEP), while 7 percent had an Individualized
Edueation 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 Individualiied 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 IIP or had an IEP represented 0 percent and 2 percent
of the population, respectively. In total, 2,486 eighth-grade Montana public-school
students were assessed. The weighted student participation rate was 96 percent. This
means that the sample of students who took part in the assessment was representative of
96 percent of the eligibk eighth-grade public-school student population in Montana.
Students' Mathematics Performance
The average proficiency of eighth-gra-1c public-school students from Montana on the
NAFP mathematics scale is 280. This proficiency is higher than that of students across the
nation (261).
Average proficiency on the NAFP 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,
NAEP 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 NAEP
scale.
9
2
THE 1993 NAEP TRIAL STATE ASSESSMENT
In Montana, 100 percent of the eighth graders, compared to 97 percent in the nation,
appear to have acquired skills in.volving simple additive reasoning and problem solving with
whole numbers (level 200). However, many fewer students in Montana (23 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 Montana performed higher than students in the nation in all of
these five content areas.
Subpopulation Performance
In addition to the overall results, the 1990 Trial State Assessment permits reporting on the
performance of various subpopulations of the Montana eighth-grade student population
defined by race/ethnicity, type of community, parents' education level, and gender. In
Montana:
White students had higher average mathematics proficiency than did
Hispanic or American Indian students.
Further, a greater percentage of White students than Hispanic or American
Indian students attained level 300.
The results by type of community indicate that the average mathematics
performance of the Montana students attending schools in areas classified
as "other" was higher than that of students attending schools in extreme
rural areas.
In
Montana,
the
average
mathematics
proficiency of eighth-grade
public-school students having at least one parent who graduated from
college was approximately 19 points higher than that of students whose
parents did not graduate from high school.
The results by gender show that eighth-grade males in Montana had a
higher average mathematics proficiency than did eighth-grade females in
Montana.
In addition, a greater percentage of males than females in
Montana attained level 300. Compared to the national results, females in
Montana performed higher than females across the country; males in
Montana performed higher than males across the country.
,
/
THE 1990 NAEP TRIAL STATE ASSESSMENT
3
Montana
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 Montana are as follows:
About half of the students in Montana (50 percent) were in schools where
mathematics was identified as a special priority.
This is a smaller
percentage than that for the nation (63 percent).
In Montana, 46 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 Montana were taking eighth-grade
mathematics (59 percent) than were taking a course in pre-algebra or
algebra
(37 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 Montana spent 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.
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 emphaEis 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
Montana
In Montana, 17 percent of the eighth-grade students had mathematics
teachers who reported getting all of the resources they meded, while
21 percen* 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 Montana, 16 percent of the students never used a calculator to work
problems in class, while 46 percent almost always did.
In Montana, 38 percent of the students were being taught by mathematics
teachers who reported having at kast a master's or education specialist's
degree. This compares to 44 percent for students across the nation.
About half of the students (47 percent) had teachers who had the highest
level of teaching certification available. This is different from 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 Montana 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.
About one-quarter of the eighth-grade public-school students in Montana
(21 percent) watched one hour or less of television each day; 6 percent
watched six hours or more. Average mathematics proficiency was lowest
for students who spent sx hours or more watching television each day.
ThE 1990 NAEP TRIAL STATE ASSESSMENT
5
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
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
District of Columbia
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Ohio
Kentucky
Oklahoma
Louisiana
Oregon
Maryland
Pennsylvania
Michigan
Rhode Island
Minnesota
Texas
Montana
Virginia
Nebraska
West Virginia
New Hampshire
Wisconsin
New Jersey
Wyoming
New Mexico
New York
North Camlina
North Dakota
Guarn
Virgin Islands
..7 3
THE 1990 NAEP TRIAL STATE ASSESSMENT
7
Montana
This report describes the performance of the eighth-grade public-school students in
Montana and consists of three sections:
This Introduction provides background information about the Trial State
Assessment a xl this report.
It also provides a profile of the eighth-grade
public-school students in Montana.
Part One describes the mathematics performance of the eighth-gade
public-school students in Montana, the West region, and the nation.
Part Two relates students' mathematics performance to
contextual
information about the mathematics policies and instruction in schools in
Montana, the West 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 LI.S.C. 1221e-1(i)(2)(C)(i)))
As a result of the legislation, the 1990 NAEP 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.
8
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
The Trial State Assessnv-nt 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 authorized the Trial State Assessment, the federal government arranged for
the National Sc nce Foundation and the U.S. Department of Education to issue a special
gxant to the Council of Chief State School Officers in mid-1987 to develop the objectives.
The development process included cartful 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 Montana, in the West 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. Defmitions of the subpopulations
referred to in this report are presented below. The results for Montana are based only on
the students included in the Trial State Assessment Program. However, the results for the
nation and thc region of the country are baseu 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. Use 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 national or regional results,
since not every state participated in the program.
National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics
(Reston, VA: National Council of Teachers of Mathematics, 1989).
4 7-
THE 1990 NAEP TRIAL STATE ASSESSMENT
9
Montana
RACE/ETHNICITY
Results are preserted 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 (includins Pacific Islander), and American
Indian (including Alaskan Native). Based on critelia described in the Procedural 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 Montana.
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 attend schools where
many of the students' parents arc 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 reporting of results by each type of community was also subject to a minimum student
sample size of 62.
PARENTS' EDUCATION LEVEL
Students were asked to indicate the extent of schooling for each of their parents -- did not
fmish high school, graduated high school, some education after high school, or graduated
college. The response indicating the higher level of education was selected for reporting.
10
THE 1990 NAEP TRIAL STATE ASSFSSMENT
Montana
GENDER
Results are reported separately 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 Fkgure 1. All 50 states and the District
of Columbia are listed, with the participants in the Trial State Assessment highlighted in
boldface type. Tenitories were not assigned to a region. Further, the part of Virginia that
is included in the Washington, DC, metropolitan statistical arra 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.
FIGURE 1
I
Regions of the Country
NORTHEAST
SOUTHEAST
CENTRAL
WEST
Connecticut
Alabama
Illinois
Alaska
Dslaware
Arkansas
Indiana
Arizona
District of Columbia
Florida
Iowa
California
Maine
ftorgla
Kansas
Colorado
Maryland
Kentucky
Michigan
HawaII
Massachusetts
Louisiana
Minnesota
Idaho
New Hampshire
Mississippi
Missouri
Montana
New Jena),
North Carolina
Nebraska
Nevada
New York
South Carolina
North Dakota
New Mexico
Pinnsybrania
Tennessee
Ohio
Oklahoma
Rhode island
Virginia
South Dakota
Oregon
Vermont
mot Virginia
Wisconsin
Texas
Virginia
Utah
Washington
Wyoming
THE 1990 NAEP TRIAL STATE ASSESSMENT
11
Montana
Guido lines 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 groups 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 significant),
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 betwecn 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
group 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 groups, the confidence interval included zero, and thus no difference could
be assumed between the groups. When three or more groups are being compared, a
Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are
discussed in greater detail in the Procedural Appendix.
12
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
..11=11
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 given
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).
7 ;)
THE 1990 NAEP TRIAL STATE ASSESSMENT
13
Montana
Profile of Montana
EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERIS11CS
Table 1 provides a profde of the demographic characteristics of the eighth-grade
public-school students in Montana, the West region, and the nation. This profile is based
on data cc _A,xted from the students and schools participating in the Trial State Assessment.
TABLE 1
I Profile of Montana Eighth-Grade Public-School
I Students
PERCENTAGE OF STUDENTS
-
WM) MEP TRIAL STATE ASSESSMENT
Montana
West
Nation
DEMOGRAPHIC SUBGROUPS
Race/Ettinicity
White
87 ( 1.1)
53 ( 1.9)
70 ( 0.5)
Black
( 01)
T ( 2.0)
18 ( 0.3)
Hispanic
3 ( 0.4)
21 ( 1.5)
10 ( 0.4)
Asian
1 ( 0.3)
4 ( 1.3)
2 (
0.5)
American Indian
8 ( 1.1)
4 ( 2.3)
2 (
0.7)
Type of Conenunity
Advantaged urban
2 ( 0.1)
14 ( 85)
10 ( 3.3)
Disadvantaged urban
0 ( 0.0)
19 ( 7.5)
10 ( 2.8)
Extreme rural
31 ( 2.8)
10 ( 3.8)
10
3.0)
Other
56 ( 2.8)
58 (10.1)
70 ( 4.4)
Parents' Eclucation
Did not finish high sch001
5 ( 0.7)
10 ( 1.3)
10 ( 0.8)
Graduated high school
23( 1.3)
19 ( 2.5)
25 ( 1.2)
Some education after high school
23 ( 0.9)
18 ( 1.2)
17 (
0.9)
Graduated college
45 ( 1.3)
42 ( 4.0)
39( 1.9)
Oendiw
Male
51 ( 1.4)
55 ( 2.1)
51 (
1.1)
Female
49 ( 1.4)
45 ( 2.1)
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 percentages 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 "1 don't know." Throughout this report, percentages less than 0.5 percent are reported as
0 percent.
20
14
THE 1990 NAEP TRIAL STATE ASSESSMENT
Monuna
SCHOOLS AND STUDENTS ASSESSED
Table 2 provides a profile summarizing participation data for Montana schools and
students sampled for the 1990 Trial State Assessment. In Montana, 100 public schools
participated in the assessment. The weighted school participation rate was 90 percent,
which means that all of the eighth-gradc students in this sample of schools were
representative of 90 percent of the eighth-grade public-school students in Montana.
TABLE 2
J Profile of the Population Assessed in Montana
EIGHTH-GRADE PUSUC 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 ot substitute schools
provided
Number of substitute schools
participating
Total number of participating
schools
90%
124
8
1GO
4
100
EIGHTH-GRADE Pt/WC-SCHOOL STUDENT
PARTICIPATION
Weighted student participation
rate after make-ups
Number of students Selected to
participate 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
0%
7%
2%
2,588
2,48$
THE 1990 NAEP TRIAL STATE ASSESSMENT
15
Montana
In each school, a random sample of students was selected to participate in the assessment.
As estimated by the sample, 0 percent of the eighth-grade public-school population was
classified as Limited English Proficient (LEP), while 7 percent hae 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 fcr the
student and describes a program of activities and/or related services neces;ary 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 2 percent
of the population, respectively.
In total, 2,486 eighth-grade Montana public-school students were assessed. The weighted
student participation rate was 96 percent. This means that the sample of students who
took part in the assessment was representative of 96 percent of the eligible eighth-grade
public-school student population in Montana.
16
THE 199U NAEP TRIAL STATE ASSESSMENT
Montana
PART ONE
ME NATION'S
REPORT
CARD
How Proficient in Mathematics Are Eighth-Grade
Students in Montana 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 scale, which ranges from 0 to 500.
This part of the report contains two chapters that describe the mathematics proficiency of
eighth-grade public-school students in Montana. Chapter 1 compares the overall
mathematics performance of the students in Montana to students in the West region and
the nation. It also presents the students average proficiency separately for the five
mathematics content areas. Chapter 2 summarizes the students' oveiall 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.
THE 1990 NAEP TRIAL STATE ASSESSMENT
37
Montana
CHAPTER 1
Students' Mathematics Performance
As shown in Figure 2, the average proficiency of eighth-grad: public-school students from
Montana on the NAEP mathematics scale is 280. This proficiency is higher than that of
students across the nation (261).2
FIGURE 2
I
Average Eighth-Grade Public-School
I Mathematics Proficiency
NAEP Uathematics Scale
200
225
250
275
300
500
Average
Proficiency
Montana
1118
0.8)
1-1414
West
2S1 ( 2.8)
Nation
281 ( 1.4)
The standard eirors 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 F4.4). If the confidence intervals for the populations do not overlap, there is a
statistically significant difference between the populations.
2 Differenms reported are staustically different at about thc 95 percent certamty level. This means that with
about 95 percent certainty there is a real difference in the average mathematics proficiency between the two
populations of interest.
18
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
LEVELS OF MATHEMATICS PROFICIENCY
Average proficiency on the NAliP 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 results from the 1990 national assessments of fourth-, eighth-, and
twelfth-grade students to defme the skills, knowledge, and understandings that characterize
four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAFP
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 the
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 impractical
to defme meaningful levels of mathematics proficiency beyond the four presented here.
Definitions of the four levels of mathematics proficiency are given 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 are not judgmental standards
of what ought to be achieved at a particular grade. Figure 4 provides the percentages of
students at or above each of these proficiency levels. In Montana, 100 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 Montana (23 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 Montana,
West region, and national results for each content area. Students in Montana performed
higher than students in the nation in all of these five content areas.
THE 1990 NAEP TRIAL STATE ASSESSMENT
19
Montana
FIGURF 3
J
Levels of Mathematics Proficiency
LEVEL 200
THE NAIRM'S
REPORT
CARD
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 identity solutions to one-step word problems and select the greatest four-digit 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 analysts, they are able to read simple bar graphs. In
the algebra dimension, these students can recognize translations of word problems to numerical sentences
and extend simple pattern sequences.
LEVEL 250
Simple Multiplicative Reasoning and Two-Step Problem Sok:ing
I
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 problems.
They are beginning to understand the relationship
between proportion and probtibility.
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
Montana
FIGURE 3
I
Levels of Mathematics Proficiency
(continued)
I
LEVEL 300
Reasoning and Problem Solving Involving Fractions, Decimals,
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 tractions 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.
rLEVEL 350
Reasoning and Problem Solving Involving Geometric Relationships,
Algebraic Equations, and Beginning Statistics and Probability
Students at this level have extended their knowledge of number 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 ar,d 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 indirect measurement. These students also can apply
then knowledge of the properties of geometric figures to solve problems, such as determining the slope of
a line.
In data analysis, these students can compute mear,_ 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 cimposition of functions.
They can determine the nth term of a sequence and give counterexamples to disprove an algebraic
generalization.
THE 1990 NAEP TRIAL STATE ASSESSMENT
21
Montana
FIGURE 4
I Levels of Eighth-Grade Public-School
I Mathematics Proficiency
LEVEL 350
State
Region
Nation
LEVEL 300
State
Region
Nation
LEVEL 250
State
Region
Nation
LEVEL 200
State
Region
Nation
iemmwail
1-44'44
11.1.1.1101W4
P-1.04
,
1-114
Flool
144
0
20
40
so
80
0 ( 0.1)
( 0.4)
0 ( 0.2)
23 (
1.4)
12 ( 2.4)
12 (
1.2)
88 ( 0.9)
63 ( 2.8)
64 (
1.6)
100 ( 0.1)
97 (
1.0)
97 ( 0.7)
100
Percentage at or Above Proficiency Levels
The standard errors are presented in parentheses. With about 95 percent certainty, the value
fo i. each population of interest is within ± 2 standard errors of the estimated percentage (95
percent confidence interval, denoted by 1-1-4).
If the confidence intervals for the populations
do not overlap, there is a statistically significant difference between the populations.
22
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
FIGURE 5
I Eighth-Grade Public-School Mathematics
I Content Ares Performance
State
Rejlon
Nation
State
Region
Nation
State
Region
Nation
State
Region
Nation
State
Region
Nation
200
225
250
275
300
Avorage
Prenciency
282 ( 1.0)
264 ( 2.6)
268 ( 1.4)
279 ( 1.4)
258 ( 3.0)
258 ( 1.7)
280 ( 0.8)
280 ( 2.6)
259 ( 1.4)
282 ( 0.8)
282 ( 3.6)
252 ( 1.8)
278 ( 0.9)
259 ( 2.4)
280 ( 1.3)
SOO
Mathematics Submits 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 mcan (95 percent confidence interval, denoted by i-H).
If the
confidence tntervals for the populations do not overlap, there is a statistically significant
difference between the populations.
THE 1990 NAEP TRIAL STATE ASSESSMENT
23
Montana
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 racial/ethnic
groups when the number of students in a racial/ethnic group is sufficient in size to be
reliably reported (at least 62 students). Average mathematics performance results for
White, Hispanic, and American Indian students from Montana are presented in Figure 6.
As shown in Figure 6, White students demonstrated higher average mathematics
proficiency than did Hispanic or American Indian students.
Figure 7 presents mathematics performance by proficiency levels. The figure shows that a
greater percentage of White students than Hispanic or American Indian students attained
level 300.
3 (i
24
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
FIGURE 6
I Average Eighth-Grade Public-School
Mathematics Proficiency by Race/Ethnicity
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 I-1-4). 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. *** Sample size is
insufficient to permit a reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
25
Montana
ME MN'S
REPORT
FIGURE 7
I Levels of Eighth-Grade Public-School
CARD
I Mathematics Proficiency by Race/Ethnicity
LEVEL 300
State
White
Hispanic
Amer. Indian
Region
White
Hispanic
Amer. Indian
Nation
White
Hispanic
Amer. Indian
LEVEL 250
State
White
Hispanic
Amer. Indian
R9Ion
White
Hispanic
Amer. Indian
Nation
White
Hispanic
Amer. Indian
LEVEL 200
State
White
Hispanic
Amer. Indian
Ragion
White
Hispanic
Amer. Indian
Nation
White
Hispanic
Amer. Indian
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 1-1-1).
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.
! 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
26 (
1.6)
4 ( 2.9)
6 ( 2.2)
16 ( 3.2)
3 ( 1.6)
P001 I *al
15 ( 1.5)
3 ( 1.1)
1
(
2.3)1
91
( 0.7)
70 ( 7.0)
80 ( 8.8)
74 ( 3.3)
41
( 5.4)
laist
74
(
1.8)
41
( 4.5)
45 (16.0)1
100 ( 0.1)
99 ( 0.0)
911
( 0.9)
99 ( 0.8)
03 ( 2.0)
*.
OS ( 0.4)
93 (
1.6)
97 ( 6.7)I
Montana
TYPE OF COMMUNITY
Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students
attending public schools in areas classified as "other" and extreme rural areas. (These are
the "type of community" groups in Montana with student samples large enough to be
reliably reported.) The results indicate that the avexage mathematics performance of the
Montana students attending schools in areas classifted as "other" was higher than that of
students attending schools in extreme rural areas.
FIGURE 8
Average Eighth-Grade Public-School
Mathematics Proficiency by Type of
Community
MEP liathematics $eale
200
225
250
275
300
500
Average
Proficiency
Montana
Extreme rural
Other
weSt
Extreme rural
Other
Nation
Extreme rural
Other
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 1.41). 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.
THE 1990 NAEP TRIAL STATE ASSESSMENT
27
FIGURE 9
LEVEL 300
sm.
Ext. rural
Other
Ext. rural
Other
Nation
Ext. rural
Other
LEVEL 250
State
Ext. rural
Other
Rai lion
Ext. rural
Other
Nation
Ext. rural
Other
LEVEL 200
slaw
Ext. rural
Other
9ion
Ext. rural
Other
Nation
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 54-4). tf 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.
! Interpret with caution
the nature of the sample does not allow aocurate determination
of the variability of this estimated mean proficiency.
18 ( 1.7)
28 ( 1.7)
( 4.8)1
10 ( 1.8)
S ( 2.3)I
12 ( 1.2)
118
( 2.4)
IS ( 0.9)
52 (12.8)1
112 ( 5.0)
SS
( 8.2)1
64 ( 2.3)
180
( 0.3)
100 ( 0,1)
00
( 1.3)1
Se
( 1.7)
97
( 2.8)1
97
( 1.0)
100
28
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
PARENTS' EDUCATION LEVEL
Previous NAEP findings have shown that students whose parents
are better educated tend
to have higher mathematics proficiency (see Figures 10 and 11). In Montana, the average
mathematics proficiency of eighth-grade public-school students having at least one parent
who graduated from college was approximately 19 points higher than that of students who
reported that neither parent graduated from high school. As shown in Table 1 in the
Introduction, a larger percentage of students in Montana (45 percent) than 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
5 percent for Montana and 10 percent for the nation.
FIGURE 10
I Average Eighth-Grade Public-School
1 Mathematics Proficiency by Parents' Education
NAEP Mathematics Scat.
0
200
225
250
275
300
500
118101?
CMS
Average
Pro &fancy
Montana
Hui
HS non-graduate
in( 2.3)
144
HS graduate
271 ( tS)
HI
Some college
in( 1.1)
College graduate
( 1.0)
West
HS non-graduate
31S ( 4.4)
HS graduate
in( 2.2)
Some college
( 340)
College graduate
fin( 2.4)
Nation
1404
hiS non-graduate
242 ( 2.0)
14
HS graduate
244 ( 1.5)
P44
Some college
2120 ( 1.7)
College graduate
274 ( 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 P4-I). If the confidence intervals for the populations do not overlap, there is a
statistically significant difference between the populations.
THE 1990 NAEP TRIAL STATE ASSESSMENT
2.9
Montana
,11.
111E WON'S
rPaRT
FIGURE II
I Levels of Eighth-Grade Public-School
.JUID
I Mathematics Proficiency by Parents' Education
LEVEL 300
State
HS non-grad.
HS greduate
Some college
College grad.
notion
HS non-grad.
HS graduate
Some college
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 grad.
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.
20
40
80
80
Percentage at or Above ProfIcleocy 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 14-4). 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.
100
36
30
THE 1990 NAEP TRIAL STATE ASSESSMENT
( 2.8)
11 ( 1.7)
20 ( 3.1)
32 ( 1.8)
2 ( 2.3)
2 ( 1.3)
15 ( 2.8)
( 3.5)
1
( 0.9)
5
( 1.5)
12
( 1.4)
21 ( 1.9)
( 3.7)
( 3.0)
( 1.9)
( 1.2)
( 8.8)
( 4.4)
( 4.1)
( 3.6)
37 ( 4.6)
56 ( 2.7)
71
( 2.6)
78 ( 2.0)
loo
00:30))
100
( 0.1)
100 ( 0.0)
( 2.2)
(
1.6)
( 0.7)
( 0.7)
( 1,9)
( 0.8)
( 0.7)
( 0.7)
Montana
GENDER
As shown in Figure 12 eighth-grade males in Montana had a higher average mathematics
pmficiency than did eighth-grade females in Montana. Compared to the national results,
females in Montana performed higher than females across the country; males in Montana
performed higher than males amass the country.
FIGURE 12
I Average Eighth-Grade Public-School
Mathematics Proficiency by Gender
NAEP liathemalks Scale
200
225
250
275
300
500
Average
Prosciana
1+4
eN
Montana
Male
Fet1111116
West
Male
Female
Nation
Male
ftil)
Female
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-I).
If the confidence intervals for the populations do not overlap, there is a
vatistically significant difference between the populations.
As shown in Figure 13, there was no difference between the percentages of males and
females in Montana who attained level 200. The percentage of females in Montana who
attained level 200 was greater than the percentage of females in the nation who attained
level 200. Also, the percentage of males in Montana who attained level 200 was greater
than the percentage of males in the nation who attained level 200.
THE 1990 NAEP TRIAL STATE ASSESSMENT
31
Montana
FIGURE 13
I Levels of Eighth-Grade Public-School
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
Stat.
Male
Female
Region Male
Female
Nation
Male
Female
0
20
40
SO
60
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 b; P+4).
If the confidence intervals for the populations
do not overlap, there is a statistically signthcant difierence between the populations.
Proficiency level 350 is not presented in this figure because so few students attained that level.
:3
32
THE 1990 NAEP TRIAL STATE ASSESSMENT
22 (
1.9)
19 ( 2.4)
13 ( 3.1)
11
( 2.2)
14 ( 1.7)
10 ( 1.3)
( 1.4)
117
( 1$)
65 ( 4,1)
61
( 3.2)
64 ( 2.0)
64
( 1,8)
100 (
0.1 )
100
( 0.1)
97
( 1,2)
( 1.0)
97 ( 09)
97
( 0.8)
Montana
In addition, a greater percentage of males than females in Montana attained level 300. The
percentage of females in Montana who attained level 300 was greater than the percentage
of females in the nation who attained level 300. Also, the percentage of males in Montana
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
Montana
TABLE 3
I Eighth-Grade Public-School Mathematics
Content Area Performance by Subpopulations
AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS
1100 NAEP TRIAL
STATE ASSESSMENT
timbers and
Operations
linalarallnana " "
CM.
Data Analysis,
Inadades' and
Probability
AlgebraFunctionsand
TOTAL
State
Region
Nation
RACUETHN1C1TY
Mite
State
Region
Nation
lapanIc
State
Region
Nation
American Indian
State
Region
Nation
TYPE OF COMMUNITY
Bennie rural
State
Region
Nation
Other
State
Region
Nation
Pralidsocw
2421 211
200
265 ( 1.0)
271 ( 3.2)
273 ( 1.8)
267 ( 3.1)
24$ ( 3.5)
248 ( 2.7)
25$ ( 3.4)
4.11
249 ( 7.8)1
280 ( 1.7)
254 ( 8.8)1
258 ( 4.3)1
253 ( 1.1)
262 ( 3,5)
206 ( 1.9)
Pra0049nay
Prolkienty
271
A1
2110 (
Prold0noV
0.esi
Pracioncy
273 ( 0.9)
ILO)
200 ( 2.0
20242
25S ( 2.4)
254
1.7)
254 (
202
124)
200 ( 1.3)
243 ( 1.4)
263 ( 0.9)
215 ( 0.7)
201 ( OA)
207 ( 3.9)
267 ( 3.0)
272 ( 4.4)
267 ( 2.6)
207 ( 2.0)
267 ( 1.5)
272 ( 1.8)
266 ( 1.4)
257 ( 6.3)
261 ( 3.'
261 ( 3.7)
260 ( 3.0
239 ( 4.2)
245 ( 4.4)
240 ( 4.7)
243 ( 4.0)
231 ( 3.4)
243 ( 3.2)
230 ( 3.4)
243 ( 3.1)
256 ( 3.1)
256 ( 4.5)
255 ( 4.4)
**ft)
1144
247 ( di)!
243 ( 8.8)1
242 ( 5.2)1
242 ( 4.0)1
275 ( 2.3)
27$ ( 1.7)
270 ( 2.2)
274 ( 1.6)
254 ( 4.6)!
252
$.4)1
253 ( 8.6)1
251 ( 8.5)1
254 ( 4.2)!
253 ( 4.5)t
267 ( 5.0)1
268 ( 4.8)1
282 ( 1.7)
251 ( 1.1)
284 ( 0.9)
280 ( 1.1)
255( 4.2)
258 ( 3,4)
250 ( 42)
258 (
257 ( 2.4)
2541( 1.7)
281 ( 22)
261 ( 1.7)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
34
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE 3
I
Eigbth-
ti
Public-School Mathematics
(continued)
I Content Area Performance by Subpopulations
AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS
,
1990 NAEP TRIAL
STATE ASSESSMENT
.
-
timbers and
Operations
_
Measurement
Geometry
-
Data Andysis,
Mad Mkt 8116
Probability
-
Algebra and
Functions
.
TOTAL
Pralkiency
!Wow
*el Mem
MI Mew
Siolisiomv
State
242 (1.0)
279 ( 1.41
200 ( 0.1 1
262 ( 0.1)
27111
Region
264 (2.6)
Nation
2036 (1.4)
25$ } 221191
rot 1.si
PARES rs' 200061106
NS non-graduate
State
272 ( 3,4)
285 ( 3.9)
270 (
264 ( 3.1)
264 (
Region
248 ( 4.2)
242 ( 82)
246 `, 4.P)
246 ( 6.2)
245 ( 6.1
Nation
247 ( 2.4)
237 ( 3.6)
242 (
240 ( 3.1)
242 (
HS imitate
State
274 ( 2.1)
266 ( 2.7)
271 ( 2.1)
272 ( 1.9)
269 ( 2.4)
Region
254 ( 2.5)
245 ( 3.0)
251 ( 3.6)
249 ( 3.2)
250 ( 2.4)
Nation
249 ( 1.1)
2411 ( 2.1)
252 ( 1.6)
233 ( 22)
253 ( 2.0)
Some ciAlitge
State
284 ( 2.0)
283 ( 2.3)
282 ( 2.7)
247 ( 1.9)
260
1.7)
Region
272 ( 2.7)
268 ( 5.3)
264 ( 3.9)
271 ( 4.9)
264
3.2)
Nation
270 ( 1.5)
264 ( 2.7)
262 ( 2.0)
209 ( 2.4)
263
2.2)
Doi Mge graduate
State
289 ( 1.4)
288 ( 1.6)
285 ( 1.2)
289 ( 1.1)
285 ( 1.1)
Region
275 ( 2.7)
271 ( 3.0)
271 ( 2.3)
276 ( 4.3)
272 ( 2.6)
Nation
278 ( 1.8)
272 ( 2.0)
270 ( 1.6)
276 ( 2.2)
273 ( 1.7)
GENDER
MMe
State
285
( 1.3)
285 ( 1.8)
253 ( 1.2)
265 ( 1.3)
279 ( 1.4)
Region
264 ( 3.8)
263 ( 3.5)
261 ( 34)
264 ( 4.1)
200 ( 3.3)
Notion
266 ( 2.0)
262 ( 2.3)
260 ( 1.7)
262 ( 2.1)
200(1.6)
Femal
State
279 ( 1.5)
274 ( 1.9)
276 ( 1.6)
279 ( 1.2)
277 ( 1.4)
Region
263 ( 2.5)
252 ( 2.9)
259 ( 2.9)
200 ( 4.0)
259 ( 2.8)
Nation
266 ( 14)
253 ( 1.6)
258 ( 1.5)
261 ( 1.9)
260 ( 14)
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 1990 NAEP TRIAL STATE ASSESSMENT
35
Montana
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, teachers, and students.
To gather such information, the students r
ating in the 1990 Trial State Assessment,
their mathematics teachers, and the princip e.!
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, the 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 STATE ASSESSMENT
37
Montana
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 strategies 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 instructional 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.
40 tj
38
1 IE 1990 NAEP TRIAL STATE ASSESSMENT
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 Montana public schools and their relationship to students'
proficiency.
Table 4 provides a profile of the eighth-grade public schools policies and staffing. Some
of the salient results are as follows:
About half of the eighth-gxade students in Montana (50 percent) were in
public schools where mathematics was identified as a special priority. This
compares to 63 percent for the nation.
3 Curtis McKnight, et al., The Underachieving Currkulum Assessing U.S. School Mathematics from an
International Perspective, A National Report on the Second International Mathematics Study (Champaign,
IL: Stipes Publishing Company, 1987).
Lynn Steen, Ed. Everybody -aunts
A Report to the Nation on the Future of Mathematics Education
(Washington, DC: National Academy Press, 1989).
. 4
THE 1990 NAEP TRIAL STATE ASSESSMENT
39
Montana
In Montana, 46 percent of the students could take an algebra course in
eighth grade for high school course placement or credit.
About three-quarters of the students in Montana (77 percent) were taught
mathematics by teachers who teach only one subject.
About half (46 percent) of the students in Montana were typically taught
mathematics in a class that was grouped by mathematics ability.
Ability
grouping was more prevalent across the nation (63 percent).
TABLE 4
I Mathematics Policies and Practices in Montana
1 Eighth-Grade Public Schools
PERCENTAGE OF STUDENTS
1900 NAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
_
Percentage of eighth-grade students In public
schools that Identified mathematics as
receiving special emphasis in school-wide
goals and objectives, Instruction, in-service
training, etc.
Percentage of elghth-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 teachers My° teach
only mathematics
Percentage of eighth-grade students in public
schools who are usignad to a mathematics
due by their abNIty in mathematics
Percentage of eighth-grade students in public
schools who receive fair or more hors of
mathematics instruction per week
Percentage
Percentage
Pmentailw
50 ( 3.0)
01 ( 8.8)
63 ( 5,9)
40 ( 2.0)
92 ( 4.7)
78 ( 4.6)
77 ( 3.0)
96 ( 1.6)
91 ( 3.3)
40 ( 2.9)
64 ( 8.3)
63 ( 4.0)
49 ( 2.9)
25 ( 5.9)
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.
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
CURRICULUM COVERAGE
To place students' mathematics proficiency in a curriculum-related context, it is necessary
to =mine the extent to which eighth graders in Montana art taldng mathematics courses.
Based on their revonses, shown in Table 5:
A greater percentage of students in Montana were taking eighth-grade
mathematics (59 percent) than were taldng a course in pre-algebra or
algebra
(37 percent).
Across the
nation,
62 percent
were taking
eigAth-grade mathematics and 34 percent were taking a course
in
pm-algebra or algebra.
Students in Montana who were enrolled in pre-algebra or algebra courses
exhibited higher average mathematics proficiency than did those who were
in eighth-grade mathematics courses. This result is not unexpected since
it is assumed that students enrolled in pre-algebra and algebra courses may
be the more able students who have already mastered the general
eighth-grade mathematics curriculum.
TABLE 5
I Students' Reports on the Mathematics Class
I They Are Taking
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
11190 NAP TRIAL STATE ASSESSMENT
I
Montana
West
Nation
Percentage
and
Prilidenay
Percenlage
and
Preidency
Percentage
and
Preiciency
What kind of mathematics class are you
taking this year?
Eighth-grade mathematics
59 ( 2.4)
63 ( 2.7)
62 ( 2.1)
27$ ( tO)
252 ( 2.4)
251 ( 1.4)
Pro-algebra
26 ( 1.9)
15 ( 2.7)
19 ( 1.9)
251 ( 1.1)
200 ( 3.6)
272 ( 2.4)
Affiebn
12 ( 1.5)
17 ( 1.5)
15 ( 1.2)
299 ( 3.8)
299 ( 4.5)
298 ( 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.
THE 1990 NAEP TRIAL STATE ASSESSMENT
41
Montana
Further, from Table A5 in the Data Appendix:*
About the same percentage of females (36 percent) and males (38 percent)
in Montana were enrolled in pre-algebra or algebra courses.
In Montana, 36 percent of White students, 35 percent of Hispanic
students, and 49 percent of American Indian students were enrolled in
pre-algebra or algebra courses.
Similarly, 38 percent of students attending schools in areas classified as
"other" and 37 percent in schools in extreme rural areas 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 thfir teachers, the greatest percentage of eighth-grade students in public
schools in Montana spent 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, tilt:, 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 Montana, 3 percent of the students spent no time each day on
mathematics homework, compared to 1 percent for the nation. Momover,
3 percent of the students in Montana 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.
42
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
The results by race/ethnicity show that 3 percent of White students,
3 percent of Hispanic students, and 6 percent of American Indian students
spent an hour or more on mathematics homework each day.
In
comparison, 3 percent of White students, 3 percent of Hispanic students,
and 5 percent of American Indian students spent no time doing
mathematics homework.
In addition, 4 percent of students attending schools in areas classified as
"other" and 2 percent in schools in extreme rural areas spent an hour or
more on mathematics homework daily.
In comparison, 3 percent of
students attending schools in areas classified as "other" and 3 percent in
schools in extreme rural areas 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
1900 NAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
_
.
Parasite",
nd
Proficiency
Pwaentese
Paraistase
Sad
Prialmay
About how much time do students spend
on mathematics homework each day?
None
3 (
44, ( 0.4)
44)
1 ( 0.3)
1 (
«14 ( 0.3)
16 minutes
38 ( 21)
42 ( 6.7)
43 ( 42)
260 ( 1.2)
255 ( 4.2)
250 ( 2.3)
30 minutes
50 ( 2.8)
43 ( 62)
43 ( 43)
263 ( 1.2)
284 ( 4.7)
203 ( 2.0)
46 minutes
0 ( 1.7)
9 ( 2.3)
1.10)
280 ( 2.6)1
270 ( 8.5)1
272 ( 51 )1
An hour or more
3 ( 0.5)
( 1.9)
4 ( 04)
252 (12.1)
276 ( 5.1)f
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 umple 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
Montana
TABLE 7
Students' Reports on the Amount of Time They
Spent on Mathematics Homework Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
11100 NAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
About how much time do you usually
spend
each
day
on
mathematics
homework?
None
15 minutes
30 minutes
45 minutes
An hour or more
Panne lap
Perverdege
Percordefe
end
and
end
Proficiency
kedelleiey
Prefirgency
( OA)
279 ( 2.9)
29 ( 1.3)
254 ( 1.3)
33 ( 1.1)
280 ( 1.3)
18 ( 0.7)
280 ( 1.4)
13 ( 0.5)
275 ( 1.9)
12 ( 1.7)
254 ( 4.2)
31 ( 43)
283 ( 3.5)
2$ ( 1.7)
251 ( 2.9)
15 ( 1.8)
287 ( 4.2)
14 ( 1.1)
251 ( 43)
The standard errors of the estimated statistics appear in parentheses.
lt can be said witii 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.
And, according to the students (Table 7 and Table A7 in the Data Appendix):
In Montana, relatively few of the students (9 percent) reported that they
spent no time each day on mathematics homework, compared to 9 percent
for the nation.
Moreover, 13 percent of the students in Montana 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,
18 percent of Hispanic students, and 21 percent of American Indian
students spent an hour or more on mathematics homework each day.
In
comparison, 9 percent of White students, 17 percent of Hispanic students,
and
7 percent of American Indian
students spent no time doing
mathematics homework.
44
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
In addition, 12 percent of students attending schools in areas classified as
"other" and 13 percent in schools in extreme rural areas spent an hour or
more on mathematics homework daily.
In comparison, 10 percent of
students attending schools in areas classified as "other" and 8 percent in
schools in extreme rural areas 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
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.
Nanona1 Council of Teachers of Mathematics. Currieultort and Evaluation Standards for School Alathonatk.t
(Reston, VA: Natronal Council of Teachers of Mathematics, 1989).
THE 1990 NAEP TRIAL STA] E ASSESSMENT
45
Montana
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.
fir; i
46
THE 1990 NAEP TRIAL STATE ASSESSMENT
.1111=1M.
Montana
TABLE 8
Teachers' Reports on the Emphasis Given to
Specific Mathematics Content Areas
.11I
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
11190 NAV TRIAL STATE ASSESSMENT
1-
Montana
West
Won
leacher
°emphasis°
categories
by
content areas
Ihromia.
Prellialsney
Perusises
lireiki10104,
ParomMes
Prolielony
Numbers and Operations
Heavy emphasis
40 ( 2.9)
42 ( 1.4)
49
290(2.0)
2117
IlLS)
290
1".ei
tittle or no emphasis
14 ( 1.3)
13 ( 2.1)
15 ( 2.1)
293 ( 2.9)
291(6.9)
217 ( 3.4)
Measunament
Heavy emphasis
9 ( 1.0)
11 ( 2.3)
17 ( 3.0)
277 ( 5.7)
251 ( 7.7)4
250 ( 5.5)
Little or no emphasis
23 ( 1.9)
36 ( 5.3)
33 ( 4.0)
2115 ( 3.3)
275 ( 8.3)
272 ( 4.0)
Geometry
Heavy emphasis
31 ( 2.5)
24 ( 8.3)
211 ( 3.5)
26e1 ( 1.5)
260 ( 25)4
2e0 ( 32)
Little or no emphasis
13 ( 1.4)
le ( 4.5)
21 ( 13)
279 ( 2.8)
277 (11.4)1
264 ( 54)
Data Analysis,Statistics, and Probabillty
Heavy emphasis
13 ( 2.3)
14 ( 3.7)
14 ( 22)
207 ( 3.0)
254 (10.8)1
259 ( 4,3)
Little or no emphasis
59 ( 2.5)
54 ( 6.3)
53 ( 4.4)
281 ( 1.4)
262 ( 4.9)
261 ( 2,9)
Algebra and Functions
Heavy emphasis
58 ( 3.0)
43 ( 5.0)
48 ( 3.0)
281 ( 13)
277 ( 5.2)
275 ( 2.5)
Little or no emphasis
10 ( 2.9)
23 ( 5.1)
20 ( 3.0)
( 3.2)1
243 ( 4.2)1
243 ( 10)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population or 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
Montana
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 Montana (50 percent) were in
public schools where mathematics was identified as a special priority. This
compares to 63 percent for the nation.
In Montana, 46 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 Montana were taking eighth-grade
mathematics (59 percent) than were taking a course in pre-algebra or
algebra
(37 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 Montana spent 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 Montana, relatively few of the students (9 percent) reported that they
spent no time each day on mathematics homework, compared to 9 percent
for the nation.
Moreover, 13 percent of the students in Montana 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 TRIAL STATE ASSESSMENT
Montana
CHAPTER 4
rixs
SIM 111/11111111111 all
111141111111111111111111111
SIM 111111111111111/ ii
1111111111111i111111111111/1111
1.111111111111111Willill
RIM II NUM
MEM :1111/.1111111
Nnossommuss.
-ma swam
MOM" ,If,gang
AM. MIMI
MINOS 11111111111111
How Is Mathematics Instruction Delivered?
Teachers facilitate learning through a variety of instructional practices. Bocause a particular
teaching method may not be equally effective with all types of students, 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 arid 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 Mathematics
(Reston, VA: National Council of Teachers of Mathematics, 1991).
THE 1990 NAEP TRIAL STATE ASSESSMENT
49
Montana
From Table 9 and Table A9 in the Data Appendix:
In Montana, 17 percent of the eighth-grade students had mathematics
teachers who reported getting all of the resources they needed, while
21 percent of the students were taught by teachers who got only sane or
none of the resources they needed. Across the natior, , these figures were
13 percent and 31 percent, respectively.
In Montana, 19 percent of students attending schools in areas classified as
"othet" and 14 percevt in schools in extreme rural areas had mathematics
teachers who got all the resources they needed.
By comparison, in Montana, 22 percent of students attending schools in
areas classified as "other" and 20 percent in schools in extreme rural areas
were in classrooms where only some or no ICSOUTCCS were available.
Students whose teachers got all the resources they needed had mathematics
achievement levels similar to those whose teachers got only some or none
of the resources they needed.
TABLE 9
I Teachers' Reports on the Availability of
I
Resources
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
-
,
111100 NAEP TRIAL STATE ASSESSMENT
Montana
Iftst
Mahon
-
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 all the resources I need.
I get most of Ow resourcos I med.
I get some of none of the resources I need
Peee.--ereago
No:1May
Ponentego
and
and
and
Proloiancy
Prelidancy
Prolitiona
17 ( 22)
15 ( 5.2)
13 ( 2.4)
265 ( 1.9)
261 ( La)
205 ( 4.2)
02 ( 3.0)
52(3.8)
Se ( 4.0)
250 ( 1.1)
266 ( 4.1)
( 2.0)
21 ( 2.7)
23 ( 6.4)
31 ( 4.2)
2110 ( 1.3)
257 ( 3.7)1
261 ( 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 for the entire population is within ± 2 standard errors
of the estimate for the sar-tple.
Interpret with caution -- the nature of the sample does not allow accurate
determination of the vari
lity of this estimated mean proficiency.
ta
50
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
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 instmction by the mathematics teachers of the assessed students.
According to their teachers:
More than half of the students in Montana (60 percent) worked
mathematics problems in small groups at least once a week; relatively few
never worked mathematics problems in small gxoups (8 percent).
The largest percentage of the students (62 percent) used objects like rulers,
counting blocks, or geometric shapes less than once a week; relatively few
never used such objects (1 percent).
In Montana, 62 percent of the students were assigned problems from a
mathematics textbook almost every day; 6 percent worked textbook
problems about once a week or less.
About half of the students (47 percent) did problems from worksheets at
least several times a week; about one-quarter did worksheet problems less
than weekly (30 percent).
Thomas Romberg, "A Common Curriculum for Mathematics," individual Differences and the Common
Curriculum
Eighty-second Yearbook of the National Society for the Study of Education
(Chicago,
University of Chicago Press, 1983).
THE 1990 NAEP TRIAL STATE ASSESSMENT
51
Montana
TABLE 10
I Teachers' Reports on Patterns of Mathematics
Instruction
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1900 MEP TRIAL STATE ASSESSMENT
Montana
West
Nation
_
or
penandamo
'Ad
Peramtags
and
Peranulais
and
About how often do students
work
problems in small groups?
Pirsialinay
Pralialanay
Praliokosy
At least ones a week
130 ( 3.0)
ST ( 8.9)
50 ( 4.4)
282 ( 1.2)
262 ( 4.2)!
260 ( 2.2)
Less than once a week
32 ( 2.9)
39 ( 7.6)
43 ( 4.1)
290 ( 1.9)
266 ( 4.5)
264 ( 2.3)
Now
( 1.8)
8 ( 2.0)
290 ( 2.3)!
277 ( 5.4)1
About how often do students use objects
Percentage
Pengentage
Percentage
like rulers, counting blocks, or geometric
awl
end
and
solids?
Pnalidiancy
Pralaiency
Proildancy
At least once a week
37 ( 2.6)
262 ( 1.7)
34 ( 8.2)
256 ( 4.9)!
,
254 ( 3.2)
LOU Man once a weak
82 ( 2.6)
57 ( 6.4)
69 ( 3.9)
281 ( 1.0)
265 ( 4.0)
263 ( 1.9)
New
( 0.4)
.4* (
8 ( 3.0)
.4")
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
Montana
TABLE 11
I Teaches' Reports on Materials for
I Mathematics Instruction
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
-
,
1800 MAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
About how often do students do problems
Proontage
mid
Peramtage
Penteitags
and
from textbooks?
ProMow
fralloissiv
Pradany
Almost ovary day
92 ( 3A)
55 ( to)
62(3.4)
234 ( 1.0)
270 ( LS)
1.1)
Swami Onos a week
32 ( 2-5)
( SA)
( 3.1)
276 ( 1.4)
251 ( 5.2)
254 ( 2.9)
About once a woak or loss
6 (
27$ (
1.6)
( 4A)
( *41
( 1.6)
200 ( 5.1)4
About how often do students do problems
on worksheets?
Perantsge
amd
Peranbie
and
Permits.
ant
Itelidancy
MO:1mm
At toast swami limas a weak
47 ( 3.3)
25 ( 5.2)
34 ( 3.6)
280 ( 1.1)
258 ( 4.3)I
256 ( 2.3)
Mout ones a wok
22 ( 2.1)
34 ( 4.6)
33 ( 3.4)
262 ( 2.7)
258 ( 4.1)
260 ( 2.3)
Lass than moldy
30 ( 2.2)
41 ( 5.6)
32 ( 3.6)
281 ( 0.8)
274 ( 4.2)
274 ( 2.7)
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 if 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 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.
tr)
THE 1990 NAEP TRIAL STATE ASSESSMENT
53
Montana
COLLABORAUNG IN SMALL GROUPS
In Montana, 39 percent of the students reported neves working mathematics problems in
small groups (see Table 12); 31 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
Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
16$0 NAEP MAL STATE ASSESSMENT
Montana
Most
Nation
-
-
Pagodas
and
Pr* !Mom
Paresnlop
and
Prot/Macy
Parvedie
End
Proadmv
How often do you work in small groups
in your mathematics class?
Al toast one* a win*
31 ( 13)
96 ( 4.6)
26 ( 2.5)
260 ( 1.4)
254 ( 42)
2941 ( 2.7)
Loss than once a week
30 ( 1.3)
2.5)
2$ ( 14)
232 ( 1.3)
271 ( 3.1)
2117 ( 2.0)
Now
30 ( 1.6)
36 ( 4.8)
44 ( 9.2)
2$0 ( 1.5)
256 ( 2.0)
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 standard errors
of the estimate for the sample.
Examining the subpopulations (Table A 12 in the Data Appendix):
In Montana, 31 percent of students attending schools in areas classified as
"other" and 33 percent in schools in extreme rural areas worked in small
groups at least once a week.
Further, 31 percent of White students, 27 percent of Hispanic students,
and 36 percent of American Indian studmts 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 (31 percent and 32 percent, respectively).
54
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
USING MATHEMATICAL OBJECTS
Students were 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 A 13 in the
Data Appendix summarize these data:
About one-quarter of the students in Montana (27 percent) never used
mathematical objects; 36 percent used these objects at least once a week.
Mathematical objects were used at least once a week by 37 percent of
students attending schools in areas classified as "other" and 35 percent in
schools in extreme rural areas.
Males were as likely as females to use mathematical objects in their
mathematics classes at least once a week (37 percent and 35 percent,
respectively).
In addition, 37 percent of White students, 30 percent of Hispanic students,
and 29 percent of American Indian students used mathematical objects at
least once a week.
TABLE 13
I Students' Reports on the Use of Mathematics
I Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS F
1FICIENCY
_
1800 NAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
How often do you work with objects hke
rulers, counting blocks, or geometric
solids in your mathematics class?
Percentage
and
Proficiency
Percentage
and
Prolidency
Percentage
and
Prolidancy
At least once a week
38 ( 1.1)
30 ( 3.5)
28 ( 1.8)
282 ( 1.2)
200 ( 4.0)
258 ( 2.6)
Less than once a week
38 ( 1.2)
28 ( 1.8)
31 ( 12)
282 ( 1.3)
209 ( 2.7)
21I9 ( 1,5)
Never
27 ( 1.2)
36(3.3)
41 ( 22)
278 ( 1.5)
258 ( 2.8)
259 ( 11)
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.
G
THE 1990 NAEP TRIAL STATE ASSESSMENT
55
Montana
MATERIALS FOR MATHEMATICS INSTRUCTION
The percentages of eighth-grade public-school students in Montana who frequently worked
mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that
these materials play a major rvle in mathematics teaching and learning. Regarding the
frequency of textbook usage (Table 14 and Table A 14 in the Data Appendix):
About three-quarters of the students in Montana (79 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 78 percent of students attending
schools in areas classified as "other" and 79 percent in schools in extreme
rural areas.
TABLE 14
I Students' Reports on the Frequency of
I Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
_
1900 NAP TRIAL STATE ASSESSMENT
Montane
West
Nation
_
How often do you do
mathematics
problems
from
textbooks
in
your
mathematics class?
nareantaga
and
Proloimay
Parcantap
and
Peaddinay
Permits,*
end
Proltaioncy
Almost every day
Ta (
1.5)
71 (
3.5)
74 (
1.9)
262 ( 0.8)
267 (
2.4)
267 ( 12)
Several times a week
13 ( 1.0)
15 (
1.5)
14 (
0.8)
2/9 (
1.1)
251 (
2.4)
252 ( 1.7)
Abota awe a week or less
(
1.0)
14 (
3.1)
12 (
1.8)
206 ( 3.2)
242 (11.2)1
242 ( 4.5)
The standard errors of the estimated StatistieS appear in parentheses.
it can he 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.
I. Interpret with caution
the nature of the sample does not allow accurate
determination of the variability of this estimated mean proriciency.
61
56
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
And, for the frequency of worksheet usage (Table 15 and Table A 15 in the Data
Appendix):
Less than half of the students in Montana (32 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 30 percent of
students attending schools in areas classified as "other" and 36 percent in
schools in extreme rural areas.
TABLE 15
I Students' Reports on the Frequency of
I Mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO MEP TRIAL STATE ASSESSMENT
Montane
West
Nation
-
How often do you do
mathematics
problems
on
worksheets
In
your
mathematics class?
Powesedaw
and
Proliciency
Pseverdies
sad
Prannalage
end
At least several times a weak
32 ( 2.1)
35 ( 4.0)
3$ ( 2.4)
278 ( 1.3)
250 ( 4.2)
293 ( 2.2)
About once a week
29 ( 1.2)
23 ( 2.6)
25 ( 1.2)
280 ( 1.4)
262 ( 2.1)
261 ( 1.4)
Less than weekly
39 ( 2.1)
41 ( 4.1)
37 ( 2.5)
284 ( 0.9)
270 ( 3.4)
272 ( 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.
Table 16 compares students' and teachers' responses to questions about the patterns of
classroom instruction and materials for mathematics instruction.
G
THE 1990 NAEP TRIAL STATE ASSESSMENT
57
Montana
TABLE 16
Comparison of Students' and Teachers' Reports
on Patterns of and Materials for Mathematics
Instruction
PERCENTAGE OF STUDENTS
1890 NAEP TRIAL STATE
ASSESSMENT
Montana
West
Nation
Patterns
of
classroom
Instruction
Perasaaage
eindlits teectIers
Pereentap
Samiteals Tendons
Percentap
Nugent. Tetbdiere
Percentage of students who
work mathematics problems In
small groups
At least once a week
31 ( 1.7)
60 ( 3.0)
35 ( 4.1)
57 ( 6.9)
20 ( 2.5)
50 ( 4.4)
Less than once a week
30 ( 1.3)
32 ( 2.9)
29 ( 2.8)
39 ( 7.8)
28 ( 1.4)
43 ( 4.1)
Never
39 ( 1.6)
( 1.9)
36 ( 4.8)
3 ( 2.2)
44 ( 29)
3 ( 2.0)
Percentage of students who
use objects like Merv, counting
blocks, or geometric solids
At least once a week
36 ( 1.1)
37 ( 2.6)
36 ( 3.5)
34 ( 6.2)
28 ( 1.8)
22 ( 3.7)
Less than once a week
36 ( 1.2)
62 ( 2.6)
25 ( 1.8)
57 ( 6.4)
31 ( 12)
89 ( 3.9)
Never
27 ( 12)
1 ( 0.4)
36 ( 3.3)
8 ( 3.0)
41 ( 2.2)
9 ( 2.6)
Materials for mathematics
Pasmeniage
Percentage
Percentage
Instruction
Stueents Teachers
Inman.* Teachers
Students Teacture
Percentage of students rho
use a mathematics todbook
Almost every day
79 ( 1.5)
82 ( 3.1)
71 ( 33)
55 ( 6.0)
74 ( 1.9)
02 ( 3.4)
Several times a week
13 ( 1.0)
32 ( 2.5)
15 ( 1.5)
38 ( 5.1)
14 ( 0.8)
31 ( 3.1)
About once a week or less
( 1.0)
6 ( 1.8)
14 ( 3.1)
9 ( 4.9)
12 ( 1.8)
7 ( 1.8)
Percentage of students who
use a mathematics worksheet
At least several times a week
32 ( 2.1)
47 ( 3.3)
35 ( 4.0)
25 ( 5.2)
38 ( 2.4)
34 ( 3.8)
About once a week
29 ( 12)
22 ( 2.1)
23 ( 2.6)
34 ( 4.0)
25 ( 1.2)
33 ( 3.4)
Less than weekly
39 ( 2.1)
30 ( 2.2)
41 ( 4.1)
41 ( 5.6)
37 ( 24)
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
Montana
SUMMARY
Because classroom instructional time is typically limited, teachers need to make the best
possible use of what is known about effective instructional delivery practices and resources.
It appears that mathematics textbooks and worksheets continue to play a major role in
mathematics teaching. Although there is some evidence that other instructional resources
ani practices are emerging, they are not yet commonplace.
According to the students' mathematics teachers:
More than half of the studer .s in Montana (60 percent) worked
mathematics problems in small groups at least once a week; relatively few
never worked in small groups (8 percent).
The largest percentage of the students (62 percent) used objects like rulers,
counting blocks, or geometric shapes less than once a week, and relatively
few never used such objects (1 percent).
In Montana, 62 percent of the students were assigned problems from a
mathematics textbook almost every day; 6 percent worked textbook
problems about once a week or less.
About half of the students (47 percent) did problems from worksheets at
least several times a week; about one-quarter did worksheet problems less
than weekly (30 percent).
And, according to the students:
In Montana, 39 percent of the students never worked mathematics
problems in small groups; 31 percent of the students worked mathematics
problems in small gioups at least once a week.
About one-quarter of the students in Montana (27 percent) never used
mathematical objects; 36 percent used these objects at least once a week.
About three-quarters of the students in Montana (79 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 Montana (32 percent) used worksheets
at least several times a week, compared to 38 percent in the nation.
THE 1990 NAEP TRIAL STATE ASSESSMENT
59
Montana
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.
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.
s National Assessment of Educational Progress, Mathematics Objectives
1990 Assessment (Princeton, NJ:
Educational "resting Servia, 1988).
National Council of Teachers of Mathematics, Curriculum and evaluation Standards for School Mathematics
(Reston, VA: National Council of Teachers of Mathematics, 1989).
60
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
Table 17 provides a profile of Montana eighth-grade public schools' policies with regani
to calculator use:
In comparison to 33 percent across the nation, 57 percent of the students
in Montana had teachers who allowed calculators to be used for tests.
A greater percentage of students in Montana than in the nation had
teachers who permitted unrestricted We of calculators (32,percent and
18 percent, respectively).
TABLE 17
I Teachers' Reports of Montana Policies on
I Calculator Use
PERCENTAGE OF STUDENTS
1000 NAEP TRIAL STATE ASSESSMENT
Pagans
W1
Nation
Percentage of elghth-grade students In public
schoolS whoae teachers permit the unrestricted
use of calculators
Percentage of eighth-grade students In public
schools whose teachers permit the use of
calculators tor tests
Percentage of eighth-grade students In public
schools whose teachers report that students
have access to calculators awned by the school
Percentage
Percentage
Ponseetais
32 ( 2.7)
20 ( 4.2)
15 ( 3.4)
57 ( 3.1)
48 ( 8.8)
33 ( 4.5)
62 ( 2.9)
72 ( 7.4)
58 ( 4.6)
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.
i''-`
) 0
THE 1990 NAEP TRIAL STATE ASSESSMENT
61
Montana
THE AVAILABILITY OF CALCULATORS
In Montana, most students or their families (98 percent) owned calculators (Table 18);
however, fewer students (56 percent) had teachers who explained the use of calculators to
them. From Table A 18 in the Data Appendix:
In Montana, 55 percent of White students, 51 percent of Hispanic
students, and 58 percent of Amesican Indian students had teachers who
explained how to use them.
Females were as likely as males to have the use of calculators explained to
them (53 percent and 58 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
Montana
West
Nation
Do you or your family own a calculator?
Perondaga
and
98 ( 0.3)
281 ( 0.8)
2 ( 0.3)
Pan:anises
and
Proficiency
56 ( 2.0)
27e ( 1.0)
44 ( 2.0)
283 ( 1.5)
Poreantaga
and
Pndkilimay
98 ( 0.8)
263 ( 2.6)
Paraentaaa.
and
Prolidoncy
SO ( 3.4)
260 ( 2.7)
41 ( 3.4)
2es ( 3.0)
Paresatsge
and
Prelkdanki
9? ( OA)
263 ( 1.3)
3 ( 0.4)
234 ( 3.8)
Paresalage
and
Prellidevey
40 ( 2.3)
25$ ( 1.7)
51 ( 2.3)
266( 1.5)
Yes
No
Does your mathematics teacher explain
how to use a calculator for mathematics
problems?
Yes
No
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
Montana
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, st
its were asked how frequently (neva,
sometimes, almost always) they used calcuuktors for working problems in class, doing
problems at home, and taking quizzes or tests. As reported in Table 19:
In Montana, 16 percent of the students never used a calculator to work
problems in class, while 46 percent almost always did,
Some of the students (11 percent) never used a calculator to work
problems at home, compared to 35 percent who almost always used one.
About one-quarter of the students (30 percent) never used a calculator to
take quizzes or tests, while 21 percent almost always did.
TABLE 19
I Students' Reports on the Use of a Calculator
I for Problem Solving or Tests
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
Percentage
and
Proficiency
Percentage
and
ProfidancY
Percentage
and
andkiencY
How often do you use a calculator for the
following tasks?
Working problems In class
Almost always
48 ( 1.7)
53 ( 2.1)
48 ( 1.6)
277 ( 0.9)
255 ( 2.6)
254 ( 1.5)
Never
18 ( 1.7)
14 ( 2.4)
23 ( 1.9)
285 ( 2.1)
265 ( 3.0)
272 ( 1.4)
Doing problems at home
Almost always
3$ ( 1.2)
29 ( 1.7)
30 ( 1.3)
283 ( 1.2)
263 ( 3.3)
261 ( 1.8)
Never
11 ( 0.9)
19 ( 1.6)
19 ( 0.9)
279 ( 2.5)
258 ( 3.7)
263 ( 1.8)
Taking quizzes or tests
Almost always
21 ( 1.4)
25 ( 1.6)
27 ( 1.4)
278 ( 1.3)
25a ( 3.9)
253 ( 2.4)
Never
30 ( 1.7)
22 ( 9.0)
30 ( 2.0)
287 ( 1.3)
270 ( 33)
274 ( 1.3)
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 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.
THE 1990 NAEP TRIAL STATE ASSESSMENT
63
Montana
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
calculator prior to the asses&ment. 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 Lalculator sections were defined as "calculator-active" items -- that is,
items that req iiied the student to use the calculator to determine the correct 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 calculrtor-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 calculato i. sections were categorized into two groups:
High -- students who used the calculator appropriately (i.e., used it for tile
calculator-active itenr 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.
ti
64
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below:
About the same percentage of students in Montana were in the High group
as were in the Other group.
About the same percentage of males and females were in the High group.
In addition, 54 percent of White students, 51 percent of Hispanic students,
and 43 percent of American Indian students were in the High group.
TABLE 20
1
Students' Knowledge of Using Calculators
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1080 NAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
"Calculator-use" group
iterlsaifts
and
Pro &slew
Pereembile
Paramisis
and
and
Pee Waxy
Preacioncy
53 ( 2.1)
SI ( 2.5)
42 ( 1.3)
218 ( 12)
273 ( 2.7)
272 ( 1.5)
47 ( 2.1)
55 ( 1.3)
275 ( 1.5)
253 ( 2A)
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
Montana
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, 57 percent of the students
in Montana had teachers who allowed calculators to be used for tests.
A greater percentage of students in Montana than in the nation had
teachers who permitted unrestricted use of calculators (32 percent and
18 percent, respectively).
In
Montana, most students or their
families
(98 percent) owned
calculators; however, fewer students (56 percent) had teachers who
explained the use of calculators to them.
In Montana, 16 percent of the students never used a calculator to work
problems in class, while 46 percent almost always did,
Some of the students (11 percent) never used a calculator to work
problems at home, compared to 35 percent who almost always used onc.
About one-quarter of the students (30 percent) never used a calculator to
take quizzes or tests, while 21 percent almost always did.
"/
66
TIIE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
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 of educating and
certifying teachers.9 Many states have begun to raise teacher certification standards and
strengthen teacher training programs. As shown in Table 21:
In Montana, 38 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 naf.on.
About half of the students (47 percent) had mathematics teachers who had
the highest level of teachhig certification available.
This is different from
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.
About three-quarters of the students (77 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, Pr *vsional Standards for the n'aching of Mathernatir.s
;Reston, VA: National Council of Teachers of Mathematics, 1991).
P
0-1
THE 3990 NAEP TRIAL STATE ASSESSMENT
67
Montana
TABLE 21
I Profile of Eighth-Grade Public-School
Mathematics Teachers
PERCENTAGE OF STUDENTS
1660 NAEP MAI. STATE ASSESSMENT
Montana
Wed
Nation
Percentage of students whose mathematics teachers
repelled having the following degrees
Sachet lor's degree
Master's or specialist's degree
Doctorate or professional degree
Percentage of students whom mathematics teachers have
the faillowing typos of teaching cortincates that ars
rectignktod by Montana
No regular certification
1
0.1)
Regular certification but less than the highest available
52
2.6)
Highest certification available (permanent or long-term)
47
2.6)
Percentage of students *two mathematics teachers have
the following types of teaching certificates that aro
recognized by Montana
Mathematics (middle school or secondary)
17 ( 3.0)
61 ( 3.0)
Education (elementary or middle School)
23 ( 3.0)
9 ( 2.6)
Other
0 ( 0.1)
2 ( 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 ± 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 teachei-s educational backgrounds -- more specifically, their undergraduate
and graduate majors and their in-service training.
68
THE 1990 NAEP 'TRIAL STATE ASSESSMENT
Montana
Teachers' responses to questions concerning their undergraduate and graduate fields of
study (Table 22) show that:
In Montana, 50 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.
Some of the eighth-grade public-school students in Montana (19 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.
TABLE 22
I Teachers' Reports on Their Undergraduate and
Graduate Fields of Study
PERCENTAGE OF STUDENTS
_
11190 NAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
What was your undergraduate major?
Paramlasa
Peroante.
Percentage
Mathematics
50 ( 2.8)
31 ( 5.9)
43 ( 3.9)
Education
38 ( 2.9)
34 (
35 ( 3.8)
Other
12 ( 2.3)
35 (5.5)
22 ( 3.3)
What was your graduate major?
Parcantaga
Porcontage
Peraintage
MaMematics
19 ( 1.7)
19 ( 4.7)
22 ( 3.4)
Education
43 ( 2.8)
36 (44)
34 ( 34)
Other or no graduate Wel study
38 ( 3.0)
45 ( 54)
40 ( 34)
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
69
Montana
Teachers' responses to questions concerning their in-service training for the year up to the
Trial State Assessment (Tabk 23) show that:
ln Montana, 38 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.
Relatively few of the students in Montana (5 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,
TABLE 23
I Teachers' Reports on Their In-Service Training
PERCENTAGE OF STUDENTS
111110 NAEP TRIAL STATE ASSESSMENT
I
Montana
Wast
Nation
During the last year, how much time in
total have you spent on
in-service
education in mathematics or the teaching
of mathematics?
None
One to 16 hours
15 hours or mom
Pimento.
Pirtientage
Prventess
5 ( 1.0)
11 ( 3.0)
11 ( 2.1)
58 ( 3.0)
45 ( 7.0)
51 ( 4.1)
38 ( 2.8)
44 ( 8.9)
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 withm ± 2 standard errors
of the estimate for the sample.
70
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
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
cpinlifications 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 Montana, 38 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 half of the students (47 percent) had mathematics teachers who had
the highest level of teaching certification available.
This is different from
the figure for the nation, where 66 percent of students were taught hy
mathematics teachers who were certified at the highest level available in
their states.
In Montana, 50 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.
Some of the eighth-grade public-school students in Montana (19 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. Lapointe, 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 Tesung service, 1988).
" Ina V.S. Mulhs, John A. llossey, Eugene U. Owen, and Gary W. Phillips, The State of Mathematics
Achievement NA Ers 1990 Assessment of the Nation and the Thal Assessment of the States (Princeton, NJ:
National Assessment of Educational Progress, Educational Testing Service, 1991).
THE 1990 NAEP TRIAL STATE ASSESSMENT
71
Montana
In Montana, 38 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 teachess who spent at least that much time
on similar types of in-service training.
Relatively few of the students in Montana (5 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.
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 role in the
education of their children. Family expectations, encouragemert, and participation in
student learning experiences are 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.
THE 1990 NAEP TRIAL STATE ASSESSMENT
73
Montana
AMOUNT OF READING MATERIALS IN THE HOME
The number and types of reading and refesence 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 west 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
_
MO NAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
,
_
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
Tires types
Four typos
Poesintage
Proicknoy
Poroonlado
and
Prat:Now
Paraminia
sad
Praliekear
12 ( 0.7)
24 ( 15)
21 ( 1.0)
2eS ( 2.1)
245 ( 4.1)
244 ( 2.0)
32 ( 12)
31 ( 1.4)
30 ( 1.0)
277 ( 1.8)
251 ( 2.4)
251 ( 1.7)
55 ( 1.0)
45 ( 111)
44 ( 1.3)
215 ( 0.5)
273 ( 3.2)
272 ( 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 data for Montana reveal that:
Students in Montana 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
Montana
A smaller percentage of Hispanic and American Indian students had all
four types of these reading materials in their homes than did White
students,
About the same percentage of students attending schools in areas classified
as "other" as in extreme rural areas had all four types of these reading
matesiab 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 Tr
State Assessment were asked to report on the
amount of television they watched each day (Table 25).
TABLE 25
I Students' Reports on the Amount of Time Spent
i Watching Television Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 MAEP TRIAL STATE ASSESSMENT
Montana
West
Nation
Posueniago
and
Proficiency
Passentago
and
Prelkiettoy
petvantago
and
Prakdoncli
How much television do you usually
watch each day?
One hour or less
21 ( 0.9)
14 ( 1.5)
12 ( 0.8)
290 ( 1.5)
260 ( 3.6)
209 ( 2.2)
Two hours
30 ( 1.2)
20 ( 1.6)
21 ( 0.9)
255 ( 1.2)
265 ( 3.6)
205 ( 1.5)
Throw hours
24 ( 1.0)
20 ( 1.2)
22 ( 0.5)
2711 ( 1.2)
282 ( 3.2)
205 ( 1.7)
Pot, to !Ivo hours
20 ( 1.1)
29 ( 1.7)
2$ ( 1.1)
24'5 ( 1.6)
263 ( 2.9)
2eo ( 1.7)
613/ hours or mars
( 0.6)
16 ( 2.0)
16 ( 1.0)
261 ( 2.9)
246 ( 2.6)
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 thr entire population is within ± 2 standard errors
of the estimate for the sample.
THE 1990 NAEP TRIAL STATE ASSESSMENT
75
Montana
From Table 25 and Table A25 in the Data Appendix:
In Montana, average mathematics proficiency was lowest for students who
spent six hours or more watching television each day.
About one-quarter of the eighth-grade public-school students in Montana
(21 percent) watched one hour or less of television each day; 6 percent
watched six hours or more.
About the same percentage of males and 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, 5 percent of White students, 10 percent of Hispanic students,
and 13 percent of American Indian students watched six hours or more of
television each day.
In comparison, 22 percent of White students,
14 percent of Hispanic students, and 12 percent of American Indian
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 Montana, average mathematics proficiency was lowest for students who
missed three or more days of school.
Less than half of the students in Montana (40 percent) did not miss any
school days in the month prior to the assessment, while 21 percent missed
three days or more.
In addition, 20 percent of White students, 17 percent of Hispanic students,
and 37 percent of American Indian students missed three or more days of
school.
76
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
Similarly, 22 percent of students attending schools in areas classified as
"other" and 19 pesvent in schools in extreme rural areas 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
1090 NAEP TRIAL
r :11E ASSESSMENT
Madam
Wad
Nation
1
How many days of school did you miss
last month?
Ons or two days
Three days or more
Pialkiemy
fralicismiv
aid
holk.may
40 ( 1.3)
43 ( 2.7)
45 ( 1.1)
244 ( 1.4)
(
245 ( 1.9)
11(12 )
282 ( 1.0)
$0 (
295 (
14)
34)
295
041.4
21 ( 0.8)
27 ( 1.1)
23 ( 1.1)
272 ( 2.0)
250 ( 3.1)
250 ( 1.9)
The standard errors of the estimated statistics appeur in parentheses. It can be mid 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.
c 2
THE 1990 NAEP TRIAL STATE ASSESSMENT
77
Montana
STUDENTS' PERCEPTIONS OF MATHEMATICS
According to the National Council of Teachers of Mathew,c.it - 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.'2
Students were asked 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 tht 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 1 (indicating very positive attitudes about the
subject), those who responded "agree" were given a value of 2, and those who responded
"undecided," "disagree," or "strongly disagree" were given a 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 1), tended to agree with the statements (an index of 2), or tended to be
undecided, to disagree, or to strongly disagree with the statements (an index of 3).
Table 27 provides the data for the students' attitudes toward math.:matics as defmed by
their pereption index. Thr following results were observed for Montana:
Average mathematics proficiency was highest for students who were in the
"strongly agree" category and lowest for students wly- were in the
"undecided, disagree, strongly disag...,!e" category.
About one-quarter of the students (30 percent) were in the "strongly
agree" category (perception index of 1).
This compares to 27 percent
across the nation.
Some of th., students in Montana (20 percent), compared to 24 percent
across the nation, were in the "undeciied, disagree, or strongly disagyee"
category (perception index of 3).
" National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics
(Reston. VA: National Council of Teachers of Mathematics, 1989).
78
THE 1990 NAEP TRIAL STATE ASSESSMENT
TABLE 27
1 Students' Perceptions of Mathematics
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
IWOO NAEP TIM STATE ASSESSMENT
Student °perception index" groups
Strongly agree
(*perception Index" of 1)
AS iv
("percep(ion index" of 2)
Undecided, (Meagre*, dranaly disagree
(.perception Index" ot 3)
271 1
44
2011
2.4)
2419(2M
25(24)
2111.1113
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 Montana 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 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.
C.,
THE 1990 NAEP TRIAL STATE ASSESSMENT
79
Montana
About one-quarter of the eighth-grade public-school students in Montana
(21 percent) watched one hour or less of television each day; 6 percent
watched six hours or more. Average mathematics proficiency was lowest
for students who spent six hours or more watching television eitch day.
Less than half of the students in Montana (40 percent) did not miss any
school days in the month prior to the assessment, while 21 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 (30 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" category and lowest for students who were in the "undecided,
disagree, strongly disagree" category.
80
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
THE 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 design, the mathematics
framework and objectives upon which the assessment was based, and the procedures used
to analyze the results.
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 Educational Testing Service. The development of the Trial
State Assessment Program benefitted from the involvement of hundreds of representatives
from State Education Agencic5 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 mathematics items were 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.
C;
THE 1990 NAEP TRIAL STATE ASSESSMENT
81
Montana
The blocks were then assembled into assessment booklets so that each booklet contained
two background questionnaires -- the first consistir; of geveral 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 I5-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.
Assessment Content
The framework and objectives for the Trial State Assessment Program were developed
using a broad-based consensus process, as described in the introduction to this report.'
The assessment framework consisted of two dimensions: mathematical content areas and
abilities. The five conte,4 areas assessed were Numbers and Operations; Measurement;
Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see
Figure A l). 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 copitive and
background question.
Item response theory (IRT) 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 subpopulations, even when all
students do not answer the same set of questions. This common scale makes it possible
to report on relationships between students' characteristic- (based on their responses to the
background questions) and their overall performance in the assessment.
I
ational Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Pnnceton,
Educational Testing Service, 1988).
82
THE 1990 NAEP TRIAL STATE ASSESSMENT
411
Montana
FIGURE AI
I Content Areas Assessed
THE NATION'S
RD
REPORT
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 of calculators, generalization of numerical
patterns, and verification of results are also included.
IMeasurement
This content area focuses on students' ability to describe real-world objects using numbers. Students are
asked to identify attributes, select appropriate units, apply meaSurement conogits, 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 acuracy. Questions
requiring estimation, measurements, and applications
of
measurements
of
length,
time, money,
temperature, mass/weight, 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 wo,.king with this knowledge. These skills are important at all levels of schooling as well as in practical
applications.
Students need to be able to model and visualize geometric figures in one, two, and three
dimensions and to communicate geomet: ic 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
tor 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.
Lb
THE 1990 NAEP TRIAL STATE ASSESSMENT
83
Montana
FIGURE A2
Mathematical Abilities
The following three categories of mathematical abilities are not to be cOnstrued as hierarchical.
For
example, problem solving involves interactions between conceptual knowledge :'d procedural skills, but
what
Is considered complex problem solving at one grade level may
considered conceptual
understanding or procedural knowledge at another.
I.Cotceptual Understanding
Students demonstrate conceptual understanding in mathematics when they provide evidence that they can
recognize, label, and generate examples and counterexamples ot concepts: can use and 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-solving situations.
Procedural Knowledge
Students demonstrate procedural knowledge in mathematics when they provide evidence of their abdity to
select and apply appropriate procedures correctly, verify and justify the 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 noncomputational
skills such as rounding and ordering.
Problem Solving
In problem solving, students are required to use their reasoning and analytic abilities when they encounter
new situations.
Problem solving includes the ability to recognize and formulate pr7blems: determine the
sufficiency and consistency of data: use strategies, data, modals, and relevant mathematics: generate.
extend, and modify procedures: use reasoning
(i.e,,
spatial,
inductive, deductive,
statistical,
and
proportional): and judge the reasonableness and correctness of solutions.
E 5
84
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
A scale ranging from 0 to 500 was created to report performance for each content area.
Each content-area scale was based on the distribution of student performance 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 defmed 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 199(1 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 defme performance at each of the four levels on the scale, NATI' analyzed sets of
mathematics items from the 1990 assessment that discriminated well between adjacent
levels. The crise, ia for selecting these "benchmark" items were as follows:
To define performance at level 200, items were chosen that were answered
correctly by at least 65 percent of the students whose proficiency was at or
near 200 on the scale.
To define 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 majority (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 higher than the percentage of students at the next
lower level who answered it correctly.
THE 1990 NAEP TRIAL STATE ASSFSSMENT
85
Montana
Once these empirically selected sets of questions had been 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 I 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 gxoups.
MATHEMATICS TEACHER QUESTIONNAIRE
The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first
requested information about the teacher, such as race/ethnicity and gender, as well as
academic degrees 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-grade mathematics teachers in a state
or territory. Rather. they represent the teachers of the particular students being assessed.
2 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.
86
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
FIGURE A3
I
Example Items for Mathematics Proficiency Levels
Level 200:
Sknple Additive Reasoning and Problem Solving with Whole
Numbers
EXAMPLE 1
A /
Tries
Ger
WM
real
o
loose
Gig
Osib
0
Sobest
7. La& bad dose Uses wan ashhe mo we sod doom Mono lusds
ha so shore gem 1 tios flak sok bee with dr boot si logio aeons
We&
'smoke brow 1010 is St
Ths kw look the ousio bah
Cis The hos Irak doe pit bails
V no les s4ch dos saber bats
0I7 *a cadre sdl.
EXAMPLE 2
DOXIS OF MIT PICKED
AT FARAWAY FARM
Tam
Med
11..
Oars OM' wak
Lasso
Owiwevii
0. HOW allay WIMP oi mein woos picked as Thurodayi
OD
SS
60
70
40
90
I don't tzar.
Grade 4
OveraN Percentage
Percentage Correct
S22
65
91
Grade 4
Overall Percent/go
Percentage Correct
MI
MI
75
91
Grade 8
Overall Percentage
Percentage COffict
78
87
fl2
Correct 73%
for Anchor Levels:
S2
114
ico
0%
for A :f4'4
Levels:
122
204
100
Correct 89%
tor Anchor Levels:
MI
nil
98
100
Level 250:
Simple Multiplicative Reasoning and Two-Step Problem Solving
I
Montana
FIGURE A3
Example Items for Mathematics Proficiency Levels
(continued)
EXAMPLE 1
7. What is the value of n 4- 5 when a
3
Answer.
EXAMPLE 2
KAM COLOR ARM
ILSULTS
Ca. si
oh
17
SO
11
The uWe thine shows the mks s Nom of hair Woe. Co At cipcle
below, ails $ code 'soh to iDisIxtSISthe &as la she table. Lthei oath
pen *I the dick mop %rub olbe thethet Mu Wee.
Ltd you two Os, eskailitor ea this isseitlos?
Yes
EXAMPLE 3
h. Utilise is pschio4 balchalle Imo boxes. Each box holds 6 baultellt. She
Us 24 bells WWI& number mew* will kelp hot linel oue how luny
beim she will othel
CD 24
6 0
cl) 24 4 ,
s, 24 + 6 0
op
r
a* 0
CD I &Wang:1w.
Grade
Cverall Percentage Correct: 75%
Paroantaos Comsat for Anchor Laval::
MI
IN
MO
MI
28
89
95
98
Grad* 8
Overall Pencentage Correct: 73%
Percentage Correct for Ancbor
ardi
202
es
92
92
Grad* 8
Overall Percentage Correct: 77%
Percentage Correct for Anchor live's:
/29
MO
3119
37
71
95
100
88
THE 19 N NAM' TRIAL STATE ASSESSMENT
Montana
FIGURE A3
I
Example Items for Mathematics Proficiency Levels
(continued)
Level 300:
Reasoning and Problem Solving involving Fractions, Decimals,
Percents, Elementary Geometric Properties, and Simple
Algebraic Manipulations
EXAMPLE 41
Ia. WIbith
As Saw* sham ohs mole si Noolvo dig
Inaftie OM'
die U.* t
QD
EXAMPLE 2
lo the said woo Au doss Is
s oar is ism leo/
lopossocsi
by milt Isio&I S hullos load. U ea mat sash is loot at loos 3S low
wool* k rsorosoico.; Li 3 Wad !soda Law way Mau WO
0 II
0
0 I
0 7
eV
DO roe use die osicuistor so ibi gosationt
0 Ws
0 No
c 4
Grade 8
Choral! Percentage Correct: 80%
Peroentage Correct for Anchor Levels:
2012
Mt
242
HQ
33
49
77
90
Grade 12
Overall Percentage Correct: 75%
Percentage Correct for Mellor Lai/leis:
MD
222
222
214
48
79
95
Grade 8
Overaii Percentage
Percentage Correct
MI
17
48
Correct: 59%
for Anchor WW2:
222
252
88
99
BEST COPY AVAILABLE
Montana
FIGURE A3
I
Example Items for Mathematics Proficiency Levels
(continued)
Level 350:
Reasoning and Problem Solving Involving Geometric
Relationships, Algebraic Equations, and Beginning Statistics and
Probability
EXAMPLE 1
01014.10so 14-17 joko io the hilIoo sus omen. of dot 4 woos
0
I
2
2
16. II Ala putts of doufigmes j cxyasout. bow fosoy dos
ll bc ia ghe
)30th fout1
CD 100
CP 10
CID 199
2D0
4) 201
EXAMPLE 2
IT. typluo how you foonyl you, UMW./
suestion 1 6.
Ammer
Grad. 8
Overall Percentage Correct 34%
Percentage Correct for Maher Levels:
Z:?2
2/11
2Ciit
201/
13
19
53
88
Grade 12
Overall Percentage Correct: 40%
Percentage Correct for Mchor Levels:
B2Q
2110
202
22
48
so
Grad* 8
Overall Percentage Correct: 15%
Percentage Correct for Anchor Levels:
22Q
221/
112
1
4
28
74
Grads 12
Overall Percentage Correct: 27%
Percentage Correct for Anchor Levels:
222
Zig
A22
122
3
22
74
90
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
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,
course offerings, and special 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. Having the student as the unit of analysis makes it possible to describe the
instruction received by representative samplet of eighth-grade students in public schools.
Although this approach may provide a differeat 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 NAEP's goal of providing
information about the educational context and performance of students.
Estimating Variability
The statistics reported by NAFP (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 repeeted,
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 NAEP) are subject to a certain
degTee of uncertainty. The uncertainty attributable to using samples of students is referred
to as sampling error.
like almost all estimates based on assessment measures, NAEP's total group and subgroup
proficiency estimates are subject to a second source of uncertainty, in addition to sampling
error. As previously noted, each student who panicipated in the Trial State Assessment
was administered a subset of questions from the totil set of questions. If each student had
been admiMstered a different, but equally appropriate, set of the assessment questions --
or the entire set of questions -- sommhat different estimates of 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
THE 1990 NAEP TRIAL STATE ASSESSMENT
91
Montana
In addition to reporting estimates of average 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
methodology called the jackknife procedure to estimate these standard errors.
Drawing Inferences from the Results
One of the goals of the Trial State Assessment Program is to make inference 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 intervals, based n the standard errors, provides a way to make
inferences about the population means and proportions in d 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-gade students in public schools in that state is between 253.6 and
258.4.
Similar confidence intervals can be constructed for percentages, providea that the
percentages are not extremely large (greater than 90 percent) or extremely small (less than
10 percent ). l'or extreme percentages, confidence intervals constructed in the above
manner may not be appropriate and procedures for obtaining accurate confidence intervals
are quite complicated,
92
'1 ile. 1990 NAEP I !UAL STATE ASSESSMENT
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 defmed 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 mathematics proficiency than students who reported spendk IS 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 a 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 population 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 difference between the proficiency
means or proportions of those groups for the sample. Ti estimate of the degree of
uncertainty -- called the standard error 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 determile
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
represents 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.
s
THE 1990 NAEP TRIAL STATE ASSESSMENT
93
Montana
As an example, suppose that one were interested in determining whether the average
mathematics proficiency of eighth-grade females is higher than that of eighth-grade male;
in a particular state's public schools. Suppose that the sample estimates of the mean
proficiencies and standard crews for females and males were as follows:
Group
Average
Proficiency
Standard
Error
-.
Female
259
2.0
Male
255
2.1
The difference between the estimates of the mean proficiencies of females and males is four
points (259 - 255). The standard error of this difference is
2.02 + 232 = 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.3
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. 'Me 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.
The procedure described above (especially the estimation of the standard error of the difference) is, in a strict
sense, only appropriate 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 siandcrd error of the difference was used.
Ct,
94
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
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. If one wants to hold the
ce.-tainty 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 described 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 Errors
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 degrec 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 subgyoups 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.
100
THE 1990 NAEP TRIAL STATE ASSESSMENT
95
Montana
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 territory, divided by the standard deviation of the proficiency in
the total population. If the true difference between subgroup and total group mean is .2
total-group standard deviation units, then a sample size of 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 terms
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
Description of Text in Report
I
p = 0
None
0 < p s 10
Relatively few
10 < p s 20
Some
20 < p S 30
About one-quarter
30 < p s 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 S. 89
Many
89 < p < 100
Almost all
p = 100
All
_
..
96
THE 1990 NAEP TRIAL STATE. ASSESSMENT
Montana
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
Montero
TABLE A5
I Students' Reports on the Mathematics Class
They Are Taking
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL
Eigh In-grade
STATE ASSESSMENT
Maihematics
Pre-algabra
TOTAt
State
Nation
36SEEM_CITY
Mita
State
Nation
Mapank
State
Nation
American Indian
State
Nation
TYPE CIF COMMUNITY
&tram nral
State
Nation
Other
State
Nation
10 is
4;1;1
$72
2.4
( 24)
61 ( 2.4)
200
50 ( 2.5)
25 ( 1.0)
50 ( 9.0)
75 ( 4,41
240 ( 24)
43 (5.8)
252 ( 4.6)
$4 ( 5.7)
aim ( e«.)
00 ( 6.3)
2.4)
74 ( 4.5)
241) ( 3.1)1
59 ( 2.3)
279
1.0)
01
2.2)
251
2.0)
24 ( 2.0)
225 ( 41.2
( 2.4
2r7 (
27 ( 9.5)
3.9)
(144
041
311( 5.0)
261 ( 4.0)
$ ( 7.2)
.4*)
25 ( 4.7)
203 ( 2.8)1
14 ( 5.0)
26 ( 2.0)
291
OA)
20
2.1)
272
23)
12 ( 1.5)
302 ( 34)
( 1.5)
300 ( 2.3)
32)
*I*
*el
( 1.5)
Imp ( «in
13 ( 5.0)
0.11
.44)
( 2.7)
.44 ( ihwt)
12 ( 4.1)
263 ( 72)1
( 22)
( *se)
12 ( 1.1)
300 ( 24)
10 ( 1.4)
294 ( 2.7)
',11MmIlIMMIr
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 pacent
cenainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the ample. 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. *** Sample size it insufficient to
permit a reliable estimate (fewer than 62 students).
1 C 3
98
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
...=111
..1m..1
TABLE AS
1 Students' Reports on the Mathematics ChisS
(continued)
They Are Taking
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
11110 NAEP TRIAL
STATE ASSESSMENT
Mgha-grads
ilalhenance
-
Prwa Ware
Algebra
_
TOTAL
State
Nation
Of
2.1
2$1 1.4
PAREIUNCENS
KS non-graduen
State
Nation
KS 'vain.
State
Nation
Sense collage
State
NaVon
College graduate
State
Nation
IMO
U.
State
Nation
Female
State
Nation
3.5)
200
211
n
SS
.. ( on
et*
oira
13 1
)
3.4)
3
1.11
241
2.1
on
03 ( t
26 ( 5.1)
(17
24$ ( la
NO 1 213
70
2
276 (
2011
22 (
1$ ( 24
277 ( 5.2)
do.
«Nri
0
1.5)
1
1.1)
21 ( 1.9
257 ( 2.1)
61 (
203
2.6
60 1 3.1
21
2.9
25
290 $ty
41
12
23)
15
13)
270 ( 2.4)
295
3.2)
55 ( 3.2)
211 ( 2.6)
15 ( 1.6)
264 ( 1.3)
206 ( 13)
53 ( 2.7)
21 ( 2.3)
304 ( 3.7
24 ( 1.1
250 ( 1.5)
271 ( 24)
303 ( 2.3
58 ( 2.9)
281 ( 1.3)
13 ( 2.1)
252 ( 1.11)
( 2.6)
275 ( 1.4)
11 ( 2.6)
251 ( 1.5)
251 2.5)
285 ( 1.8)
1$ ( 14)
275 ( 24)
20 ( 2.3)
278 ( 2.1)
20 ( 2.3)
260 ( 3.0)
13 ( 1.4)
301 ( 4.0)
15 ( 1.2)
220 ( 2.5)
10 ( 1.9)
290 ( 4.2)
15 ( 1.7)
293 ( 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. The percentages may t t total 100 percent because a small number of students
reported taking other mathematics courses. ! Interpret with caution - the 112-are 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
4
THE 1990 NAEP TRIAL STATE ASSESSMENT
99
Montana
TABLE A6
Teachers' Reports on the Amount of Time
Students Spent on Mathematics Homework
Each Day
PERCENTAGE Of STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1111* NAEP TRIAL
STATE ASSESSMENT
-
Nom
16 Minutes
30 Minuiss
46 Minis. I An Naar ar
Mars
TOTAL
State
10
2
020( 1.2
411( 4.2
300 (
Nation
RAOVETNNICITY
White
State
Nation
14111Panic
State
Nation
American Indian
State
Nation
TYPE OF COMMUNITY
Extreme rurat
State
3 ( OA)
1 (
222 ( 12
SS 13)
220
1
*** ( 4")
2112 ( 22
2112
2.7)
1 ( 03)
VT 70
ii
3A
3 ( 21
34 ( ILO)
IS ( 71
)
"de cm*
11 1
1 1 01)
48 1 7.II)
34 ( RS)
13
1
245 ( 3.444
251 ( 4.2)4
ser i see
*Mr ( .rev.
5 ( 2.1)
35 ( 0.5)
45 ( 7.0)
9 ( SA)
"P" ( 5")
291 ( 49)4
25$ ( SAP
"11 ( "*)
0 , 0.0)
74 (31S)
22 (2112)
0 ( 0.0)
rt. ( in
540 ( ..45)
at* c on
( ***)
Nation
Other
State
Nation
43 ( 7.4)
277 ( 1.II)I
0$ (141)
253 ( 5.4)4
34 ( 2.2)
211 ( 1.4)
37 ( 4,3)
258 ( 3.1)
47 ( 8.1)
200 ( 2.3)
14 (101)
14,)
204
1.8)
40 Si)
53
21)
205 ( 2.5)
5 ( 2.0)
.44
$ ( 5.8)
( 2,2)
54*
10
2.4)
278 ( 1.0 s
2 ( 1.6)
*45(5.5)
10 ( 73)
4 ( 0.3)
4 ( 1.1)
2$2 MAY
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
t.)
100
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE Ab
Teachers' Reports on the Amount of Time
(imntinued)
Students Spent on Mathematics Homework
Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRULL
STATE ASSESSINENT
,
Nolte
15 Minutes
30 Minutes
45 115kades
.
An Hour or
Mont
.
TOTAL.
.91,00911,
rialzdancy
3 04)
4.
1
03)
gel
2.1)
1 ( 04)
«.41
5 ( 1.4)
«e
«44)
( 0.5)
( «in
4 ( 0.5)
HP* (
( 0.9)
44. (
2 ( 0.4)
( 0.3)
( ".)
3 ( 0.5 )
(
1 ( 0.3)
Mr* ( trirl
3 ( 0.4)
*I* ( *41
I ( 0.4)
Poisems99
an0
Prellielemy
$I ( 2,0)
200 ( 12)
43 ( 4.2)
268 ( 2.3)
39 ( OA)
elk.)
49 ( 83)
240 ( 2.5)
41 ( 3.9)
272 ( 13)
43 ( 5.2)
249 ( 3-1)
37 ( 4.1)
262 ( 1.7)
44 ( 5.4)
266 ( 2.6)
38 ( 3.3)
265 ( 1E)
40 ( 4.7)
265 ( 25)
37 ( 2.8)
252 ( 1.4)
44 ( 4.4)
257 ( 2.9)
39 ( 33)
277 ( 1.5)
41 ( 44)
255 ( 23)
Porotatigs
and
frolialow
W (
2115 ( 12
43 (
200 ( 2.0)
49 ( 7.5)
( 141
40 ( 8.1)
248 ( 3.7)
44 ( 3.7)
271 ( 2.4)
44 ( 5.5)
258 ( 23)
50 ( 4.1)
2118 ( 3.2)
43 ( 5.8)
270 ( 3.8)
52 ( 3.3)
290 ( 1.5)
44 ( 41)
277 ( 3.0)
52 ( 2 8)
287 ( 1.4)
43 ( 4.3)
260(2.0)
4$ ( 33)
279 ( 2.3)
43 ( 4.7)
264 ( 2.8)
Pmedlage
and
trelialow
II)
290
mop
10
1.9)
272 ( 53)1
( 42)
*el
8 ( 1.7)
t
7 ( 2.8)
.4,41
9 ( 3.1)
44* (
( 1.5)
7 ( 2.1)
Orli (
5 (1.8)
*.it
441
11 I, 2.3)
287 ( 6.1)1
5 ( 1.8)
( 1.9)
273 ( 7.3)1
( 2.0)
278 ( 3.8)1
( 2.0)
272 ( 5.7)1
Pwoolios
and
PralkiWICY
( 04)
282 (12.1)
4 ( 0.9)
270 ( 5.1)1
2
1.41
4 ( 1.3))
3 ( 0.9)
14* ( 41
3 ( 1.0)
2 ( 1.1)
(
4 ( 1.0)
3 ( 0.5)
5 ( 1.3)
41
3 ( 0.6)
5 ( 1.3)
279
71/4
3 ( 0.8)
( *41
4 ( 0.9)
( ***)
State
Nation
PARENTS' EDUCATION
143 noriraduats
State
Nation
It5 graduate
State
Nation
Sento college
State
Nation
College graduate
State
Natioi
GENDER
M.
State
Nation
Female
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 rtithin ± 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
101
Montana
TABLE A7
I Students' Reports OD the Amount of Time They
I Spent on Mathematics Homework Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
11100 MEP TMAL
STATE AlISESSMENT
None
15 Mknomo
30 Mimi's
M Minsios
An Hour or
Mono
Nation
Beigiangant
Nle
State
Nation
Moo*
State
Nation
Arassican Indian
State
Natim
ECEIZSZLIMM
bongo nra1
State
Nation
Other
State
Nation
el
so 12
11101
1$1
V* Li
tal
$.1t
It IS
15
2741
`
7
$9
9011)
37
5.4)
14
4.1
11 SA
37
30
.12;1
17 Li
14
71.;
240
344
241 ( 43)
(
10 I 44
12 tit)
ipLi
30 (i0.0)
27 ( 111.7)
24 114.2)
9 ( 41.1
«e«
( 1.5)
91 (
270 ( 1.7)
203
2.2
200
3.5
( 2.3)
30
4.6
10 ( 09)
20 ( 14)
271
3.1)
2E4 ( LS)
( 1.0)
$0 ( 12)
3$ (
270
31
255
23
251
32
1.7
2.0
2.9
5.1
1.7
1.3
)
15 (
271 (
1$ (
10
AS
15
1.3)
2.4)
3.9)
0.8)
t7)
1.1)
13
267
7
(
270 (
1$ (
( 24)
2413 ( LS)
214 ( 2.3
207
2.1)
250 (
4.2)
1.5)
2.7)
2.2)
1.1)
0.9)
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
determination of the variability of this estimated mean proficiency. "* Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
r
102
THE 1990 NAEP TRIAL STATE ASSESSMENT
Maxima
TABLE A7
I Students' Reports on the Amount of Time They
(wiltinued)
I Spent on Mathematics Homework Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1SS0 NAB MAL
STATE ASSESSMENT
15 INNAss
30 Mutes
41 Wide'
An Near w
Mom
121ti
State
Nation
DiRnatiffiriAngii
I99 non-gradate
State
Nation
HS graduate
State
Nation
letne college
State
Nation
College graduate
State
Nation
GENDER,
maw
State
Nation
Female
State
Nation
teItt.o..
*kW
- No*
249
ow
24
30 4.1
17
241 ( 4.2)
250
.6170 i 1.1
32 2
i .8*.
272 ( 1
2
294 ( 2
27 (
277 9
31 ( 1
9 ( 1
0 ( 1.1)
$1
2.3 )
IS tA
*do ( .4,6
223
..204
*** (
11,10
Ma
9 ( 12}
SO
2.1
a
14
211t1
274
2115 ( SS)
275 ( 2.0)
271 ( 22
279 ( SA
271
24)
209 ( *2)
291 ( 1.4
227
2.1
2155
1
10 ( 1.1)
29 (
14
1
7 ( OA)
31 ( 3.4
111
2
1$
1.2
292 i
14
1
205
3.9)
204
2.1)
ase 24
INS
222
3.9)
237
LS)
294 12
11
1.1)
11
1.1)
30
12)
S4
2.4)
32
20 12
19
12
14
41 I
11 (
2211( 4.1
273 ( 4.0)
2030 ( 14)
277
1.7
275 ( 1.0
273
3.5
240 ( 4.1)
203 ( 1.5)
NO 2.0)
2IN 1 2.4
219
*3
7 ( OA)
29 ( 2.0)
34 (
$6
1.7
1$ ( 13)
17 ( 1.0
14 (
13
1:3
( OA)
211 ( 1.8)
The standard errors of the estimated statistics appear in parenthesei. 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).
THE 1990 NAEP TRIAL STATE ASSESSMENT
103
Montana
TABLE A8
I Teachen' Reports on the Emphasis Given To
Specific Mathematics Content Areas
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
tit= NAEP TRW
STATE ASSESSMENT
timbers and Operations
Maasurament
Own fry
Heavy
Emphasis
Little or No
EMphasis
Heavy
Emphasis
Uttie or No
Em aslsJ
Heavy
Emphasis
Little or No
Emphasis
State
Nation
862fidifflrM
%Mite
Nation
217
2E1 13
206 .22
4.0
MO 14
ne
14
9
02 1.11
.2;3
410 44
'44' 14
ft 4A)
ill
14;
State
3411
240
111
07 4.3
215 13)
223 ,16)
Niapanic
*tr. g
41
ifez?
6
La.5.4
State
Nation
d
.41)
I
1
( *)
MS
*** "
Irb
**
4.4)1
)
471.17)
23( 4.11
SA)
24
4
Amens= Indian
State
Nation
254 ( SAN
(
( NWT
45 ( 4.0)
11 ( 42)
11 ( 3.1)
29
7.3)
2$ ( 4,$)
44 (115)
I .0.71}
7 17)
13 15.5)
! (0")
243 106)1
*** (
..e.)
es* (
ipih,
*a/
10 (10.7I
TYPJL2F COMMUNITY
Ulnae rural
State
2111
2.6
12A
205 (101
44
7.4
$
14 (
111
22
3.7)
14 (
Nation
53 12.4
3.11
0 (41
32 11.7
9 11)
II
7.11
)
276 4A
257
7.1
INN!
NI
OM*
f11/1
2.5 al
...)
Itee
Other
Nation
130
2.3
MO
72
4.11
2.5
14
286
3.4)
247
10 22
10
3.41
34
6.3)
26
4.0
24
4.3
250
7.1
270 ( 4.111)
926 52
14
1.7
6 ( OA
41
2.4)
36
2.9)
11 ( 03)
State
AMMMIC
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 pescentages may not total 100 percent because the "Moderate emphasis"
category is not included.
Interpret with caution - the n2ture 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).
104
THE 1990 MARI' TRIAL STATE ASSESSMENT
Montana
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
Nurtiben and Operations
Measurement
Geometry
heavy
Emphasis
Little or No
Emphasis
,
Heavy
Emphasis
Little or No
Emphasis
Heavy
Emphasis
Little or No
Emphasis
TOTAL
Percentage
and
Pro Odom
Parontege
and
Prvildency
Porantae Poundage
and
and
Prole lona P. necioncy
Percentags
and
Praliciany
Paranta.
ind
Prolkiency
State
40 ( 2.6)
14 ( 1.3)
9 ( 1.0)
33 (
31 ( 2.5)
13 ( 1A)
280 ( 2.0)
23 ( 2.9)
277 ( 5.7)
285 ( 3.3 )
288 ( 1.5)
279 ( 2.8)
Nation
49 ( 31)
15 ( 2.1)
17 ( 3.0)
33 ( 4.0
28 ( 3.8)
21 ( 3.3)
280 ( 1.8)
287 ( 3.4)
250 ( 5.8)
272 ( 4.0)
260 ( 3.2)
264 ( 5.4)
PARENTS' EDUCATION
NS non-graduate
State
32
***)
( *al
Wit* (
***
*al
111 ( *el
Nation
00 ( 0.9)
7 ( 2.3)
22 ( 5.3)
25 ( 5.3)
32 ( 6.3)
20 ( 0.7)
251 ( 3.4)
***)
.41
( 441
( *el
HS graduate
State
44 ( 3.4)
9 ( 2.1)
10 ( 1.3)
32 ( 4.0)
26 ( 2.9)
14 ( 2.2)
273 ( 2.8)
( '1')
262 (10.8)
269 ( 4.7)
279 ( 3.9)
265 ( 5.1)
Nation
55 ( 4.8)
11 ( 2.6)
17 ( 3.9)
27 ( 5.0)
27 ( 4.5)
24 ( 5.1)
259 ( 2.9)
( ")
251 (
8.1)1
253 ( 4.7)4
255 ( 4.2)
246 ( 4.8y
Som college
State
30 ( 4.1)
16 ( 1.7)
6 ( 1.8)
30 ( 2.9)
29 ( 31)
11 ( 1.7)
280 ( 3.1)
301 ( 4.1)
(
444)
293 ( 51)
285 ( 42)
288 ( 4.8)
Nation
47 ( 4.4)
17 ( 3.3)
12 ( 2.7)
39 ( 5.5)
27 ( 5.0)
23 ( 4.1)
265 ( 2.8)
264 ( 4.1)?
(
)
279 ( 4.5)
202 ( 4.8)?
270 ( 4.7)
Cottage graduate
State
40 ( 3.4)
16 ( 2.0)
8 (
1.1)
36 ( 2.6)
35 ( 3.5)
14 ( 1.0)
288 ( 2.3)
297 ( 3.8)
289 ( 5.3)
293 ( 3.6)
290 ( 2.81
288 ( 3.5)
Nation
44 ( 4.1)
19 ( 2.4)
16 (
3.3)
37 ( 3.6)
26 ( 3.4)
21 ( 2.9)
269 ( 2.0)
298 ( 3.4)
264 ( 7.2)l
283 ( 3.8)
270 ( 3.3)
260 ( 8.4)
GENDER
Male
State
37 ( 2.7)
14 ( 1.9)
9 ( 12)
33 ( 2.2)
31 ( 3.2)
14 ( 1.5)
282 ( 2.0)
299 ( 4.1)
279 ( 51)
290 ( 5.0)
288 ( 2.4)
281 ( 3.4)
Nation
48 (
261 (
4.1)
2.5)
14 (
237 (
2.1)
4.4)
17 (
258 (
3.3)
6.7)
32 (
275 (
3.9)
4.8)
29 (
263 (
4.1)
3.8)
20 (
2er (
3.3)
8.8)
Femal
State
42 ( 3.4)
13 ( 1.8)
8 (
1.8)
34 ( 2.4)
30 ( 3.1)
11 ( 1.8)
278 ( 2.9)
286 ( 4.3)
275 (
7.4)1
280 ( 31)
283 ( 2.8)
277 ( 3.8)
Nation
51 ( 3.9)
15 ( 2.4)
17 ( 3.2)
35 ( 4.3)
27 ( 3.9)
23 ( 3.5)
260 ( 2.0)
286 ( 3.3)
241 ( 54)
288 ( 4.1)
250 ( 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 withM ± 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).
1 1 0
THE 1990 NAEP TRIAL STATE ASSESSMENT
105
Montana
TABLE A8
I Teachers' Reports on the Emphasis Given To
(cmitinued)
I Specific Mathematics Content Areas
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
Data Analysis, Statistics, and
Probability
Algebra and Functions
Heavy Emphasis
Little or No
Emphasis
Heavy Emphasis
,
Little or No
Emphasis
TOTAL
Percentage
and
Proficiency
Percentage
and
Proficiency
Permit:spa
and
Proficiency
Penoentage
and
Proficiency
State
13 ( 2.3)
59 ( 2.5)
58 ( 3.0)
10 ( 2.9)
287 ( 3.0)
281 ( 1.4)
281 ( 1.5)
268 ( 3.2)1
Nation
14 ( 2.2)
53 ( 4.4)
46 ( 3.6)
20 ( 3.0)
2$9 ( 4.3)
261 ( 2.9)
275 ( 2.5)
243 ( 3.0)
RACESETH ICITY
White
State
13 ( 2.3)
58 ( 2.6)
58 ( 3.0)
9 ( 2.7)
288 ( 3.0)
284 ( 1.3)
285 ( 1.6)
271 ( 2.7)1
Nation
14 ( 2.4)
53 ( 5.0)
4a ( 4.2)
18 ( 2.8)
276 ( 4.1)
271 ( 3.1)
281 ( 3.0)
251 ( 3.3)
Hispanic
State
5 (
(
3.1)
"4)
62
58 ( 8.3)
.41
8 (
44-4
3.3)
4.0.)
Nation
56 (
246 (
6.3)
4.4)
46 (
257 (
5.9)
4.0)1
18 (
044.
( 4.2)
American Indian
State
7 ( 3.1)
66 ( 6.7)
53(7.5)
16 ( 6.6)
4" ( 4")
257 ( 5.8)
253 ( 5.8)
Nation
3 ( 4.2)
82 (29.1)
*** (
16 (21.5)
«a* ( .4*)
87
.41
TYPE OF COMMUNITY
Extreme rurai
State
( 5.8)
00 (
279 (
6.6)
3.0)
4$ (
277 (
6.7)
3.3)
15 ( 7.9)
..*)
Nation
5
5.4)
85 (16.9)
33 ( 8.1)
42 (18.0)
(
254 ( 6.7)l
241 ( 5.9)t
Other
State
1$ ( 2.2)
58 ( 2.8)
65 ( 2.1)
8 ( 1.2)
289 ( 2.8)
282 ( 1.4)
283 ( 1.8)
263 ( 3.7)
Nation
15 ( 2.9)
53 ( 5.2)
47 ( 4.3)
17 ( 3.3)
267 ( 4.7)
260 ( 3.4)
276 ( 2.8)
245 ( 4.4)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 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).
106
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A8
I Teachers' Reports on the Emphasis Given To
(wntinued)
i Specific Mathematics Content Areas
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
IWO NAEP TRIAL
STATE ASSESSMENT
Data Ma Von, Statistics, and
Probability
Algebra and Functions
Heavy Emphasis
Little or No
Emphasis
Hesavy Emphasis
Little or No
Emphasis
TOTAL
Percents,*
and
Pro Money
PIWOOrage
and
Proadency
Penmeall
and
Prolidancy
peraanlage
and
Proficiency
State
13 ( 2.3)
59 ( 2.5)
58 ( 3.0)
10 ( 2.9)
287 ( 3.0)
281 ( 1A)
281 ( 1.5)
266 ( 32)1
Nation
14 ( 2.2)
53 ( 4.4)
46 ( 3.6)
20 ( 3.0)
209 ( 4.3)
261 ( 2.9)
275 ( 2.5)
243 ( 3.0)
PARENTS' EDUCATION
HS non-graduat
State
17 ( 4.9)
60 ( 4.8)
55 ( 5.5)
6 ( 2.0)
264 ( 4.6)
264 ( 4.2)
Nation
9 (
***
3.0)
53 (
240 (
7.7)
6.2)
G4r1
29 (
( 6.9)
44)
HS graduate
State
14 ( 3.6)
59 (
271 (
3.4)
2.5)
54 (
273 (
3.7)
2.2)
11 ( 3.0)
*ate)
Nation
17 ( 3.7)
54 ( 5.4)
44 ( 4.8)
23 ( 3.9)
261 ( 8,0)1
247 ( 2.9)
265 ( 3.5)
239 ( 3.4)
Some college
State
11 (
IP**
( 2.3)
***)
58 (
288 (
3.7)
3.3)
56 (
282 (
3.7)
2.9)
9 ( 3.4)
***)
Nation
13 ( 2.5)
57 ( 5.8)
48 ( 4.8)
17 ( 3.1)
270 ( 3.7)
278 ( 3.0)
College graduate
State
12 ( 2.2)
58 ( 2.8)
61 ( 3.4)
10 ( 3.3)
293 ( 4.4)
287 ( 1.7)
289 ( 1.5)
272 ( 5.0)1
Nation
15 ( 2.4)
53 ( 4.4)
50 ( 3.9)
18 ( 2.4)
282 ( 4.5)
275 ( 3.8)
288 (
0)
249 ( 4.0)
GENDER
Male
State
14 ( 2.4)
58 ( 2.6)
58 ( 3,5)
10 ( 2.7)
292 ( 3.6)
284 ( 1.6)
283 ( 2.2)
267 ( 3.0)1
Nation
13 ( 2.2)
54 ( 4.7)
44 ( 4.1)
22 ( 3.6)
275 ( 5.8)
260 ( 3.5)
276 ( 3.2)
243 ( 3.0)
Female
State
12 ( 2.6)
59 ( 3.0)
58 ( 3.3)
9 ( 3.3)
281 (
3.2)1
278 ( 1.9)
280 ( 2.0)
269 ( 4.5)1
Nation
16 ( 2.4)
53 ( 4.5)
48 ( 3.6)
18 ( 2.9)
263 ( 4,4)
262 ( 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
rehable estimate (fewer than 62 students).
1 2
THE 1990 NAEP TRIAL STATE ASSESSMENT
107
TABLE A9
I Teaches' Reports on the Availability of
Resources
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATiCS PROFICIENCY
ISSO NAEP TMAL
I OM MI So Rowan I
I OM Mast of Ma
I Clot Sawa ar Nana of
STATE ASSESSMENT
Need
Nalwarcas I Need
No Ramouroas I Need
State
Nation
BASIMIESIU
MOM
State
Nation
iiispanic
State
Nation
Amartain Indian
State
Nation
nnieeatiMODI
&Irmo rural
State
Nation
Omer
State
Nation
14 ( U)
ta
731 ;11
34
7.7)
- 411
2441
1.7)1
214) 1244
244 ( 2441
13 (
77 I ft
.40
10 ( U)
0( 7.4)
72 (2r11)
22 120.71
oh* (
2113
2.7)1
14
4.41)
2
2.6)
eei
3.111
2.4
11
2.011
205
10
2.2
NI ( 6.5)
271 ( 2.2)
54 (104)
280( 84)1
50 ( 3.1)
2$1 ( 14)
SII ( EA)
2414 ( 2.1)
20 ( 4.0)
277 ( 24))
43 (10.3)
257 ( 5.0)1
22 ( 3.2)
202
1.1)
2213
4.2)
54)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population it within ± 2 standard errors
of the estimate for the sample.
I Interpret with caution
the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
I 7 3
108
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A9
J Teachers' Reports on the Availability of
(continued)
Resources
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1860 NAEP TRIAL
I Get AN the ItillOWCAIS 1
1 (1111 Wet OS MS
1 Get law sr None of
STATE ASSESSMENT
Need
Remands I Need
the Reeserces I Need
TOTAL
State
Nation
PARENTS EDUCATtON
HS ooniraduate
State
Nation
HS graduate
State
Nation
Some college
State
Nation
Whigs graduate
State
Nation
GENDER
M.
State
Nation
Female
State
Nation
111.1840.0
,c80818mW
17 (
1.8
13 ( 1.4
205 ( 42)
"1"111:111.411.
Ofivialsoir
280
t.111
al
4.0
02
15 ( SI)
441)
88 (
MIS (
54 (
244 (
24
5.7
2.7)
1$ ( 2.7)
81 ( 3.4)
278 ( 2.1)
270( 2.4)
10 ( 2.5)
54 ( 42)
253 ( 4.8)4
25$ ( 12)
18 ( 33)
$2 ( 44)
294 ( 4.8);
282 ( 1.8)
13 ( 3.3)
82 ( 4.3)
2e0 ( 2.5)
17 ( 2.2)
2es ( 2.0)
83 (
28$ (
3.1)
1.3)
15 ( 2.9)
56 ( 4.9)
276 ( 54)4
275 ( 2.2)
le ( 2.1)
82 ( 33)
267 ( 2.4)
264 ( 12)
13 ( 2.6)
57 ( 4A)
284 ( 5.0)1
205 ( 2.8)
18 ( 2.6)
62 ( 3.2)
263 ( 2.7)
278 ( 1.8)
13 ( 2.4)
55 ( 44)
206 ( 3A)
264 ( 2.0)
21 .343414
38 13
943
23
22
25$ ( 22
22 (
201 ( 2.8
2$ ( 4.1
on ( 3.8)
18 ( 5.1)
209 ( 24)
30 ( 5.1)
273 ( 3.7)
21 ( 3.1)
2613 ( 2.4)
30 ( 4.0)
254 ( 3.3)
20 ( 2.7)
277 ( 2.1)
32 ( 4.7)
257 ( 3.0)
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.
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).
1
4
THE 1990 NAEP TRIAL STATE ASSESSMENT
109
Montana
TABLE AlOa I Teachers' Reports on the Frequency of Small
I Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
111110 NAEP TRIAL
STATE ASSESSMENT
I
I At Laast Owe a Wank
Less Than Om* a Week
Now
TOTAL
INWOMINNIM
AINIMMIIRS
GO ( $.0)
14401101410112,
SI
ant
Prolkleacv
State
242 ( 1.2)
20131 11:11
Nation
40 ( 4A)
43
4,1)
6
2.0)
200 ( 22)
294 ( 211)
277 ( 5.4)4
SMail_4NICITY
%Ma
State
00 ( 3.1)
32 ( 3.1)
9 ( 1.9)
245 ( 1.2)
244
1.4)
241 ( 2.6)4
Nation
49 ( 4.6)
43
4.5)
( 2.3)
245 ( 2.7)
271
2.2)
285 ( 4.9)4
HIspank
State
54 ( 45)
.+4
041
34 ( 8.5)
iNhe
4.041)
(
00. (
Nation
64 ( 7.2)
246 ( 2.6)
32 ( 8.9)
247 ( 8.3)4
4 ( 1.4
d.,41
Anworlext Indian
State
56 ( 8.4)
267 ( 46)4
34 ( 5.4;
254 ( 5.8)4
6 ( 2.9))
Nation
18 (24.3)
( 441
80 (27.2)
444
2 ( $1)
.44.)
TYPE Of COMMUNITY
Extrante rural
State
54 ( 7.4)
34 ( 7.0)
12 ( 5.6)
277 ( 2.1)1
277 ( 4,0)1
281 ( 52)!
Nation
35 t14.6)
255 ( 5.5)1
56 (17.1)
258 ( 5.9)1
( 6.6)
4144,
Other
State
85 ( 22)
30 ( 2.1)
5 ( 0.4)
244 ( 1.5)
252 ( 2.3)
Nation
50 ( 4.4)
44 ( 4.5)
( 1.6)
244.4 (2.4)
264 ( 25)
277 ( 6.3)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** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
110
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A:Oa I Teachers' Reports on the Frequency of Small
(continued)
I Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO !IAEA =AL
STAT
SSE11111 ENT
E A
At Least Ones a Weak
Less Thee Once a Week
-
Never
12104,
State
Nation
31,41420,4,
pielaisiow
222
IS)
1:11
20 4A)
43
4.1
200
3.2)
204
23)
14111111102010
oil
Pn$41444y
'2110
23
277 ( SA
EMETEIESAIEN
N$ nonirsdisste
State
( 7.1)
20
6.5)
4 ( 25)
271 ( 3.4)
***
emt)
Nation
10 ( 14)
6.531
1.41
le graduate
244 ( 3.2)
24430
State
5$
270
1
34 ( 44)
273 ( 2.6)
i0
2.9)
Nation
41
4.1
41 ( 5.1)
0 C 2.5)
some =foga
252 ( 2.1
257 ( 2.7)
State
57 (
265 ( 2.2
35 ( 3.2)
203 ( 3.0)
2.8)
.*)
Nation
$1 ( 5.2
42 ( &I)
( 2.3)
266 ( SA)
286 ( 3.2)
College graduate
State
63 ( 3.2
29 ( 24)
8 ( 1.7)
219( 1.4)
287 ( 2.5)
286 ( 3.3p
Nation
46 ( 52)
43 ( 4.4)
11 ( 2.7)
271 ( 2.6)
276 ( 3.0)
265 ( 4.1)/
0040ER
M.
State
CO ( 3.8)
33 ( 34)
7 ( 1.7)
248 ( 1.5)
293 ( 24)
279 (
3.1)1
Nation
50 ( 4.5)
42 ( 4.0)
( 2.1)
281 ( 3.0)
285 ( 3.1)
278 ( 5.3)1
Female
State
80 ( 3.2)
31 ( 3.2)
9 ( 2.1)
277 ( 1,3)
277 ( 3.7)
241 ( 3.7)1
Nation
50 ( 4.7)
43 ( 4.7)
( 2.1)
259 ( 2.2)
283 ( 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).
1
6
THE 1990 NAEP TRIAL STATE ASSESSMENT
111
Montana
TABLE A 10b I Teachers' Reports on the Use of Mathematical
I Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL
STATE ASSESSMENT
Al Least Once a Week
Lees Than Once a We*
Never
TOTAL
Poressise
and
11411444a4y
$7 (2.0)
242
1.7)
22
3.7)
for043144.
2:11
State
Nation
254 ( 3.2)
253
1
RAMTNNICITY
Mite
State
31 ( 2.8)
( 2.5)
208 ( 1.5)
213 (
Nation
17 ( 4.0)
72 ( 4.2
201 ( SA)!
( 2.1
Hispanic
State
43 ( 7.8)
511 7.7)
Nation
30 ( 7.5)
55 (
247 ( 3.8)
245 ( 3.8)1
American Indian
State
22 ( 8.5)
73 ( 115)
Mir (
201 ( 3.4)
Nation
71 (34.8)
22 (34.8)
TYPI Of COMMUNITY
ladreme rural
State
32 ( 64)
67 1 Oh)
275 ( 3.7)
279 ( 1.6)
Nation
27 (14.9)
( *on
05 (143)
262 ( 2.8)1
Other
State
40 ( 2.7)
50 ( 23)
235 ( 2.0)
211 ( 1.4)
Nation
19 ( 4.3)
72 ( 5.0)
253 ( 3.9)1
263 ( 2.2)
1 (OA)
441
1101 2.7)
21115
guy
( 2.8)
".)
5 ( 2.2)
Mr* (011r9
01 0.0)
*MP
*41
1 ( O.?)
(
( 3.9)
( *41
1 ( 0$)
251 ( 7.41
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.
! 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 e-'imate (fewer than 62 students).
112
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montww
TABLE AlOb I Teachers' Reports on the Use of Mathematical
(c*ntinued)
I Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
11100 NAEP TRIAL
STATE ASSESSMENT
At Least Ones a Vittek
LOIS Than Once a Meek
Never
TOTAL,
Pementage
and
lorseskagl
Pirosolsgs
SRI
Prolioisecy
Percaulses
and
Widow
State
$7 (
282 (
2.5)
11)
82 (
261 ( 1.0
*H.
0.4)
041
Nation
22 ( 37)
Oa (
2.5)
254 ( 3.2)
203 ( 1,9)
242 ( 5.9)1
PARENTS' EDUCATION
NS non-graduate
State
36 ( 82)
81 ( 6.1)
3 ( 12)
269 ( 3.1)
Nation
25 (( 5.6)
06 (
243 (
7.2)
2,2)
9 ( &SI
.40)
HS graduate
State
32 ( 3.3)
06 ( 3.2)
2 ( 0.8)
269 ( 2A)
273 ( 1.7)
(
Nation
23 (
248 (
4.11)
4.0)I
TO (
255 (
5.3)
22)
7 ( 2.8)
(4 )
Sem cealge
State
38 ( 3.4)
00 ( 3-3)
286 ( 2.5)
262 ( 2.1)
Nation
18 (
281 (
4.0)
4.4)!
73 (
269 (
4.3)
2.3)
9 ( 2.4)
0..)
College graduate
State
39 ( 3.4)
00 ( 3.4)
1 ( 0.3)
219 ( 1.8)
267 ( 1.5)
Nation
20 ( 3.9)
09 ( 3,7)
11 ( 2.5)
266 ( 3.5)1
274 ( 22)
297 ( 4.2)1
GENDER
Mato
State
36 (
284 (
3.2)
2,9)
03 (
265 (
32)
1.1)
1 ( 0.3)
4.1
Nation
22 ( 41)
09 ( 4.1)
8 ( 2.0)
255 ( 4.1)
265 ( 2.1)
287 ( 72)!
Renal'
State
38 ( 3.0)
00 ( 3.1)
2 ( 0.6)
280 ( 22)
270 ( 1.5)
Nation
21 ( 3.6)
89 ( 4.2)
10 ( 3.3)
254 ( 3.3)
2t? ( 1.9)
278 (
8.0)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.
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).
1 s
THE 1990 NAEP TRIAL STATE ASSESSMENT
113
Montww
TABLE AI la I Teachers' Reports on the Frequency of
Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
16190 NAEP TRIAL.
STATE ASSESSMENT
Ahmed Every Day
Several Times a tffilat
a
About Once Week or
LAM
Niait
State
Nation
awl
Poldisionw
:2$4
SA
267 t*
Porsemesp
Pnikflaaat
2
278 11
3.1
264 ( 24)
BagalaNTY
White
State
63 ( 3.1)
31 ( 2.6)
286 ( 1.1)
261 ( 1.2)
Nation
84 ( 3,7)
26 ( 3.2)
272 ( 1.9)
264 ( 2.4)
Hispanic
State
50 ( 9.0)
*en
39 (( 9.1)
Nation
61 ( el)
32 ( 53)
251 ( 3.1)
240 ( 4.3)I
American Indian
State
51 ( 7 .0)
45 ( 7.3)
283 ( 4.0)
250 ( 4.2)1
Nation
15 (25.11)
*** (
63 (263)
TYPE Of COMMUNITY
Extreme rural
State
61 ( 0.7)
31 ( 4.6)
281 ( 1.6)
271 ( 3.8)
Nation
SO (10.0)
40 (10.0)
208 ( 4.0)1
247 ( 7.0)1
Other
State
02 ( 24)
32 ( 3.0)
285 ( 1.4)
278 ( 1.3)
Nation
63 ( XS)
31 ( 3.5)
287 ( 2.3)
255 ( 3.1)
Peresaisips
Noe
Preildwity
14)
279
1.4
240
5.1
( 14)
262 ( 3-1)1
( 23)
264 ( 5,4)4
$ ( 2.6)
( mon
9 ( 2.3)
114.11 ( MO)
4 ( 23)
44,)
2 ( 3.0)
4* (
7 ( 54)
( 441
8 ( 0.7)
279 ( 3.8)
0 ( 14)
257 ( 54)I
The stardard 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).
114
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE Alla I Teaches' Reports on the Frequency of
(continued)
Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1990 NAEP TRIAL
STATE ASSESSMENT
Aknoet Every Day
Several Then a Wolk
About Ottoo a Week or
Lass
TOTAI-
State
Nation
PARENTS' EDUCATKIN
KS non-graduate
State
Nation
fitt graduate
State
Nation
Sam coils,'
State
Nation
College grutuat
State
Nation
GENDER
Male
State
Nation
Female
State
Nation
PerialMage
11Ri
01110101111113/
05 ( 6.3)
269 ( 2.3)
07 ( 5.5)
245 ( 3.2)
01 ( 4.1)
274 ( 1.5)
61 ( 4.4)
257 ( 2.5)
62 ( 4.2)
2118 ( 2.3)
68 ( 42)
272 ( 2.7)
61 ( 3.1)
290 ( 1.4)
Of ( 4.0)
261 ( 2.2)
61 ( 3.1)
287 ( 1.5)
80 ( 3.7)
2ea ( 2.1)
62 ( 3.4)
281 ( 1.3)
85 ( 3.6)
266 ( 1.6)
0101110161190
and
trelklem.
I 111
254
2.9
28 ( 5.5)
( don
27 ( 5.2)
32 ( 3.1)
266 ( 3.4)
34 ( 3.7)
250 ( 2.9)
33 ( 3.9)
277 ( 2.1)
26 ( 3.7)
258 ( 5.2)
33 ( 2.6)
263 ( 2.0)
31 ( 3.9)
265 ( 3.1)
33 ( 23)
280 ( 2.0)
33 ( 34)
256 ( 3.6)
31 ( 2.7)
272 ( 2.0)
28 ( 3.3)
253 ( 2.5)
illanspiege
iM6
241/1100181
II
'MS 9.0
7
1.0
280
9..1
( 23)
7 ( 2.7)
15)
***
141
( 20)
e
1.9))
to*
1.6)
3.1)
.hen
***
7
1.2)
261 ( 8.7)4
( 2.1))
7 ( 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).
THE 1990 NAEP TRIAL STATE ASSESSMENT
115
Montana
TABLE Al lb I Teachers' Reports on the Frequency of
Mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1S110 NAEP TRIAL
Al Laist Swami Tknas
STATE ASSESSMENT
a Ws*
About Oncto a Weak
Less than %%aft
,
TOTAL
Paressdase
and
firsidistray
feraudaga
and
Pralidelav
ParaNdep
and
Predidsony
State
47 ( 3.3)
22 ( 2.1)
00 ( 22)
2$0 ( 1.1)
2$2 ( 2.7)
241 ( OA)
Nation
34 ( 3.8)
3$ ( 3.4)
32 ( SA)
250 ( 2.3)
200 ( 2.3)
274 ( 2.7)
RACE/ETHNICITY
Mite
State
4$ ( 3.4)
23 ( 2.2)
30 ( 23)
282 ( 1.1)
288 ( 2.1)
254 ( 1.0)
Nation
32(4.1)
33 ( 3-5)
35 ( 3.8)
264 4 21)
264 ( 2.7)
279 ( 2.9)
Hispanic
State
40 ( 8.7)
( *41
17 ( 8.5)
044 (
43 ( 9.1)
( *41
Nation
41 ( 7.7)
2Sf 5.3)
33 ( 7.5)
242 ( 12)1
244 ( 5.1)1
257 ( 2.3)'
American Indian
State
49 ( 7.9)
200 ( 4.1)1
20 ( Si)
244 ( 9.9)1
31 ( 6.0)
..**)
Nation
10 (113.6)
76 (362)
0114 ( 444 )
13 (18.5)
( 0,1
TYPE OF COMMUNITY
Extreme nwal
State
59 ( 7.5)
18 ( 4.8)
23 ( 48)
280 ( 1.7)1
269 ( 7.1)1
277 ( 2.0)
Nation
27 (14.3)
49 (12.7)
24 (WA)
258 ( 6.7)1
(
Other
State
42 ( 2.8)
24 ( 1.9)
34 (2.1)
279 ( 1.5)
288 ( 2.5)
282 ( 1.0)
Nation
30 ( 44)
35 ( 43)
36 ( 42)
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 ± 2 standard errors
of the eptimate 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 insufacient to permit a
reliable estimate (fewer than 62 students).
1 2 1
116
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE Al lb
Teaches' Reports on the FIN
(continual)
I
Mathematics Worksheet Use
f
PERCENTAGE OF 5
DENTS AND
A'ffERAGE MATHEWTt5 PROFICIENCY
MU NAEP TRIAL
STATE ASSESSMENT
At Lead Sew* naps
Week
About Once a Week
-
Lass Sun Weekly
State
Nation
1261MILMEN&USE
NS nsn-graduate
State
Nation
AS graduate
State
Nation
Same college
State
Nation
CoStge graduate
State
Nation
OENWR
M.
State
Nation
FORUM
Stine
Nation
SS
2,4
all 19
2410( Iwt)
Nod
Preltrimmy
2AI
3111
SA
274
2.7)
*a 44
29 &Si
40 (
s.
38 I Ili
230 ( 3.2)
*ft (
2$0 ( 4.5)I
:0 I 42.1i
35 53)
20$
)
21 ( 2.2)
3$
27304 I 234.7))
30
4.8)
250 ( 2.8)
250 ( 2. )
263 ( 3.4)
47 ( 11.8)
22 ( 2
31 ( 2.7)
242 ( 2.5)
2170 (
210 ( 2.8)
33 (
201 (
32 ( 4
22033$71
422.8.11
4.73
50 ( 3.5)
22 ( 2.
29 ( 2.5)
1.3)
35
3.1)
290 ( 2
11
26 ( 1.0)
32 (
264
2.9)
271 ( 24
299 ( 2.9)
3$ ( 3.5)
50 ( 3,8)
283 ( 1.2)
$5 ( 4.1)
257 ( 3.2)
45 ( 3,8)
278 ( 1.8)
34 ( 4,1)
254
2.1)
20
2.7
287
4
35
25 ( 2
270 ( 3
32 ( 3.
rAl ( 2
The standard errors of the estimated statistics appear in parentheses.
certainty that, for each population of interest, the value for the entire po
of the estimate for the sample.
! Interpret with caution - the nature
determination of the variability of this estimated mean proficiency. ***
reliable estimate (fewer than 62 students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
30 ( 27)
284 ( 1.8)
31 ( 3,5)
275 ( 3,2)
31 ( 2.1)
278 ( 1.3)
34 ( 4,1)
273 ( 2.8)
t can be said with about 95 percent
ulation is within ± 2 standard errors
the sample does not allow accurate
ample size is insufficient to permit a
117
Montana
TABLE Al2
I Students' Reports on the Frequency of Small
I Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1 1100 NAEP TRIAL
STATE AS SESSMENT
At Least Ones a WiaA
Leas Than One* a Wm*
New
TOTAL
State
Nation
291
300
1.4
1
210
RACE/ETHNICITY
*tits
State
Nation
Hispanic
State
Nation
Amarican Indian
State
Nation
TYPE QF COMMU4ITY
Extrema rural
State
Nation
Odor
State
Nation
OM 31)
2014
131
$i
1.0
27
2.9
1.7
11,*1)
242 ( SA
37 ( 5,21
1
Si 1
29
272 ( 14)
22 24
250 ( SA)
SO ( 5.5)
27 ( 3.7)
252 ( 4.0)I
VIM
31 ( 5.1)
S$
( ***)
111441)
33 ( 3.9)
29 ( 2.1)
276 ( 2.7)
200 ( 2.1)
34 (10.6)
27 ( 3.5)
249 ( 5.3)I
264 ( 3.5)i
31 ( 1.7)
Si ( 14)
252 ( 1.5
263 ( 1.7)
27 (
.02}
26 ( 1.7)
200 ( 3.3
264 ( 2.1)
240 2A
121 El
41
$11
217
5.1)
5.0)
335.0)
ow
SS ( S.5)
277 ( 23)
SS (11A)
250 ( 6.2)I
IS ( 1.5)
200 ( 14)
41 ( 3.3)
262 ( 22)
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 vidue for the entire population is within t 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
detertni.nation of the variability of this estimated mean proficiency. *" Sample size is Msufficient to permit a
reliable estimate (fewer than 62 students).
118
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A 12
I Students' Reports on the Frequency of Small
(mitinued)
I Group Work
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
STATE ASSESSMENT
MAD TRIAL
AI Least Ono a Week
Lass Than Once a Week
New
/Ea
State
Nation
MagatliffAlt_ON
HS nan-graduata
State
Nation
Hi graduate
State
Nation
S ense college
State
Nation
College graduate
State
Nation
OENDER
M.
State
Nation
Fem.*
Stire
Nation
foregalk.
Problems/
$1 ( 13)
NO 1A)
2$
24)
258
2.7)
40 ( GI)
444 ( .4)
29 ( 4.5)
242 ( 3.4)
30 ( 2.9)
242 ( 2.4)
26 ( 3.0)
251 ( 3.7)
29 ( 2.5)
225 ( 2.1)
27 ( 3.9)
285 ( 31)
32 ( 22
2116 ( 2.0)
211 ( 3.0)
270 ( 2.7)
32 ( 2.1)
202 ( 1.7)
31 ( 21)
259 ( 3.3)
31 ( 1.9)
277 ( 2.0)
20 ( 2.4)
257 ( 2.8)
rod
Pralidemqt
$0 (tS)
222 (1,$)
Perameass
and
Orideimlif
ell
241( 14 )
44 ( 2.9
267 ( 2.0)
261 (
25 ( 04)
35 ( 5.9)
( 4.)
0.11r41, ( Oil
29 ( 3.0)
42 ( 4.5)
244 ( 3.0)
242 ( 2.7)
30 ( 2.3)
40 ( 2.8)
271 ( 3.3)
274 ( 2.4)
28 (
1.11)
43 ( 3.4)
261 ( 21)
252 ( 1.7)
31 ( 3.1)
40 ( 2.8)
287 ( 3.0)
279 ( 2.4)
27 ( 2.4
46 ( 3.8)
268 ( 3.3)
268 ( 2.1)
30 ( 1.9)
38 ( 2.2)
290 ( 14)
266 ( 1.7)
2$ ( 1.9)
44 ( 31)
278 ( 2.8)
275 ( 22)
32 ( 2.1)
37 ( 14)
200 ( 2.2)
263 (
1.5)
20 ( 1-7)
41 ( 24)
2011 ( 21)
262 ( 1.8)
29 ( 1.7)
41 (
1.9)
279 ( 1.3)
278 ( 2.2)
27 (
1.11)
47 ( 3.2)
200 ( 1.7)
260 ( 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 insufficient to permit a reliable estimate (fewer than 62
students).
THE 1990 NAEP TRIAL STATE ASSESSMENT
119
Montana
TABLE A 13
I Students' Reports on the Use of Mathematics
Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1690 AMP TRIAL
TE ASSIIIIIMENT
STA
At Load Once a Week
Loss Than Once a Week.
Plover
12M12
State
Nation
MadatiaM
WINN
State
Nation
diaper*
State
Nation
American Indian
State
Nation
Typg OF COMMUNITY
Extreme nrid
State
Nation
Other
State
Nation
Pansmitro
torieriew
( 1.2)
Oa 13)
$1
1.2)
20.
15)
Peromease
Old
$1911$01/49$
27 (
279 (
41 ( 2,2
2311( 1.9)
37 ( 1.3)
37 ( 1.2)
26
1M5 ( 1.2)
205 ( 13)
so
Vt 13)
33 ( 1A)
40
2116 ( 23)
275 ( 1.9)
(
SO ( 53)
31 ( ILO)
Se ( 9.11)
6.11 ( 001
f ill
IMb ( OM)
1111 ( 4.2)
23 i 2.0)
40 ( 4.0)
241 ( 4A)
253 ( 4.3)
240 ( 1A)
29 ( 4A)
23 ( 3.4)
257 ( 4.2)
36 ( 5.1)
257 ( 5.4)
36 ( 3.4)
04* ( 4.43
37 ( 12)
.... ( .**)
2$ f LA)
... ( *An
35 ( 2.2)
4ff 2.0)
23 ( 2.5)
279 ( 2.5)
27$ ( 1.7)
274 ( 3.3)
21 ( 3.1)
( 44,41
37 ( 4.7)
262 f 4.7)1
43 ( 5.0)
251 ( 5.2)(
37 ( 1.4)
$4 ( 1.6)
29 (
.6)
2413 ( 1.5)
265 ( 1.1)
277 (
1.6)
27 ( 2.0)
$1 ( 1.4)
41 ( 2.4)
259 ( 2A)
270 ( 1.8)
200 ( 2.2)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
120
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A13
I Students' Reports on the Use of Mathematics
(c4mtinued)
I Objects
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1910 MEP TRIAL
STATE ASSESSMENT
At Least Once a Weak
Lass Than Onoa a Weak
Mow
TOTAL
lIt 1.1)
( 1.2)
20 ( 1.11)
State
Nation
minnizsarm
21$ ( 2A)
141 mergracktate
State
31 ( 4.1)
Nation
27 ( 4.2)
237 ( 3.0)
1111 graduate
State
32 ( 2.8)
271 ( 2.3)
Nation
27 ( 2.7)
250 ( 2,4)
Soma cottage
State
37 ( 2.5)
2161 2.7)
Nation
29 ( 29)
281 ( 3.5)
Collage graduate
State
40 ( 1.5)
217 ( 1.3)
Nation
30 ( 23)
269 ( 3.0)
GENDER
Maio
State
37 ( 1.7)
264 ( 1.3)
Nation
32 ( 2.0)
256 ( 2.9)
Female
State
35 ( 1.9)
279 ( 2.1)
Nation
25 ( 2.0)
257 ( 3.0)
(
.40 ( SIM
34
$.1)
24
2.7
;4:012.3
253 ( 3.5
24047
31 ( 2.8)
(
2/2 ( 2.7)
270 ( 2.11
111 ( 2.4)
43 ( 3.3
216(2.7)
263 ( 2.1)
37 ( 2.1)
29 ( 1.9)
213 ( 1.8)
2/9 ( SM
38 ( 2.3)
36 ( 2.8)
274 ( 2,2)
203 ( 2.1)
38 ( 1.9)
25 ( 2.0)
290 ( 1.5)
264 ( 2.2)
32 ( 2.0)
38 ( 2.8)
271 ( 2.0)
275 ( 2.0)
35 ( 1.8)
27 ( 1.9)
206(2.1)
241 ( 2.1)
30 ( 13)
3111( 2.2)
271 ( 2.1)
200 ( 1.6)
37 ( 1.4)
27 ( 1.5)
270 ( 1,3)
272 ( 1.0)
31 ( 1.9)
414 ( 2.6)
266 ( 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 insufficient to permit a reliable estimate (fewer than 62
students),
THE 1990 NAEP TRIAL STATE ASSESSMENT
121
Montana
TABLE A14
I Students' Reports on the Frequency of
Mathematics Textbook Use
PERCENTAGE Of STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
-
11190 NAEP 'TRIAL
STATE ASSESSMENT
Newt Every Day
Several Times a Week
About Onc
Week or
e a
LOU
a
TOTAL
earameaga
ame
Prwealang
71(1.5)
242 ( OA)
74 ( 1.1)
2ti ( 1,2)
PeeReelees
PrweWataaff
13( 1.0)
14)
14 OA)
252
1.7)
flet,***11.
000110111gat
See (3.2)
12 ( 14)
242 ( 4.5)
State
Nation
RACEIETHNICITY
Witte
State
79 ( 1.6)
13 ( CO)
1 ( 1.0)
265 ( Me)
242 ( 1.7)
270 ( 3.4)
Nation
711( 2.5)
13 ( 0.8)
11 ( 2.2)
274 ( 14)
258 ( 2.2)
Hispanic
State
OA)
23 ( 5.2)
9 ( 4.0)
'41
Nation
61(3.7)
21 i 2.9)
17 ( 2.7)
249 ( 2.3)
242 ( 5.1)
224 ( 3.4)
American Indian
State
78 ( 4.3)
14 ( 3.7)
( 2.2)
251 ( 3.7)
***
44P*)
*4114P)
Nation
61 ( 4.4)
.. (
22 ( 30)
17 ( 4.0)
TYPE OF COMMUNITY
Darlene rural
State
79 ( 2.0)
13 ( 1.7)
7 ( 1.8)
278 ( 1.9)
279 ( 3.0)
237 ( 8.1)1
Nation
ee (113)
203 ( 4.2)1
15 ( 3.6)
444 ( 4
17 ( 5.2)
aaa)
Other
State
78 ( 1.7)
13 ( 1.1)
a ( 1.2)
204 ( 0.9)
279 ( 2.2)
205 ( 3A)
Nation
75 ( 2.2)
14 ( 1.0)
10 ( 1.9)
26? ( 1.6)
252 ( 2.0)
239 ( 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.
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).
1 r:
122
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A 14
I Students' Reports on the Frequency of
(continued)
Mathematics Textbook Use
PERCENTAGE OF STUDENTS AND,
AVERAGE MATHEMATICS PROFICIENCY
_
IWO NAIND TRIAL
TAU ASSEINUENT
Almost Dray Day
Several Timm a Weak
.
About Moe a Week er
Lass
Air
TOTAL
Se
Nation
muntsasass
NI nen-gradusts
State
Nation
NS graduate
State
Nation
enta college
State
Nation
College graduate
State
Nation
oeNDER
U.
State
Nation
Female
State
Nation
71 (
20 (
$45 (
24)
23)
10
1$
tee
$.0)
*On
2 .0)
( al
11 (43)
411
11 ( «le)
77 (
272 (
3.4)
1.7)
14
272
( 1.6)
(
111
71 ( SS)
111 ( 1A
13 ( 22)
254 ( 1D)
248 ( 3.2
239 ( 3.4)1
40 (
205 (
2.3)
1$
200
( 2.3
( 3.2)
5 ( 1.4)
oedi ( «ft
00 ( 2.0
11 ( 1.2
9 ( 1.7)
270 ( 1.9
79 ( 1.7)
13 ( 1.3)
1 (
1.0)
209 ( 1.1)
2$5 ( 3.0)
276 ( 4.2)
77 ( 2.7)
13 ( 0.9)
10 ( 2.3)
279 ( 1.6)
200 ( 2.3)
237 ( 6.4)1
77 ( 1.7)
14 ( 1.2)
( 1.1)
2116 ( 1.1)
242 ( 2.7)
209 ( 4.3)
72 ( 2.4)
13 ( 1.2)
12 ( 2.1)
20. ( 14)
242 ( 24)
242 ( 61)
00 ( 2.0)
13 ( 1.3)
7 ( 1.2)
279 ( 1.3)
276 ( 2.2)
261 ( 54)
78 ( 1.1)
13 ( 1.0)
11 ( 1,6)
205 ( 13)
250 ( 24)
242 ( 3.8)
The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insuffic4ent to permit a
reliable estimate (fewer than 62 students).
1 f's
THE 1990 NAEP TRIAL STATE ASSESSMENT
123
Montana
TABLE A1S I Students' Reports on the Frequency of
Mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL
sun mussuar
At Least Several Timm
a Weak
._
About Once a Weak
Leas Thin Weakly
TOTAL
State
Nation
BAMETEELY
White
State
Nation
Hlipank
State
Nation
American Indian
State
Nation
TYPE OF COIMMUNITY
Extreme rural
State
Nation
Other
State
Nation
ihrbkiolat
I
se 1,221
2$
12)
1.4)
25
12)
2491
14)
$22
32 ( 23)
20 ( 13)
sitlis
210 ( 1.1)
25 ( 2.2)
144 1 1
41
202 ( 2.5)
WM 1.5
271
2$ (
2$( 4.5)
45 1
... ( .4*
I *In
44 ( 4.1
2$
230 ( 33)
247
31 ( 4.0)
31
24$ ( 5.0)
250
41 ( 4.2)
30
ae ( 5.2)
275 ( 3.1)
42 (10.1)
249 ( 4.0)1
30 ( 2.4)
277 ( 12)
36 ( 2.9)
252 ( 3.0)
( 3.4)
$2
( 2.3)
241
( 4.7)
33
( 3.2)4
205
(11.3)
23
24 ( 2.4)
277 ( 3.0)
30 ( 4.4)
250 (
3.4)1
31 (
111)
251 ( 14)
25 ( 12)
261 ( 2.1)
( 43
( 13
( 5$)
( 4.0S
(124)
40 ( 544)
200 (
2$ ( 7.5)
207 ( 7.3)1
30
1.0)
2111
1.0)
30
29)
272
14)
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
rehable estinnte (fewer than 62 students).
124
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A15 1 Students' Reports on the Frequency of
(continued)
I Mathematics Worksheet Use
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL
STATE ASSESSMENT
At Least Several Times
a Week
About Onc a Week
Leas Than Wieldy
TOTAL
Permodepo
add
Pralitioacy
Verodoliso
and
Podidiesay
Persold.
and
Pregkdietv
State
$2 ( Li)
2Sf 1,2)
39 ( 2.1)
27$ ( 1$ )
220 (1.4)
214 ( 0.9)
Nation
3$ ( 2.4)
25 (12)
37 ( 24)
253 ( 22)
201 ( 1.4)
272 ( 1.9)
PARENTS' EDUCATION
HS non-graduete
State
2S ( 5.3)
30 ( 5.0)
45 (( 14)
Nation
41 ( 4.5)
30 ( 2.7)
22 ( 4.0)
235 ( 3.1)
243 ( 2.7)
253 (2.8)
HS graduate
State
31 ( 34)
30 ( 2.4)
39 ( 2.9)
206 ( 2.6)
270 ( 3.3)
276 ( 2.1)
Nation
40 ( 3.2)
29 ( 22)
32 ( 3.6)
247 ( 2.7)
256 ( 2.5)
262 ( 22)
Som college
State
3$ ( 3.4)
2$ ( 3.1)
39 ( 3.8)
271 ( 2.2)
268 ( 35)
26$ ( to)
Nation
34 ( 3.4)
26 ( 22)
40 ( 33)
259 ( 2.3)
269 ( 2.8)
271
211)
College gracluat
State
33 ( 2.7)
29 ( 1.8)
30 ( 2.5)
284 ( 1.4)
286 ( 1.7)
291 ( 1.5)
Nation
38 ( 2.8)
22 ( 1.8)
41 ( 2.6)
264 ( 2.6)
273 ( 2.5)
285 ( 23)
GENDER
M.
State
33 ( 2.3)
28 ( 1.8)
39 ( 2.5)
279 ( 1 A)
264 ( 2.0)
287 ( 13)
Nation
39 ( 2.7)
2$ ( 1.6)
35 ( 2.7)
253 ( 2.7)
263 ( 2.3)
274 ( 2.4)
Female
State
31 ( 2.6)
29 ( 1.6)
40 ( 24)
273 ( 2.0)
277 ( 2.4)
2S1 ( 13)
Nation
37
25)
25 ( 1.5)
38(23)
253 ( 2.1)
250 ( 1 A)
( 2.2)
The standard errors of the esfunated statistics appear in parentheses.
It ean 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 ettimate (fewer than 62
students).
1 3o
THE 1990 NAEP TRIAL STATE ASSESSMENT
125
Montana
TABLE AIS
Students' Reports on Whether They Own a
Calculator and Whether Their Teacher Explains
How to Use One
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1110 NMP TMAL
STATE ASSESSMENT
.
,
Own a Calculator
Teacher Opiates Calculator Use
Yes
I
No
Yes
,
I
No
Mai
State
Nation
Emaniffma
woe
state
Nation
Hispanic
State
Nation
ARIENiCal Indian
State
Nation
TYPE OF COMMUNITY
Extrema niral
State
Nation
Mee
State
Nation
gi2it
:311
17 ( 0.4)
2113 ( 1.3)
91 ( 03)
214 ( OA)
10
70
031.5i2
90 ( el)
264 (3.1)
12 (1.2)
245
2.7)
65 ( 13)
257 ( 3.4)
N ( 3.1)
eee
frollakmar
1 ( 0.3)
( eel
2
03)
10 ( 0.7)
grop.
,44)
( 1.2)
44
5
1)
( 1".)
6 ( 3.1)
44e ( eee)
ad
!Isom,
214
49 ( 2.p
2511
1.7)
SS ( 2.2)
212 ( 1.0)
46 ( 2.6)
211 ( 13)
Si ( 6.5)
**IP
44/
3.41
54 ( 5.6)
253 ( 3.9)
71 (16.7)
vv. (
161
141610111,06
44 (
213 ( 1
111 ( 2.3
2116 ( 1.5)
45 ( 2.2)
215 ( 1.6)
54 ( 2.0)
273 ( 1$)
49 ( 6.5)
*MI
37 (
245 ( 2.9)
42 ( 53)
261 ( 4.6)1
29(197)
*44, )
a6 ( OA)
278 ( 1.$)
00 ( 1.3)
257 ( 34)1
96 ( 0.3)
202 ( 1.0)
01(0.5)
213 ( 1.7)
1
4
to,
2
*14(444)
5
2$3
( OA)
***)
( 1.3)
( 1M1
( 0.3)
( 0.5)
( 54)
57 (
270 (
42 (
251 (
55 (
210(
50 (
251 (
5,0)
2.0)
8.7)
41)1
11)
1.1)
2.7)
2,1)
43 (
279 (
56 (
261 (
45 (
244 (
50 (
206 (
5.0)
2.2)
e.1)
4.4)1
13)
2.0)
2.7)
20)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
! Interpret with caution - the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
126
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE AlS
Students' Reports on Whether They Own a
(wiltinued)
Calculator and Whether Their Teacher Explains
How To Use One
PERCENTAGE Of STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1460 NAEP TRIAL
STATE ASSEUMUT
_
Own a Cakaatar
,.
Teacher Scabs Calm Mar Use
Yes
No
I
Yes
.
No
_
TOTAL
State
Nation
PAR$TS' EDUC
HS
te
State
Nation
NS graduate
State
Nation
Some college
State
Nation
College graduate
State
Nation
OENKR
M.
State
Nation
Female
State
Nation
Nes
Stalkissio
OS (
241 (
97 (
243 (
99 (
240 (
92 (
243 (
0.3)
0.4)
04)
1.3)
2.3)
2.3)
1.5)
2.0)
2 ( 0.3)
imp (
( 0.4)
234 ( 3.4)
(
do* (
iC 1.0
2:1.1242
11(0.8)
271 ( 1.8)
97 ( OA)
255 ( 1.5)
11(0.5)
2 (
3 (
(
0.4)
0.4)
0.5)
$4 ( 2.
270 (
54 ( 3.0
252 ( 1A)
se ( ti
263 ( 1.7)
242 ( 1.7
96 ( 0.9)
4 ( 0.9)
a ( 3.2
23$ ( 14)
(
205 ( 2.4)
99 ( 0.4)
1 ( 0.4)
55 ( 2.2
287 ( 1.1)
(
245 ( 1.3)
99 (
275 (
0.2)
1.8)
1 ( 0.2)
( mkt )
46
266
( 2.6
( 2 2
98 ( 0.4)
2 ( OA)
56
2.1)
254 (
)
2$1
1.7)
97 ( 0.5)
3 ( 0.5)
31 ( 2.5.
234 ( 1.7)
.441
2$1 ( 2.1)
00 ( 04)
( 0.4)
53 ( 2.5)
27$ ( 13)
27$ ( 1.4)
97 ( 0.5)
3 ( 04)
47 ( 24)
282 ( 1.3)
(
2511 ( 1.7)
51
2.3)
14)
243
42.14
2? R4)
47
4i ( 2.7)
273 ( 1.7)
40 ( s.a)
256 ( 2.0)
44 ( 3.1)
265 ( 2.7)
52 ( 3.2)
264 ( 2.2)
45 ( 2.2)
290 ( 1.7)
54 ( 2.6)
(
26014)
42 ( 2.1)
287 ( 1.7)
49
2.9)
206(2.1)
47
2.5)
279 ( 1.8)
53 ( 2.5)
263 ( 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 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
127
Montalto
TABLE A19
I Students' Reports on the Use of a Calculator
I for Problem Solving or Tests
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
INO NAEP TRIAL
STATE ASSESSMENT
Wad
Problems in
Class
Doing Problems at Homo Taking Quizzes or Tests
Almost
Always
Neve r
Almost
Always
Never
Almost
Always
4
Never
TOTAL.
State
Nation
RACEfETHNICITY
White
State
Nation
Hispanic
State
Nation
American Indian
State
Nation
TYPE OF COMMUNITY
Extra'''. rural
State
Nation
Other
State
Nation
Perom44. persim4904 Poivoilme P4ralmbps Powlso Poombee
4414
and
sed
4444
494
eml
Posioinev Polielem
4/41941.444
114.4114*NW
Pro04192149 PrskieNW
44(
19 171
277 ( 0.9
44 ( 1.5
254 ( 14)
2123
14
46 ( 1.7)
1C ( 1.7)
281 ( 1.0)
287 ( 2.2)
40 ( 1.7)
24 ( 2.2)
262 ( 1.7)
278 ( 1.3)
49 ( 6.3)
15 ( 5.2)
.N ( .4.41
9.4.444 ( 404.)
51 ( 23)
16 ( 34)
an ( 2.3)
252 ( 3.3)I
48 ( 5.9)
15 ( 44.2)
251 ( 4.0)
*** ( ***)
33 ( Se)
23 ( 4.9)
44 ., (
444444)
4.4.4 ( ***)
45 ( 3.1)
17 ( 4.5)
274 ( 2.1)
279 ( 2.1$
46 ( 7.4)
29 ( 6.5)
246 ( 4.3)1
208 (
47 ( 2.0)
14 (
1.4)
279 ( 1.0)
297 ( 23)
48 ( 13)
22 ( 2.0)
254 ( 2.1)
272 ( Ca)
351 1.2
11
0.9)
21
1.4)
30( 1.7
1.2
279
2.5)
270 (1.3)
217( 1.2
:I
19
09)
27 (1.4)
30( 2.0
(11.1
292
1.2)
2511( 2.4)
274( 13
SS ( 1.4)
10 (
21 ( 1.4)
31 ( 13)
236 ( 1.1)
285 ( 2.0
279 ( 1A)
290 ( 1.4)
$1 ( 1,5)
15 ( 1.2
25 (13)
82 ( 28)
270 ( 1.7)
20 ( 28)
283 ( 2.0)
278 ( 1-2)
26 ( 73)
op. i 4.4,4)
22 ( 63)
4.4,4 ( 494)
23 ( 5.8)
444 ( In
29 ( 6.3)
i 441
26 i 3.2)
21 ( 2.1)
26 ( 22)
22 i 3.1)
296 ( 4.8)
244 ( 3.1)
237 ( 3.2)
256 ( 4.2)
32 ( 4.1)
258 ( 5.0)4
14 ( 3.5)
- ( -)
26 ( 4.3)
250 ( Lep
22 ( 5.0)
.-- ( -)
15 ( 4.9)
32 (10.1)
20 ( 62)
21 ( 7.3)
( .....)
444 ( *41
*44. ( in
444 ( 441
31 ( 2.3)
10 ( 1.7)
24 ( 3.5)
215 ( 4.6)
278 ( 2.8)
280 ( 18)
275 ( 2.4)
284 (
1.7
20 ( 2.5)
23 ( 33)
24 ( 6.6)
37 ( 8.3
( -)
263( 4.4$
(
)
270 ( 4.0
37 ( 1,4)
11 ( 1.1)
20 ( 1.3)
30 ( 1.2
295 ( 1.5)
279 ( 3.3)
276 ( 1.5)
239 ( 1.7
32 ( 1.7)
18 ( 1.1)
27 ( 1.8)
29 ( 2.1
263 ( 2.3)
263 ( 2.8)
253 ( 2.7)
275 ( 13
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 becauee the "Sometimes" 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).
r..
-
128
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
=1.
TABLE A19 1 Students' Reports on the Use of a Calculator
(continued)
I for Problem Solving or Tests
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1920 NAEP TEAL
STATE ASSES$MENT
,
Westing Problems in
Class
..
Doing Problems at Name
-
Taking Quizzes or Tests
Almost
I
_
Always
Never
Almost
I
Always
..
Never
Almost
1
Atways
,
NeVef
121M
State
Nation
feanniasano.
KS non-graduate
State
Nation
149 eradiate
State
Nation
Soma college
State
Nation
College graduate
State
Nation
Mate
State
Nation
Female
State
Nation
0,66411006600 14111"1"..
8100
600
Prailisting tfinsisketv Prolimipow alnilhOmpf 1,00014,1W
,.
277 AO M
42 11
_If g
sol 11
21.4.1 20.1)
Ai
.1144
or 1.3
4.
1.5
,
22
1.2
30
1.3
12 ( OA}
27
1.4
IQ
2.0
264
1.2
271i
1.4
18111
IA
21121( 13
2811 2A
274
1.3
50 ( IA )
12 ( 2.9)
3.1
44*
.4.)
84 $A
21 3.11)
240
2.2
n
4$ ( Si)
17 (
249( 2.0)
275 ( 2.11
52 ( 2.5)
20 ( 2.4
249 ( 1.4)
285 ( 2.7)
44 ( 2.7)
13 ( 2.3)
273 ( 2.3)
218 ( 5.4)
48 ( 2.4)
28 ( 2.2)
Nil ( 2.1)
272 ( 2.5)
47 ( 2.4)
17 ( 1.9)
364 ( 1.4)
292 ( 2.4)
45 ( 1.9)
25 ( 2.4)
255 ( 1.7)
284 ( 13)
47
2.1)
14 (
280
1.4)
NO ( 3.4
50
1.7)
20 ( 2.0
255
1.9)
275 ( 2.2)
45
2.0
17 ( 2.4)
274 ( 1.4
281 ( 2.5)
46
2.0
26 ( 2.1)
252
1.7
269 ( 11)
29 ( 5.11)
4.,....
.9711
13 ( aildt)
23 ( 4.4)
281
02 1 2.21
$8t 1 Zill
244 SA
244
4.2
237 ( 2.3
101 ( 2.5)
15 ( 2.3)
24 ( 2.5)
273 ( 2.1)
21$ ( 5.9)
297 i
29 ( 1.9)
11 ( 1.5)
2$ ( 1.11
250 ( 2.4)
25$ ( 2.4)
248 ( 2A
32 ( 3.0)
$ ( 19)
21 ( 24)
255 ( 2.9)
""" ( ")
279 ( 3.8)
24 ( 2.0)
20 ( 13)
2e( 2.4)
297 ( 3.0)
28$ ( 12)
255 ( le)
39 ( 13)
10 ( 1.3)
20 ( 1.7)
289 ( 14)
289 ( 3.2)
283 ( 1.9)
33 ( 2.0)
18 ( 1.4)
26 ( 1.8)
274 ( 2.2)
278 ( 2.8)
26$ ( 2.6)
33 ( 1.8)
12 ( 1.0)
20 ( 1.5)
287 ( 2.1
280 ( 2.9)
278 ( 2.1)
29 ( 1.8
19 ( 1.3)
27 ( 1.5)
264 ( 2.8)
263 ( 2.5)
250 ( 10)
37 ( 13)
10 ( 1.4)
23 ( 1.1)
279 ( 2.1)
278 ( 3.9)
273 ( 1.5)
32 ( 1.6)
18 ( 1.2)
27 ( 1.5)
250 ( 1.7)
261( 24)
251 ( 24 )
22 ( 3.3)
.... i Hi
24 ( 3.2)
251 ( 4,15)
20 ( 3.2)
279 ( 29)
27 ( 2.2)
216 ( 2.0)
29 ( 3.0)
247 ( 4.2)
35 ( 2.5)
275 ( 2.0)
31 ( 2.0)
295 ( 1.4)
33 ( 2.7)
285 ( 2.0)
27 ( 1.7)
294 ( 1.9)
26 ( 2,1)
277 ( 1.a)
33 ( 2.3)
262 ( 1.8)
33 ( 2.1)
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).
THE 1990 NAB? TRIAL STATE ASSESSMENT
129
Montana
TABLE A20 I Students' Knowledge of Using Calculators
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAP TRIAL
ITATE ASSEISMENT
-
Itigh "Caloutater4iss" Group
_
Muir "Calaisier-tiar Ora.
MIK
State
Nation
sectanmsm
White
State
Nation
Nispani,
State
Nation
American Indian
State
Nation
TYPE Of COMMUNITY
Extreme nevi
State
Nation
Other
State
Nation
14 ( al)
2211 ( 1.4
VS
44 ( 141
21
277 ( 1.1
310
!:
2$4
4.2)
311
1 Loi
42)
ite 1 1
iii ( 43
OS (
43 ( 4.5)
57 ( 44)
285 ( 4.3)
11 ifti
.g
20 (12.0)
44. I ***)
sob ( )
51 ( 2.1)
41) ( 2.1)
243 ( 11)
272
2.1)
$0 ( 5.2)
61
5.4)
222 ( 44)1
241
42)1
( 2,9)
47 ( 2.5)
2e ( 4.7)
275 ( 1.11)
42 ( 1.4)
511 ( 1.4)
271 ( 19)
255 ( 2.0)
The standard errors of the estimated statistics appear in parentheses.
It can be said with about 95 percent
certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors
of the estimate for the sample.
Interpret with caution -- the nature of the sample does not allow accurate
determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
"
;
130
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A20
I
Students' Knowledge of Using Calculators
(continued)
I
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1300 NAEP TRIAL
I
E ASES
STAT
S SMENT
IRO "Ca twister-We" Group
"Calculator-Uses Grow
TOTAL
State
Nation
PARERTS' gpucAnc*
HS non-graduate
State
47 ( 8.4)
53 ( 8.4)
Nation
34 ( 3.31
40 ( 3.3)
24$ ( 4.4)
242 ( 2.4)
HS graduate
State
47 ( 2.4)
53 ( 2S)
Nation
40 ( 2.2)
40 ( 22)
Some college
,04Witkfte.
47.1
$ 15.11
1.3)
255 ( 14)
ColMge graduate
State
50 ( 2.7)
44 ( 2.7)
291 ( 1.8)
,
293 ( 2.2)
Nation
48 ( 2.0)
54 ( 2.0)
282 ( 2.1)
28$ ( 1.9)
GENDER
Male
State
51 ( 3.1)
49 ( 3.1)
291 ( 1.5)
277 ( 1.7)
Nation
39 ( 20)
61 ( 2,0)
274 ( 2.0)
258 ( 2,3)
Female
State
58 ( 24)
44 ( 24)
281 ( 14)
273 ( 2.0)
Nation
45 ( 1.8)
65 ( 14)
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 ± 2 standard errors
of the estimate for the sample.
*** Sample siu is insufficient to permit a reliable estimate (fewer than 62
studenu).
THE 1990 NAEP TRIAL STATE ASSESSMENT
131
Montana
TABLE A24
I Students' Reports on Types of Reading
I Materials in the Home
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
MO NAEP TRIAL
TE ASSEISMENT
STA
Zero to Two TYPits
_
Throw TYPIK
Fair TYiws
TQTAL
ParteillP
Priediewi
12 ( 0.7)
259 ( 2.1)
21 ( 1,0)
244 ( 2.0)
10 ( OA)
274 ( 2.2)
10 ( 1.1)
251 ( 22)
22 ( 7.0)
am. ( 641
44 ( 3.0)
237 ( 3.4)
20 ( 4.0)
249 ( 4.2)
29 (11.1)
em ( *#1
13 ( 1.0)
205 ( 3.2)
17 ( 4.9)
(
12 ( 1.0)
272 ( 2.8)
22 ( 1.5)
244 ( 2.6)
State
Nation
Bagainingan
State
Nation
Hispanic
State
Nation
Anworican
State
Nation
TYPE OF COMMUNITY
Extreme rural
State
Nation
Other
State
Nation
Pommies*
PrOakacv
32 ( 1.2)
277
30
1.0)
255
1.7)
31 ( 13)
251 ( 14)
29 ( 1.3)
( 1,5)
38 ( 8.3)
( +41
30 ( 2.4)
244 ( 4.3)
40 ( 5.0)
2S5 ( 4.3)
40 ( 4.9)
( 41
33 ( 14)
275 ( 2.2)
33 ( 3.2)
253 ( 43)t
33 ( 1.6)
278 ( 22)
30 ( 1.3)
259 ( 22)
Peromills
Proisiesty
52 ( 1.0)
266 ( 0.4)
48 ( 1.3)
272 ( 14!
511 ( 1.1
227 ( OA)
36 ( 1.3)
276 ( 1.7)
40 ( 5.4)
edne
.D40)
26 ( 2.3)
233 ( 2.4)
34 ( 5.6)
263 ( 4.4)4
31 ( 0.2)
gin
54 ( 1.6)
252 ( 14)
50 ( 5.1)
263 ( 5.6)1
55 ( 1.2)
258 ( 0.9)
48 ( 1.5)
272 ( 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 cautioii - the nature of the sample does not allow accurate
determination of the variability of this estir...ated mean proficiency. * Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
13k
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A24
I Students' Reports on Types of Reading
(continued)
Materials in the Home
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
10110 NAEP TRIAL
STATE ASSESSMENT
Zero to Two Typos
Three Types
Four npos
TOTAL
Peramags
ftellolenay
0101280011
aid
Prailkamay
State
12 ( 0,7)
32 ( 12)
( 2.1)
277 ( 1,6)
Nation
21 ( 1.0)
30 ( 1.0)
244 ( 2,0)
258 ( 1.1)
PARENTS' FOUCATKIN
Hil nan-graduate
State
26 (
*FR ( 4.8)
111**)
43 ( 6.3)
Nation
47 ( 4.0)
28 ( 3.0)
240 ( 3.4)
243 ( 3.3)
NI graduate
State
17 ( 1.5)
37 ( 2.6)
262 ( 3.8)
272 ( 3.1)
Nation
26 ( 22)
33 ( 1.9)
248 ( 22)
253 ( 2.7)
8ortw college
State
11 ( 1.3)
38 ( 2.()
271 ( 4.8)
282 ( 2.5)
Nation
17 ( 1.5)
32 ( 1.7)
251 1 4.0)
282 ( 2.8)
Coif's. graduate
State
8 ( 0.9)
25 ( 1.8)
281 ( 3.7)
281 ( 2.5)
Nation
10 (
254 (
0.8)
2.8)
28 ( 1.8)
2es ( 2 5)
GENDER
Male
State
12 ( 0.9)
33 ( 1.5)
273 ( 24)
281 ( 2.3)
Nation
21 (
1.5)
31 ( 1.5)
244 ( 2.3)
259 ( 2.1)
State
12 ( 1.1)
32 ( 1.9)
286 ( 3.5)
273 ( 2.0)
Nation
22 (
1.2)
29 ( 1.4)
244 ( 2.2)
251 ( 1.9)
PINVINIMOS
Pnii0411019
55 (1
( 0.11
411 ( 1.3
'272 ( 15)
!it
4.3)
25 I 24
246 ( 33)
45 ( 2.6)
274 ( 1.9)
40 ( 1.7)
260 ( 2.1)
SO ( 2.3)
266 ( 2.0)
51 ( 2.0)
274 ( 1.9)
87 ( 1.5)
290 ( 1.2)
82 ( 2.0)
280 ( 1.8)
55 ( 1,3)
288 ( 1.1)
48 ( 1.4)
273 ( 2.0)
58 ( 1.7)
262 ( 1.4)
49 ( 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 ± 2 standard errors
of the estimate for the sample.
*** Sample size is insuricient to permit a reliable estimate (fewer than 62
students).
1
S
THE 1990 NAEP TRIAL STATE ASSESSMENT
133
Montana
TABLE A25
I Students' Reports on the Amount of Time Spent
I Watching Television Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1890 NAEP TRIAL
STATE ASSESSMENT
_
One Hour or
Less
Two Hours
I Three Koos
I
Far t o Rye
Hass
Six Heirs or
More
TOTAL
Poosalage
sad
ProOdeng
21 ( 0.9)
22012
0141
209 ( 2.2)
22 ( 0.9)
292 ( 1.4)
13 ( 1.0)
276 ( 2.5)
14 ( 4.1)
eke ( 441
14 ( 2.4)
fro
*on
12 ( 3.0)
*al
13 ( 5.0)
glio)
19 ( 1.8)
285 ( 3.3)
tio*
*al
21 ( tO)
292 ( 1.6)
12 ( 1.0)
268 ( 2.6)
Pereadage
Pidialency
$0 ( 1.2)
285 ( 12)
21 ( 0.9)
26$ ( 14)
30 ( 1.3)
267 ( 1.1)
23 ( 1.2)
275 ( 2.2)
22 ( 6.4)
tnielt
20 ( 2.5)
245 ( 3.2)
25 ( 3.1)
17 ( $A)
4,to
,po)
28 ( 1.4)
282 ( 1.8)
30 ( 1.8)
266 ( 1.7)
21 ( 1.0)
209 ( 2.3)
Veresolage
ad
Paddatcy
24 ( 1.0)
27$ ( 1.2)
22 ( OA)
265 ( 1.7)
24 ( 1.1)
281 ( 1.2)
24 ( 1.1)
272 ( 1.9)
27 ( 5.6)
oo)
19 ( 2.4)
242 ( 5.6)
25 ( 3.7)
.6.0*
doo)
21 (10.5)
27 ( 1,5)
276 ( 1.7)
22 ( 1.3)
278 ( 1.9)
23 ( 12)
265 ( 2.1)
Paromaile
and
Prolkisacy
20 ( 1.1)
275 ( 1.6)
26 ( 1.1)
260( 1.7)
19 ( 1.1)
276 ( 1.6)
27 ( 1.4)
267 ( 1.7)
31 ( 3.1)
247 ( 3.5)
25 ( 3.7)
254 ( 5.4)1
thio ( too)
( 1.7)
271 ( 3.0)
26 ( 2.7)
256 ( 3.6)1
20 ( 1.5)
277 ( 1.8)
27 ( 1.2)
250 ( 2.2)
liersemlaga
aM
Prollaisocy
( 0.6)
261 ( 24)
16 ( 1.0)
245 ( 1.7)
5 ( 0.6)
264 ( 3.4)
12 ( 1.2)
253 ( 2.6)
10 ( 3-5)
do. ( ..00)
17 ( 1.7)
236 ( 3.8)
13 ( 3.3)
.441
.4o)
5 ( 1.0)
254 ( 4.6)
7 ( 0.7)
263 ( 3.7)
17 ( 1.4)
246 ( 2.5)
State
Notion
RAa
HNIC1TY
White
State
Nation
Hispanic
State
Nation
American Indian
State
Nation
TYPE OF COMMUNITY
Extreme rural
State
Nation
Other
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 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.
*I'. Sample size is insufficient to permit a
reliable estimate (fewer than 62 students).
1
134
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A25 I Students' Reports on the Amount of Time Spent
(continued)
I Watching Television Each Day
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROPCIENCY
1910 NAV TRIAL
STATE ANIESSUEXT
,
Ono Noir sr
Lass
Illso Hours
Theo Hours
Four 10 Ms
Hours
lb( Hours or
Moro
191A
State
Nation
26BIBILENSAM?N
HS nor-grodusto
State
Nation
HS aroduste
State
Nation
S ense caego
State
Nation
College grockato
State
Nation
GENIX4
M.
State
Nation
FonsaIo
State
Nation
24,011fory
21
12 (
111.11
1$ (
210 (
1 (
240 (
17 (
295 (
10 (
11**
24 (
294 (
17 (
262 (
18 (
293 (
11 (
269 (
23 (
267 (
14 (
269 (
Parlislonsr
ad
PrOsisnew
Prelbelsw
aNd
Prallelsowi
021
f
OA)
2.2)
51)
2.2)
OH)
2.9
1.0
4.7)
2.0)
3.1)
1.4)
INk11)
1.5)
2.0)
1.3)
2.6)
1.3)
2.3)
0.9)
3.3)
1.6)
1.9)
1.1)
23)
la)
316
12)
21
0.9)
2111
1.1)
24 ( 4.11
It* (
20 ( 3,1)
,m
*es)
23 ( 2.0)
275 ( 3.0)
17 ( 1.4)
257 ( 23)
36 ( 2.0)
2111 ( 3.4)
25 ( 2.4)
275 ( 2.7)
31 ( 2.3)
269 ( 1.7)
22 ( 1.6)
260 ( 2.5)
28 ( 1.8)
268 ( 1.7)
22 ( 1.2)
207 ( 2.6)
31 ( 2.2)
251 ( 2.4)
20 ( 1.3)
269 ( 2.2)
( 12
11
22 ( 01
201 (1.
20 ( 3.9)
21 ( 21)
29 ( 2.4)
371 ( 2.0)
23 ( 2.0)
220 ( 32)
22 ( 22)
240 ( 2.?)
23 ( 2.6)
2.0 ( 3.5)
23 ( 1.5)
263 ( 2.1)
23 ( 1.1)
277 ( 2.2)
25 ( 2.0)
279 ( 1.7)
22 ( 1.0)
267 ( 22)
23 ( 1.6)
276 ( 1.7)
23 ( 1.4)
264 ( 1.8)
IA)
276
1.6)
21
1.1)
2410
1.7)
21 ( 4.7)
( *el
2$ ( 2.9)
244 ( 32)
22 (
291
2.9
321 2.3
253 ( 23)
22 ( 2.0)
275 ( 2.0)
26 ( 2.2)
261(23)
17 ( 1.8)
282 ( 2.8)
25 ( 1.5)
270 ( 2.4)
22 ( 13)
261 ( 2.1)
2$ ( 1,3)
262 ( 2.1)
18 ( 1.6)
267 ( 23)
26 ( 1.6)
258 ( 1.9)
6( 0.41)
201 ( 22)
16 ( 1.0)
245 ( 11)
14 ( 3.0)
( .41
20 ( 3.4)
ok
( 1.6)
.1*. 0441
19 ( 1.6)
( 3.0)
5 ( 1.4)
44. (
14 ( 1.5)
242 ( 3.4)
et* (
12 ( 1.1)
255 ( 32)
( 1.0)
246 ( 4.6)
17 ( 1.5)
248 ( 2.5)
5 ( 0.8)
15 ( 12)
241 ( 22)
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).
THE 1990 NAEP TRIAL STATE ASSESSMENT
135
Montana
TABLE A26 I Students' Reports on the Number of Days of
School Missed
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1800 NAEP 'TRIAL
STATE ASSESSMENT
None
Ono or Two Days
Throe DIP or More
TOTAL
istionlaips
ard
Prato"
40( 13)
State
284 ( 1.4)
Nation
4$ ( 1.1)
( 13)
WE/ETHNICITY
Mite
State
41 ( 1.5)
210 ( 14)
Nation
43(1.2)
273 ( 19)
Hispanic
State
29 ( 7.1))
Nation
41 ( 3.3)
245 ( 4.6)
American Indian
State
20 ( 4.4)
263 ( 5.3)1
Nation
23 ( 0.6)
TYPE OF COMMUNITY
Extreme rural
State
41 ( 2.3)
281 ( 1.9)
Nation
43 ( 4.4)
257 ( 4.1)I
Other
State
40 ( 1.7)
288 ( 1.9)
Nation
45 ( 1.3)
285 ( 2.2)
fleumires
and
Prallolow
214
2:1111( 1,5)
Parsiolsia
awl
4Prallakmay
30 ( 1.3)
20 ( OM
2115 ( 02)
( la)
34 ( 1.2)
23 ( 12)
272 ( 1.7)
251 ( 2.1)
54 ( 0.5)
17 ( 4.7)
cm.
.14./
( 44)
32 ( 22)
27 i 2.6)
250 ( 3.3)
295 ( 3.1)
31 ( 5.7)
37 ( 4.0)
240 ( 4.4)
250 ( 3.9)
39 ( 5.1)
M 5.2)
4,41
40 ( 1.9)
278 ( 1.8)
32 ( 4.2)
244 ( 6.8)l
38 ( 1.7)
283 ( 1.3)
32 ( 1.1)
2418 ( 1.8)
19 ( 2.0)
209 ( 3.4)
25 ( 3.9)
*41
22
09)
273
2.5)
2?
1.1)
251 ( 24)
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).
136
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A26
I Students' Reports on the Number of Days of
(continued)
School Missed
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
1NO NAEP TRIAL
STATE ASSESSMENT
None
One or Two Days
Three Days or Mora
TOTAL
Portents.
awl
Proficiency
State
40 < 1.3)
244 ( 1.4)
Nation
45 ( 1.1)
266( 1.8)
PARENTS EDUCATION
NS non-gracklate
State
33 ( 5.0)
Nation
36 ( 3.2)
245 ( 3.0)
HS graduate
State
43 ( 2.8)
277 ( 1.3)
Nation
43 ( 2.1)
255 ( 2.0)
Some college
State
36 ( 2.3)
284 ( 3.7)
Nation
40 ( 1.8)
270 ( 3.0)
College graduate
State
42 ( 2.1)
290 ( 1.9)
Nation
51 ( 1.8)
275 ( 2.1)
GENDER
Male
State
44 ( 1.6)
287 ( 1.5)
Nation
47 ( 1,8)
( 2.0)
Female
State
36 ( 2.2)
281 ( 1.7)
Nation
43 ( 1.4)
264 ( 23)
iterundsle
*WI
Proliciemy
SO
262
1.0
32 00
200
1.5)
34 ( 5.4)
26 ( 3.1)
249 ( 3.3)
36 ( 2.6)
271( 2.2)
31 ( 1.9)
257 ( 2.6)
43 ( 2.4)
267 ( 1.4)
37 ( 1.6)
271 ( 2.5)
30 ( 2.5)
286 ( 1.6)
33 ( 1.2)
277 ( 1.7)
36 ( 1.4)
283 ( 1,8)
31 ( 1.4)
287 ( 2.1)
42 ( 1.7)
280 ( 1.5)
32 ( 1.1)
< 1.7)
Porasula.
and
Prolk4oky
21 ( 0.11)
272 ( 2.0)
23 < 1.1)
250 ( 1.0)
33 ( 4.5)
38 ( 63)
237 ( 3.1)
22 ( 2.8)
250( 4.1)
27 ( 1.0)
249 ( 2.4)
21 ( 2.1)
273 ( 2.6)
23 ( 1.6)
253 ( 3.1)
10 (
1.5)
264 ( 2.3)
16 ( 1.3)
2155 ( 3.1)
21 ( 1.4)
278 ( 3.5)
22 ( 14)
250 ( 2.6)
22 (
1.3)
208 ( 2.4)
25 ( 1.3)
250 ( 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).
THE 1990 NAEP TRIAL STATE ASSESSMENT
137
Montana
TABLE A27
I Students' Perceptions of Mathematics
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
IWO NAEP TRIAL
STATE ASSESSMENT
Womb/ Agree
AV
Undecided, Disagree,
Siren* Disagree
Jr
TOTAL
Pers1966.1
and
Pre lolsogy
Peramines
adi
Prelicidecy
liertediage
and
Prdidefacy
State
30 ( 1A)
50 ( 1.4)
20 ( 1.1)
202 ( 1.2)
278 (.1.0)
267 ( 1.6)
Nation
27 ( 1.3)
49 ( 1.0)
24 ( 1.2)
271 ( 13)
262 ( 1.7)
251 ( 1.8)
RACEIETHNiCITY
%Mite
State
30 ( 1.4)
51 ( 1.5)
111 ( 1.1)
204, ( 1.2)
262 (
1.0)
271 ( 1.4)
Nation
28 ( 1.8)
43 ( 1.3)
26 ( 13)
279 ( 2.0)
272 ( 1.8)
257 ( 2.0)
NisPank
State
38
41 ( 4.5)
..64)
45 ( 7.0))
17 ( 4.9)
rtm,)
Nation
24 ( 23)
( 2.6)
28 ( 2.1)
257 ( 5.5)
244 ( 2.2)
230 ( 3.8)
American Imilan
State
28 ( 5.2)
40 ( 4.2)
33 ( 43)
( **I )
256 ( 4.3)
247 ( 4.4)1
Nation
1
23
*OA ( 7.4)
(
48
.pw (14.9)
.44)
29
(mtip ( 9.5)
04*)
TYPE Of COMMUNITY
EN:trent* mai
State
32 ( 3.5)
47 ( 2.8)
21 ( 23)
287 ( 1.4)
278 ( 2.1)
265 ( 3.0)
Nation
34 ( 2.8)
49 ( 2.2)
17 (
;.4)
270 ( 3.9)1
262 ( 4.1)1
......
(
...**)
ONW
State
29 ( 03)
52 ( 1.8)
19 ( 1.2)
204 ( 1.7)
260 (
1.2)
268 ( 13)
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 stanrlard 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).
/
138
THE 1990 NAEP TRIAL STATE ASSESSMENT
Montana
TABLE A27
I Students' Perceptions of Mathematics
(continued)
I
PERCENTAGE OF STUDENTS AND
AVERAGE MATHEMATICS PROFICIENCY
,
1990 NAEP TRIAL
STATE ASSESSMENT
StroisidY *Rim
AV.*
Undecided, Disagree,
Stanch Ditumiree
TOTAL
Mi
Pm Galaxy
PgrailleaP
and
PireNdage
sod
941414811Cy
State
30 ( 1.4)
50 ( 14)
20 ( 1.1)
292 ( 12)
279 ( 1.0)
267 ( 1A)
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
19 (
***
3.7)
***
43 (
.44 ( 4.3)
441
37 ( 4.3)
41
Nation
20 ( 2,6)
50 ( 3.3)
30 ( 3.6)
*44 (
*AM)
243 ( 2.6)
238 ( 4.3)
HS graduate
State
23( 2.3)
54 ( 2.5)
23 ( 1.9)
285 ( 2.2)
270 ( 2.0)
261 ( 3.7)
Nation
27 ( 2.1)
47 ( 2.3)
26 ( 2.0)
262 ( 2.7)
255 ( 2.3)
245 ( 2.4)
Some college
State
34 ( 2.3)
49 ( 2.6)
17 ( 2.3)
294 ( 2.7)
261 ( 2.1)
268 ( 2.9)
Nation
26 ( 2.5)
47 ( 2.4)
25 ( 1.8)
274 ( 3.1)
267 ( 1.9)
258 ( 3.2)
College graduate
State
34 ( 2.1)
51 ( 2.0)
15 (
1.4)
295 ( 1.5)
265 ( 1.4)
276 ( 2.5)
Nation
30 ( 2.3)
51 ( 18)
19 (
1.6)
280 ( 2.4)
274 ( 2.2)
296 ( 2.5)
GENDER
Mal.
State
30 ( 1.6)
50 ( 2.0)
20 ( 1.7)
295 (
1.4)
282 ( 1.7)
271 ( 1.9)
Nation
26 (
1-5)
48 ( 1.2)
24 ( 1.4)
273 ( 2.3)
263 ( 2.0)
251 ( 2.4)
Female
State
30 ( 2.2)
51 ( 2.1)
19 ( 1.7)
289 (
1.7)
27$ ( 1.4)
2133 ( 2.5)
Nation
26 ( 1.7)
50 ( 1.7)
25 ( 1.9)
269 ( 2.1)
262
1.8)
252 ( 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 insufficient to permit a reliable estimate (fewer than 62
students).
4 4
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 (ETS), 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 considerable
contributions to the program, especially its management of the National Assessment Planning Project. That
project resulted in the mathematics framework and objectives for the assessment and recommendations
about reporting the results of the program. In particular, we note the significant contributions of Ramsay
Selden, 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 deseive
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 interpreting the results.
Under the NAEP contract to ETS, Archie Lapointe served 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 services. 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 processing of the materials were the responsibility of NCS, under the direction
of John O'Neill and Lynn Zaback.
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 generation 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 Ku lick, 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 Koffler wrote the text for the report.
Kent Ashworth was responsible for coordinating the cover design and fmal 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.
U.S. GOVERNMENT PRINTING OFFICE 1491 0 - 293-276 QL 8 WK. 22)
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