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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<X < New., ;K.,' . !N. ... Z.X,,. . ' 0 20 40 00 80 Pen:setae* at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certaitty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 100 3 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 1 ( 0.8) 4 ( 1.0) 11 ( 2.0) 21 ( 1.8) 2 ( 2.3) 2 ( 1.3) 18 ( 2.8) 21 ( 3.5) 1 ( 0.9) ( 1.5) 12 ( 1.4) 21 ( 1.9) 40 ( 2.9) 47 ( 2.5) 72 ( 2.5) 77 ( 2.0) 44 ( 8.8) 81 ( 4,4) 75 ( 41) TS ( 3.6) 37 ( 4.6) IS ( 2.7) 71 ( 2.6) 79 ( 2.0) 16 ( 1.1) la ( 1.1) 114 ( 0.7) ( OM) 10 ( 32) 97 ( 1.6) 110 ( 0.7) ( 0.7) ( 1.0) ( 0.8) ( 0.7) 10 ( 0.7) Texas GENDER As shown in Figure 12, there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in Texas. Compared to the national results, females in Texas performed lower than females across the country; males in Texas performed no differently from males across the country. FIGURE 12 I Average Eighth-Grade Public-School i Mathematics Proficiency by Gender MEP allatheinaticis Scab 200 225 250 275 300 500 The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in Texas who attained level 200. The percentage of females in Texas who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in Texas who attained level 200 was similar to the percentage of males in the nation who attained level 200. 37 THE 1990 NAEP TRIAL STATE ASSESSMENT 31 Texas FIGURE 13 I LevelS of Eighth-Grade Public-School I Mathematics Proficiency by Gender LEVEL. 300 Ms lie Male Female Region Male Female Nation Male Female LEVEL. 250 State Male Female Region Male Female Nation Male Female LEVEL 200 Stets Mate Female Region Male Female Nation Male Female 20 40 so so 100 Parcantaga at or Abovs Proficiwcy Lewis 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 14-9. 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. 38 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 12 ( 1.2) ( 1.1) 13 ( 3.1) 11 ( 2.2) 14 ( 1.7) 10 ( 1.3) 00 ( 2.2) 27 ( 2.1) OS ( 4.1) 01 ( 3.2) 64 ( 2.0) 54 1-0) 07 ( 0.7) 97 ( 0.8) 97 ( 1.2) ( 1.0) 27 ( 0.9) 97 ( 0.8) Texas In addition, there was no difference between the percentages of maks and females in Texas who attained level 300. The percentage of females in TC,XLS who attained level 300 was similar to the percentage of females in the nation who attained level 300. Also, the percentage of males in Texas who attained level 300 was similar to the percentage of males in the nation who attained level 300. CONTEN Jr AREA PERFORMANCE Table 3 provides a summary of conttnt area performance by race/ethnicity, type of community, parents' education level, and gender. 3D THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Texas TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 111SCI NAEP TRIAL STATE ASSESSMENT Nialiblaperareder Milailnalent "MN" Data Analysis, Statiltk*probabuy' and Algebra and Rilenatil jam Pralkiency firsidincy Pracknow Prefidenty State Region 24112) 253 ( 20 ( 1.4 3.01 255 ( 220 ( 2 25i ( 02 ( 34 Nation 225 ( 1.4) 258 ( 1.7 05 ( IA 202 ( 11 PAOVETHNICITY DR*. State 275 ( 1.1) 220 ( 1.5) 272 1.2 275 1.7) Region 271 ( 3.2) 287 ( 3.9) 227 3.01 272 4.4) Nation 273 ( 12) 227 ( 2.0) 267 1.5 272 1.8) Waft State Region 244 ( 250 ( 2.2) 5.8)1 222 ( 2.8) 240 (10.7)4 234 ( 249 ( 2.0) 5.7)4 227j 244 k 8.7 Nation 244 ( 3.1) 227 ( 3.6) 234 ( 21) 231 ( 3.8 Hispanic State 249 ( 1.6 240 ( 2.0) 247 ( 2.1) 240 ( 22) Region 248 ( 3.5 235 ( 42) 245 ( 4.4) 240 ( 4.7) Nation 248 ( 2.7) 238 ( 3.4) 243 ( 3.2) 232 ( 3.4) Type OF COMMUNITY Advantaged urban State 278 ( 2.5)1 273 ( 3.8)4 278 ( 2.8)1 280 ( 3.0)r Region 284 ( 34)1 253 ( 2.7)4 279 ( 8.9)1 2841 ( Nation 263 ( 3.2)1 261 ( 3,2Y 277 ( 5.2)4 285 (4.8)1 Disadvantaged urban State 250 ( 2.5)1 239 ( 3.0)1 245 ( 2.3)! 240 3.2)1 Region 200 ( 5.4)! 250 ( 81)1 250 ( 4.5)1 255 8.3)4 Nation 255 ( 3.1)1 ( 41)1 248 ( 3.7)1 247 4.0)1 Extrense flrat State 267 ( 3.5)! 250 ( 4.5)1 200 ( 3.2)1 259 ( 4.5)1 Region 254 ( $.0)1 254 ( .1.6)1 252 ( 9.4)4 253 ( 11.8)1 Nation other 258 ( 4.3)1 254 ( 4.2)1 253 ( 4.5)1 257 ( 5.0)1 State 261 ( 1.8) 252 ( 1.9) 257 ( 11) 250 ( 2.6) Region Nation 262 ( 200 ( 3.5) 1.9) 255 ( 257 ( 4.2) 2.4) 258 ( 259 ( 3.4) 1.7) 25e ( 4.2) 201 ( 2.2) Ptilidletty 2681 OS (2.4 260 13 272 1.4) 22? 2.8) 286 1.4) 78 237 2.7 242 2.1 243 4.01 243 3.1 275 ( 2.6)4 279 ( 2.9)! 277 ( 4.8)1 244 2.0)1 254 ( 4.0)I 247 ( tap 201 ( 3.7)1 251 ( 81)1 256 ( 4.6)4 251255 261 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 4 0 34 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE 3 I Eighth-Grade Pabik-SChaal Mathematics (wntinued) i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS MO NAEP TRIAL STATE ASSSMENT SE Numbers Ind Operations Measurement Data AniNYINI1' OsoknetryiStatistics, and Pmbabeity Aigetwa and Functions Zetak State Region Nation imainummensw NS neniradmato Stats Region Nation tt$ 'radiator State Region Nation lass Maga State Region Nation College graduate State Region Nation IMRE mats State Region Nation Female State Region Nation 0:2 247 1 2.4 253 243 ( 249 244 ( DO 254 245 ( SA 251 250 2.4 7111 la 11411 ( 2.1 252 1 El 2111 253 a 13 285 131 272 3.7 254 2.7 270 1.51 269 1.7 275 ( 2.7) 271 3.0 272 2.01 27$ ( 12) Preadlear 053i 1.7 is. 2 24214 237 fIngaissor 231 i TA 21/111 *42 2 $410001$11141 21: 1, ..) 2242:1111 240 3.1) PrallsitM8Y 2So: I ;.!4] 200( 1.3) 2221 0 342 ( 204 ( 1.5) "4208 (221 280 1.4) 283 2.5) 228 14) 258 12 263 *Si 242 33 250 ( 12) 252 ( 22) 2$3 ( 12) 1.10 22$ 20$ 3.9) 271 262 2.0) 249 272 ( 275 271 ( 23 271 270 ( 1 275 230 ( 1.5) 258 251(34 ) 234 200 ( 1.7) 262 258 ( 1.8) 255 250 ( 2.9) 200 252 ( 15) 281 ( 2.1 2.1} ( 42} 264 3.2) ( 2.4 263 2.2) 273( 12 43 272 ( 22 22 273 ( 13 ( 2.0) ( it) ( 2.1) ( 12) ( 4.0) ( 1.2) 257 ( 1.7) MAIO "1.61 258 ( 1.7) 259 ( 22) 260 ( 14) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each popllation of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. 41 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Texas ME NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuihie in and of itself, but it becomes more useful for improving instruction and sett Licy when supplemented with contextual information about schools, teachers, and studeals. 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, instniction, 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 understandi4 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 ane instruction -- fundamental aspects of the educational process in the country. 4 2 THE 1990 NAEP TRIAL STATE ASSESSMEM 37 Texas 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 da&SIDOM3. 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 tr-7'llooks or worksheets. Also, it is widely recognized that home eineironment has an ex or nous 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 matematics homework. Pan Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instnictional practices -- how instrur-tion is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 eumines students' home support for learning. 43 35 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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 refomis 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 incluse in the proportions of students in high-school mathematics programs.3 This chapter focuses on curricular and instructional content issues in Texas 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 three-quarters of' the eighth-grade students in Texas (77 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 Underw.hteving Currkuhun: AsseSslag US. 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 Counts: A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). 4 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Texas In Texas, 85 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Almost all of the students in Texas (92 percent) were taught mathematics by teachers who teach only one subject. More than half (63 percent) of the students in Texas were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was equally prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in Texas Eighth-Grade Public Schools PERCENTAGE OF STUDENTS IMO NAEP TRIAL STATE ASSESSMENT Texas Wsrai Nation _ Percentage of eighth-grade students in public schools that Identified meithemetics as recebine *WM emphests in school-wide goals and objectives, instruction, In-service training, etc. Percentage of eighth-grade public-school students who are Whored a cane In atgebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who teach esty maiwmatios Percentage of elghth-grade students In public schools who are swiped $o a mathematics class by their ability In mathematics Percentage of eighth-grade students In public schools who receive low or more hoin of mathematics kisanictkn per week 77 ( 42) 61 ( 6.6) 63 ( 5.9) 65 ( 3.4) 92 ( 42) 76 ( 4.13) 92 ( 22) 96 ( 1.0) 91 ( 3.3) 63 ( 32) 64 ( 6.3) 133 ( 4.0) 30 ( 3.3) 25 ( 54) 30 ( 44) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 45 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas CURRICULUM COVERAGE To place students' mathematics proficiency in a cuniculum-related context, it is necessary to examine the extent to which eighth graders in Texas are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in Texas were taking eighth-grade mathematics (72 percent) than were taking a course in pre-algebra or algebra (26 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algpbra. Students in Texas who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the mow able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 Students' Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Texas West Nation _ Per011110.11 and Pralicliney Pereentage and Prelkiency Pereentage and Preedency What kind of mathematics class are you taking this year? Eighth-grade mathematics 72 ( 2.0) ( 2.7) 02 ( 2.1) 249 ( 1.4) 252 ( 2.4) 251 ( 1.4) Pre-aigebra 14 ( 1.5) 1$ ( 2.7) 19 ( 1.9) 274 ( 2.6) 2OS ( 3.8) 272 ( 2.4) Algebra 12 ( 1.0) 17 ( 1.8) 15 ( 1.2) 226 ( 1.6) 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. 4 C THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Texas Further, from Table A5 in the Data Appendie About the same percentage of females (26 percent) and males (25 percent) in Texas were enrolled in pre-algebra or algebra courses. In Texas, 33 percent of White students, 15 18 pement of Hispanic students were enro courses. t of Black students, and in pm-algebra or algebra Similarly, 31 percent of students attending schools in advantaged urban areas, 20 percent in schools in disadvantaged urban areas, 20 percent in schools in eAreme rural areas, and 27 percent in schools in areas classified as "other" were enrolled in pre-algebra or algebra COMM MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in Texas spent either 15 or 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes daily. Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix): In Texas, 5 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 2 percent of the students in Texas and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations race/ethnicity, type of community, parents' education level, and gender. 4 7 42 THE 1990 NAE.P TRIAL STATE ASSESSMENT Texas The results by race/ethnicity show that 2 percent of White students, o percent of Black students, and 2 percent of Hispanic students spent an hour or mon on mathematics homework each day. In comparlsoD, 2 percent of White students, 8 percent of Black students, and 6 percent of Hispanic students spent no time doing mathematics homework. In addition, 1 percent of students attending schools in advantawd urban areas, 3 per.ent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 2 percent in schools in areas classified as "other" spent an hour or more on matlzmatics homework daily. In comparison, 2 percent of students attending schools in advantawd urban areas, 4 percent in schools in disadvantaged urban areas, 1 percent in schools in extreme rural areas, and 6 pacent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY -N- MO NAEP TRIAL STATE ASSESSMENT Texas Wed Nikko , About how much time do students spend on mathematics homework each day? Sono 18 minutes 30 minutes AO mintdos An hour or more PeraNdies Persuerge .01018110 and amil OM Paisions, Pmficims, 14110140023 ( 1.1) 232 ( 4.8)Ilei 1214 41 ( 34) 256 ( 1.8) T ( 1.2) 2SS ( SA) 2 C 01) ( 0.3) 42 ( 8J) 288 ( 4.2) 43 ( CI) 264 ( 47) 4.11 10.114 1 1 Et 221 Ili 104 14) 272 5.7$ 24 The standard errors of the estimated statistics appear in par, ntheses. 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). 48 THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Texas TABLE 7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1010 NAEP TEAL STATE ASSESSMENT TWOS Watt Nation About how much time do you usually spend each day on mathematics homework? Parestases soul Paramisp and redisaw Paraudage wawa None 12 ( 1.0) 12 ( 1.7) 9 ( 01) 257 ( 2.2) 254 ( 4.2) 251 ( 2.6) 15 minutos 243 ( 1.0) 31 ( 45) 31 ( 2.0) 259 ( 1.5) 263 ( 3.5) 264 ( 1.9) 39 ininsass 30 ( 1.0) 28 ( 1.7) 32 ( 1.2) 259 ( 1.5) 201 ( 2.9) 203 ( 1.9) 45 alkyls, 10 ( 0.7) 15 ( 1.5) 10 ( 1.0) 255 ( 2.1) 267 ( 4.2) tea ( 1.0) An hour or more 15 ( 10) 14 ( 11) 12 ( 1,1) 238 ( 2.6) 261 ( 4.3) 250 ( 1.1) The standard errors of the estimated statistics appear in parentheses. It con 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. And, according to the students (Table 7 and Table A7 in the Data Appendix): In Texas, some of the students (12 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 15 percent of the students in Texas 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 14 percent of White students, 16 percent of Black students, and 17 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 14 percent of White ,tudents, 10 percent of Black students, and 11 percent of Hispanic students spent no time doing mathematics homework. 4 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas In addition, 11 percent of students attending schools in advantaged urban areas, 14 percent in schools in disadvantaged urban areas, 20 percent in schools in extreme rural areas, and 16 peseent in schools in areas classified as "other" spent an hour or more on mathematics homework day. In comparison, 13 percent of students attending schools in advantaged urban areas, 13 percent in schools in disadvantaged urban areas, 17 percent in schools in extreme rural areas, and 12 percent in schools in areas classified as "other" spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of rnathanatics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurements Because the Trial State Assessment questions welt 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 leam 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. Alvbra and Function& Teachers were asked about emphasis placed on one topic: algebra and functions. National Council of Teacher: of Mathematics, Currkultan and Evaluation Standardr for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, l989). THE 1990 NAEP TRIAL STATE ASSESSMENT 1 0 45 Texas 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 =Oak? and "little or no emphasis" and the average student proficiency in each content arta. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student oerformance 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 and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 51 46 THE 1990 NARA TRIAL STATE ASSESSMENT Texas TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ----., 1810 NAEP TRIAL STATE ASSESSMENT Texas West Nation ImiIIMMINIMPImIgmlmININEMIMPIMPEINIPIIMI11011111.1.1.111MPPOIMPIMMOINNIIIMIIIIMIMIV Illowilese Pomo.. tPreldelt* pniisksw PfZEW4/ 61 SA) 42 ( 7.4) 257 ( 1.7) 237 RS) NO( 7 ( 1.4) 13 ( 2.1) 15 ( 279 ( 41) 291 ( EA) 287 29 ( 11 ( 2A) 17 246 ( SA) 251 ( 7.7)1 Stio 19 ( 2.4) 16 ( 53) 3.3(4.0) 200 ( 3.7) 275 ( 63) 272 37 ( 3.0) 24 ( 63) 28 257 ( 2.4) 260 ( 2.8)4 200 12 ( 2.0) 15 ( 4.5) 21 255 ( 4.8) 217 (11.4)1 264 20 ( 2.5) 14 ( 3.7) 14 252 ( 4.4) 264 (10.6)1 2641 47 ( 3.3) 54 ( 63) 53 253,( 2.3) 262 ( 4.9) 261 52 ( 2.5) 43 ( 5.6) 46 264 ( ..9) 277 ( 5.2) 275 13 ( 1.9) 23 ( 5.1) 20 237 ( 3.6) 243 ( 4,2)1 243 1.8) 2.1) ( 3.4) ( 3.0) (5.6) ( 4.0) ( 33) ( 3.2) ( 11.3) ( SA) ( 2.2) ( 4.3) ( 44) ( 2.0) ( 3.6) ( 2.5) ( 3.0) ( 3.0) Teacher °emphasis" categories by content ARMS Numbers and Oparalions Heavy emphasis Little or no emphasis Measurement Heavy emphasis Little or no emphasis Geometry Heavy emphasis Little or no emphasis Data Analysts, Statistics, and Probability Heavy emphasis Little or no emphasis Algebra and Fiectlans Heavy emphasis Uttle or no emphasis 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. 52 THE 1990 NAEP TRIAL STATE ASSESSMENT 47 Texas SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students ate 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 three-quarters of the eighth-grade students in Texas (77 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Texas, 83 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. i=r percentage of students in Texas were taking eighth-grade rkaa tics (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 uch day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework =eh day, while students reported either 15 or 30 minutes daily. In Texas, some of the students (12 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 15 percent of the students in Texas and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed huvy 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 Sevi'llons and Measurement had lower proficiency in these content areas : students whose teachers placed little or no emphasis on the same . areas. 5 0 48 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas CHAPTER 4 pigs -ISZ-3 11111111111 1111111111111111111111, UN I OS 1141_111111Mii 211111111V1111111111ills Min U SIR Mal MUM ..111111/.111111 "IMMO hirilles IMMO& IMMO 1Iu ir.111110111 111111112111M11 MINI MISUSE How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with ail 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 lnd 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 Mat.hemaucs, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). 5 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Texas From Table 9 and Table A9 in the Dsta Appendix: In Texas, 20 percent of the eighth-grade students had mathematics teachers who =ported getting all of the resources they needed, while 29 percent of the students were taught by teachers who got only some or new of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Texas, 34 percent of students attending schools in advantaged urban areas, 20 percent in schools in disadvantaged urban areas, 16 percent in schools in extreme rural areas, and 18 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in Texas, 21 percent of students attending schools in advantaged urban areas, 29 percent in schools in disadvantaged urban areas, 27 percent in schools in extreme rural areas, and 31 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had 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 1010 kW TRIAL STATE ASSESSMENT Texas West Nation Which of the following statements is true about how well supplied you are by your school system with the instructional materials and other resources you need to teach your class? I got all the reeourses I wit I get moot of the resources I now I got some or none of Ihe resources I need. Peresolage Pereentage Pen:adage and and and Prallelaw Pielalency Prallkienqf 20 ( 20) 15 ( 5.2) 13 ( 2.4) 257 ( 3.0) 2191 ( 5.9)4 205 ( 42) 51 ( 3.3) 02 ( SA) SI ( 4.0) 259 ( 1.5) 200 ( 4.1) 2115 ( 2.0) 29 ( 3.1) 23 ( 31 ( 4.2) 249 ( 2.9) 257 ( 3.7)1 201 ( 2.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent oestainty 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 or the sample does not allow accurate determination of the variabilhy of this estimated mean proficiency. rJ SO THE 1990 NAEP TRIAL STATE. ASSESSMENT Texas PATFERNS 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.7 Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers art making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table I 1 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: Less than half of the students in Texas (39 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics problems in small groups (10 percent). The largest percentage of the students (70 percent) used objects Wm rulers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (6 percent). In Texas, 62 percent of the students were assigned problems from a mathematics textbook almost every day; 8 percent worked textbook problems about once a week or less. Less than half of the studeats (41 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (27 percent). 7 Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Curriculum: Eighty-mond Yearbook of the National Society for the Study of Educadon (Chicago, IL University of Chicago Press, 1983). 5 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 51 Texas TABLE 10 I Teachers' Reports on Patterns of Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Texas West Nation IPInieniop end Pre 'Mow 99 ( 3.9) 256 ( 2.5) 257 11 10 ( 1.7) 250 ( 4.0) Percentage and Prelicioncy Perowilose and Predideen, ST ( 5.9) 262 ( 4.234 30 ( TA) 299 ( 4.5) ( 2.2) Percentage and Proficiency Perenniee end Prolidrey 50 ( 4.4) ( 2.2) 43 ( 4.1) 264 ( 23) 8 1 2.0) 277 ( 5.434 Percentage and Proficiency About how often do students work problems in small groups? At least once a week Less than once a week About how often do students use objects like rulers, counting blocks, or geometric solids? At least once a week 24 ( 3.0) 34 ( 82) 22 ( 3.7) 249 ( 2.5) 256 ( 4.9)1 254 ( 3.2) LASS than once a week 70 ( 3.0) $7 ( 6.4) 257 ( 1.5) 26$ ( 4.0) 263 ( 1.9) Never 6 ( 259 ( 1.4) 5.9)1 ( 3.0) 4411 9 ( 282 ( 2.6) 5.934 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 Texas TABLE 11 I Teachers' Reports On Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1210 NAEP TRIAL STATE ASSESSMENT Tons Wad Nation About how often do students do problems from textbooks? Aimed wiry day Swears! times a weak About ones a week or loss About how often do students do problems on worksheets? At host savoral times a we* About ones a gook Loss than moldy POrallempa Widows 42 ( 3.2) 254 ( 1.7) 29 ( 3.1) 2111 ( 23) ( 1.2) 254 ( 53) Pirsislose Parommase sni Awl Proficiency ardkaisoly 2106 14 Ali !a .Sf 44 Percuely awl Prlikionoy 41 ( 3.2) 256 ( 2.1) 32 ( 3.5) 253 ( 2.5) 27 243.31 503. Parasologe lieftfidotair 25925 34 25S 41 274 524 ( 4A) ( 4.1) ( 5.6) ( 4.2) Paramilage sad 34 ( SI) 254 ( 23) 33 ( 34) 240 ( 2.3) 32 ( 3.0) 274 ( 2.71 The standard errors of the estimated statistics appear in parenthetes. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population I. 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). 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. 58 THE 1990 NAEP TRIAL STATE ASSESSMENT 53 Texas COLLABORATING IN SMALL GROUPS In Texas, 48 percent of the students reported never working mathematics problems in small groups (see Table 12); 23 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 _ NM NW TRIAL STATE ASSESSMENT Texas West Nation - Puromilage Mid Proildanow Peraintase and Patiolinelf 14,001551P ant Prele4511511 How often do you work in small groups in your mathematics class? At least once a week 23 ( 2.0 ( 4.5) 25 2.5) 259 ( 23) 2541 ( 42) 251 ( 2.7) lass than once a week 28 ( 1.5) 29 ( 20) 28(14 ) 264 ( 1.11) 271 ( 3.1) 20? ( 2.0) 4 ( 2.4) 44 ( 2.9) 254 ( 1.5) 2r8 2"1.01 241 ( 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 ± 2 standard errors of the estimate for the sample, Examining the subpopulations (Table A 12 in the Data Appendix): In Texas, 28 percent of students attending schools in advantaged urban areas, 21 percent in schools in disadvantaged urban areas, 26 percent in schools in extreme rural areas, and 23 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 22 percent of White students, 23 percent of Black students, and 25 percent of Hispanic students worked mathematics problems in small groups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (21 percent and 25 percent, respectively). 5.9 54 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as ruless, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: Less than half of the students in Texas (19 percent) never used mathematical objects; 28 percent used these objects at least once a week. Mathematical objects woe used at least once a week by 26 percent of students attending schools in advantaged urban areas, 34 percent in schools in disadvantaged usban areas, 30 percent in schools in extreme rural areas, and 26 percent in schools in areas classified as "other". Males were as likely as females to use mathematical objects in their mathematic$ ClaS3C3 at least once a week (29 percent and 26 percent, respectively). In addition, 23 percent of White students, 28 percent of Black students, and 34 percent of Hispanic 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 PROFICIENCY IMO MEP TRIAL STATE ASSESSMENT T.xa. Nation How ofton do you work with objects like rulers, counting blocks, or ;Isometric solids in your mathematics class? lloroontogo one Pnellolonoy Poroodogo one Pneloloncy Percentage and Pinikkos, M lust once a mail 28 ( 2.0) 36 ( 3.5) 2S ( 1.8) 253 ( 1.9) 200 ( 4.0) 2561 2.6) Lass than ance a Wook 33 ( 12) 25 ( 1.6) 31 ( 12) 204 ( 1.0) 209 ( 2.1) 20S ( 15) Mow 39 ( 2.2) 36 ( 3.3) 44 ( 2.2) 250 ( 12) 256 ( 2.8) 259 ( 16) The standard errors of die estimated natistics appear in parmitheses. 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. Co THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Texas MATERIALS FOR MATHEMA11CS INSTRUCTION The percentages of eighth-grade public-school students in Texas who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table A 14 in the Data Appendix): About three-quarters of the students in Texas (72 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 74 parent of students attending schools in advantaged urban areas, 67 percent in schools in disadvantaged urban areas, 85 percent in schools in extreme rural areas, and 72 percent in schools in areas classified Ss "other". FABLE 14 I Students' Reports on the Frequency of i Mathematics Tintbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL, STATE ASSESSMENT Texas West Nation How often do you do mathematics problems from textbooks In your mathematics clan? Pantontass and Ponglolancy Peraniele and Prat:fancy POWWOW end INalkdancy Almost ovary day 72 ( 1.7) 71 ( 3.5) 74 ( 1.9) 202 ( 1.3) 24/ ( 2.4) 247 ( 1.2) Several limos a weak 10 ( 1.2) 15 ( 1.5) 14 ( 0.4) 249 ( 2.2) 251 ( 2.4) 252 ( 1.7) About once a mak or kw 12 ( 1.2) 14 ( 3.1) 12 ( 11) 247 ( 3_2) 242 (11.2) 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 61 56 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas And, for the frequency of worksheet usage (Table 15 and Table A 15 in the Data Appendix): About half of the students in Texas (45 percent) used worksheets at least several times a week, compared to 38 percent in the nation. Worksheet3 were used at least several times a week by 38 percent of students attending schools in advantaged urban areas, 51 percent in schools in disadvantaged urban areas, 39 percent in schools in extreme rural areas, and 45 percent in schools in areas classified as "other". TABLE 15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT Texas How often do you do mathematics problems on worksheets in your mathematics class? Parmidap sad Praildancy Perosniage and Predidoncy Perangsge died Praliokiney At least several Nines a week 45 ( 2.2) 35 ( 4.0) 35 ( 2.4) 252 ( 1.7) 250 ( 42) 253 ( 2.2) About ono a weak 25 ( 1-2) 23 ( 2.6) 25 ( 12) 253 ( 12) 262 ( 2.1) 201 ( 14 ) Lass than moldy 30 ( 2.3) 41 ( 4.1) 37 ( 24) 236 ( 2.0) 270 ( 3.4) 272 ( 1.9) The standtrd errors of the estimated statistics appear in parentheses. it can be said with about 95 percer certainty that, for each population of interest, the value fro the entire population is within ± 2 standard errors of the estimate for the sample. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. 62 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 Texas TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instrudion PERCENTAGE OF STUDENTS 1990 MEP TRIAL STATE ASSESSMENT Texas Wed Nation _ .. Patterns of clawoom instruction Pere~ et students who work problems In email groups At least once a week Less than once a week Never Permits,* et students %Wm um Ojeda Me niers, counting Medea sr geemalic sands At least once a week Less than once a week Never Materials for mathematics instruction Percentage et students vain um a mathematics textbook Almost every day Several times a week About once a weak or less Pernentege of students Me use a methematics worksheet At least several times a week About once a week Less than weekly $4111 310 22 1.4 2$ $3 1 Iftramtap Peramispo Per~ Obibole Tawasn 1111rials Tosoloss Sepliele tmillsre 72 92 71 3.5 55 74 52 ( *4) 12 1,2 $ 1,2 14 $.1 9 4,* 12 1A 11 LI) 10 1.2 29 3.1 15 141 30 51 14 0,1 111 SA) 45 (2.2 41 3.2 4.0) 3.6) 25 (1,2 32 3.51 23 2.9) 24 4.9 25 1.2 13 (3.4) 30 (2.31 27 $.3 41 4.1) 41 $ U. It (sa) 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 erhnate for the sample. 63 58 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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 mathematic; teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachess: Less than half of the students in Texas (39 gement) worked mathematics problems in small groups at least once a week; relatively few never worked in small groups (10 pervent). The largest percentage of the students (70 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (6 percent). In Texas, 62 percent of the students were swiped problems ftom a mathematics textbook almost every day; 8 percent worked textbook problems about once a week or less. Less than half of the students (41 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (27 percent). And, according to the students: In Texas, 48 percent of the students never worked mathematics problems in small groups; 23 pacent of the students worked mathematics problem in small groups at least once a week. Less than half of the students in Texas (39 percent) never used mathematical objects; 28 percent used these objects at least once a week. About three-quarters of the students in Texas (72 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. About half of the students in Texas (45 percent) used worksheets at least several times a week, compared to 38 percent in the nation. G4 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Texas 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 arc important tools for mathematics and students need to be able to use them wisely. Tha 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 We 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 .7bjectives: 1990 Assessment (Princeton, NI: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curricubtm and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas Table 17 provides a profile of Texas eighth-grade public schools' policies with regard to calculator use: ln comparison to 33 percent across the nation, 22 percent of the students in Texas bad teachers who allowed calculators to be used for tests. About the same percentage of students in Texas and in the nation had teachers who permitted unrestricted use of calculators (12 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of Texas Policies on I Calculator Use PERCENTAGE OF STUDENTS MO NAEP TRIAL STATE ASSESSMENT Texas Percentage of eighthgrode students in public schools whose teachers permit the unrestricted Poiventage Perowdepo Peremisse use of calculators 12 ( 2.5) 20 ( 4A) 16 ( 2.4) Percentage of eighth-grade students in public schools WhOSe teachers permit the use of cakulators for tests 22 ( 3.6) 46 ( 33 ( 4.5) Percentage of elghth-grade students in public schools whose teachers report that students have access to calculators owned by the school Ti ( 3.7) 72 ( 1.4) 511 ( 4.51 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. cc THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Texas ME AVAIILARTLITY OF CALCULATORS In Texas, most students or their families (96 percent) owned calculators (Table 18); however, fewer students (56 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In Texas, 54 percent of White students, 54 percent of Black students, and 59 percent of Hispanic students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (54 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 MOO NAP TRIAL STATE ASSESSMENT Taw West Nation Penmen le and alvalciaanY 98 ( 0.5) 259L 1.2) 4 ( 0.5) 235 ( 2.9) Parcentala and Mrallabanay Pereentaw Sad Pralkilancw 90 ( 00) 203 ( 2.5) 4 ( 00) ( 441 Parcaniage and Madam" PortfiNtive int Madam 97 ( 0.4) 203 ( 1.3) 3 ( 0.4) 234 ( 3.8) Parvialago and Proackin99 Do you or your family own a calculator? Vol No Does your mathematics teacher explain how to use a calculator for mathematics problems? Yu 56 ( 2.4) 59( 3.4) 49 ( 2.3) 258 ( 1.8) 200 ( 2.7) 258 ( 1.7) No 44 ( 2.4) 41 ( 3.4) 51 ( 24) 259 ( 1.5) 205 ( 3.0) 208 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 6" THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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 put of the Trial State Assessment, students mine asked how frequently (never, sometimes, almost always) they used calculatc. c working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In Texas, 19 percent of the students never used a calculator to work problems in class, while 51 percent almost always did. Some of the students (17 percent) neves used a calculator to work pmblems at home, compared to 26 percent who alma always used one. About one-quarter of the students (29 percent) never used a calculator to take quizzes or tests, whil! 27 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 MAEP TRIAL STATE ASSESSMENT Tens West Nation , Illereentase and Prellokmoy 51 ( 1.4) 251 ( 1.8) 19 ( 1.7) ( 1.5) 26 ( 13) 259 ( 2.0) 17 ( 0.9) 282 ( 1.9) 27 ( 14) 262 ( IS) 29 ( 1.6) 271 ( 13) 1144441s. one Prellelawy 5$ ( Li) 255 ( ZS) 14 ( 2.4) ASS ( 10) 29 ( 1.7) 2,33 ( 13) 19 ( 1.0) 358 ( 3.7) 25 ( 1.6) 21511( 34) 22 ( 2.0) 270 ( 13) 1416141010 1418001141f 4 ( 2S4 ( 23 272 2.14°f,1.11. 2111 27 253( 104 274 14) 13) ( 1.9) ( 14) fa] ( 1.4) AA) ( ix) How often do you use a calculator for the following tasks? Working prc4)lains in class Almost always Never Doing problems at home Almost always Never Taking quizzes or tests Almost always Never 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. 68 THE 1990 NAEP TRIAL STATE ASSESSMENT 63 Texas 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 assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the 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 uid not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of thc Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorizal into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they weir presented. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas The data presented in Table 20 and Table A20 in the Data Appendix are highligAted below: A smaller percentage of students in Texas wen in the High group than were in the Other group. A smaller percentage of 'llales than females were in the High group. In addition, 52 pescent of White students, 44 percent of Black students, and 43 percent of Ifispanic students were in the IBA group. TABLE 20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11110 NAEP MAL STATE ASSESSMENT , _ Tants 1 Wig , Nation "Calculator-uso" group Mir 01111111NelP lad firsikiemay 47 ( 1.2) 205 ( IA) 53 ( 11) 251 ( 14) Paraminge Ihreentap an* and Orsicioncy Prolktioncy 2rsi 224.7i 82 ( 2.0) 2S3 ( 2A) 42 ( 13) 272 ( 1A) 511( 1.3) 255 ( 1.5) The standard errors of the estimated statistics appear in parenthetes. It can be said with about 9$ percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. 70 THE 1990 N OP TRIAL STATE ASSESSMENT 65 Texas 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 calculatiors 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, 22 percent of the students in Texas had teaehers who allowed calculators to be used for tests. About the same percentage of students in Texas and in the nation had teachers who permitted unrestricted use of calculators (12 percent and 18 percent, respectively). In Texas, most students or their families (96 percent) owned calculators; however, fewer students (56 percent) had teachers who explained the use of calculators to them. In Texas, 19 percent of the students never used a calculator to work problems in class, while 51 percent almost always did. Some of the students (17 percent) never used a calculator to work problems at home, compared to 26 percent who almost always used one. About one-quarter of the students (29 percent) never used a calculator to take quizzes or tests, while 27 percent almost always did. 71 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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 Texas, 38 percent of the students were being taught by mathematics teachers who reported having at last 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 mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of the students were taught by mathemafics teachers who were certified at the highest level available in their states. Many of the students (86 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematks (Reston, VA: National Council of Teachers of Mathematics, 1991). 72 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 Texas TABLE 21 I Profile of Eighth-Grade Public-School I Mathematics Teachers PERCENTAGE OF STUDENTS 1111113 NAEP TRIAL IITATE ASSESSMENT Texas West Sedan I I Percentage of students whew mathematics teachers reported lievtng the *Soft degrees Bachelor's degree Master's or specialist's degree Doctorate or professional degree Percentage at Wards whew statheatatice teachers hew the Mewing types at teaching certNicales that are reaegiked by Twos No regular certification Regular certification but less than the highest available Hi °Net certification available (permanent Of long-term) Percentage of students whose teethematics teachers haw the Mowing types al teaching aertMcales Mat we recognized by Texas Mathematics (middle school or secondary) Education (elementary or middle school) Other The standard errors of the estimated statistics appear in parentheses. It can be said with about 9$ percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the tample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, these is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergaduate and graduate majors and their in-service training. 73 68 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table n) show that: In Texas, 36 percent of the eighth-grade public-school students were being taught mathematics by teacWs- who hW an undergraduate major in mathematics. In comparison, 43 percent of the students sauss the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in Texas (15 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 I Graduate Fields of Study PERCENTAGE OF STUDENTS 111110 NAEP TRIAL STATE ASSESSMENT Taxes What was your undergraduate major? Perembie Mathematics 1234 43 3.5) Education Other 4,336 21 ( 3.2) Se 00 3$ 3S SA) n 3.3) What was your graduate major? Perventage Percentage Pareentep Mathematics 13 ( 2.3 4.? &WNW 30 ( 3.01 SO 441 w5.11 Ober or no graduate level stue 40 ( 3.0 46 OA 401 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population Is within * 2 standard errors of the estimate for the sample. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT 69 Texas Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In Texas, 38 percent of the eighth-grade public-school students had teachers who spent at last 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 staining. Some of the students in Texas (13 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or thi, 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 MO NW TRIAL STATE itilESSIAIENT Twos Wost Nation , During the last year, how much time In total have you spent on In-service education in mathematics or the teaching of mathematics? Nano Ono to 15 hors III Amos or more Paramise Poroonlose Porcarta. 13 2A 11 ( 3.0 11 ( 2.1) 4. 3.91 45 ( 51 ( 4.1) 3, 44 ( 8.9) SS( 3.5) Tbe 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. 75 70 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas SUMMARY Recent results from international studies have shown that students fiom 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 teachess. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; howeves, it is likely that relevant training and experience do contsibute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In Texas, 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 three-quarters of the students (73 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In Texas, 36 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 studcnts across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in Texas (15 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 Testing Service, 19811). I I Ina VS. Mullis, John A. Dorsey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement- NAEP's 1990 Asscsment of the Nation and the Mal Assessment of the States (Princeton, NJ: National Atsessment of Educational Progress, Educational Testing Service, 1991). 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas In Texas, 38 percent of the eighth-grade public-bchool students had teachers who spent at least 16 hours on in-service education dedicated to mdhanatics or the teaching of mathanatia. Across the nation, 39 permit of the students had tachas who spent at last that much time on similar typal of in-savice training. Some of the students in Texas (13 percent) had mathematics teachers who spent no time on in-serviee education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathandim teachers who spent no time on similar in-service training. 7" 72 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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, encouragement, 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. 7S THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Texas AMOUNT OF READING MATERIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning anti schooling. Students participating in the Trial State Assessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP MAL STATE ASSESSMENT Tens West Nation , Does your family have, or receive on a regular basis, any of the following items: more than 25 books, an encycloPadik, newspapers, magazines? Zero to two types Three types Four types Parcenta. and Parcantags 11Peramtase and and Oniiiraionev Prallialanka 30 ( 1.3) 24 ( 1.5) 21 ( 1.0) 243 ( is) 245 ( 4.1) 244 ( 2.0) 29 ( 1.0) 31 ( 1.4) 30 ( 1.0) 250 ( 1.7) 258 ( 2.4) 255 ( 1.7) 42 ( 1.1) 45 ( 1.2) 4$ ( 1.3) 222 ( 14) 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 Texas reveal that: Students in Texas 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. 79 74 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas A smaller percentair of Black and Hispanic students had all four types of these reading materials in their homes than did White students. A greater percentage of students attending schools in advantaged urban areas than in disadvantaged urban areas or areas classified as "other" and about the same percentap of students in schools in advantaged urban areas as in extieme rural areas had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER L AY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 23 I Students' Reports on the Amount of Thne Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111110 MEP TRIAL STATE ASSESSMENT Teas Walt Nation How much talavislon do you usually watch each day? Ono hoer or loss Two hours Throe hours Four to Ow hours ebt haws or more 1 Awl:~ and Prallokosy 1$ ( 0.7) 261 ( 24) 15 ( 0.8) 262 ( 2.2) 23 ( CO) 264 ( 1.6) 25730 0.1 1.41 if ( 0.0) 243 ( 2.0) Peronassa end Prollobacy 14 ( 1.5) 260 ( 2.6) 20 ( 1.6) 265 ( 3.8) 20 ( 1.2) 262 ( 32) 29 ( 1.7) 263 ( 2.9) 1$ ( 2.9) 240 ( 2.6) isaresitege and Proldany 12 ( OA) 269 ( 2.2) 21 ( OS) 25$ ( 16) 2E1 43 a1.71 2$ ( 1.1) 250(1.7) 111 ( 1.0) 243 ( 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. S THE 1990 NAEP TRIAL STATE ASSESSMENT 75 Texas From Table 25 and Table A25 in the Data Appendix: In Texas, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Some of the eighth-grade public-school students in Texas (13 percent) watched one hour or less of television each day; 15 percent watched six hours or more. About the same pacentage of males and females tended to watch six or more hours of television daily. Similarly, about the same parentage of males and females watched one hour or less pa day. In addition, 10 parent of White students, 30 percent of Black students, and 15 percent of Hispanic students watched six hours or more of television each day. In comparison, 12 percent of White students, 7 percent of Black students, and 15 percent of Hispanic 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 absented= to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the numba 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 Texas, average mathematics proficiency was lowest for students who missed three or more days of school. About half of the students in Texas (49 percent) did not miss any school days in the month prior to the assessment, while 18 percent missed three days or more. In addition, 16 percent of White students, 19 parent of Black students, and 21 percent of Ifispanic students missed three or more days of school. S I 76 THE 1990 NAEP TRIAL. STATE ASSESSMENT Texas Similarly, 16 percent of students attending schools in advantaged urban areas, 22 percent in schools in disadvantaged urban MU, 21 percent in schools in extreme niral areas, and 16 percent in schools in areas classified as "other" missed three or more days of school. TABLE 26 I Students' Reports on the Number of Days of i School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1NO NAEP TRIAL STATE e';1...711aINT Tow Pamodap aid Prellidossy Parsenlis. 010 Mallow PerWatilla ant Prastaly How many days of school did you miss last month? Nana 49 ( 1.0) 43 ( 2.n 45 (1.1) 251 ( 1.4) 2415 ( 3.5) 205 ( 1.5) Oast or two days 33 ( GS) 30 ( 1.4) 32 ( 0.9) 225 t 1.4) 265 ( 3.0) 2911 ( 13) Throe daYs or more 15 ( 0.9) 27 ( 1.5) 23 ( 1.1) 249 ( 1.9) 230 ( 3.1) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 77 Texas STUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not only to master essential skills and concepts but also to develop confidence in their mathematical abilities and to value mathematics as a discipline." Students were asked if they agreed or disagreed with five statemests 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 o m good in mathematics. Value of mathematics, inJuding 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 id not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is weful for solving everyday problerns. 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 witti the statements (an index of 1), tended to agree with the statements (an index of 2), or torded 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 mathematics as defined by their perception index. The following results were observed for Texas: 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. Less than half of the students (31 percent) were in the "strongly agree" category (perception index of 1). This compares to 27 percent across the nation. About one-quarter of the students in Texas (22 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). 12 National Council of Teachers of Mathematics, Curruk,unt and Evaluaaon Standards for School Marhemattcs (Reston, VA: National Council of Teachers of Mathematics, 1989). S 75 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY UM NAEP TRIAL STATE ASSESSMENT Texu West Nation imJrmnpail=1MIMINM Student "perception index" groups Perambige and IvreSeen 'evening aid Peg Winn Pereentep min Pm *tom Strongly agree 31 ( 1.0) 27 ( 1.9) 27 ( 1.3) ("percepuon index" of 1) 248 ( 1.7) 273 ( 3.9) 271 ( 11) Ayes 48 ( 1.0) 48 ( 1.5) 4 ( 1.0) ("perception index" of 2) 257 ( 1A) 282 ( 2.4) 202 ( 1.7) Undecided, disagree, strongly disagree 22(1.1) 25 ( 2.1) 24 ( 1.2) ("perception Index" of 3) 24( 1.9) 24 ( 2.9) 251 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. The data related to out-of-school factors show that: Students in Texas who had four types of reading materials (an encyclopedia, newspapers, imtgazines, 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 ihe 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. 84 THE 1990 NAEP TRIAL STATE ASSESSMENT 79 Texas 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 houn or more. Average mathematics pioficiency was lowest for students who spent six hours or more watching television each day. About half of the students in Texas (49 percent) did not miss any school days in the month prior to the assessment, while 18 percent missed three days or mote. Average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students (31 percent) were in the "strongly agree" relating to students' paceptions of mathematics. Average proficiency was highest for students who war in the "strongly spree category and lowest for students who war in the "undecided, disagree, stroll* disagsw" earegorY. 85 80 THE 1990 NABP TRIAL STATE ASSESSMENT Texas NE 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 ,3f the assessment design, the mathematics framework and objectives upon which the assessment was bawd, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Counal 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 Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the progam. Assesment Design The 1990 Trial State Assessment was based on a footred 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. SC THE 1990 NAEP TRIAL STATE ASSESSMENT $I Texas The blocks were then assembled into assessment booklets so that each bookletcontained two background questionnaires -- the first consisting of general background questions and the second consisting of mathematics background questions and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three IS-minute blocks of mathematics items. ThU3, the entire assessment required approximately 55 minutes of student time In accordance with the BIB design, the blocks were assigned to the assessmentbooklets so that each block appeared in exactly three booklets and each block appeared with evesy other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets were *kale,' or intaleaved in a systems& sequence so that each booklet appeared an appropriate number of times in the sample. The studcuts 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 content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure Al). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponsc. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiencyfor 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 perfonmance 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' characteristics (based on their responses to the background questions) and their overall performance in the assessment. National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Prinexton, NJ: Educational Testing Service, 1988). 8" 82 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas FIGURE Al I COntent Areas Assessed Numbers and Operations This content area focuses on students' understanding of numbers (what, numbers, fractions, dadmala, integers) and their application to real-world situations, as well as computational end 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 eppropriate units, apply measurement concepts, and communicate measurement-related Ideas to others. Questions are included that require an ability to read instruments using metric, customary, or nonstandard units, with emphasis an precision and accuracy. Questions requiring estimation, measurements, and appileattons 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 arid on their skills in working 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 geometric Ideas. In addition, students should be able to use informal reasoning to establish geometric relationships. Data Analysis, Statistics, and Probability This content area focuses on data representation and analysis across all disciplines and reflects the importance and prevalence of these activities in our society. Statistical knowledge and the ability to interpret data are necessary skills In the contemporary world. Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysis. Algebrl_ notions 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Texas FIGURE A2 I Mathematical Abilities The following three categories of mathematical abilities are not to be construed as iiierarchical. For example, problem solving involves interactions between conceptual knowledge and procedural skills, but what Is considered complex probiem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. Conceptual Understanding Students demonstrate conceptual understanding In mathematics when they prot,Ide evidence that they can recognize, label, and generate examples and counterexamples of concepts; can use and Interrelate models, diagrams, and varied representations of concepts; can Identify and apply principles; know and can *poly 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 evidenceof their ability to select and apply appropriate procedures correctly, verity 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 trie 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 u rounding and ordering. !problem Solving in problem solving, students are required to use their reasoning and analytic biollities when they encounter new situations. Problem solving includes the ability to recognize and formulate problems; determine the sufficiency and consistency of data; use strategies, data, models, and relevant mathematics; generate, extend, and modify procedures; use reasoning (i.e., spatial, inductive, deductive, statistical, and proportional); and judge the reasonableness and correctness of solutions. S THE 1990 NAEP TRIAL STATE ASSESSMENT Texas A scale ranging &am 0 to 500 was created to report pafonnance for each content amt. Each content-area scale was based on the distribution of student performance across all three grades assessed in the 1990 nadonal assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale WU created as an overall measure of students' mathematics proficiency. The composite scale weal" weighted average of the five content area scales, where the v ',eight 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, paformance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In contrast, the NAEP scale anchoring is accomplisheo by describing what students at selected levels 1.1now and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels 200, 250, 300, and 350 -- on the 04o-500 scale. Although pmficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics items fror, the 1990 assessment that discriminated well between adjacent levels. The criteria 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. 90 THE 1990 NAEP TRIAL STATE ASSESSMENT 85 Texas Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize theknowledge, 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 successiblly. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.' Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administratorin 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 processthat involved extensive development, field testing, and review by external advisory groups. MAMEMATICS 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 *,sie use of various instructional approaches. Because of the nature of the sampling fo,. the Trial State Assessment, the responses to the mathematics teacher questionnaity do not necessarily represent all eighth-grade mathematics teachers in a state or territoiy. Rather, they represent the teachers of the particular students being assessed. a Since there were insufficient ntunbers of eighth-grade questions at levels 200 and 350, oneof the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 9 1 86 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 20Ch Simple MOM Reseoning and Problem llohrIng odds Whole 1 Numbers EXAMPLE 1 (?) 4111 lab Oft law T. Lade MO am hip bone al dr roe des erg deo diderer bra al Mb se Arra beer If dr lib realm web dr liar el bib deem ribleb adi bre lb berm bib la id 0 The los rid dr war leie The boa rah Es pNb. b 0 Tie ira rib dr Maw kb 0 be art NIL EXAMPLE 2 20101 OF NLIT AT FAMAWAT RUMS Ale did liar ape OM. IAA 001.1 IAMB bydrali 11. Haw saw bawl a aro, wen picied as Tirsiari SS OS ED 70 0 20 0 20 I 11We brew. rd 9 2 Grade 4 Overall Percentage Ow** iss Pim*. Minot for Anchor Lew* 2122 Mt 222 85 91 100 Grade 4 awaN Percentsge Corroct Parmtve Coma for Anchor Law* 202 2211 220 220 73 91 100 Grade 8 Overall Percentwo Minot 89% Perverstsge Correct for Anchor Levels: 2I/2 2120 SO 220 78 87 98 100 THE 1990 NAEP TRIAL srAm ASSESSMENT 17 Texas FIGURE A3 I Example Items for Mathematics Proficiency Levels (cooliaded) [Level 250: Simple MuldplIcadve Reasoning and Twoaap Problem Solving EXAMPLE 1 7. What is the 'slut of + 5 when n is 3 1 Answer: EXAMPLE 2 Th lat artheilsrsideshiasAssmemoiamiai farazil hale aga. Oa tag dais paes doe a jaag ids :Ta Os mum ab : "Ws. OW yr UN *a otaims, fa ihis analog I* "a Ci EXAMPLE 3 Kabala is podia Web& ass book be bet halal boosiells. Ms 24 balk MA swabar massmos wig bap ha had sus hew mum ism she ail use CD24-440 24 +0..0 026 +4...0 14 Is R CD 44srs famw. Grade $ Cheral roveratas Comet 76% Parasalogs Coma far Anew Lasts IRO MR MI 3131 91110 11110 Grade Mandl paroanawa Comsat 73/4 Pm**. *mkt far Anchor Law* 310 333 X0 1111 21 II 02 SI Grade 8 Oarall Pawleys COITOCO 77% Pam*. Coniat for Mahar LOW* 8011 202 AIR 37 71 06 100 se nm 1990 NAN TRIAL STAIR ASSEIRAENT Texas FIGURE A3 j Example Items for Mathematics Proficiency Levels (continued) EXAMPLE i si ths fieswissiesiss dm nook et Nimplesdoe ees ma*WV *OW EXAMPLE 2 bibs 1.14 Weit thaa Ow it WNW..iti hoe e lemma 17 ego mad I bit* Rag.1111.11, took is tra. bow SS for agebwildi be nembiessi by a WsmeiUm sort tidebela 1 $ 7 DO ma dig isastisvg so shio*twee Cs Vas Cs No ME 1990 MAE? TRIAL STATE ASSESSMENT Grado Nona Poronntago Correct 00% Porosnoies Cannot for Mohor Lewis: 2011 200 33 40 TT 00 94 Grade 12 Overall Potonte0.0 Cornet 7511. Isorosnow Wreck for Anchor Unfair 202 2211 MR ER 70 06 Grade 8 OvIrral PIIMINISIGO Correct 50 Poroontago Gonad for Mohor Lovoic EY2 WO 200 MO 17 48 Oa 00 BEST COPY AVAILABLE 59 MX= FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving invoking Geometric Relationship% Algebraic Equation% and Beginning Statistics and Probability EXAMPLE 1 Q0001000 1,0-17 mit whorollawieg maw .1 ihn4iymeas. It 0 H. Mikis pram al det4lowss * kw way dm MN ha la Ai 100* maw CP 100 ED 101 11P4 MO 301 EXAMPLE 2 hipihe bre yea fowl yes swat as pram IL Arrow go Grade Oweral Percentage comet 34% Percentege Comm* for Andior Leak 202 IA 2211 222 13 19 53 $11 Grade 12 04erall Perventege Correct 40% Pawnees Correct for Anchor Levels; MO RAI 222 222 22 411 00 Grade $ Omni Pementege COITII0t: 15% Pensentegs Coned tor Anchor Lents: 202 212 2112 1 4 2$ 74 Grade 12 Natal Percentage Com* 27% Percentage Correct for Anchor Ureic 222 202 MI 3 22 74 0 r 0 MR 1990 NAB? TRIAL SIAM AssissmENr Texas SCHOOL CHARACTERISTICS AND POUCIES 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 samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEP's goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state ui tetritory were assessed. Virtually all statistics that are based on samples (including those in NAEP) are subject to a certain degree 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 participated in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropriate, set of the assessment questions -- or the entire set of questions -- somewhat d;fferent 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. 96 THE 1990 NAM,' TRIAL STATE ASSESSMENT 91 Texas In addition to reporting estimates of average proficiencies, proportions of students 4 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 uncestainty me called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics pmficiency statistics reflect both KW= 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 UM a methodology called the jackkvife procedure to estimate these standard errors. Drawing Inferences from the Results One of the goals of the Thal State Msessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and tenitory based on the particular sample of students assessed. 011e Wei the restiltS from the sample -- takiag into account the uncertainty associated with all samples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population tilt% ns and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a AS percent confidence ituerval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of intemst (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 t 2 standard errors = 256 t 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for petrentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. 9 7 92 THE 1990 NAEP TRIAL. STATE ASSESSMENT Texas 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 dermed by shared charactesistics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defined by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaite. 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 spending 15 mbsutes or less? To answer the question posed above, one begins by comparing the avensge mathematics prificiency for ere 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, these 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 gement 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 differmce between the proficiency means or proportions of those groups for the sample. Ms 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 wean or proportion is used, the standard error of the difference can be used to help detenrkine whether differences between groups in the population are real. The diffesence 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. 98 THE 3490 NAEP TRIAL STATE ASSESSMENT 93 Texas As an example, suppose that one wcre interested in determining whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard errors for females and males were as follows: Group Avorogo 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 Ni 2.02 + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state? Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two goups, the confidence interval included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to alight 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 statir.ically significant. 3 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 standard error of the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas 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 chapta of this report, many different groups are being compared (i.e., multiple sets of confidence intervals are being analyzed). When one considers sets of confides= 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 certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed desaiption 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 standarderrors subject to a large degree of uncertainty are followed by the symbol "!". In such cases, the standard errors -- and any confidence intervals or significance tests involving these standard errors -- should be interpreted cautiously. Further details concerning procedures for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defined 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 (Mvaataged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and/or background variable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probability of .8 or greater. 100 THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Texas The effect size of .2 pertains to the tile difference between the average proficiency of the subgroup in question and the average proficiericy 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. Descriting 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 rnapitude 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 p = 0 None 0 < p 5 10 Relatively few 10 < p S 20 Some 20 < p 5 30 About one-quarter 30 < p 5 44 Less than half 44 < p 5 55 About half 55 < p 5 69 More than half 69 < p S 79 About three-quarters 79 < p 5 89 Many 89 < p < 100 Almost all p = 100 All 10 1 96 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas ME 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 97 Texas TABLE A5 I Students' Reports on the Matheraatics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pm-algebra Algebra , TOTAL Peronhes fenamia. asNI ana 0:011144magr Proldeny 274 2 784! 2 10 1.9 251 1.4 272 ( 2.4 State Nation RACE/ETHNICITY WNW State es ( 2A) 10( 2.2) 203 ( 1.3) 213( 2.7 Nation 50 ( 23) 21 ( 2.4 259 ( A) 277 ( 2.2 Black State 83 231 ( 3.0) ( 11 ( «b. ( 2.71 Nation 72 ( 4.7 18 3.8) 232 ( 3.4 248 ( 8.4) Hispanic State 77 ( 2.3) 11 ( 12) 240 ( 13) 283( 28) Nation 75 240 ( 4.4) ( 2.4) 13 3.9) *01 TYPE OF COMMUNITY Modantagal urban State SO ( 44) 15 4.8) 245 ( 2.3)1 Nation SS ( 94) 22 209 ( 2.5)1 44* ) Disadvantaged urban State 78 237 3.9) ( 2.2)1 ( 13) ***) Nation 65 ( 0.0) 10 4.1) 240 ( 4.0)1 *MI ( Extreme twig State 79 7.3) 1 0 ( 5.9) 255 3.0)1 Nation 74 249 4.5) 3.1)1 14 5.0) ea* ( *el Other State 70 ( 3.0) 16 ( 2.4) 2413 ( 2.0) 271 3.3) Nation 51 ( 2.2) 20 2.1) 251 ( 2.0) 272 23) 290 244 17 1 2.11 21 i 4.45 «Fe en 1$ ( 2.5) 14 ( 34 2S7 ( t2 10 4.1) 044, * 7 2.2) ( do.) 12 1.1 04 2.7 10 1.41 204 2.7 vmsommo The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for eivh 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. 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 98 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE AS I Students' Reports on the Mathematics MI6 (continued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY NM NAEP TRIAL I Eighth-grade STATE ASSESSMENT L Ma Sumacs Pre-algebra Algsbra TOTAL Pommy and Praia law 2411 02 2.1) 01 14) State Nation PARENTS' EDUCATION HS nowgradttats State 81 ( 2.7) 241 ( 1.8) Nation 77 ( 3.7) 241 ( 2.1) 1111 graduate State 78 ( 2.6) 243 ( 1.8) Nation 70 ( 2.6) 249 ( 1.9) Sem college State 70 ( 3.6) 257 ( 1.9) Nation 00 ( 3.1) 257 ( 2.1) College greduate State 01 ( 2.6) 200 ( 1.0) Nation 53 ( 2.7) 259 ( 1.5) GENDER M. State 72 ( 2.3) 251 ( 1.8) Nation 63 ( 2.1) 252 ( 1.6) Pamela State 71 ( 2.3) 247 ( 1.6) Nation 61 ( 2.8) 251 ( 1.5) Parasodaga and Priladiacy Parcodee sot Iftlialasay 14 12 ( 274 200 ( 19 1.9 ( 12 272 ( 2.4) 295 ( 2.4 12 ( 2.4) op* 13 3.4) ( 264 SA 18 2.4 208 10 ( 2 9) 21 2713 15 205 21 278 13 274 18 275 14 274 20 200 4 ( 0.5) 'I ..**) ( 1.2) Ifts ( 441 8 ( 1.1) 277 ( $2) 12 ( 1.9) Of/ 1.9) 3.2) 2.0) 1.7) 1.7) 2.3) IMP ( ( 2.9) 15 ( ( 2.8) 295 ( ( 1.7) 21 ( ( 9.1) 305 ( ( 2.3) 24 ( ( 2.8) 903 ( ( 1.7) 12 ( ( 3C0 ( ( 1.8) 15 ( ( 2.9) 299 ( ( 1.8) 12 ( ( 31) 293 ( 2.3) 15 ( 3.0) 293 1.3) 2.5) 1.2) 2.5) 1.4) 24) 1.7) 24) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. *** Sam ). le size is insufficient to permit a reliable estimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Texas TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP MAL STATE ASSESSMENT 15 It.inutes 30 Minides 4$ Minutes An Nam or Mara TQTA State Nation Migaintinn WM* State Nation Rack State Nation State Nation reAgf,422VEMILY Arluantapd urban State Nation Disadvantaged State Nation Eidevone nral State Nation Other State Nation Pdroolass Prwandaga and and Praadaraw Pradiailinv 2 ( 1.2) ( *en ( 0.9) eori, 4 ( 2.9) ( *en Erie lin 0 0.0) ( 0.0) O 0.0) .111. ( eel ( 1.6) 230 ( 5.4)1 ow, *on I 0.4) 4. 3.2 212 1 4342 200 23 413 4.4) 287 12) 39 4.5) 285 2.2) 47 ( 231 ( 2.3 55 ( 7.6 232 ( 3.1 441 ( 3.2) 242 ( 2.2) 46 ( 7.6) 245 ( 3.0)1 37 ( 9.6) 269 ( 3.0)1 81 (11.3) 273 ( 3.1)1 51 ( 8.5) 230 ( 24)1 41 (124) 235( 2.1)1 40 (15.1) 4.) OS (142) 253 ( 5.4)1 47 ( 3.8) 254 ( 2.2) 37 ( 423) 258 ( 3.1) Panameass Parasonage and and Pagenbany lindideacy 411 ( 1.2) 251 ( to 289 ( 43 ( 4.3 10 ( tO ( 2..e) 272 ( 43 ( 4.4) 7 ( 1.5) 271 ( 1.7) 202 ( 11.0)? 45 ( 5.1) 11 ( 2.4) 270 ( 2.7) 277 ( Lap 39 ( ( 22) 240 ( 22 ( (gm) 40 ( el 3 ( 1.2) 249 ( 5.3) ( ***) 39 ( 3.0) ( 1.6) 246 ( 2,2) 34 ( 63) 13 ( 2.9) 251 ( 4.2)1 53 ( 274 6.0) ( 3.5) ( 24)1 iNpe) 32 ( 8.8) 5 ( 3.4) ***) 28 230 5.4) 14 34)1 ( 3.3) ***) 38 9.4) 12 52) 253 ( 9.0)1 53 255 14.7) ( 5.4) 4.4)1 *we ***) 14 10.9) ( 5.8) 30 4.0) ( 1.4) 259 2.1) 2130 ( 9.4)1 49 ( 5.1) 10 ( 2.4) 205 ( 24) 278 ( 84)t PorainIa. and Prellaiancy 2 (0.7) sum 4 ( 0.9) 27$ ( 2 0.9) O 11* 4 0.9) 279 ( &as 0.3) INN1 2 ( 0.8) gmt ( *el 2 ( 1.0) go.* ( .44) 7 ( 2.1) ***) 1 ( 1.0) IN* ( ***) 0 ( 0.0) 3 ( 22) ow* ( 10 ( 8.2) 0 ( 0.0) 10 ( 7.3) 2 ( 02) 282 1112)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). 105 100 THE 1993 NAEP TRIAL STATE ASSESSMENT Texas TABLE A6 Teachers' Reports on the Amount of Time (continued) Students Spent on Mathematics Homework Each Day PERCENTAGE OF STULJENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1990 NAEP TRIAL STATE ASSESSMENT Nene 15 ilkinges 30 Mufti _ 45 Minutes _ , An Now or Mont TOTAt. State Nation PARENT*" ERMATKN4 Peraddage and Ptyalin./ 5( 1.1) 232 ( 4.5)1 1 ( 0.3) 444. 5 ( 2.1) ( 1 ( 0.8) 5 1.11) ( 0.5) ( ( 0,9) ( «0,1 ( 0.9) 110** 4 ( 1.4) f+D) 0 ( 0,3) ***) ( 1.4) ( ***) ( 0.3) doe ( 4 ( 1.0) ( «in 1 ( 0.4) *44 ( Paresatage and Pi *Mew 49 ( 34) 252 ( 14) 43 ( 4.2) 258 ( 23) 411 ( 4.1) 242 ( 23) 49 ( 83) 240 ( 2.8) SO ( 4.0) 240 ( 2.4) 43 ( 5.2) 249 ( 3.1) 49 ( 4.4) 290 ( 2.5) 44 ( 5.4) 265 ( 2.6) 43 ( 3.6) 266 ( 2.4) 40 ( 4.7) 285 ( 24) 4/ ( 34) 254 ( 2.0) 44 ( 4.4) 257 ( 2.9) 45 ( 3.2) 251 ( 2.3) 41 ( 4.4) 255 ( 2.3) Pandataila and firsIdem 41 258 43 2813 41 244 40 241 38 251 44 258 43 267 43 270 41 212 44 277 3$ 282 43 268 43 255 43 284 3.0) 4-3 ( 2 ( 3.3) 2.9) ( 1,1) ( 3.7) ( 3.9) ( 2.5) ( 5.11) ( 2.7) ( 4.3) ( 2.8) ( 54) t 3.8) ( 3.8) ( 2.0) ( 4.1) ( 3.0) ( 33) ( 2.3) ( 4,3) ( 2.9) ( 3.0) ( 22) ( 4.7) ( 2.8) Payee., and Pre Scisaty 7 ( 1.2) 209 ( 0.3) 10 ( 1.9) 272 ( 5.7)1 8 ( 1.7) **4.) 1.7) *Mk MIMI a ( 1.1 ) 9 ( 3.1) *in 5 ( 1.8) 0. 7 ( 2.1) tre 11411 9 ( 1.9) 282 ( 7.9)1 11 ( 23) 287 6.1)1 ( 1.3) 268(8.0) 9 ( 1.9) 273 ( 73)1 7 ( 1.3) 270 ( 8.1)1 11 ( 2.0) 272 ( 5.7)1 Pardeatip and Madam 2t. 4 278 2 ( ( 4 ( 1 (04) .e 3 ( OM* 4 ( 2 ( *14(44*) 5 irk* 2 5 279 2 0.7) opin 0,9) 5.1)4 1.0) 1.31 di**) 1.0) *** 0.5) On 1.0),) 1.1) ( 1.3) ( 111111 0.9) ( ( 1.3) ( 7.7)1 ( 0.7) ( *01 148 non-wacksato State Nation 118 graduate State Nation Same college State Nation College graduate State Nation GENDER MN* State Nation Fan181* 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 far 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 estitnate (fewer than 62 students). 106 THE 1990 NAEP TRAL STATE ASSESSMENT 101 Texas TABLE A7 I Students' Reports on the Amount of Time They i Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP MAL. STATE ASSESSMENT Nem - 15 Mimeos 30 Minutes 48 Minutes An Noir or MOM , TOTAL 44344414. and Pr44/41344$ 12 257 $ 251 14 271 10 224 10 404 464 11 243 12 444 13 8 4440 13 12 4404 444 44. 12 252 9 250 2.2 04 2.3) ( 1.6) ( 1.6) ( 1.0) (3.4) ( 1.8) ( ( 1.5) .44) ( 1.2) ( 3.1) ( 1.8) ( .41 ( 2.3) 2.5) ( 441 ( 1.0) ( 3.7) 4441 ( 444/ ( 2.3) ( 1.1) ( 2.8) ( 1.0) ( 36) Parambips mid Prelisitacg 24 I.0 216 1 31 2.0 ) 266 14 2$ 1.5) 274 13) 33 2.4) 270 ( 1.9) 2$ ( 2.4) 223 3.2) 24 2.5) 241 3.3) 25 ( 1.2) 248 ( 2.5) 27 ( 3.0) 248 ( 3.8) 32 ( 24) 275 2.8)1 41 12.5) 278 ( 3.0)1 24 ( 2.5) 244 ( 3.7)1 24 ( 3.3) 253 ( 4.9)1 24 ( 2.8) 98 ( 4.8) 200 ( 3.5)1 25 ( 1.4) 259 ( 2.4) 30 ( 1.8) 263 ( 2.3) 1114m4138$ NW 1440liony SO ( 1.0) 2741( IA) 22 ( 1.2) 243( 1.9) 30 ( 1.4) 273 i.15) 32 12) 270 ( 2.1) 28 ( 2.9 234 ( 2.7) 33 ( 2.7) 237 ( 3.5) 30 ( 1.5) 240 ( 1.9) 30 ( 2.0) 248 ( 3.4) 31 ( 2.8) 278 ( 2.8)! 31 ( 8.8) 280 ( 4.0)1 30 ( 2.8) 247 ( 3.4)1 31 ( 3.0) 247 ( 4.7)1 22 ( 4.3) 31 ( 2.9) 255 ( 5.1)1 31 ( 1.3) 259 ( 2.0) 32 ( 1.3) 264 ( 2.3) 114111011131$11 aid Pralaboacf 13( 255( 2.1 10 f 1.0 203( 1.4 14 0.9) 273 2.2) 1$ 0.9) 277 ( 2.2) 24 ( 23$ ( 3.1 18 ( 2.3 240 ( 3.0) 17 243 2.7 17 2.1 241 ( 4.3) 13 ( 1.8) ( 441 12 ( 3.3) 444 ( 19 ( 2.3) 241 ( 3.5)1 20 ( 1.9) 260 ( 4,8)1 17 ( 2.8) 4414 .41 18 ( 3.8) ( .41 18 ( 0.9) 258 ( 2.9) 15 ( 1.1) 267 ( 2.1) POMMIIIIIII and 44,11411111314, 15( 1 241( 12( 1.1 264( 3.1 14 ( 1.0) 274 ( 3.3) 11 ( 13) 288 ( 3.3) 10 ( 1.9) .44 10 ( 1.9) 232 ( 3.7) 17 ( 1.4) 247 ( 3,5) 14 ( 1.7) 4.1 11 ( 1.4) ( 3.4) 4.4 ( 14 ( 2.8) 14 ( 2.2) ( .") 20 ( 3.1) 44. ( 441 ( 2.r) 18 ( 1.3) 255 ( 2.9) 13 ( 1.1) 258 ( 3.8) State Nation AffinTIEVIU Mite State Nation Mac* State Nation Hispanic State Nation TYPE OF COMMUNITY AdVantacod urban State Nation Disadvantaged urban State Nation Wrenn mai State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with shout 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). .107 102 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE A7 I Students' Reports on the Amount of Time They (Continued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . 12Wi NAEP TRIAL s AESU um NI IENT N ana 15 Motes 30 IMO. 45 Minutes 1 An Hour or Yoro TM& SAtte Nation Eggsmggssagg 14$ noniroarato State Nation HS graduate State Nation Remo collage State Nation Canoga graduate State Nation GENDER Mal* State Nation Funail State Nation 13 1.61 17 &OS 'ft...) 249 SA) 248 4.2) 1.5) 11 C tsi «b. a 1.2} 13 ( 1.8) 272 ( 3.2) ( 0.9) 235 ( 32) 14 ( 1,2) 255 253 32 11 1.1 11 ( 12) 250 ( 2.1) 7 ( 0.9) 245 ( 4.1) 520 I 3 290 ( 32 25 ( 1/) 33 ( 2.2 2113 32 2111$ ( SA 30 2. 27 274 24 ) 7$ ) 25 2.0 i.5) 31 44) 2 24$ 2.7 245 4.4 32 24 $ 1 MN, 22 Si 1 254 2.4) 38 ( 2.1 2.9 ( 279 ( 1. SI ( 2.0 275 ( 2. ( 274 SA 14 I .1.1 13 4:1 10 1. 272 1$ 12 14 1 *TS 701 ta 27 14) 223 2.0) $4 2.4) 234 22) 25 1,3 256 2.0 29 2.0 283 1 31 2320 280 30 257 35 200 4.4) 12 2.4 1,4) 13 2.0 15 255 15 SS 15 223 17 217 1.2 IS 1.2 3.0 02 2.9 14 24 Si 24 13 1$ 239 SA The standard errors of the estimated statistics appear in parenthetes. 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). 1 S THE 1990 Nit EP TRIAL STATE ASSESSMENT 103 Texas TABLE AS I Teachers' Reports on the Emphasis Given To I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Webers and Operadens M.ea Oestestry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation Ifisents_r_t Witte State Nation BIM* State Nation Hispanic State Nation TYPE OF CommenfiTy Advantaged urban State Nation Disadvantaged State Nation Extreme rural State Nation Other State Nation Paraluirp jyroalleas Posvor4a. P468911,8113 Awasiasse loircontapo and ARO OM Me Priapism Pirdaisnar Priikking Pradiney Fralkftrav 2Lfa 40 3.$ 15 2.1 260 1.1 287 3.4 Sa ( 4.5) 8 1.7) 270 ( 1.7) 210 48 ( 3.7) 18 2.4 207 ( 2.2) 200 3.5 58 ( 6.7) 4 1 tin ZOO ( 3.11 .. ") 54 ( 7.9 11 ( 3.3) 243 ( 43) *** ( ) 55 ( 3.8) 8 ( 2.1) 248 ( 1.9) "" ( -n 47 ( 11/) 8 ( 2.2) 248 ( 4.8) "" ( ***) 57 ( 3.2) 5 ( 2.2) 272 ( 2.7$ "4' ( ***) 26 (13.0) 18 ( 4.2) ". ( ...) ... ( ...) 95 ( 9.5) 8 ( 3.5) 247 ( 3.1)1 *** ( ***) 4$ (12.1) 9 ( 4.0) 255 ( 03)4 11* ( "") SS (18.1) 6 ( 8.2) 17 3. 250 2e 4,3) 281 14 3.4 250 8.9 30 8.2) 218 5.2 25 7.4 228 ( 2.6 )4 32 ( 239 ( 3.5 23 ( 4.1 *" ( ***) to 19 ( 7.5) ( ***) 9 ( 7.0) "" ( ***) 46 (10.5) 239 ( 4.3)4 39 (10.3) 239 ( 34)4 24 (12.8) 231,1 272 4,0f 20 ( 3.1) 278 ( 4.2) 38 ( 4.7) 277 ( 43) 14 ( 4.5) *** ( ***) 23 ( 5.7) 2311 ( 6.1)4 20 ( 3.3) 248 ( SA) 34 ( 5.8) 255 ( 4.4)1 12 ( 4.7) ~ ( ***) 40 ( 6.5) ". ( ..") 20 ( 6.0) 250 ( 6.2)4 21 ( 8.5) ( ***) 14 ( 7.9) 14.04 280( 32 2341 541 37 $.3) 10( 2.2 270 4.8 27 4.4 22 34 205 $.3 273 5.11 40 ( 11 ( 3.7) 211$ ( WI ". ( `") 33 ( 7.0 24 ( 7.3) 242 ( &SP 291 ( 4.79 38 ( 3.8 15 ( 2.9) 248 ( 3.1 241 ( 5.11$ 21 ( 0.3 18 ( 5.5) *** ( *** "" ( *ft) 31 ( 8.7) 12 ( 3-3) 200 ( 4.7)! *" ( "1 36 ( 3.4) 13 3.2) 267 ( 49)4 l'e ( ***) 54 ( 99) 11 ( 3.7) 242 ( 3.39 *** ( ***) Xi (11.6) 18 ( 7.3) 24$ ( 3.2), *** ( "e) 35 ( 9.2) 9 ( 8.4) 283 ( el)4 *** ( 444) 41** ( eft) t4i ( MN) i 1,111 NO ( Mt) 33 (12.4) 8 ( 3.8) 8 ( 4.0) 32 (11.7) 9 ( 6.1) 18 ( 7.9) 257 ( 7.1)4 *** ( ***) *** ( -) 295 ( 9.1)4 *** ( ) ". ( `e) 80 ( 4.3) 8 ( 1.11) 2$ ( 43) 20 ( 3.4) 33 3.3) 13 ( 2.8) 238 ( 2.2) 278 ( ikay 245 ( 4.0)4 200 ( 4.3 256 3.3) NS ( 9.2)4 52 ( 4.1) 113 ( 2.7) 18 ( 3.9) 34 ( 5.3 23 4.8) 24 ( 4.3) 280 ( 2.3) 2$8 ( 3.8) 253 ( 7.1)4 270 ( 4.8 259 ( 3.9) 295 ( 5.7) "MINIM 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 olution - 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). 104 1 f: THE 1090 NAEP TRIAL STATE ASSESSMENT Texas TABLE ASI Teaches' Reports on the Emphasis Given to (continued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 NOUP MAL STATE 12$111041MT atunhers and Operations GIMIMOITY "limy Emphasis Little .x No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis /2IeL State Nation ffil IlitiMENADSVI NI noniradole State Nation Ns grailluab State Nation Sam cape State Nation Coley graduate State Nation MEE Mai State Nation Female State Nation 45 10 ft( 3.7) 9 2.1 0 44 17(II 'I CT.; 3:1:11 "71 2.4) en 2401 L7 0 0.0 1 2.3 2360 la 26 (6.3 ell! It; 20 0.7) 951 3.4 IA* 4"4 "11 flirt' 150 2.9 1 1. 29 4.4 V LS 29i 9.0 .:11 .V. ate ***I 4.1 245 45 ON( 3.7 251 0.1 SS 4. 20( 4.2 241 41 27 2?( 4,-, 24 51 STO 2.4 It1 142:1 47 44 17 3.3) 12( 2.7 SO SA) 27 ItIl 23I :IS rI 1.71 257( 5.3 20( 4.SI 42I V..1 17 4.4 11I 2.1? 1.5 204 4.11 ( 4") VA 45) 02 4.1 270( 4.7) 57 6.2 9( 11 261 44111 22c 3.0 0 4.1) 13( 21 20 IS 2911( 2.4 254( .2 263 II 270 1.11) 230 OA) 09 2.1 44 4.1I 4731 274 16( 1.3 23111 SA 51 20 2A) 271 6.4 OS 1.4) 21 2.9 0 $.7 5 1.1 0( SA 19( 2A 36 3.1 1$ 2.1 1 150 2.1 279 41 441 14 2.1 17( 3.3 32 3.9 210 4.1 20 3.3 ( 3.2 021 4.0 259 2.1 254 5.1 361 2.5 267 4.4 253( &T 215 4.3 20 3.1 20 OA faI 1:1 7i 1.41 30( 3.1 19( 2.1 241 4.5 ft591 5.9 25 2.2 SO1 3.3 341 5.4 20 4.1 256 3.3 20 5.0 1? 3.2 SI 4.3 23 3.5 11( 2.21 51 29 15 2.4 IWO 2.0 20 3.3 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 witlim *2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included.t Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permita reliable estimate (fewer than 62 students). no THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Texas 4.111M/IPIM.M TABLE AS I Teachers' Reports on the Emphasis Given To (continued) i Specific Mathematics Content Areas PENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1810 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra and Rind Ions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation RcritTmeciTy whit. Slate Nation track State Nation Hispanic State Nation TYPI Of COMMUNITY Advantaged urban State Nati on Disadvudapd urban State Nation Extrma nral State Nation Mir State Nation Snoods* aid flidlaioncy ale.01161.11 nod Itallalatur iltdidansy 250 4.4 209 ( 43 14 2,2 SS 44) 2#11) 261 2.1) 47 ( 3.3) 52 2.$ 2Si 1.0 2/5 46 237 it) 243 2.1) 20 3.0 19 ( 3.2 200 3.91 141 2.4 276 4.1) 2$ I 2295.3 141 3.4) ONO ( 0.19 23.2 24:1 4.11 15 ( 4.1) 22 ( 6.0) ( 441 lIt 6.6) 7.3) 232 4.7)1 11 OA) *In 5.8) . *41 5 ( 54) *an 33) 206 5.1 15 2.91i 257 4.7 50 ( 4.2) 270( 3.0) $3( 5.0) 271 ( 3.1) 41 ( 5.1) 223 ( 4.1) 53 ( 82) 22$( 4.3) 45( 237 ( 3.3 56 ( 6.3 246 ( 4.4) 37 ( 7.1) OM ( 4.0)1 05 (10.4) 284 ( 7.4)1 41 7.411) 240 5.7)1 34 11.4) 23ti ( 02)1 58 264 T.5)1 85 119) 254 15.7)1 4.3) 252 32) 53 12) 2410 14) 577 2 I 4 42 281 3.0 47 ( 4.6) 244 ( 2.9) 30 ( 1.4) 253 ( 6.3) 50 ( 3.4) 250 ( 2.4) 46 ( 5.9) 257 ( 4.0)1 51 7,9 278 3.6 41 8,9 298 7.9)1 53 ( 741) 253 ( IA)1 53 (If A) 254 ( 6.3)1 " 33( 8,11 *al 54 44) 205 2.5) 47 43) 276 2.5) 12 ( 3.8 18 24 3.3) I g 0.8 27 ) 226 2.2)i 15 2.2) 223 3.8) 18 41 «a* coom 11 3,2) Illf 0.1 18 5.3) ". i "1 2.7) 20 0.41 26 (17.7 42116.011 241 45.5 1$ 222 44 17 3.3 245 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 percentages may not total 100 percent because the "Moder...4 emphasis" category is not included. 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). 106 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE AS I Teachers' Reports on the Emphasis Given To (continued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEW TICS PROFICIENCY 1NO NAEP TRIAL STATE ASSESSMENT Data Analysis, Statisticik and Rub* lity Algebra and Rmattans Heavy Emphasis Little or No Emphasis HeavY EmPhasts Lae or No Emphasis yoTAL. state Nation 12anntigartATM NS non-waduate State Nation NS graduate State Nation Some coNage State Nation cola", graduate State Nation GEI4DeR Male State Nation Female State Nation 1St 3,21 50 237 3.3 ( 3.05 53 ( 1.7 ( 23 ( 45 ( 32) 244 ( S2 17 ( 3.7 242 ( ( SA 281 ( 247 ( 2.9 22 ( 3.7) 45 ( 3J) 271 t 5.1) 264 ( 3.5) 1?. ( 2.5) ( 2TO ( 5.6) 3.7) 20 ( 2.6) 47 ( 4.0) 27$ ( 8.3) 271 ( 3.7) 15 ( 2.4) 53 ( 4.4) 262 ( 4.5) 275 ( 3.6) 19 ( 2.6) 47 ( 3.4) 251 ( 10) 135 ( 2.9) 13 ( 2.2) $4 ( 4.7) 275 ( 5.6) 280 ( 15) 21 ( 2.6) 47 ( 3.8) 25$ ( 4.1) 251 ( 2.8) 10 ( 24) 53 ( 4.5) 253 ( 44) 262 ( 2.6) 42 ( 43 246 ( 2$ ( 5.21 or* 2344 I 3 23.41 44 ( 265 ( 15) 50 ( 4.1) 272 ( 't.1) 45 ( 45) 271$ ( 10) 57 ( 3.0) 27$ ( 2.5) 50 ( 3.9) 52 ( 2.7) 284 ( 2.2) 44 ( 4.1) 27$ ( 3.2) 51 ( 3.3) 264 ( 2.3) 46 ( 3.6) 274 ( 2.7) 16 ( 22) 211 ti 16 ( as) 237 ( 0.3) 23 ( &I) 239 ( 3.4) 10 2.71 *el i.po *n1 17 (3.1) 9 ( 2.0) ( 04* 249 ( 4.0) 18 ( 2.4 14 ( 2.4) 240 ( 4.7) 22 ( 34) 243 ( 3.0) 12 ( 1.9) 233 ( 4.1) 16 ( 2.9) 244 ( 39) 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). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT 107 Texas TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , ISIO NAEP TRIAL 10st AM the Reseurese 1 I Set Meet et the 1 ON Son yr Nene o( STATE ASSESSMENT Need Mow= I Need the Nesearoes I Need , State Nation MaiMMINO. State Nation Mack State Nation Hispanic State Nation mg_w_imadyx_Tv Advantaged urban State Notion Disadvantaged urban State Nation Etdrama nral State Other state Nation 22 4.3 51 1/I ri U 271 275 170 61! 1 5 51 0 241 SAY iti OS 1 se so 3.4 17 $ 11 240 ( 73 23 i 1 44:1 rti 250 2.1 144 Se $4 TA 27$44 al 27$ $.011 M 2.2 911 SA 272 ( 11.51 200 ( 13$ 20 C 5.0) 24410 04 10 9.7) 2 24) 2531 41 205 1LS 11 24 2$1 &Of 8.1111 40 1$.1 1141 ae $$$ 11 3$1 30 t 7. 200 ( 43 255 ( 1.4 34 (1044 ST 257 .2« fire* 43 $1 2S0 2.3) $4i) SS SA) 41' 0 3.0 0 204 2.1) ors g 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 accunte determination of the variability of this estimated mean proficiency. "" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 108 1 t) THE 1990 NAB!' TRIAL STATE ASSESSMENT Texas TABLE A9 I Teachers' Reports on the Availability of (wntinued) Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MAEP TRIAL I Dot All the Rosourcas I I Oat Most of the I Get Soma or Was of STATE ASSESSMENT Nited Rosources I Nood the Resources I Rood TOTAL Porosnhega Prelklancy and Prolakoncy Pertamisp and 1114v641incy State 20 ( 2.9) 51 ( 3.3) 23 ( 3.1) 257 ( 3.0) 256 ( 1.6) 249 ( 2.8) Nation 13 ( 2.4) 58 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 261 ( 2.9) PARENTS' EDUCATION HS non-graduate State 19 ( 4.0) 52 ( 5.0) 29 ( 4.0) 241 ( 4.4)1 247 ( 2.2) 23411 ( 3.1) Nation ( 2.6) 54 ( 5.7) 38 ( 8.3) ( 244 ( 2.7) 243 ( 3.5)1 NI graduate State 17 ( 3.1) 49 ( 4.1) 34 ( 4.3) 245 ( 4.8) 249 ( 2.5) 245( 11) Nation 10 ( 2.5) 54 ( 4.9) 36 ( 4.9) 253 ( 4.8)! 256 ( 1.3) 256 ( 2.6) Some collage State 20 ( 3.9) 57 ( 4.2) 23 ( 35) 267 ( 3.5) 266 ( 2.2) 255 ( 4.1)) Nation 13 ( 3.3) 62 ( 4.3) 25 ( 4.1) *fh* IMO) 269 ( 2.5) 267 ( 348) Cottage graduate State 22 ( 3.7) 51 ( 3.6) 27 ( 3.6) 270 ( 3.1) 272 ( 2.5) 262 ( 3.5) Nation 15 ( 2.9) 56 ( 4.9) SO ( 5.1) 276 ( 5.4)1 270 ( 2.2) 273 ( 3.7) GENDER Male State 21 j 3.0) 491 3.4) 30 ( 3$) 259 ( 4.1) 259 ( 2.0) 253 ( 2,9) Nation 13 1 2.0) 57 ( 4.0) 30 ( 4.0) 284 ( 5.0)1 265 ( 2.6) 264 ( 3.3) Femal. State 19 ( 3.1) 52 ( 3.5) 291 3.0) 255 ( 3.5) 256 ( 2.1) 2451 2.9) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 266 ( 3.9) 284 ( 2.0) 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 Minute for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Semple size is insufficient to permh a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 109 Texas TABLE AlOa I Teachers' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL TATE ASSESSMENT At Least once a Week Lass Than Ono a weak Never 1411416011114, 214{ 31( 2.5 50 4.4 20D 2.2 36 ( 4.3) 273 2.3) 40 44) 205 ( 2.7) 43 ( SS) 232 ( 2.3) 47 ( 0.1) 240 ( 3.4) 42 ( 242 ( 3.0 84 ( 7.2 24$ ( 2.$) 41 (11.3) 270 ( 3.1)1 39 (22.9) ( *el 44 (102) 230 ( 4.0)1 70 (MT) 241 ( 4.8)1 22 ( 9.4) eye .hm) 33 (14.$ ) 255 ( 5.5)1 42 ( 40) 250350 43.41 2110 2.4) Perassnage and Pindidisury SO 2$7 43 204 55 26$ 43 271 42 237 43 238 47 245 32 247 51 274 41 273 40 246 21 249 267 51) 256 4$ 257 44 264 ( 3.0) ( 1.0) 4.1) ( 2.3) ( 4.0) ( 1.7) ( 4.5) ( 2.2) ( 5.9) ( 2.2) ( 7.0) ( 4.0) ( 5.0) ( 16) ( 0.9) ( 6.3)1 (10.5) ( 3.8)1 (17,9) ( 6.0)1 8.3) ( 2.8)1 ( 9.0) ( 0.7)1 ( 64) ( 3.7)1 (17.1) ( 5.9)1 ( 4.5) ( 16) ( 4.5) ( 2.8) Parcentaga and Preardaacy 10 ( 250 ( 4.0 $ ( 2.0 277 ( 5A)1 8 ( 2.2) 267 ( 3.5)1 8 ( 2.3) 255 ( 4.9)1 45 ( 3.2) 111** d441 9 ( 4.1) 44 ( **) ( 2.1) 244 ( 3A)1 4 ( 14) ( ( 4,1) 441 20 (12.2) 444. 16 ( 4.0) 247 ( 4.6)1 0 ( 8.5) 0 ( 0.0) 1144 ( M.* ) 9 ( 9.6) it ( fin 11 ( 2.4) 24$ ( 84)1 ( 1.8) 277 ( 8.3)1 State Nation RACUETHNICITY Mats State Nation Mack State Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extrema rural Stade Nation Myr State Nation 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 esthnate 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 ttudenu). 1 4. 110 THE 1990 NAEP TR1"L STATE ASSE&SMENT Texas TABLE AlCia I Teachers' Reports on the Frequency of Small (cpntinul) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a W. _ Less Min Once a Week Never TOTAL Percletage and Preached pereentaff owl Preached Pereenlase and Prolidend State 38 ( 3.6) 50 ( 1.6) 10 ( 1.7) 255 ( 2.5) 257 ( 1.6) 250 ( 4.0) Nation 50 ( 4.4) 43 ( 4.1) 8 ( 2.0) 200 ( 2.2) 204 ( 2.3) 277 ( 5.4)1 PARENTS' EDUCATION HS noniraduat State 33 ( 4.9) 243 ( 3.0) 54 ( 4.8) 244 ( 2.5) 13 ( 2.8) op* ( *on Nation 00 ( 6.4) ( 1.4) 244 ( 3.2) 244 ( 3.2)1 Mit ( IMP) HS graduate State 42 ( 4.5) 243 ( 3.3) 48 ( 4.4) 252 ( 1.8) 10 ( 1.0) ***) Nation 40 ( 48) 45 ( 5.1) 2.5) 252 ( 2.6) 257 ( 2.7) Some college State 37 ( 4.6) 264 ( 3.5) 50 ( 4.0) 265 ( 2.4) ( 1.8) oke) Nation 51 ( 52) 42 ( 5.1) 7 ( 2.3) 268 ( 3.1) 268 ( 3.2) *Or* ( *41 College graduate State 42 ( 4.4) 47 ( 3.8) 11 ( 23) 272 ( 3.0) 270 ( 2.1) 258 ( 5.9)1 Nation 48 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 275 ( 3.0) 285 ( 4.9)1 GENDER Male State 40 ( 3.9) 50 ( 3.7) 10 ( 1.8) 257 ( 3,0) 258 ( 1.8) 251 ( 4.1) Nation 50 ( 4.5) 42 ( 4.0) ( 2.1) 281 ( 3.0) 2SS ( 3.1) 278 ( 5.3)1 Femal State 39 ( 4.1) 51 ( 3.8) 10 ( 1.8) 254 ( 2.7) 255 ( 1.9) 249 ( 4.7) Nation 50 ( 4.7) 43 ( 4.7) 7 ( 2.1) 25S ( 2.2) 2e3 ( 2.1) 275 ( 0.0)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. 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). THE 1990 NAEP TRIAL STATE ASSESSMENT 111 Texas TABLE Al Obl Teachers' Reports on the Use of Mathematical I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111110 MEP TRIAL STATE ASSESSMENT , _ At Least Once a Week _ Lees Than Once a Week atom . TOTAL Pergentana and Polk Macy novanimip and PonSaissa Paroanfana and Proldnnay State 24 ( 8.0) 70 ( 3.0) 1.4) 244 ( 2.5) 257 ( 1.5) 25a ( 50)1 Nation 22 ( 34.7) 254 ( 3.2) Oa ( 4.9) 1.0) ( 2.8) 242 ( 5.9)4 RACE/ETHNICITY Mite State 19 ( 3.6) 77 ( 3.6) 4 ( 12) 207 ( 2.1) 270 ( 1.7) Nation 17 ( 4.0) 72 ( 4.2) 10 ( 2.7) 261 ( 3.8)1 240 ( 2.1) 288 ( 6.2)I Slack State 36 ( 5.5) 81 ( 6.0) 3 (1.8) 232 ( 3.0)1 234 ( 2.2) Nation 22 ( 5.9) 233 ( 5.9)1 70 ( 6.3) 241 ( 2.9) 8 32) ( 01 Hispanic State 2$ ( 4.0) 64 ( 4.3) 8 ( 2.4) 241 ( 2.6) 245 ( 1.8) 240 ( 4.4)4 Nation 39 ( 7.5) 55 ( 7.3) 247 ( 3.8) 245 ( 3.8)1 TYPE OF_COMMUNITY Advantaged urban State 86 ( 4.5) ( 1.0) ( 274 ( 2.8)4 Nation 23 (14.4) 63(11.5) 278 ( 5.8)1 Disadvantaged urban State 29 ( 7.3) 66 ( 8.9) 235 ( 2.8)1 244 ( 2.6)1 4414 ( 44r1 Nation 39 (11.4) 59 (12.1) 2 ( 1.8) 247 ( 7.5)1 253 ( 7.0)1 Extreme rural State 28 (18.0) 64 (18.2) 041,* *41 200 ( 5.9)1 Nation 27 (14,9) 65 (14.6) 8 ( 3.9) 44,4 ( *41 282 ( 2.8)1 Other State 25 ( 3.6) 68 ( 3.4) 7 ( 2.3) 252 ( 3.4) 257 ( 1.9) 253 ( 7.3)! Nation 19 ( 4.3) 72 ( 5.0) ( 3.3) 253 ( 3.9)1 263 ( 2.2) 281 ( 7.1)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. ! 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). 112 1 `i 7 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE Alt% I Teachers' Reports on the Use of Mathematical (cmtinued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IOW NAEP TRIAL STATE ASSESSMENT Al Least Once a Weak Lass Than Once a Weak Now TOTAL, parommlago aW Praksheacy Ihroodage aml Prollokocy State 24 ( 3.0) 70 ( 240 ( 2.5) 257 ( 1.5 Nation 22 ( 3.7) 05 ( 234 ( $.2) 253 ( 12 PARENTS' EDUCATION HI normraduate State 24 ( 3.6) $$ ( 41) 242 ( 3.7) 243 12) Nation 23 ( 5.8) 90 72) 243 2.2) 143 graduat State 26 ( 33) 70 3.8 244 ( 43) 249 2.01 Nation 23 ( 41) 70 53 246 ( 4.0)1 255 ( 22) Some college State 21 ( 3.5) 73 ( 3.6) 256 ( 3.7) 207 ( 23) Nation 1$ ( 4.0) 73 ( 4.3) 201 ( 4.4)1 209 ( 2.3) College graduate State 22 ( 3.0) 72 ( 3.3) 201 ( 3.5) 271 ( 2.0) Nation 20 ( 3.9) 09 ( 3.7) 206 ( 3.5)4 274 ( 2.2) GENDER Male State 2e ( 32) 09 ( 3.3) 242 ( 3.0) 259 ( 1.7) Nation 22 ( 4.1) 55(4.1) 255 ( 4.1) 20$ ( 2.1) Female State 23 ( 2.9) 70 ( 31) 249 ( 2.0) 250 ( 1.8) Nation 21 ( 3.0) 09 ( 4.2) 254 ( 3.3) 262 ( 1.9) 110990990. ail 11Proilissir 7 31) .e. .4.1 SS) 44* I 4+1 5 1 .2 7 ( 21 NIP ( Mb ..! f !..q el i 2.4) 5 i 1.5) .01.1 11 ( 2.5) 297 ( 4.2)4 5 ( 13) 44..) ( 2.0) 247 74)1 7 1.6) 255 52)1 10 3$) 278 8.0)4 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ." Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I. s THE 1990 NABP TRIAL STATE ASSESSMENT 113 Texas TABLE Al la 1 Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once I Weak or Lass TOTAL Pereeniase awl Proliclency Pereentege and Prolisiency Pervade. erri Proficiency State 02 ( 3.2) 29 ( 3.1) ( 1.2) 256 ( 1.7) 251 ( 2.3) 254 ( 58) Nation 62 ( 3.4) 31 ( 3.1) 7 ( 1.13) 267 ( 1.6) 254 ( 2.9) 200 51P RACE/ETHNICITY Whit^ State 66 ( 3.9) 27 ( 3.9) 8 ( 1.5) 271 ( 1.6) 288 ( 1.8) 278 ( 3.9)4 Nation 64 ( 3.7) 2$ ( 32) ( 2.3) 272 ( 1.9) 284 ( 3.4) 264 ( 5.4)4 Black State 56 ( 7.2) 31 ( 8.7) 14 ( 4.7) 2113 ( 3.0) 233 ( 2.5)1 Nation 50 ( 7.7) 41 ( 7.9) 2 ( 1.4) 244 ( 4.0) 233 ( 3.9)1 IMPIt ( NMI Hispanic State 60 ( 4.5) 31 ( 4.3) 8 ( 2.1) 248 ( 1.0) 241 ( 24) 242 ( 4.1)4 Nation 61 ( 251 8.8) ( 3.1) 32 ( 240 5.3) ( 4.3)4 $ ( ( 2.3) *41 TYPE OF COMMUNITY Advantaged urban State 54 (122) 31 (10.1) 15 ( 7.4) 274 ( 3.5)1 270 ( 2.1)1 Nation 63 (15.9) 14 (14.8) 283 ( 7.3)1 Diudvantagad urban State 59 ( 9.7) 24 ( 7.7) T ( 4.1) 240 ( 3.1)4 237 ( 3.6)1 "" ( 4" ) Nation 60 (10.7) 31 (11.1) 4 ( 2.2) 252 ( 4.7)1 243 ( 8.0)I "" ( 4") Extrema rural State $6 ( 261 ( 3.2) 3.6)1 14 ( ( 8.2) *el 0 ( ''" ( 0.0) '") Nation 50 (10.5) 208 ( 4.0)1 40 (10.0) 247 ( 7.6)1 10 ( *44 ( 7.3) Other State 00 ( 42) 31 ( 4.0) 9 ( 1.7) 251 ( 2.3) 253 ( 2.4) 253 ( 7,9) Nation 83 ( 3.9) 31 ( 3.5) ( 1.9) 207(2.3) 265 ( 3.1) 257 ( 5.8)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. "'it Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE Al la I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Almost Every Day , Several Times a Week About Once a Week or Less TOTAL State Nation nagnumssmi NS nanireduate State Nation Ns graduate state Nation some college State Nation Waage graduate State Nation 22110 Maie state Nation Female State Nation oat Progialmeqf Parowlia and Prelkienci Perosiell. aid Prailidency 92 $.2) 29 250 1. 2541 2.3 254 5.9) 3.141 31 31 7 1.1) 207 iA 254 2.0) 200 5.1)1 08 4.43) 244 2.0) 87 5.5) 246 3.2) 152 ( 3.5) 250 ( 2.2) St ( 4A) 257 ( 2.5) 20" 23.9.41 OS 4.2) 272 2.7) 61 ( 3.9) 272 ( 2.2) 51 ( 4.0) 261 ( 2.2) 92 ( 32) 210 ( 1.9) SO ( 37) 269 ( 2.1) 63 ( 3.6) 256 ( 2.0) 05 ( 3.6) 253 ( 1.6) 27 ( 4.4) 240 3.6) 27 5.2) 31 ( 3A) 7 2.2) 8 ( 2.1) 8 (1.8) 24S 2A) 34 ( 3.7) 250 ( 2A) Welt Mil ( 1.5) gran 3D (4.0) 256 32) 8 (( 1.3) .41 28 3.7) ( 1.9) OS 5.2) ( *4.) 23 ( 3.8) it ( 1.3) 285 ( 2A) 288 ( 7.4) 31 20$ ( 3.9) ( 3.1) 3 ( .44 ( 3.1) 29 ( 32) 9 ( 1.2) 263 ( 3.1) 253 ( 0A) 33 ( 34) 7 ( 1A) 256 ( 3A) 201 ( 67)1 39 ( 2.4) 7 ( 1.3) 249 ( 2.3) 256 ( 5.0) 21 ( 3,3) 7 ( 2.2) 233 ( 2.3) 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. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 11 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1.2 0 THE 1990 NAF.P TRIAL STATE ASSESSMENT 115 Texas TABLE Alibi Teachers' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Least Several Tithes STATE ASSESSMENT a Week About Once a Week Less than Weekly TOTAL Poundage and Pro /Monty Panonlap and Prod/dem Parandaga and Prallidency State 41 ( 3.2) 32 ( 3.5) 27 ( 3.3) 255 ( 2.1) 253 ( 2.5) 250 ( 3.4) Nation 34 ( 3.6) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 250 ( 2.3) 274 ( 2.7) RACE/ETHNICITY Whit* State 43 ( 4.1) 31 ( 4.5) 26 ( 3.9) 268 ( 2.1) 206 ( 2.6) 277 ( 2.8) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 266 ( 2.7) 279 ( 2.9) Mad( State 39 ( 6.9) 28 ( 6.5) 32 ( 7.9) 234 ( 2.5)1 234 ( 2.5)) 231 ( 4.4)1 Nation 45 ( 75) 31 ( 7.8) 23 ( 6.3) 232 ( 3.1)1 243 ( 2.3)1 248 ( 7.0)1 Hispanic State 39 ( 4.0) 3$ ( 4.3) 25 ( 3.8) 242 ( 2.3) 243 ( 2.5) 248 ( 2.6) Nation 41 ( 7.7) 26 ( 5.3) 33 ( 7.5) 242 ( 3.2)1 244 ( 5.131 257 ( 2.3)1 TYPE OF COMMUNITY Advantaged ',ban State 45 ( 8.5) 28 ( 9.3) 27 (10.6) 273 ( 2.6)1 275 ( 53)1 269 ( 2.8)) Nation 59 (13.9) 273 ( 3.4)1 20 ( 6.0) 21 ( 8.2) ***) Disadvantaged urban State 36 ( 8.7) 28 ( $.0) 38 ( 9.4) 240 ( 4.0)1 237 ( 3.0)1 251 ( 5.7)1 Nation 50 (13k 22 (11.2) 211 (10.7) 237 ( 2.4)1 258 ( 8.3)I 263 ( 4.1)I Extreme rtral State 38 (10.9) 261 ( 6.1)1 36 (13.4) 249 ( 3.1)1 28 (103) ( *41 Nation 27 (14.3) 42 (12.7) 24 (10.1) 258 ( 6.7)1 Other State 43 ( 4.0) 33 ( 4.0) 24 ( 3.4) 253 ( 2.7) 255 ( 2.9) 201 ( 4.7) Nation 30 ( 4.4) $5 ( 4.3) 36 ( 4.2) 256 ( 3.3) 259(2.6 9 272 ( 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 estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate &termination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 116 1 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE Al ib I Teachers' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1110 NAEP TRIAL STATE ASSESSMENT . _ At Lust Seurat Times a Week _ About Ones a Week Lass thin Moldy TOTAL 040,431$010 Preldency kraals. ad Pnoldsaar loanadapi ad Pretbismy State 41 ( 3.2) 32 ( $.5) 27 ( 0.3) 255 ( 2.1) 253 ( 15) 200 ( 14) Nation 34 ( 34) $3 ( $.4) $2 ( 3.0) 258 ( 2.3) 200 ( 2.3) 274 ( 2.7) PARENTS" EDUCATO3N RS non-graduate State 38 ( 4.4) 30 ( 4.0) 28 ( 3.9) 244 ( 3.5) 239 ( 3.2) 248 ( 2.9) Nation 3$ ( 0.0) 29 ( &3) 98 ( 8.9) 229 ( SS) 250 ( 4.5)I IlS "'sante State 41 ( 42) 38 ( 4.3) 23 ( 3.8) 248 ( 2.7) 248 ( 3.0) 250 ( 4.0) Nation 36 ( 5.3) 30 ( 4.5) 90 ( 4.8) 250 ( 3.8) 2$0 ( 21) 263 ( 3.4) Some college State 41 ( 3.8) 30 ( 4.5) 28 ( 4.1) 25.9 ( 10) 290 ( 3.1) 270 ( 3.7) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 293 ( 2.8) 288 ( 4.2) 278 ( 2.8) College graduate State 42 ( 3.8) 29 ( 3.9) 29 ( 4.1) 270 ( 2.5) 26$ ( 3.0) 270 ( 4.8) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.8) 271 ( 2.4) 2139 ( 2.9) GENDER M. State 41 ( 3.2) 31 ( 3.7) 28 ( 3.8) 258 ( 2.4) 255 ( 2.8) 262 ( 3.8) Nation 3$ ( 4.1) 35 ( 3.8) 34 ( 3.5) 257 ( 3.2) 201 ( 2.8) 275 ( 3.2) Female State 41 ( 3.5) 34 ( 3.8) 25 ( 3.3) 254 ( 2.3) 251 ( 2.8) 257 ( 3.8) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution the nature of the sample does not allow accurate detennthation of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT 117 Texas TABLE Al2 I Students' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT _ At Least Once a Weak Ana Than Once a Weak NNW TOTAL. State AMEMELY %bite 0.111110111.11 assl MOW" 23 950 20 115 294 2.7 Nation 27$ ( 2.0 22 ( 27 ( 24 10 ( 2 277 all 29 1. 44 *A so 11 46 $.31 State lalack 26$ ( $.1 272 1 00 12) Nation 23 1 234 ( 3.0 2$ ( 3.0 114 I 2 245 4.6 24 48 295U 2341 3.1 State NIspank Nation 242 ( 39 37 ( 5.2 250 } SA) 3431 9 240 1.9 41 99 241 ( 24 25 ( 201 1 4111 State 'NPR OF COMMUNITY Advantaged urban Nation 222 ( 3.911 27 (13.9 State 2$ ( 0.9 IhIrt ( Oil Disadvantaged urban 27 ( 3.7) 41540 2141 tr 1133:14 208 5.4 I 279 3.5 Nation 245 ( 44)1 $1 52) 237 11.4)1 20 2.8) 2401 5151 44) 93 2ra { 5.0)1 250 SAY 27 1.5) 58 State 245 47 &trims rural Nation 249 5.21 203 0.4)1 $4 U.1.2) 284 5.0}I 27 9.5 $1 72 281 $.2 43 0 11 State 26 ( 6.9) 254 ( 3.5)1 250 ( 52 Other . Nation 2$ 2.1 200 $.3) 27 2.0) 1114 1.1 265 20 1.9) MI 12 202 22 254 2.31 48 32 45 $.8 State The standard errors of the estimated statistic: appear in parentheses. It be suld with about 95 percent certainty that, for each population of interest, the value for the entire populk n is within * 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determlnation of the variability of this estimated mean proficiency. *** Sample tize is insufficient to permit a reliable estimate (fewer than 62 students). Us 1 r. n - t.) THE 1990 NAM' TRIAL STATE ASSESSMENT Texas TABLE A 12 Students' Reports on the Frequency of Small (continued) i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT , At Least Once a Wok LASS Than Ono a Week Never I TOTAL Percentage and Proallelency fleromitsfill and Pralldsacty Porosniaps and Predidency State 23 ( 2.0) 2$ ( 1.5) 48 ( 258 ( 2.3) 204 ( 1.8) 254 ( 1.$ Nation 28 ( 2.5) 2$ ( 1.4) 44 ( 2.9 258 ( 2.7) 207 ( 2.0) 261 ( 1.8) PARENTS' EDUCATION NS non-graduato State 19 ( 2.8) 28 ( 2.8) 53 ( 3.5) 241 ( 3.7) 281 ( 2.7) 240 ( 2.1) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4.5) 242 ( 3.4) 244 ( 3,0) 242 ( 2.7) HS graduate State 21 ( 2.3) 246 ( 3.5) 2$ ( 2.3) 2se ( 2.3) 50 ( 3.1) 246 ( 2.0) Nation 28 ( 3.0) 28 ( 14) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some college State 25 ( 3.4) 31 ( 2.9) 43 ( 3.5) 203 ( 3.1) 274 ( 2.8) 262 ( 2.2) Nation 27 ( 3$) 27 ( 2.4) 46 ( 3.8) 265 ( 3.8) 268(3.3) 268(2,1) Coffey' graduat State 25 ( 2.9) 29 ( 2.2) 48 ( 2.9) 277 ( 3.1) 277 ( 2.1) 270 ( 241 Nation 28 ( 3.0) 28 ( 1.9) 44 ( 3.6) 270 ( 2.7) 278 ( 2.8) 275 ( 2.2) GENDER Mat State 25 ( 2.1) 29 ( 1.8) 48 ( 2.8) 290 ( 2.9) 266 ( 2.3) 256 ( 1.9) Nation 31 ( 2.9) 23 ( 1.7) 41 ( 2.9) 259 ( 3.3) 268 ( 2.8) 262 ( 14) Fonsat State 21 ( 2.2) 28 ( 1.8) 51 ( 2.8) 258 ( 2.4) 283 ( 2.1) 253 ( 1.9) Nation 26 ( 2.4) 27 ( 1.8) 47 ( 3.2) 257 ( 2.8) 298 ( 1.7) 200 ( 1.8) The standard errors of thr estimated SUltisties 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. / 9 1. 1., THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Texas TABLE A 13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11110 NAEP TRIAL TE ASSELIMENT STA At Least Once a Week Less Than Once a Week Never 19.16k State Nation Matangarf State Nation kook State Nation Meanie State Nation TYPE Of COMMUNITY Advantaged tartan State Nation Disadvantaged urban State Nation Ekklm rtswi State Nation Othsv State Nation 111015151115115 15111 101155k11101 P4F0140110 Pf9.810841 $3 ( 1.$ 31 219 { 1 12 peormiagi Proildisql N 24-2 M .71 41 ( 2.2 25$ ( 1.6 23 38 ( 1.8) 29 ( 2.7) 20 2.4 278 ( 1.8) 273 ( 1.8) 27 1 33 ( 1.8) 40 ( 2.5) NI ( 275 ( 1.8) 208 ( 1.8) 235 21 i 43.101 27 ( 239 ( 2.7 48 ( 4.4) 231 21) 27 ( 34) 27 ( 3.2 48 4.5) 234 ( 3.7) 245 ( 4.5) 232 2.8) 34 ( 2.8) 24 ( 1.5) 39 ( 2.5) 244 ( 2.1) 21$ ( 1.9) 243 ( 2.2) 3$ ( 42) 23 ( 2.0) 40 ( 4.0) 241 ( 41) 253 ( 4.3) 240 ( 1.9) 28 ( 8,1) 272 ( 49)i 38 (10.3) 278 ( 8.1)1 $4 ( 53) 240 3.711 25 $15 248 5.3)1 30 ( 11.8) 202 ( 5.3)1 21 ( 3.1) 20 2$) 252 2.1) 27 2.0) 258 21) 39 ( 4,0) 261 ( 2.9)1 33 ( 41) 2114 ( 32)1 2$ ( SA) 2$0 ( 19 ( 2.1) 258 ( 5.7)1 SS ( 5.7) 206 ( 5.1)1 ( 4.7) 202 ( 4.7)1 32 1.9) 262 2.1) 31 1.4) 270 ( 11) 35 ( 0.0) 215 ( 31)1 32 (11,1) 2V. ( 5.9)1 38 ( 3.1) 24e ( 2.8)3 48 ( 5.4) 248 ( 41)3 25 ( 5.5) 251 ( 3.0), 43 ( 5.0) 251 ( 52)3 41 ( 3.3) 263 ( 2.4) 41 ( 2.4) 280 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be saW 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" 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE A13 I Students' Reports on the Use of Mathematics (mitinued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Ottin a Week - Less Than Once a Week Never TOTAL Pernsrbge And Prefickncy Peewees, ami Pro alma Pen maw vont Proacisacw State 26 ( 2.0) $3 ( 1.2) 36 ( 22) 253 ( 1.9) 264 ( 1.6) 25. ( 1.7) Nation 26 ( 1.8) 31 ( 1.2) 41 ( 22) 256 ( 2.6) 269 ( 1.5) 2511( 1.6) PARENTS' EDUCATION NS non-graduate State 29 ( 2.5) 2$ ( 2.3) 43 ( 2.6) 242 ( 3.3) 245 ( 2.0) 244 ( 2.1) Nation 27 ( 4.2) 20 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) liS graduate State 27 ( 2.6) 32 ( 2.0) 41 ( 3.1) 246 ( 3.1) 254 ( 2.1) 244 ( 2.5) Nation 27 ( 2.7) 31 ( 24) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some coitego State 2$ ( 3.0) 34 ( 2.8) 3$ ( 3.3) 253 ( 3.1) 272 ( 2.6) 260 ( 2.9) Nation 29 ( 2.8) 38 ( 2.3) 35 ( 2.6) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) Collage graduate State 20 ( 2.8) 37 ( 2.0) 37 ( 2.7) 266 ( 2.3) 27$ ( 2.0) 274 ( 2.3) Nation 30 ( 2.5) 32 ( 2.0) 30 ( 2.6) 200 ( 3.0) 276 ( 2.0) 275 ( 2.0) GENDER M. State 29 ( 2.2) 32 ( 1.7) 39 ( 2.3) 255 ( 2.3) 208 ( 1.8) 258 ( 22) Nation 32 ( 2.0) 30 ( 1.$) 3$ ( 2.2) 258 ( 2.9) 271 ( 2.1) 200 ( 1.8) Famal State 26 ( 2.3) 34 ( 1.8) 34 ( 2.7) 251 ( 2.2) 261 ( 2.1) 255 ( 2.0) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 268 ( 1.5) 257 ( 1,9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard error . of the estimate fOr the sample. 126 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Texas TABLE A14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 18110 NAEP TRIAL STATE ASSESSMENT Nowt Every Day SOVIIIIM UMW a Week About Once a Weak er, tise TOTAL Illwasalaaa and Prallalancy 1Parasalay and frallabacy aad dralidona State 72 ( 1.7) 10 12 ( 202 ( 13 Ste 22 247 ( 32 Nation 74 ( tO 14 0.8 12 ( 1.$ 207 ( t2) 232( 1,7) 242 ( 45) RACEMTNNICITY White State 78 ( 2.0) 13 ( 1.3) 9 ( 12) 275 ( 1.3) ne 2.6) 268 ( 3.2) Nation 78 ( 2.5) 13 OA) 11 ( 2.2) 274 ( 1.3) 258 2.2) 252 ( 5A)4 Mack State 59 ( 4.0) 21 2.9) 20 ( 42) 235 ( 2.3) 232 2.1) 233 ! 4.0)1 Nation 71 ( 2.8) 15 1.7) 14 ( 3.2) 240 ( 2.9) 232 ( 3.1) 223 ( 6.1)1 Hkpanic State 89 ( 2.5) 18 ( 2.1) 12 ( 1.3) 248 ( 1.8) 240 ( 2.8) 234 ( 3.6) Nation 81 ( 3.7) 21 ( 2.0) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) TYPE OF COMMUNITY Advantaged urban State 74 ( 5.8) 278 ( 3.1)1 14 ( 2.3) 12 ( 5.1) ( 441 Nation 73(11.1) 285 ( 4.6)! 13 ( 1.7) «pa) 14 (10.4) 444. Dludvantaged urtan State 67 ( 5.2) 20 ( 3.5) 13 ( 3.3) 249 ( 3.1)1 239 ( 2.1)1 213 ( 3.2)1 Nation de ( 2.8) 15 ( 2.5) 15 ( 2.2) 253 ( 3.7)1 243 ( 44)1 235 ( 8.5)1 Barone nral State 8$ ( 5.7) 4 ( 2.6) 265 ( 2.8)1 Nation 68 (113) 15 ( 3.6) 253 ( 4.2)! Other State 72 ( 1.7) 18 ( 1.3) 12 ( 13) 201 ( 1.8) 248 ( 32) 248 ( 4.4) Nation 75 ( 2.2) 14 ( 1.0) 10 ( 1.9) 207 ( 1.8) 252 ( 2.6) 239 4.3)? MN& 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). 1 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE A14 I Students' Reports on the Frequency of (ccultinued) I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Om* a WINN or Lass TOTAL State Nation Ememithmet HS nee-gradtate State Nation HS graduate State Nation Some ceitegs State Nation College graduate State Nation GENDER M. State Nation Fame!. State Nation awl Pailislava 72 1.7) 282 4.3) 74 1.9) 207 tZ 71 ( 3-2) 245 ( 2,0) 84 ( 3.4) 245 ( 2.3) 73 ( 23) 25371 ;41 2511 ( 1.8) 74 ( 3.1) 2419 ( 1.9) 80 ( 2,0) 270 ( 1.9) 74 ( 2.0) 278 ( 1.3) 77 ( 2.7) 270 ( 1.8) 73 ( 1.0) 283 ( 1.4) 72 ( 2.4) 203 ( 14) 71 ( 2.0) 200 ( 111) 78 ( 1.8) 255 ( 1.3) moo 114111888111118 1 248 211 14 04t7 24 241 2.4 111 2.01 .40 17 ( 2.1) 241 2.7) 19 14) 249 3.2) ?..44 11 ( 1.2) 14 ( 1.4) 243 ( 13 ( 0.9 210 ( 2.8 18 ( 1.5) 251 ( 18 ( 1.2 232 ( 2.5 18 ( 1.4) 247 13 1.0 250 2.5 IS 1* ago at ie te - me 4.ek ,0 12 ( 1A1 281 4. 10 2.94 287 11.4 11 947 4.5 2.1 242 247 2.9 11 1 242 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). 123 THE 1990 NAEP TIUAL STATE ASSESSMENT 123 Texas TABLE A15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Wk ee About Once a Week Less Than Wieldy TOTAL Perostite fa and "rackety PerambRNI ant Pradelty Percents. and Preldency State 45 ( 2.2) 26 ( 1.2) 90 ( 252 ( 1.7) 258 ( 1.7) ( 2.0 Nation 38 ( 2.4) 25 ( 1.2) 37 ( 2.5 253 ( 2.2) 261 ( 14) 272 ( 1.9) RACEMTHNICITY Wt. State 40 ( 2.7) 29 ( 1.9) 34 ( 3.0) 269 ( 1.6) 273 ( 2.2) 279 ( 2.0) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 262 ( 2.5) 269 ( 1.5) 277 ( 2.0) Black State 53 ( 4.2) 22 ( 2.9) 26 ( 3.6) 233 ( 2.4) 233 ( 2.9) 238 ( 3.5) Nat Ion 4$ ( 3.6) 32 ( 2.7) 20 ( 3.1) 232 ( 4.3) 241 ( 2.9) 241 ( 4.4) Hispanic State 49 ( 2.7) 25 ( 1.4) 26 ( 2.6) 241 ( 1.9) 245 ( 2.4) 251 ( 2.8) Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 238 ( 3.9) 247 ( 3.3) 24$ ( 34) TYPE OF COMMUNITY Advantaged urban State 36 ( 7.7) 24 ( 2.6) 36 ( 6.5) 270 ( 3.1)1 262 ( 3.2)! 280 ( 4.1)1 Nation 50 ( 271 ( 9.0) 3.3)1 19 ( *4. 4.9) 31 292 ( 9.3) ( 5.3)1 Disadvantaged urban State 51 ( 4.9) 25 ( 3.5) 24 ( 3.2) 240 ( 2.6)1 240 ( 3.8)1 254 ( 4.9)1 Nation 37 ( 5.8) 23 ( 3.0) 41 ( 0.7) 240 ( 4.8)1 253 ( 4.1)1 255 ( 4.2)1 Extreme rural State 3e ( 8.2) 28 ( 5.1) 34 6.5) 260 ( 8.0)1 1411. ) 271 7.1)1 Nation 42 (10.1) 30 ( 44) 28 7.5) 249 ( 4.0)1 256 ( 3.4)1 267 ( 7.3)1 Other State 45 ( 2.2) 25 ( 1.7) 30 ( 2.8) 252 ( 2.3) 256 ( 2.3) 264 ( 2.7) Nation 38 ( 2.9) 26 ( 1.2) 38 ( 2.9) 252 ( 3.0) 261 ( 2.1) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with evut 95 permnt 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. "1* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE AB I Students' Reports on the Frequency of ("mtinued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 16110 NAV TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Less Than Weekly - 19.1AL State Nation talmtimmigi NS noninktuate State Nation NS graduate State Nation Seim college State Nation College graduate State Nation 9-P-ME Male State Nation Fames State Nation Paramdella awl Preiakacy Peresatage owl Povilalsny Pardentafe and Pralloiency 45 ( 2.2) 25 ( 1.2) 30 ( 23) 252 ( 1/) 258 ( 1.7) 286 ( 20) 38 (24) 25 ( 1.2) 37 ( 25) 253 (2.2) 261 ( 14) 272 ( 49 ( 10) 28 ( 2.0) 25 ( 2.8) 243 ( 2.11) 248 ( 2.8) 242 ( 2.5) 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) 45 ( 2.8) 26 ( 2.1) 27 ( 3.2) 242 ( 23) 252 ( 23) 253 ( S.1) 40 ( 3.2) 29 ( 2.2) 32 ( 3.8) 247 ( 2.7) 258 ( 2.5) 289 ( 2.2) 44 ( 3.3) 23 ( 2.3) 33 ( 2.9) 200 ( 2.5) 284 ( 25) 274 ( 2.5) 34 ( 3.4) 28 ( 2,2) 40 ( le) 250 ( 23) 289 ( 2.5) 271 ( 2.8) 42 ( 3.0) 22 ( 1.7) 38 ( 3.1) 267 ( 2.3) 274 ( 2.4) 281 ( 2.1) 38 ( 2.8) 22 ( 1.6) 41 ( 2.13) 264 ( 2.8) 273 ( 2.5) 265 ( 2.3) 48 ( 2.3) 2S ( 1.4) 29 ( 2.3) 253 ( 2.0) 200 ( 2.0) 270 ( 2.3) 30 ( 2.7) 25 ( 1.8) 35 ( 2.7) 253 ( 2.7) 263 ( 23) 274 ( 2.4) 44 ( 2.5) 25 ( 32 ( 2.8) 252 ( 2.0) 257 ( 2.3) 282 ( 25) 37 ( 2.5) 25 ( 1$) 38 ( 2.8) 253 ( 2.1) 250 ( 1.11) 260 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 Texas TABLE Al8 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Imlalm. 1990 NAEP TRIAL STATE ASSESSMENT - Own a Calculator Teacher Explains Ca It:dater Use Yes . No Yes No TOTAL Putentaga and Prolkiency Percentage and Pto Idiocy Paraantaia and Pro Many Percentage Sod Pm Ilaismw State 913 ( 0.5) 4 ( 0.5) 58 ( 2A) 44 ( 2.4) 259 ( 1.2) 235 ( 2.9) 258 ( 1.6) 259 ( 14) Nation 97 ( 04) 3 ( OA) 49 ( 2.3) 51 ( 2.3) 283 ( 1.3) 234 ( 3.8) 258 ( 1.7) 248 ( 14) RACE/ETHNICITY White State 98 ( 54 ( 32) 46 ( 3.2) 274 ( 1.1) ( ***) 272 ( 1.8) 274 ( 1.3) Nation 90 ( 0.3) 2 ( 0.3) 46 ( 2.8) 54 ( 24) 270 ( 1.5) 41.41 2e8 ( 1.8) 273 ( 1.8) Slade State 93 ( 1.2) T ( 1.2) 54 ( 4.1) 48 ( 4.1) 235 ( 1.6) Of* ( 0.041 234 ( 2.7) 238 ( 2.4) Nation 93 ( 14) ( 1 4) 53 ( 4.9) 47 ( 4.9) 237 ( 2.6) &Mt ( 441 23S ( 3.6) 239 ( 2.7) Hispanic State 94 ( 0.9) 8 ( 0.9) 59 ( 3.2) 41 ( 32) 245 ( 1.5) 237 ( 3.7) 246 ( 1.8) 244 ( 2.3) Nation 92 ( 12) 8 ( 1.2) 83 ( 4.3) 37 ( 4.3) 245 ( 2.7) 243 ( 3.4) 245 ( 2.9) TYPE OF COMMUNITY Advmtaged urban State 98 ( 0.9) 53 ( 5.3) 47 ( 5.3) 277 ( 2.3)! *** ( 276 ( 3.1)1 276 ( 2.5)f Nation 99 ( 1.0) 1 ( 1.0) 45 (12.2) 55 (12.2) 281 ( 3.5)1 "P" ( 278 ( 2.5)f 285 ( 6.4)1 Disadvantaged urban State 93 ( 1.4) 63 ( 5.7) 37 ( 5.7) 24$ ( 24)! ( 244 ( 3.3)1 247 ( 2.6)1 Nation 94 ( 1.2) 250 ( 3.5)1 8 ( 12) *J. ( 53 ( 74) 247 ( 4.1)1 47 ( 7.5) 251 ( 3.0)1 Extreme rural State 99 ( 0.5) ( 0.5) 00 (11.8) 40 (11.8) 282 ( 3.2)1 259 ( 5.7)1 267 ( 3.1)1 Nation 96 ( 1.3) 257 ( 34)1 4 ( 12) 4.0.1 42 ( 8.7) 251 ( 4.8)1 58 ( $.7) 261 ( 44)! Other State 98 ( 0.5) 4 ( 0.5) 56 (3.1) 45 ( 3.1) 258 ( 1.8) 258 (2.2) 2$8 ( 2.3) Nation 97 ( 04) 3 ( 0.5) 50 (2.7) 50 ( 2.7) 263 ( 1.7) 233 ( 5.4) 258 ( 2.1) 288 ( 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. 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). 126 131 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE A18 Students' Reports on Whether They Own a (wiltinued) Calculator and Whether Their Teacher Explains How To Use One PERCEN'AGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Ow a Calculator Teacher Explain. Calculator Use Yes No , Yes No - TOTAL Poreentagle and Pndideacy Penootaga add Praia/Maw lisiventaga and Pro Idiocy Panaida. and Pro Palmy State 06 ( 05) 4 ( 0.5) $6 ( 2.4) 44 ( 2A) 230 ( 1.2) 235 ( 2.9) 258 ( 1.6) 259 ( 1,5) Nation 97 ( 0.4) 3 ( 0.4) 441 ( 2.3) 51 ( 2.3) 263 1.3) 234 ( 3.8) 258 ( 1.7) 203 ( 1.5) PARENTS' EDUCATION HS non-graduato State 92 ( 244 ( 1.3) 1.6) *** ( ***) 51 ( 24$ ( 3.7) 2.0) 44 ( 242 ( 3.7) 2.2) Nation 92 ( 1.6) 8 ( 1.6) 53 ( 4.6) 47 ( 4.6) 243 ( 2.0) 242 ( 2.9) 243 ( 2.5) HS graduate State 4 ( 0.9) 56 ( 3.1) 44 ( 3.1) 249 ( 1.6) tellt **) 249 ( 2.0) 249 ( 2.1) Nation 97 ( 0.5) 3 ( 0.6) 54 ( 3.0) 46 ( 3.0) 255 ( 1.5) ( ".) 252 ( 1.9) 258 ( 2.0) Some college State 97 ( 0.6) 3 ( 0.8) 55 ( 3.8) 45 ( 3.8) 266 ( 1.7) ( "") 263 ( 2.3) 269 ( 2.3) Nation 96 ( 0.9) 4 ( 0.9) 48 ( 3.2) 52 ( 3.2) 268 ( 1.8) ( "it) 265 ( 2.4) 268 ( 2.2) Canoga graduate State 99 ( 0.4) 55 ( 2.6) 45 ( 2.6) 274 ( 1.3) 273 ( 2.0) 274 ( 1.7) Nation 99 ( 0.2) ( 0.2) 48 ( 2.6) St ( 2.6) 275 ( 1.6) ( v") 268 ( 2.2) 280 ( 1.9) GENDER Mai. State 96 ( 05) 58 ( 2.9) 42 ( 2.9) 261 ( 1.5) ( 200 ( 1.7) 259 ( 2.1) Nation 97 ( 05) 3 ( 0.5) 51 ( 2.8) 49 ( 2.6) 264 ( 1.7) 258 ( 2.1) 262 ( 2.1) Facial State 95 ( 0.7) 54 ( 2,4) 48 ( 2.4) 258 ( 1.4) ( "4) 255 ( 1.9) 258 ( 1.7) Nation 97 ( 0.5) 47 ( 2.5) 53 ( 2.5) 262 ( 1.3) 258 ( 1.7) 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). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 Texas TABLE A19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Working Problems in Mos Doing Problems at Nome Taidng Quines or Teets Almost Always Never Almost Always Never Almost Always , NOW TOTAL State Nation RACE/ETHNICITY White State Nation Wick State Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation Diudvantaged urbmn State Nation Extreme nral State Nation after State Nation Nrcontaeo Parents. Porawdop Paco lige Pecomitio Okanossese end ant in* and Mil aNd Pro &Ian ProOtisnay Pnicifiviv Pideimp Peskisinav Pralitimay 51 19 1.7 2$ 1.5 251 1.5 26$ 14 25. 2.0 21:2 1.1 4$ 1.5 23 19 30 1.3 12 OA 254 1.5 272 14 201 1.2 263 1 41 ( 1.9) 22 ( 2.3) 20 1.8) 17 ( 207 ( 1.0) 280 ( 1.7) 273 17) 277 ( 1.9 46 ( 1.7) 24 ( 2.2) 31 1.5) 18 ( 1.2 262 ( 1.7) 27$ ( 1.3) 270 1.7) 269 ( 2.3) 62 ( 2.0) 13 ( 2.5) 30 ( 2.3) 12 ( 1.3) MI ( 3.0) 231 ( 1.8) ' ( "IP) 234 ( 2.9) ( ") 230 24) 11 51( 3.2) 20( 3.9) 31 ( 2.9) 18 ( 1.0) SS 3.3) 24 31 292 ( 24) 249 ( 4.0) 223 ( 3.3) 241 ( 5.5) 230 34) 251 441 54 ( 19) 1$ ( 1.8) 24 ( 1.9) 19 ( 1.5 20 ( 2.1 1.11 240 ( 1.8) 256 ( 2.2) 246 ( 2.4) 249 ( 24) 240 ( 24 252 2.0 51 ( 24) 16 ( 3.5) 28 ( 9.2) 21 ( 2.1) 26 f 2.7 22 3.1 230 ( 2.8) 252 ( 3.3)4 238 ( 4.8) 244 ( 31) 237 ( 3.2 256 ( 4.2 2:12 ji? ;4 27 1.4 216 2.4 En 14 24 271 1 2.5 311 1.4 25 14 32 2.11 283 ( 24 279( 1.2 47 ( 3.6) 19 ( 3.4) 90 ( 2.7) 13 ( 1.4) 30 ( 31) 27 3.2) 271 ( 24)4 280 ( 2.5)1 277 ( 2.5$ *** ( ***) 272 ( 4.0)4 283 51 ( 5.4) 23 (10.7) 22 ( OM 14 ( 2.4) 31 ( 3.8) 20 as 270 ( 4.7$ *** ( ***) 274 ( 4.ss - ( -) 261 ( 7.5$ NB 4.2 54 ( 3.4) 21 ( 3.8 19( 20 30 ( 3.2 239 ( 24)4 254 ( 3.9 245 5.0 251 4.8 2r17 ii 2: 1 $4111 SQ ( 3.1) 22 ( 44 30 3.3 24 2.2 241 ( 3.8)4 259 ( 5.4)4 246 5.2 254 4.6 240 4.2 262 5.0$ 51 ( 5.8) 20 ( 7.1) 25 ( 5.4) 10 ( 3.7) 23 ( 44) 29 ( 2.7) 256 ( 42)1 " ( ') "4 ( "1 4.4 ( 4") 4" ( 4") 275 ( 4.1s 46 ( 7,4) 29 ( 0.5) 20 ( 24) 23 ( 34) 24 ( 2.8) 31 ( 33) 248 ( 4.3)4 268 1 2.1)4 *** ( ***) 263 ( 448 " ( ***) 270 ( 4.0 s 51 ( 14) 19 ( 2.1 21 1.9 ill 1.3 20 11 30 2.1 250 ( 2.3) 269 2.4 257 2.7 203 21 250 34 271 1. 48 ( 1.9) 22 2.0 32 1.7 1$ 1.1 27 14 2$ 2.1 254 ( 2.1) 272 14 203 2.3 263 2.8 232 2.7 VI 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 "Sometimes" category is not included. 1 Interpret with caution -- the nature of the sample does nc,;. allow =orate determination of the variability of this estimated mean proficiency. *** Sample size is intuffIcient to permit a reliable estimate (fewer than 62 students). 123 11.13 t.r3 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE A19 I Students' Reports on the Use of a Calculator (continued) 1 for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT "king PIN* la" ki Class Doing Ptob lents at Home Taking Quizzes or Tests Almost Always Never Almost Always Never Almost Always Never TOTAL State Nation PARENTS EDUCATION 145 noniraduate State Nation graduate State Nation Some college State Nation College graduate State Nation DENDER Male State Nation Female State Nation Pannegage Pa'amtage Perm haw Paralegals 11,44rosntege lieniegsgs and and wed and and and Pralkieney Pro latency Pra Wang Pesisisrari Pra edam PrOteksasy 51 1.4) 19 ( 1.7) 25 1.5) 17 251 1.8) 206 ( 1.5) 259 262 46 1.5) 23 ( 1.9) 30 1.3 19 254 1.5) 272 ( 1.4) 261 11 263 60 ( 2.3) 19 ( 2.4) 22 ( 2.8) 24 ( 2$6 ( 2.0) 251 ( 3.0) 242 ( 2.7) 249 ( 54 ( 2.3) 19 ( 3.8) 26 ( 3.1) 22 ( 240 ( 2.3) "1' ( ***) 244 ( 3.8) 244 ( 54 ( 2.0) 18 ( 2.0) 25 ( 2.1) 15 ( 242 ( 2.0) 259 ( 3.4) 24? ( 21) 254 1 52 ( Ls) 20 ( 24) 29 ( 1.9) 16 ( 249 ( 1.4) 265 ( 2.7) 250 ( 2.4) 256 ( 52 ( 2.4) 19 ( 2.4) 24 ( 2.3) 14 ( 258 ( 2.3) 279 ( 2.5) 268 ( 3.0) *** ( 46 ( 2.8) 25 ( 2.8) 26 ( 2.0) 20 ( 255 ( 2.1) 272 ( 2.5) 267 ( 3.0) 268 ( 47 ( 2.1) 21 ( 2.2) 30 ( 2.0) 17 ( 267 ( 2.3) 281 ( 2.2) 273 ( 2.8) 276 ( 45 ( 1.9) 25 ( 2.4) 33 ( 2.0) 15 ( 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 63 ( 1.7) 18 ( 1.8) 25 ( 1.8) 20 ( 253 11) 271 ( 2.0) 259 ( 2.3) 264 ( 50 1.7) 20 ( 2.0) 29 ( 1.8) 19 ( 255 1.9) 275 ( 2.2) 264 ( 21) 253 ( 49 ( 11) 21 ( 1.9) 27 ( 1.8) 15 ( 249 ( 1.9) 206 ( 1.9) 258 ( 2.4) MO ( 46 1 2.0) 26 ( 2.1) 32 ( 1.8) 18 ( 232 ( 1.7) 209 ( 1.8) 259 ( 1.7) 263 ( 0.9) 27 ( 1.5) 20 1.9) 252 ( 2.5) 271 0.9) 27 ( 1.4) 30 11) 253 ( 2.4) 274 1.7) 26 ( 20 21) 240 ( 2.6 250 2.6) 32 ( 3.6 24 4.2) 237 ( 2.3) 251 1.9) 28 ( Li) 25 3.9) 241 ( 2.7) 262 1.5) 24 ( 1.6) 27 2.4) 248 ( 2.8) 265 1.5) 24 ( 2.7) 33 ***) 255 ( 3.5) 279 1.9) 26 ( 2.4) 35 3.2) 255 ( 3.5) 275 1.5) 28 ( 2.2) 32 2.5) 280 ( 3.5) 282 1.4) 26 ( 1.8) 33 2.8) 263 ( 2.8) 2115 1.2) 27 ( 1.7) 23 2.5) 253 ( 3.0) 274 1.3) 27 ( 1.5) 26 2.5) 258 ( 3.0) 277 1.0) 28 ( 1.7) 32 2.1) 251 ( 2.3) 268 1.2) 27 ( 1.8) 33 2.1) 251 ( 2.4) 271 1-8 -- 1.3 2.0 1.3 ( 2.4) ( 2.5 ( 3.2 ( 4 ( 2.0) 1 2.4) ( 2.2) ( 2.0) ( 2.6) ( 2.3) ( 2.5) ( 2.0) ( 2.3) ( 1.9) ( 2.7) ( 2.0) The standard errors of the estimated stafistics 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 permst a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 329 Texas TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO MAEP TRIAL "Calculater.tiss" "Calculator-Us." STATE ASSESSMENT Nigh Group Other Group , MILL State Nation NACVETHNICITY Milts State Nation Black Stee Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation Pow lap and Pro Salem 47 1.2 205 14 42 1.31 272 1.6 52 ( 272( 1.15 44 ( 1.4 277 ( 1.7) 44 ( 3.2 240 ( 2.5 37 ( 3.4 24$ ( 3.9) 43 ( 2.1 250 ( 1.6 36 ( 4.2 254 ( 4.11) 4$ ( 2.3) 279 ( 3.4)1 50 ( 3.8) 265 ( 4.9)1 43 ( 3.1) 251 ( 3.1)1 35 ( 4.2) 262 ( 5.6)1 45 ( 4.3) ( 4.3)1 39 ( 5.0) 209 ( 4.4)1 49 ( 1.8) 265 ( 2.0) 42 ( 1.4) 271 ( 1.9) Perambee mad Praildency 63 ( 1.2 251 ( 14 SI ( 1031 255 ( 1.5) 48 ( 1.e) 265 ( 1.6) 58 ( 1.4) 263 ( 1.7) 56 ( 3.2) 231 ( 2.1) 63 ( 3.4) 231 ( 3.0) 57 ( 2.1) 240 ( 2.2) 84 ( 4.2) 238 ( 3.0) 52 ( 2.3) 272 ( 3.0)1 50 ( 3.8) 275 ( 4.4)1 57 ( 3.1) 241 ( 2.3)1 62 ( 4.2) 244 ( 3.9)1 55 ( 4.3) 254 ( 3.1)1 61 ( 5.6) 245 ( 4.3)1 51 ( 1.6) 249 ( 2.1) 56 ( 1.4) 235 ( 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. 1 Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. I 130 THE 1990 NAEP TRIAL STATE ASSESSAENT Texas TABLE A20 1 Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL "Calculator-Use" "Calculator-Use" STATE ASSESSMENT High Grow Other Grow TOTAL Percentage and Pre Ildency Peroonlop an0 Prolksisnqf State 47 ( 1.2) 53 ( 1.2) 265 ( 1.4) 251 ( 14) Nation 42 ( 1.3) 51 ( 1.3) 272 ( 1.0) 255 ( 14) PARENTS' EDUCATION H5 non-graduate State 43 ( 2.8) 57 ( 2.6) 249 ( 2.8) 240 ( 2.1) Nation 34 ( 3.3) 118 ( 3.3) 248 ( 4.4) 242 ( 24) NS graduate State 42 ( 2.9) 50 ( 2.9) 255 ( 1.9) 243 ( 2.4) Nation 40 ( 2.2) 00 ( 2.2) 263 ( 2.0) 249 ( tit) Some college State 50 ( 2.7) 50 ( 2.7) 269 ( 2.8) 259 ( 2.9) Nation 48 ( 2.2) $2 ( 22) 277 ( 2,8) 258 ( 2.5) College gradiate State 54 ( 2.1) 4$ ( 2.1) 279 ( 1.9) VS ( 2.3) Nation 4$ ( 2.0) 54 ( 2.0) 2$2 ( 2.1) 208 ( 1.9) GENDER Mak State 44 ( 1.8) 56 ( 1.5) 207 ( 2.0) 25S ( 1.8) Nation 39 ( 2.0) tli ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State Si ( 1.4) 49 ( 1A) 283 ( 1.8) 249 ( 1.8) Nation 45 ( 1.8) 55 ( 1.8) 209 ( 13) 254 ( 13) 4P The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 136 THE 1990 NAEP TRIAL. STATE ASSESSMENT 131 Texas TABLE A24 I Students' Reports on of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 111110 NAEP TRIAL STATE ASSESSMENT Zero to ilvo Typos Throe Typos Four Types TOTAL Offiwam and Proadency Ponisitag in* Pivilalency Permisis Sid Pnellaimuy State 30 ( 1.3) 29 ( 1.0) 42(1.1) 24$ ( 1$) 256 ( 1.7) 299 ( 14) Nation 21 ( 1.0) 30 ( 1.0) 46 ( 1.3) 244 ( 2.0) 255 ( 1.7) 272 ( 1.5) RACE/ETHNICITY Milts State 15 ( 1.1) 30 ( 1.3) , ..4) 258 ( 2.3) 259 ( 1.9) 27itt 1.3) Nation 16 ( 1.1) 29 ( 1.3) 58 ( 1.5) 251 ( 2.2) 268 ( 1.5) 278 ( 1.7) Made State 35 ( 3.0) 30 ( 2.8) 35 ( 3.1) 231 ( 2.5) 233 ( 3.3) 230 ( 2.5) Nation 34 ( 1.9) 30 ( 22) 33 ( 2.4) 232 ( 3.2) 233 ( 3.9) 245 ( 3.3) Hispanic State 40 ( 2.0) 27 ( 1.9) 27 ( 1.7) 238 ( 2.0) 245 ( 1.9) 255 ( 22) Nation 44 ( 3.0) 30 ( 2.4) 20 ( 2.3) 737 ( 3.4) 244 ( 4.3) 253 ( 2.4) TYPE OF COMMUNITY AdvaMaged urban State 17 ( 2.8) ***) 32 ( 275 ( 14) 3.2)1 52 ( 281 ( 35) 3.2)1 Nation 13 ( *114 ( 3.8) *441 28 ( 2.1) 4-* ) 61 ( 287 ( 4.9) 3.6)1 Disadvantaged urban State 40 ( 3.9) 30 ( 2.7) 31 ( 2.9) 236 ( 1.8)1 243 ( 3.8)1 258 ( 3.2)1 Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.0) 243 ( 2.9)1 247 ( 3.7)1 257 ( 4.9)1 Extrema rural State 32 ( 4.0) 44 ( 4.6) 250 ( 2.7)1 276 ( 4.6)1 Nation ***) 33 ( 253 ( 3.2) 4.3)1 50 ( 263 ( 5.1) 5.6)! Other State ( 1.8) 27 ( 1.3) 42 ( 1.4) 243 ( 2.5) 251 ( 2.4) 267 ( 1.8) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 1.5) 244 ( 2.6) 259 ( 2.2) 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 caution -- the nature of the sample does not allow accurate determination of the variability ci..his estimated mean proficiency. *** Sample size is Msufficient to permit a reliable estimate (fewer than 62 students). 132 137 THE 1990 NAEP TRIAL STATE ASSESSMENT Texaf TABLE A24 I Students' Reports on Types of Reading (cmitinued) i Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Throe Types Four Twee TOTAL Perawea. Peraralast wd Pre Ndomay frelishmea State 30 243 ( ( 1.S Me 1. Nation 21 ( 1.0 30 tO 244 ( 2.0 256 12 PARENTS' EDUCATION NI1 non-waate State 52 ( 2.5) 20 ( 2.1) 239 ( 1.6) 11 24 ( 2.3) Nation 47 ( 4.0) 2S ( 3.0) 240 ( 3.4) 243 ( 3.3) HI graduate State 33 ( 2.3) 2.2) Nation 240 28 ( 2.5) ( 2.2) 33 1.9 247 243 ( 2.2) 253 2. Some camp State 10 ( 2.2) 34 ( 2.4) 250 ( SA) 204 ( 2.5) Nation 17 ( 1.5) 32 ( 11) 251 ( 4.0) 202 ( 2A) College graduate State 14 ( 1.4) 211 ( 1.5) Nation 258 ( 10 ( 3.8) 0.8) 270 ( 2.8) 28 ( 1.6) 254 ( 2.8) NO ( 2.6) RENDER Male State 20 ( 1.0) 211 ( s 244 ( 2.1) 256 ( 2.2) Nation 21 ( 1,5) 31 ( 14) 244 ( 23) 25S ( 2.1) Female State 30 ( 1.5) 29 ( 1A) 242 ( 1.8) 255 ( 2.1) Nation 22 ( 1.2) 29 ( 1.4) 244 ( 2.2) 258 ( 1.0) 40 1173 SI LI 2671 NO 2.41 40 1. 2Y1 Li 274 1.91 2.3) 54 2.0 1.7) 50 270 1 HO 1.8 82 AI 270 2.0 1.6) 48 1.4 VI 40208 1.9) 1:5) 40 13) 270( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certairity that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. 138 THE 1990 NAEP TRIAL STATE ASSESSMENT 133 Texas TABLE A25 I Students' Reports on the Amount of Time Spent i Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One Hair or Less Two Hours Three Hours Four to Five Hours Ilbt Hews or Moro TOTAL Pennontasa and Pro*dam Pormentapo and Prodkdancy Ponanhopo and Praidancy Paraantago and Pre Adana Pantentage and Pre *buy State 13 ( 0.7) 19 ( 0.8) 23( 1.0) 251 ( 2.9) 202 ( 2.2) 264 ( 1.0) 2:07 1 243 2.0 Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 1.1 I 16 1.0 209 ( 22) 206 ( 1.8) 205 ( 1.7) 200 1.7) 245( 1.7) State 12 ( 1.1) 22 ( 1.2) 26 ( 1.4) 29 ( 1.3) 10( OA) 278 ( 2.7) 270 ( 2.4) 27$ ( 1.8) 270 ( 1.5) 260( Nation 13 ( 1.0) 23 ( 1.2) 24 ( 1.1) 27 ( 1.4) 12 ( 1.2 275 ( Z.5) 275 ( 2.2) 272 ( 1.9) 267 ( 1.7) 253( 2.6 Black State 7 ( 1.3) 444 ( 14 ( 1.6) 1111h* *el 16 ( 2.1) **It ( 041 34 ( 2.8) 238 ( 2.9) 30( 3.0) 233( 3.3) Nation 13 ( 1./) 17 ( 2.1) 32 ( 1.8) 32 ( 2.2) 239 ( 7.0) 23$ ( 5.0) 239 ( 4.0) 233( 2.5) Hispanic State 15 ( 1.3) 19 ( 1.4) 21 ( 1.7) 31 ( 1.4) 15( 1.5) 245 ( 4.1) 246 ( 2.8) 24$ ( 2.4) 240 ( 13) 233( 3.0) Nation 14 ( 2.4) 20 ( 2.5) 19 ( 2.1) 31 ( 3.1) 17 ( 1.7) 245 ( 3.2) 242 ( 5.6) 247 ( 3.5) 236 ( 3.8) TYPE OF COMMUNITY Advantaged ieban State 15 ( 2.2) 18 ( 1.9) 279 ( 4.6)1 29 ( 1.9) 278 ( 3.1)1 29 ( 1.7) 277 ( 3.7)1 10 ( 1$) 44,1 Nation 18 ( 1 .4) ( ***) 25 ( 4.3) .44, 21 ( 1.8) 30( 4.3) 5.1.) ( 2.0) Disadvantaged urban State 11 ( 1.3) .44 .44) 19 ( 1.9) 247 ( 3.0)1 22 ( 2.1) 251 ( 3.2)1 29( 2.9) 240 ( 3.6)1 19 ( 2.6) 234 ( 3.3)1 Nation 9 ( 1.2) 17 ( 3.1) 19 ( 2.1) 34( 2.4) 20 ( 3.2) 250 ( 4.0)1 255 ( 5.0)1 251( 4.7)! 238 ( 4.5)1 Extrem rural State MN. ( 4441 19 ( 2.5) 4-41 22 ( 3.3) 29 ( 1.0) 19 ( 3.2) ( «61 Nation 14 ( 3.3) 19 ( 2.6) fen 23 ( 2.0) ( «el 26 ( 2.7) 256 ( 3.6)1 Other State 13 ( tO) 20 ( 1.1) 22 ( 1.3) 31 ( 1.1) 14 ( 0.9) 259 ( 4.0) 262 ( 2.7) 261 ( 2.2) 250 ( 1.8) 244 ( 3.1) Nation 12 ( 1.0) 21 ( 1.0) 23 ( 1.2) 27 ( 1.2) 17 ( 1.4) 26$ ( 2.6) 209 ( 2.3) 265 ( 2.1) 259 ( 2.2) 248 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. t. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE A25 I Students' Reports on the Amount of Time Spent (amtinued) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11110 NAEF TRIAL STATE ASSESSMENT Ons How or Loss Two Hours neva Has w Four to Me HMI Six Hours or More IMAk Ststa Mon man: jarmss H. newaradusts State Nation HS graduate State Nation Some coleys State Nation Collage 'Mast* State Hatton MAW State Nation Foaule State Nation loopp 04,44,9910 Parools. Perveplip sod and Walltissig Pnilidency Pralolsoy PreSelow Prollabow , OA) 1.0) 201 202 2.2) 204 1.0) 12 AS 21 0.9) 22 0.6) 211$ 2.2 2011 ( 1.11) 205 1.7) 15 243 2.0 10 1.0 245 ( 1.7) 1$ i1.1) 19 1.6) 2.4) 29 ( 2.0) 10 2.3) 1 242 2.8) 250 2.3) 241 1A) 233 3.2) 12 ( 2.2) 20 3.1) 21 2.1) 23 2A) 20 2.4) 244 33) sift ( .41 12 13) 16 ( 1.6) 20( 34( 1.9) 10( 1.6) 247 4M 253 ( 32) 20 ( 2.9 24$ 2.2) 239 ( 3.3) 3 1.0) 17( 1.4) 23 ( 2.0 32 2.3) 19 ( 1.0) 242 ( 4.7) 257 ( 2.11) 259 ( 3.2 253 24) 24$ ( 3.0) 11 c 1.5) 19 ( 2.1) 27 2.5) 30 ( 2.3) 12 i 1A , ) 206 34) 260 2.9) 2615 ( 2.6) .1.*1 10( 14) 25 2.4) 23 2.6) 23 ( 2.2) 14 ( 13) "I ( ***) 275 2.7) 209 ( 3.5) 267 ( 2.5) 242 ( 3.4) 13 1.3) 22 ( 1.4) 27 ( 1.4) 27 ( 1.7) 11 ( 12) 279 260 2.3) 277 ( 2.4) 271 ( 2.4) 254 ( 32) 17 1.3 22 1.6) 23 ( 1.1) 25 ( 1.5) 12 ( 1.1) 262 260 24) 277 ( 2.2) 270 ( 2.4) 255 1 3.2) 12 OA) 20 ( 1.0) 22 1.4) 31( 261 262 1 2.6) 265 1.9) 261 11 22 ( 1.2) 22 1.0) 26 25111 ( 3.3 267 ( 2.6) 267 ( 2.2) 262 1.0) 19 1.3) 24 ( 1.4) 29 ( 201 32) 262 2.5) 263 ( 2.2) 253 14 1.1) 20 1.3) 23 ( 1.4) 2$ 209 ( 26) 289 2.2) 264 ( 1.8) 258 15( 14 244 ( 1.3 17 ( 2.1) 246 ( 1.2) IS ( 1.5) 241 ( 1.0) 15 ( 1.9) 241 ( 1.1) 2.7) 1.5) 2.5) 12) 2.5) 1.2) 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 4 0 THE 1990 NAB? TRIAL STATE ASSESSMENT 135 Texas TABLE A26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Norsa One or TWO Days Three Days or More 1 TOTAL, Porconisso and firolidency leasenlass and PnelicleOcy 'wooed's* and Proficiency State 49 ( 1.0) 33 ( 0.9) 16 ( 0.9) 261 ( 1.4) 250 ( 1.0) 249 ( 1.9) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 285 ( 1.8) 200 ( 1.5) 250 ( 1.9) NACE/ETHNICITY White State 50 ( 1.5) 34 ( 1.4) 16 ( 1.1) 277 ( 1.3) 272 ( 1.3) 26$ ( 2.4) Nation 43 ( 1.2) 34 ( 12) 23 ( 12) 273 ( 1.8) 2/2 ( 1.7) 258 ( 2.1) Sack State 50 ( 3.4) 90 ( 3.4) 19 ( 2.7) 238 ( 2.2) 234 ( 3.4) 227' ( 3.3) Nation 58 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 47 ( 1.4) 33 ( 1.8) 21 ( 1.8) 248 ( 1.4) 248 ( 2.3) 239 ( 2.7) Nation 41 ( 3.3) 32 ( 22) 27 ( 2.8) 245 ( 4.8) 250 ( 3.3) 235 ( 3.1) TYPE OF COMMUNITY Advantaged urban State 50 ( 279 ( 2.8) 2.3)1 34 ( 2.9) 277 ( 3.1)1 18 ( ( 2.3) 441 Nation 47 ( 284 ( 2.3) 4.4)1 38 ( 2.8) 279 ( 4.5)1 15 ( ( 3.7) 441 Disadvantaged urban State 45 ( 2.7) 33 ( 22) 22 ( 2.5) 250 ( 2.7)1 247 ( 3.0)1 234 ( 3.2)1 Nation 42 ( 3.3) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 258 ( 42)1 238 ( 8.3)i Wrens* nral State 51 ( 283 ( 1.3) 3.9)1 2$ ( 2.8) 284 ( 4,8)1 21 ***, 3.7) Nation 43 ( 44) 32 ( 4.2) 25 3.9) 257 ( 4.1)1 264 ( 5.8)1 Other State 50 ( 1,4) $3 ( 1.1) 18 ( 1.0) Nation 260 45 1.9) 1.3) 25832 } 2A1.1 249 ( 23 ( 24) 1.1) 285 22) 200 ( 1.9) 251 ( 2,4) 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. 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). 136 141 THE 1990 NAEP TRIAL STATE ASSESSMENT Texas TABLE A26 I Students' Reports on the Number of Days of (continued) I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MD NAEP TRIAL STATE ASSESSMENT , None One or TWo Days Tem Days or More TOTAL State Nation PARENTS' EDDCATt011 IIS non-graduate State Nation KS graduate State Nation Sont college State Nation 4tge graduate -"due Nation GENDER M. State Nation Female State Nation glegvenlain and draidancy 43 ( 2.3) 244 ( 2.2) 30 ( 3.2) 245 ( 3.0) 47 ( 1.8) 251 ( 2.1) 43 ( 2.1) 255 ( 2.0) 48 ( 2.8) 206 ( 2.7) 40 ( 1.8) 270 ( 3.0) 53 ( 1.4) 277 ( 1.4) 51 ( 1.0) 275 ( 2.1) 5.4( 1.4) 263 ( 1.7) 47 ( 1.6) 266 ( 2.0) 44 ( 1.5) 259 ( 1.8) 43 ( 1.4) 264 ( 2.3) 5.1818011110. Pareenlape and Praidanty Podding, 33 ( 258 ( 32 ( 1 0.0 18 ( 248 ( 23 ( 1.1 ( 1.5 250 ( 34 ( 2.1 23 ( 2.5) 240 ( 241 ( 22) 25 ( 3.1 30 ( 3.6) 249 ( 3.3 237 ( 3.1) 35 ( 2.0 1111 ( 1.5) 250 ( 2.1) 230 ( 3.5) 31 ( 1.9) 27 ( 1.9) 257 ( 2.8) 249 ( 2.4) 37 ( 22) 15 ( 1.9) 209 ( 2.3) 4144 () 37 ( 1.8) 23 ( 1.8) 271 ( 2.5) 253 ( 3.1) 31 ( 1.5) 16 ( 1.3) 272 ( 2.4) 264 ( 3.0) 33 ( 1.2) 18 ( 1.3) 277 ( 1.7) 265 ( 3.1) 30 ( 1.2) 18 ( 1.1) 282 ( 2.1) 249 ( 2.9) 31 ( 1.4) 22 ( 1.4) 287 ( 2.1) 250 ( 2.6) 38 ( 1.4) 20 ( 1.3) 257 ( 1.8) 249 ( 2.2) 32 ( 1.1) 25 ( 1.3) 266 ( 1.7) 250 ( 1.8) 4. 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). 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 1:7 Texas TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT , $troll* *CH Alive Undecided, Disagree, SPengly Diem*. Brat 11148rootage an. Preliciancy anril Praibleacy State 31 ( 1.0) 44 ( to 2011( 1 .7) 267 1.4 Nation 27 ( 13) 49 1.0) 271 ( 1.9) 242 V? RACE/ETHNICITY Mite State ( 1.6) 47 ( 14) 283 ( 1.7) 271 ( 1.5 Nation 25 ( 1.6) 4$ ( 1.3 279 ( 2.0) 272 ( 1.8) Black State 36 ( 2.3) 46( 2.3 241 ( 2.3) 234 ( 2.3 Nation 32 ( 25) 52 ( 2.3) 247 ( 4.1) 239 ( 3.3) Hispanic State 25 ( 1.4) 49 ( 1.5) 254 ( 2.1) 248 ( 1.6) Nation 24 ( 2.5) 4$ ( 2.6) 257 ( 53) 244 ( 2.2) TYPE OF COMMUNITY Advantaged gaban State 31 ( 2.8) 45 ( 2.8) 286 ( 3.3)1 276 2.5)1 Nation 17 ( 3.2) 55 ( 24) 2$0 ( 4.1)1 Disadvantaged urban State 31 ( 1.8) 4$ ( 1.5) 253 ( 3.2)1 243 ( 2.7); Nation 26 ( 2.9) 41(2.9) 260 ( 5.6)1 249 ( 4.6)1 Extreme rural State 28 ( 34) *di 51 263 ( 4.2) ( 4.0)1 Nation 34 ( 24) 49 ( 2.2) 270 ( 3.9)1 212 ( 4.1)4 Other State 31 ( 1.4) 47 ( 1.4) 258 ( 22) 257 ( 2.0) Nation 27 ( 1.4) 4$ ( 1.2) 271 ( 2.4) 263 ( 2.2) Paraside. Praikisegt 22 ( aa ( 24 ( 231 ( 1 202 1 20 1.! 257 2A 18 32) 222 S 1114 227 4.2 236 2.9 24 2.1 234 ( 33 24 2.5) 208 23)I 24 4.2) 441 21 ( 2.1) 2;1761 31 240 4.5)1 201 17 1.4 eel 22 ( 243 2.7 25 1.4 250 1 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. ! 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 Texas TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Stron* A. Undecided, Magna STATE MLSESSMENT kW** Strongly Mare* TOTAL mad loroliciency one Preacioncy Percesda. Md ilvtviciency State ( 1,0) 4$ ( 1.0) 22 ( 1.1) 268 ( 1.7) 257 ( 1.4) 248 ( 1.9) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 1.9) 262 ( 1.7) 251 ( 1A) PARENTS' EDUCATION NS non-graduat State 27 1 243) 46 ( 2.7) 27 ( 2.0) 251 ( 2.5) 243 ( 22) 237 ( 2,5) Nation 20 ( ( 2.6) *41 50 ( 243 ( 3.3) 2.6) 30 ( 238 ( 3.8) 4-3) 145 gracksate State 28 ( 2.0) Si ( 1.8) 22 ( 1.7) 256 ( 22) 246 ( 1.9) 240 ( 3.1) Nation 27 ( 2.1) 47 ( 2.3) 26 ( 2.0) 262 ( 2.7) 255 ( 2.3) 24$ ( 2.4) Some collage State 35 ( 2.4) 46 ( 2.7) 20 ( 1.9) 275 ( 2.8) 263 ( 1.9) 258 ( 3.3) Nation 28 ( 24) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 256 ( 3.2) College graduate State 36 ( 2.2) 47 ( 2.0) 17 ( 1.8) 282 ( 2.3) 273 ( 1.7) 260 ( 2.6) Nation 30 ( 280 ( 2.3) 2.4) 51 ( 274 ( 1.6) 2.2) 19 ( 2es ( 1.8) 24) GENDER Mal* State 31 ( 1.5) 49 ( 1.5) 21 ( 1.3) 271 ( 2.0) 259 ( 1.6) 246 ( 2.2) Nation 28 ( 1.5) 445 ( 1.2) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Fon= le State 31 ( 1.4) 47 ( 1.5) 23 ( 1.6) 266 ( 22) 258 ( 1.7) 245 ( 2.4) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 269 ( 2.1) 262 ( 1.8) 252 ( 1.0) The standard errors of the estimated statistics appear in ptrentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 144 THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center far Education Statistics (NCES), Educational Testing Seivice (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 Coortfinators, 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 Natioaal Assessment Planning Project. That project resulted in the mathematics framework aid objectives for the assessment and recommendations about reporting the results of the prop dm. 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 US. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza worked closely and collegially with ETS Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathemalics 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 Mazza), with consultation from Eugene Johnson and Donald Rock. John Barone 13111111ge4 the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffier, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldftll, 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 cliaraderistics 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 teat 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 repot. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowie:, Laura McCandey, and Craig Pizza Debra Kline coortfinated the efforts of the data analysis staff. Stephen Koffier wrote the text for the report. Kent Ashworth was responsible for coordinating the cony design and final printing of this report. Special thanks are also due to many individuals for their invaluable assistance in reviewing the reports, especially the editors who improved the text and the analysts who checked the data. 1 4.4, US. GOVERNMENT PRINTING OFFICE : 1991 0 - 293-213 QL 3 (BK. 33) 14G