ED 330 580 INSTITUTION SPONS AGENCY DOCUMENT RESUME SE 052 090 The State of Mathematics Achievement in Texas: The Trial State Assessment at Grade Eight. Educational Testing Service, Princeton, N.J.; National Assessment Princeton, NJ. National Center for Washington, DC. REPORT NO ETS-21-ST-02; IS3N-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) of Educational Progress, Education Statistics (ED), 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 Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing . IDENTIFIER National Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; *Texas; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In Texas, 2,542 students in 101 public schools were assessed. This report describes the mathematics proficiency of Texas 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 far 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 1,ackground of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, Texas students had an average proficiency of 258 compared to 261 nationwide. Many fewer students (Texas-10%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achie ment in TEXAS The Trial State Assessment at Grade Eight THE NATION'S REPORT I CARO I IN BEST COPY AVAILABLE U 5 DEPARTMENT OF EDUCATION Oztse crt rth.atooar fiersearcr, and fmurovement U)I'C TI0NA RNOURCFS INFORMATION CFNTFR tERICt n's dot ument Ras Peen reproduced as Irom Me person or Organization onginatmg r Manor changes nave peen made to tmprOrd reproctuct.on Clualitv Ponts ot vie* or oPrnons stated fn th,sdccu ment do not necessann, reforeSent C"C191 poston or p(mcv Prepared by Educational Testing Senme under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education 2 What is The Nation's Reaort Card? THE NATION'S REPORT CARD, the National Assessment of Educational Progress (NAEP), is the only nationally representative and continuing assessment of what America's students know and can eao in various subject areas. Since l9fi9. te.sessments have been conducted periodically in reading, mathematics. science, writing, history/geography, and other fields. By making objective information on student performance available to policymakers at the national, state, and local levels. NAEP is an integral part of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics. the U.S. Department of Education. The ('ommissioner of Education Statistics is responsible, by law, for carrying out the NAEP project through competitive awards to qualified organi/ations. NAEP reports directly to he Commissioner, who is also responsible for providing continuing reviews, including validation studies and ..olicitation 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 subject areas to be 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 or the National Assessment; and ensuring that all items selected for use in the National Assessment are free from racial, cultural, gender. or regional bias. The National Assessment Governing Board Richard A. Boyd, Chairman Executive Director Martha Holden Jennings Fotmdation Cleveland, Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.O.C.L.S. Saratoga Springs. New York Franck Alexander Associate Superintendent California Department of Education Sacramento, California David P. Battini High Schist)! 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. Boehlje Attorney Gaass. Klyn. & Boehlje Pella. [owl, Linda R. Bryant Teacher Greenway Middle School Teacher Center Pittsburgh. Pennsylvania Honorable Michael N. Castle Governor of Delaware Curvet State Office Building Wilmington. Delaware Honorable Naomi K. Cohen State ot Connecticut House of Representatives Legislative Office Building Hartfold, Connecticut Chester E. Finn, Jr. Professor of Education and Public Policy Vanderbilt University Washington, D.C. Michael S. Glode Wyoming State Board of Education Saratoga, Wyoming Christine Johnson Principal Abraham Lincoln High School Denver. Colorado John Lindley Principal South Colby Elementary School Pi...! Orchard, Washington Carl J. Moser Director of Schools The Lutheran Church - Missouri Synod International Center St. Louis, Missouri Mark D. Musick President Southern Regional Education Board Atlanta. Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith. Arkansas Matthew W. Prophet. Jr. Superintendent Portland Oregon School District Portland. Oregon Honorable William T. Randall Commissioner of Education State Department of Education Denver, Colorado Dorothy K. Rich President Home and Schixil Institute Special Projects Office Washington, D.C. Honorabk Richard W. Riley Attorney Nelson. Mullins, Riley and Scarborough Columbia. South Carolina Thomas Topuzes Attorney Law Offices of Frank Rogoiienski Coronado, California Herbert J. Walberg Professor of Education University of Illinois Chicago, Illinois Assistant Secretary for Educational Research and Improvement t Ex -Officioi U.S. Department of Education Washington. DC Roy Truby Executive Director. NAGB Washington. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement In TEXAS The Trial State Assessment at Grade Eight 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 US. 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 available directly from the participating States. For ordeling information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or cal11-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). library of Central, Catalog Card Number: 91-61478 ISBN: 04868544-9 The work upon which this publication is based was performed for the National Carter for Education Statistics. Office of Educational Research and Improvement, by Educational Testing Service. Eduestienal Testing Service is an equal opporturtityftffinnstive action employer. Educational Testing Servicc, ETS, and are registered uidanarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of Texas 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Profieent in Mathematics Are Eighth-Grade Students in Texas Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 Levels of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race/Ethnicity 24 Type of Community 27 Parents Education Level 29 Gender 31 Content Area Performance 13 THE 1990 NAEP TRIAL STATE ASSESSMENT !11 PART TWO Finding a Context for Understanding Students/ Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics' 39 Cuniculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Thliveral" 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instructwri 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 Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 7 iv THE 1990 NAEP TRIAL STATE ASSESSMENT Texas THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1985, 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 assessme! rt-, that NAEP has conducted since its inception. 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 twelv?.. For the Trial State Assessment, eighth-grade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the 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. THE 1990 NAEP TRIAL STATE ASSESSMENT Texas In Texas, 101 public schools participated in the assessment. The weighted school participation rate was 97 percent, which means that all of the eighth-grade students in this sample of schools were representative of 97 percent of the eighth-grade public-school students in Texas. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 5 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 8 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 2 percent and 5 percent of the population, respectively. In total, 2,542 eighth-gade Texas 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 Texas. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from Texas on the NAEP mathematics scale is 258. This proficiency is no different from that of students across the nation (261). Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal specffically 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-gxade students to define the skills, knowledge, and understandings that chalacterize four levels of mathematics performance -- levels 200, 250, 300, and 350 on the NAEP scale. 9 2 THE I990 NAEP TRIAL STATE ASSESSMENT Texas In Texas, 97 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning Ind problem solving with whole numbers (level 200). However, many fewer students in Texas (10 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; Gmmetry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in Texas performed comparably to 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 Texas eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In Texas: White students had higher avei age mathematics proficiency than did Black or Hispanic students. Further, a greater percentage of White students than Black or Hispanic students attained level 300. The results by type of community indicate that the average mathematics performance of the Texas students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural areas, or areas classified as "other". In Texas, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 30 points higher than that of students whose parents did not graduate from high school. The results by gender show that there appears to be no difference in the average mathematics proficieney of eighth-grade males and females attending public schools in Texas. In addition, there was no difference between the percentages cf males and females in Texas who attained level 300. Compared to the national results, females in Texas perfo-med lower than females across the country; males in Texas performed no differently from males across the country. THE 1990 NAEP TRIAL STATE ASSESSMENT 3 Texas 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 Texas are as follows: About three-quarters of the students in Texas (77 percent) were in schools where mathematics was identified as a special priority. This is about the same percentage as that for the nation (63 percent). In Texas, 85 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 1 exas were taking eighth-grade mathematics (72 percent) than were taking a course in pre-algebra or algebra (26 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 Texas spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent 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 emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 1 1 4 THE 1990 NAEP TRIAL. STATE ASSESSMENT Texas In Texas, 20 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 29 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Texas, 19 percent of the students never used a calculator to work problems in class, while 51 percent almost always did. In Texas, 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 nation. About three-quarters of the students (73 percent) had teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in Texas who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of these materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. Some of the eighth-grade public-school students in Texas (13 percent) watched one hour or less of television each day; 15 percent watched six hours or more. Avtrage mathematics proficiency was lowest for students who spent six hours or more watching television each day. THE 1990 NAEP TRIAL STATE ASSESSMENT 5 Texas INTRODUCTION THE NATION'S REPORT CARD 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 Februaiy 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West VirOnia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Texas This report describes the performance of the eighth-grade public-school students in Texas and consists of three sections: This Irtroduction provides background information about the Trial State Assessment and this report. It also provides a profile of the eighth-grade public-school students in Texas. Part One describes the mathematics performance of the eighth-grade public-school students in Texas, the West region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Texas, 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 tune 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)(1) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(i))) As a result of the legislation, the 1990 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 t.tate or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 14 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patteme after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP throu3h June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council of Chief State School Officers in rind-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,' the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the wades for the national program, the fmal 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-gxade public-school students in Texas, in the West region, and for the nation. Results also are provided for groups of students defmed by shared characteriitics -- race/ethnicity, type of community, parents' education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for Texas are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the regton of the country are based on the nationally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. 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. 3 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 9 Texas RACE/ETHNICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on caiteria 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 Texas. 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 metropo;tan statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The 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 finish 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. 6 10 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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 Figure I. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. THE NATION'S REPORT CARD FIGURE 1 I Regions of the Country NORTHEAST SOUTHEAST CENTRAL WEST Connecticut AlabaNi Illinois Alaska Delaware Arkansas Indiana Arbxma District of Columbia nark la Iowa California Maine Georgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana Now Jersey North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohio Oklahoma Rhode island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming 17 THE 1990 NAEP TRIAL STATE ASSESSMENT 1 1 0. Texas Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual background questions. 7,t 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 ofeighth 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 conider both the magnitude of the difference "ixtween the means or propertions 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 a-s 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 between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not con*ain the value zero. When a statement indicates that the average proficiency orproportion ef 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 it greater detail in the Procedural Appendix. 12 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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 proficiemcies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT 13 Texas Profile of Texas EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in Texas, the West region, and the nation. This profile is based on data collected from the students and schools participating in the Trial State Assessment. TABLE 1 I Profile of Texas Eighth-Grade Public-School 1 Students PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Texas West Nation DEMOGRAPHIC SUBGROUPS Percentage Percentage Percentage Race/Ethnicity White 47 ( 2.1) 63 ( 1.9) 70 ( 0.5) Black 13 ( 1.3) ( 2.0) 16 ( 0.3) Hispanic 36 ( 2.1) 21 ( 1.5) 10 ( 0.4) Asian 2 ( 0.0) 4 ( 1.3) 2 ( 0.5) American Indian 1 ( 0.2) 4 ( 2.3) 2 ( 0.7) Type at Community Advantaged urban 1$ ( 3.4) 14 ( 8.5) 10 ( 3.3) Disadvantaged urban 17 ( 3.6) 19 ( 7.5) 10 ( 2.8) Extreme rural 9 ( 2.8) 10 ( 3.6) 10 ( 3.0) Other 59 ( 5.3) 56 (10.1) 10 ( 4.4) Parents Eckscation Did not finish high school 17 ( 1.1) 10 ( 1.3) 10 ( 0.8) Graduated high school 23 ( 1.1) 19 ( 2.5) 25 ( 1.2) Some education after high school 15 ( 0.8) 16 ( 1.2) 17 ( 0.9) Graduated college 34 ( 1.5) 42 ( 4.0) 30( 1.9) Gender Male 50 ( 1.0) 55 ( 2.1) 51 ( 1.1) Female 50 ( 1.0) 45 ( 2.1) 49 ( 1.1) 411111INIMM 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 RacelEthrt..city may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 20 14 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Texas schools and students sampled for the 1990 Trial State Assessment. In Texas, 101 public schools participated in the assessment. The weighted school participation rate was 97 percent, which means that all of the eighth-grade students in this sample of schools were representative of 97 percent of the cighth-grade public-school students in Texas. TABLE 2 1 Profile of the Population Assessed in Texas EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution Weighted school participation rate after substitution Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating schools 107 4 92 10 101 EIGHTH-GRADE PUBLX-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 Parcentage 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 96% 3,049 196 5% 2% a% 5% 2,657 2,542 In Texas, one school in the original sample initially declined and then decided to participate after a substitute for that school had been provided. Although the substitute school also participated. estimates are based on the -Ile including the original school and not the substitute school. 0 1. THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Texas In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 5 percent of the eighth-grade public-school population was classifiet. as Limited English Proficient (LEP), while 8 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assesqment, a student had to be categorized as Limited English Ptoficient 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 cr.: had an IEP represented 2 percent and 5 percent of the population, respectively. 'n total, 2,542 eighth-grade Texas 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 Texas. 2 2 16 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Texas Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Nurnbz.rs 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 Texas. Chapter 1 compares the overall mathematics performance of the students in Texas 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' overall mathematics performance for subpopulations defined by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. 0 i".,) t.) THE 1990 NAEP TRIAL STATE ASSESSMENT 27 Texas CHAPTER 1 Students' Mathematitl Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from Texas on the NAEP mathematics scale is 258. This proficiency is no different from that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School 1 Mathematics Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for earl population of interest is within t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-4-1), If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 Differences reported are statistically different at about the 95 percent certainty 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. 2 4 18 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of %hat 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 NAEF scale. To defme 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 defming 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 define 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 arc based solely on stuck= 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 Texas, 97 percent of the eighth graders, compared to 97 percent in thc nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in Texas (10 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 Texas, West region, and national results for each content area, Students in Texas performed comparably to students in the nation in all of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 Texas FIGURE 3 I Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships Involving whole numbers. They can sOive 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-diglt number in a list. In measurement, these Students can reed a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numerical sentences and extend simple pattern sequences. LEVEL 250 Simple Multiplicative Reasoning and Two-Step Problem Solving Studemrt at this level have co:tended 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 measure=nt 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 probability. In algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions. 9 6 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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 fractions and decimals, including pictorial representations. They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expressions, including those with exponents and negative integers. In measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sami. le bias. In algebra, they can graph points in the Cartesian plane and parrot m simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open linear sentences and inequalities by substitution, and checking and graphing an interval representing a compound inequality when it is described in words. They can determine and apply a rule for simple functional relations and extend a numerical pattern. LEVEL 350 Reasoning and Problem Solving Involving Geometric Relathmships, Algebraic Equations, and Beginning Statistics and Probability Stuuents at this level have extended their knowledge of number and algebraic understanding to include some properttes of exponents. They can recognize scientific notation In a calculator and make the transition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles 7Iva, problems. They can find the zircumferences of circles and the surface areas of solid figure In geometry, they can apply the Pythagorean theorem to solve proNems involving indirect measurement. These students also car, apply their knowledge of the properties of geometric figures to solve problems, such as determining the slop-. of a line. In data analysts, these students can compute means from frequency tables and determine the probability of a simple event, In algebra, they can identify an equation describing a linear relation provided in a table and solve literal equations and a system of two linear equations. They ore developing an understanding of linear functions and their graphs, as well as functional notation, including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. THE 1990 NAEP TRIAL STATE ASSESSMENT 21 Texas 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 0 20 40 60 so 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by H-I). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2S 22 THE 1990 NAEP TRIAL STATE ASSESSMENT 0 ( 0.1) 0 ( 0.4) 0 ( 0.2) 10 ( 0.9) 12 ( 2.4) 12 ( 1.2) SS ( 1.8) 83 ( 2.8) 84 ( 1.6) 97 ( 0.6) 97 ( 1.0) 97 ( 07) Texas FIGURE 5 I Eighth-Grade Public-School Mathematics I Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation 0 200 225 250 275 300 Averse, Proficiency 262 ( 1.2) 244 ( 2.0) 266 ( 1.4) 253 ( 1.4) 258 ( 3.0) 258 ( 1.7) 258 ( 1.4) 20( 2.6) 250 ( 1.4) 256 ( 1.7) 262 ( 3.6) 262 ( 1.8) 258 ( 1.5) 259 ( 2.4) 260 ( 1.3) 500 MatMinattes Subsea!" Proftelonty 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 1-14). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. AmWr THE 1990 NAEP TRIAL STATE ASSESSMENT 23 Texas 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 perfomiance results for White, Black, and Hispanic students from Texas are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black or Hispanic students. Figure 7 presents mathematics performance by proPciency levels. The figure shows that a greater percentage of White students than Black :-/r Hispanic students attained level 300. 30 24 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas FIGURE 6 I Average Eighth-Grade Public-School Mathematics Proficiency by Race/Ethnicity * '.'tk> 10414: 10410fi 0: Texas White Black Hispanic west White Black Hispanic Nation White Black Hispanic ':'14; s N , so. I is) sas its) t *Ai 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 P+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. 31 THE 1990 NAEP TRIAL STATE ASSESSMENT 25 Texas 111E NATION'S REPORT FIGURE 7 1 Levels of Eighth-Grade Public-School CARD I Mathematics Proficiency by Race/Ethnicity LEVEL 300 Stat. White Black Hispanic Region White Black Hispanic Nation White Black Hispanic LEVEL 250 State White Black Hispanic White Black Hispanic Nation White Black Hispanic LEVEL 200 Stat. White Black Hispanic Region White Black Hispanic Nation White Black Hispanic 0 20 40 60 80 Parcintaga at or Abova Proficloncy Lents 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 11-0-1). 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. 1 00 32 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 111 ( 1.5) 1 ( 0.5) 3 ( 0.7) 16 ( 3.2) ( 5.0)1 3 ( 1.6) 15 ( 1.5) 2 ( 1.3) 3 ( 1.1) 79 ( 1.6) 25 ( 2.7) 42 ( 2.3) 74 ( 3,3) 44 (12.9)1 41 ( 5.4) 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) ( 0.3) 2.1) 05 ( 1.4) se ( 0.8) N ( 3.0)1 93 ( 2.0) at) ( 0.4) 19 ( 3.1) 93 1 6 ) Texas TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, &advantaged urban areas, extreme ntral areas, and areas classified as "other". (These ate the "type of community" groups in Texas with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Texas students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural areas, or areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community Tams Advantaged urban Disadvantaged u, ban Extreme rural 1-thwavol Itag Other went Advantaged urban 11,4 tkiji Disadvantaged urban Ai (.30 Extreme rural IN ( 1.3$ Other t $4) Nation Advantaged urban 4 ,011 Disadventaged urban NIP .1 SS, Extreme rural IN 1,4.1$ Other 141 The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is withth ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1.4-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 Texas FIGURE 9 LEVEL 300 litats Adv. urban Dtsadv. urban Ext. rural Other Region Adv. urban Dtsadv. urban Ext. rural Other Nation Adv. urban Dtsadv. urban Ext. rural Other LEVEL 250 State Adv. urban Otsadv. urban Ext. rural Other Regkin Adv. urban Otsadv. urban Ext. rural Other Nation Mv. urban Dtsadv. urban Ext. rural Other LEVEL 200 State Adv. urban Dlsadv. urban Ext. rural Other Region Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proftciency by Type of Community 20 ( 3.3)1 ( 1.3)1 10 ( 2.5)1 ( 1.1) 31 ( 3.1)1 ( 3.5)1 ( 4.3)1 10 ( 1.8) 26 ( 4.8)1 ( 2.1)1 ( 2.3)1 12 ( 1.2) 62 ( 2.9)1 a ( 3.4)1 16 ( 5.1)1 ( 2.4) 13 ( 3.3)1 57 ( 8.0)1 62 (12.8)! 62 ( 5.0) 83 ( 4.6)1 4$ ( 5.0)1 511 ( 8.2)1 64 ( 2.3) 100 ( 0.0) s-104 96 ( 1-2)i ( 1.4)1 97 ( 1.0) 0 20 40 80 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the valuz for each population of interest is within ± 2 standard errors of the estimated percentage (95 peroent confidence interval, denoted by 1-14). If the confidence intervals for the populations do not overlap, there is a statisti=lly 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. 100 ( 0.0) ( 2.0)1 ( 1.3)1 111 ( 1.7) 100 ( 0.0) 11 ( 14)1 07 ( 2.8)1 07 ( 1.0) 100 3 4 25 THE 1990 NAEP MAL STATE ASSESSMENT Texas PARENTS' EDUCATION LEVEL Previous NAEP &dings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In Texas, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 30 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, about the same percentage of students in Texas (34 percent) and in the nation (39 percent) had at least one panmt who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 17 percent for Texas and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School I Mathematics Proficiency by Parents' Education MEP Mathamatios Seale 200 225 250 275 1-4nas 300 500 Average Preaching); at, N4 Texas HS non-groduate HS graduate Some college College graduate West HS non-graduate HS graduate Some college College graduate Nation HS non-graduate HS graduate Some college College graduate ( 4.4) ( 2.2) 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-11-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 35 THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Texas ITIE Pi& 1$ FIGURE 11 I Levels of Eighth-Grade Public-School 1 Mathematics Proficiency by Parents' Education LEVEL 300 Nate HS non-grad. HS graduate Some college Canoga grad. Region HS non-grad. HS graduate Some college C0nags grad. Nation HS non-grad. MS graduate Some college Collage grad. LEVEL 250 SO Se MS non-grad. MS graduate Some COONS College grad. Rag/an MS non-grad. HS graduate Some college Collage grad. NOW MS non-grad. MS graduate Some college College grad. LEVEL 200 State KS non-grad. MS graduate Some college Collage grad. Ne MS non-grad. HS graduate Some college liaga grad. Ratko HS non-grad. HS graduate Soma college Cot lege grad. 30 .. h