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DOCUMENT RESUME ED 330 581 SE 052 091 TITLE The State of Mathematics Achievement in Virginia: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE XF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assess%ent; 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 IDENTIFIERS Yational Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP): *Virginia ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial St,ite 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 represEmt 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 Virginia, 2,661 students in 104 public schools were assessed. This report describes the mathematics proficiency of Virginia eighth-graders, compares their overall performance to students in the Southeast region of the United States and the nation (using data from 'Lhe NAEP national assessments), presents the average proficienc separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, parents' educational level, and gender). To provide a context for the assessment data, participating students, their mathematics teachers, and principals completed questionnaires which focused on: instructional content (curriculum coverage, amount of homework); delivery of math instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, Virginia students had an average Proficiency of 264 compared to 261 nationwide. Many fewer students (Vrginia-15%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS U.S. DEPARTMENT OF EDuCATION The STATE of Othce F ducAbortor Rebeffcro and trnr)rovement EntiCAT1ONA&_ RESOURCES INFORMATION CENTE R sERIC1 reedacument has Deer% ref:Joao-al as cc, lefelvee 'reel the DerSoft CV Of garItZtspn at e aties Whop rrienves have been made thiptore rarooduetnah Quattv Pcnnts view op+mons stated thshICIOCth Mehl ao hat neceSserly repeesent offic.al A It! ot RI oosoion or pol.cy CIZ 4.; in VIRGINIA The Trial State Assessment at Grade Eight THE NATIONS REPORT I CARD BEST COPY AVAILABLE Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD, the National Assessment of Educational Progress (NAEP). is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1969. assessments have been conducted periodically in reading. mathematics. science. writing, history/geography, and other fields. By making objeetive information on student performance available to polieymakers at the national, state, and local levels. NAEP is an integral pan of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics. the U.S. Department of Education, The Commissioner of Education Statistics is responsible. by law, for canying out the NAEP project through competitive awards to qualified organitations. NAEP reports directly to the Commissioner, who is also responsible for providing continuing reviews, including validation studies and solicitation of public comment, on NAFP's conduct and usefulness. In 1988, Congress created the National Assessment Governing Board (NAGS) 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 (Aijectives; developing test specifications; designing the assessment methodology: developing guidelines and standards for data analysis and for reporting and disseminating results: developing standards and procedures for interstate. regional, and national comparisons: improving the form and use of the National Asses.anent: and ensuring that all items selected for use in the National Assessment are free from racial, cultural, gender, or regional bias. The National Assessment Governing Board Richard A. Boyd, Chairman Executive Director Martha Holden Jennings Foundation Cleveland. Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.O.C.E.S. Saratoga Springs, New York Franck Alexander Associate Superintendent California Department of Iducation Sacramento, California David P. Battini High School History Teacher Cairo-Durham High School Cairo. New York Parris C. Battle Teacher Horace Mann Elementary, Scho-,: Miami. Florida Mary R. Blanton Attorney Cromwell. Porter, Blanton & Blanton Salisbury. North Carolina Boyd W. Boehlje Attorney Gauss, 'Gyn. & Boehlje Pella. Iowa Linda R. Bryant Teacher Greenway Middle School Teacher Center Pittsburgh, Pennsylvania Honorable Michael N. Castle Governor of Delaware Carve! State Office Building Wilmington, Delaware Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hartford. Connecticut Chester E. Finn. Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.C. Michael 5, Glode Wyoming State Board of Education Saratoga, Wyoming Christine Johnson Principal Abraham Lincoln High School Iknver, Colorado John Lindley Principal South Colby Elementary School Port Orchard. Washington ari J. Maser DireLtor of Sehools 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 Willlam T. Randall Commissioner of Education State Department of Education Denver. Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington, D.C. Honorabk Richard W. Riley Attorney Nelson. Mullins, Riley and Scarborough Columbia, South ("angina Thonum Topuzes Attorney Law Offices of Frank Rogoirenski Coronado, Califorma Herbert J. Walberg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary tor Educational Research and Improvement tEx-Officio) U.S. Department of Education Washington, D.C. Roy Trilby Executive Direa or, NAGB Washington, D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of 1111r entaties Achievement In VIRGINIA The Trial State Assessment at Grade Right Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education 4 U.S. Department of Education Lamar Alexander Seottary Office of Educational Research and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson I. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Deparunent 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 gmnch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). library of Congress, Catalog Card Number: 91-61478 ISBN: 048685-14-9 The work upon which this publication is based was perfotmed for the National Center fa. Education Statistics, Office of Educational Research and Improvement, by Educational Testing Service. Educational Testing Service is an equal opportunity/affirmative actim employer. Educiaiional Testing Sankt. ETS. and are tegistered trademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION 7 Overview of the 1990 Trial State Assewsment 8 This Report 9 Guidelines for Analysis 12 Profile of Virginia 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Virginia Public Schools? 17 Chapter 1. Students' Mathematics Performance 1 S I xvels of Mathematics Proficiency Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race/Ethnicity 24 Type of Community 27 Parents Education Level 29 Gender 11 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics? 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics instruction Davered" 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used' 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics' 67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the flame 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 iv THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia ME NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history a provision authorizing voluntary state-by-state assescments on a trial basis, in addition to continuing its primary mission, the national asselPments that NAEP has conducted since its inception. As a result of the legislation, the 1990 NAEP piogram included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the 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 1 Virginia In VirOnia, 104 public schools participated in the assessment. The weighted school participation rate was 99 percent, which means that all of the eighth-grade students in this sample of schools were representative of 99 percent of the eighth-grade public-school students in Virginia. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 2 percent of the cighth-grade public-school population was classified as Limited English Proficient (LEP), while 8 percent had an Individualized Education Plan (MP). 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 aetivities 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 1EP represented 1 percent and 5 percent of the population, respectively. In total, 2,661 eighth-grade Virginia public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligible eighth-grade public-school student population in Virginia. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from Virginia on the NAEP mathematics scale is 264. 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 specifically what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to defme the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia In Virginia, 98 patent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in Virginia (15 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in Virginia 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 Virginia eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In Virginia: White students had higher average mathematics proficiency than did Black or Hispanic students but lower mathematics preficiency than did Asian students. Further, a greater percentage of White students than Black or Hispanic students but a smaller percentage of White than Asian students attained level 300. The results by type of community indicate that the average mathematics performance of the Virginia 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 Virginia, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 40 points higher than that of students whose parents did not graduate from 'aigh school. The results by gender show that there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in Virginia. In addition, there was no difference between the percentages of males and females in Virginia who attained level 300. Compared to the national results, females in Virginia performed no differently from females across the country; males in Virginia performed no differently from males across the country. I 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 3 Virginia 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 Virginia are as follows: About three-quarters of the students in Virginia (74 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 Virginia, 97 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. About the same percentage of students in Virginia were taking eighth-grade mathematics (46 percent) as were taking a course in pre-algebra or algebra (51 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 Virginia 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 instnictional emphasis on Numbers and Operations and Measurement had towel proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. I 1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia In Virginia, 22 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 31 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 Virginia, 27 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. In Virginia, 32 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. More than half of the students (68 percent) had teachers who had the highest level of teaching certificatica available. This is similar to the figure for the nation, where 66 percent of students were taught by teachers who were certifilcl at the highest level available in their states. Students in Virginia 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 Virginia (13 percent) watched one hour or less of television each day; 16 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 5 Virginia NE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maly land Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Quo lina Indiana North Dakota Guam Virgin Islands .13 THE 190 NAEP TRIAL STATE ASSESSMENT 7 Vfrginia This report describes the peormance of the eighth-grade public-school students in Virginia and consists of three sections: This Introduction provides background information about. the Trial State Assessment and this report. It also provides a profile of the eighth-grade public-school students in Virginia. Part One describes the mathematics performance of the eighth-grade public-school students in Vuginia, the Southeast region, and the aation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Virginia, the Southeast region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survey instilment 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 (1)(2)(C)0) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(1)(2)(C)(0)) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represeat the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 14 8 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and pa. :mod after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council of Chief State School Officer in mid-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,' the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refmed by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in igade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-grade public-school students in Virginia, in the Southeast region, and for the nation. Results also are provided for groups of students defmed by shared characteristics -- race/ethnicity, type of community, parents' education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for Virginia are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nationally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAEP program was necessary beatuse the voluntary nature of the Trial State Assessment Program did not guarantee representative national or regional results, since not every state participated in the program. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 1 5 9 Virginia RACE/ETHNICITY Results are presented for students of different racial/ethnic groi .ps based on the students' self-identfication of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Pmcedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for raciallethnic 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 Virginia. 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 pmfessional 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 meti. politan 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 gradumed college. The response indicating the higher level of education was selected for reporting. 16 10 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia 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 1. 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 Vuginia will be to the Southeast. FIGURE 1 I Regions of the Country NORTHEAST SOUTHEAST 1 CENTRAL WEST Connecticut Delaware District of Columbia Maine Maryland Massachusetts New Hampshire New Jersey New York Pennsylvania Rhoda island Vermont Virginia Alabama Arkansas Florida Georgia Kentucky Louisiana Mississippi North Carolina South Carolina Tennessee Wri Olga West Virginia IWnoIs Indiana Iowa Kansas Michigan Minnesota Missouri Nebraska North Dakota Ohio South Dakota Wisconsin Alaska Arizona California Colorado Hawaii Idaho Modena Nevada New Mexico Oklahoma Oregon Tens Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT 11 Vitsinia Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difterence between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistical1), signifkant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) -- regardless of whether the sample means or sample proportions appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the difference is not statistically significant), the means or proportions are described as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the apparent magnitude of the difference 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 differenck between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two goups, 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 disct.....4ed in greater detail in the Procedural Appendix. 18 12 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia It is also important to note that the conftdence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). 9 THE 1990 NAEP TRIAL STATE ASSESSMENT 13 Virginia Profile of Virginia EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERIS17CS Table I provides a profile of the demographic characteristics of the eighth-grade public-school students in Virginia, the Southeast 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 Virginia Eighth-Grade Public-School I Students PERCENTAGE OF STUDENTS 1860 NAEP TRIAL STATE ASSESSMENT WSW& Southeast Nation DEMOGRAPHIC SUBGROUPS Raceighnicity White Black Hispanic Asian American Indian Typo of Community Advantaged urban Disadvantaged urban Extreme rural Other Patents' Education Did not finish high school Graduated high school Some education after high school Graduated college Gender Male Female Percentage Percentage Percentage 66( 1.5) 63 ( 3.0) 70 ( 0.5) 23 ( 1.5) 32 ( 3.0) 16 ( 5 ( 0.5) 3 ( 01) 10 ( 0.4 4 ( 0.4) 1 ( OA) 2 ( 04 ( 0.2) 0 ( OA) 2 ( 0.7 25 ( 3.9) 0 ( 0.0) 10 ( 3.3) 4 ( 1.3) 2 ( 2.3) 10 ( 2.8) 11 ( 1.7) 9 ( 5.3) 10 ( 3.0) 00 ( 4.3) 89 ( 5.8) 70 ( 4.4) 10 ( 0.7) 14 ( 2.1) 10 ( OA) 27 ( 1.0) 27 ( 1.8) 25 ( 1.2) 18 ( 0.8) 1$ ( 11) 17 ( 0.9) 41 ( 1.5) 32 ( 3.3) 39 ( 1.9) 49 ( 0.9) 49 ( 2.8) 51 ( 1.1) 51 ( 0.9) 51 ( 2.8) 49 ( 1.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages for Race/Ethnicity may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 2 0 14 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Virginia schools and students sampled for the 1990 Trial State Assessment. In Virginia, 104 public schools participated in the assessment. The weighted school participation rate was 99 percent, which means that all of the eighth-grade students in this sample of schools were representative of 99 percent of the eighth-grade public-school students in Virginia. TABLE 2 I Profile of the Population Assessed in Virginia EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution ea% 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 106 1 104 104 THE 1990 NAEP TRIAL STATE ASSESSMENT EIGHTH-GRADE PUISLX-SCHOOL, STUDENT PARTICIPATION Weighted student participation rate after make-ups 04% Number of students selected to participate in the assessment 3206 , Number of students withdrawn from the asseSsment 105 Percentage of students who were of Limited English Proficiency 2% Percentage of students excluded from the assessment due to Limited English Proficiency 1% Percentage of students who had an Individualized Education Plan 8% Percentage of students excluded from the assessment due to Individualized Education Plan status 5% Number of students to be assessed 2,836 Number of students assessed 2,061 21 15 Virginia In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 2 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 proigam 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 1 percent and 5 percent of the population, respectively. In total, 2,661 eighth-grade Virginia public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligible eighth-grade public-school student population in Virginia. 22 16 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia ME NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Virginia Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAEP mathematics scale, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficiency of eighth-grade public-school students in Virginia. Chapter 1 compares the overall mathematics performance of the students in Virginia to students in the Southeast 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. 9 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 17 Virginia CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-gxade public-school students from Virginia on the NAEP mathematics scale is 264. This proficiency is no different from that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency NAEP Mathematics Scala 0 200 225 250 275 300 500 Avarage Proficiency tt4 Virgin Pa 264 ( 1.5) t-1.4 Southeast 253 ( 2.7) ret Nation 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 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. a 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. 24 Is THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia 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 specics of what the students know and can do in the subject. To describe the nature of students' proficiency in greoer detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to 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 are based solely ;in student performance on the 1990 mathematics assessment. The levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In Virginia, 98 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in Virginia (15 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 Virginia, Southeast region, and national results for each content area. Students in Virginia performed comparably to students in the nation in all of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 Virginia 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 solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-Step word problems and select the greatest four-digit number in a list. In measurement, thedie students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coin& 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 Students at this level have extended their understanding of quantitative reasoning with whole niimbers 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 identity solutions to other elementary two-step word problems. In these basic problem-solving situations, they can Identify missing or extraneous information and have some knowledge of when to use computational estimation. They have a rudimentary understanding of such concepts as whole number plaCe value, "even," "factor," and "multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion arid probability. In algebra, they are beginning to deal Informally with a variable through numerical substitution in the evaluation of simple expressions. 26 20 THE 1990 NAEP TRIAL STATE ASSESSMENT 1 Virginia FIGURE 3 I Levels of Mathematics Proficiency (continued) i 300 Reasoning and Problem Solving involving Fractions, Decimals, Percents, Eiementary 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 pletorial representstions. They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expressions, including thoSe with exponentS and negative integers. In measurement, these Students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and prOpertieS of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, cOmpute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open linear sentences and inequalities by substitution, and checking and graphing an interval representing a compound inequality when it is described in words. They can determine and apply a rule for simple functional relations and extend a numerical pattern. LEVEL 350 Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to Include some properties of exponents. They can recognize scientific notation on a calculator and make the transition between Scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and t les to solve problems. They can find the circumferences of circles and the surface areas of so, figures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirect measurement. These students also can apply their knowledge of the properties of geometric figures to solve problems, such as determining the slope of a line. In data analysis, these students can compute means from frequency tables and determine the probability of a simple event. In algebra, they can identify an equation describing a linear relation provided in a table and solve literal equations and a system of two linear equations. They are developing an understanding of linear functions and their graphs, as well as functional notation, Including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. 2 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 Virginia FIGURE 4 I Levels of Eighth-Grade Public-School Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 Stift Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation Percentage 1 ( 0.4) o ( 0.0) (I ( 0.2) 20 40 so 80 1 00 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 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 28 22 THE 1990 NAEP TRIAL STATE ASSESSMENT 64 ( 1.6) 52 ( 3.2) 54 ( 1.6) 98 ( 0.4) 94 ( 2.2) 97 ( 0.7) Virginia FIGURE 5 I Eighth-Grade Public-School Mathematics Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation 0 200 225 250 275 300 Average Proficiency 2611 ( 1.4) 259 ( 2.9) 266 ( 1.4) 259 ( 1.8) 246 ( 3.8) 258 ( 1.7) 261 ( 1.5) 249 ( 2.6) 239 ( 1.4) 264 ( 1.8) 250 ( 3.3) 262 ( 1.8) 265 ( 1.6) 254 ( 2.7) 260 ( 1.3) 500 Mathematics Subseal. Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. _ 4) THE 1990 NAEP TRIAL STATE ASSESSMENT 23 Virginia CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessmeat included reporting on the performance of various subgroups of the student population defiled by race/ethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY The Trial State Assessment results can be compared according to the different racial/ethnic groups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Black, Hispanic, and Asian students from Virginia are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black or Hispanic students but lower mathematics proficiency than did Asian students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Black or Hispanic students but a smaller percentage of White than Asian students attained level 300. 3 0 24 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia FIGURE 6 I Average Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity Average Proficiency illommemral Virginia Mite Black Hispanic Asian Southeast White Black Hispanic Asian Nation Mite Black Hispanic Asian SO ( 15) *Ai 4 gi) 313 ( 2.3) 5441 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 14-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 31 THE 1990 NAEP TRIAL. STATE ASSESSMENT 25 Virginia TIE NATION'S REPORT FIGURE 7 I Levels of Eighth-Grade Public-Sebool CARO Mathematics Proficiency by Ract/Etbnicity LEVEL 300 Stat White Black Hispanic Asian 11.9147n White Slack Hispanic Asian Nation White Black Hispanic Asian LEVEL 250 State White Black Hispanic Asian R91an White Black Hispanic Asian Nation White Black Hispanic Asian LEVEL 200 State White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispan c Asian 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-4-I). 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 determinaLon of the variability of this estimated mean proficiency, ". Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 19 ( 1.9) 2 ( 0.7) 6 ( 2.6) 40 ( 5.4) 11 ( 2.7) 2 ( 1.6) ( "I) 15 ( 1.5) 2 ( 1.3) 3 ( 1.1) 31 ( 82)1 73 ( 1.5) ( 2.5) 40 ( 5.0) 04 ( 2.8) 86 ( 3.6) 27 ( 5.1)* 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) 90 ( 5.6)! 99 ( 0.3) 94 ( 1.1) 90 ( 3.5) 100 ( 0.0) 98 ( 1.3) ( 5.3) *4.) ( .41 99 ( 0.4) 66 ( 3.1) 93 ( 1.6) 97 ( 2.5)1 100 32 26 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TYPE OF COMMUMTY Figure 8 and Figure 9 pmsent the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, disadvantaged urban areas, extresue rural areas, and areas dassifkd as "other". (These are the "type of community" groups in Virginia with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Virginia 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-Scbool Mathematics Proficiency by Type of Community MAEP Mathematics Scale 225 250 275 300 500 AIWA"! PirdiCiefICY 14 1-4.4 11polOISIMEMIIMIIMMI Virghfia Advantaged urban Disadvantaged urban Extreme rural Other Southsast Advantaged urban Disadvantaged urban Extreme rural Other Nation Advantaged urban ( Disadvantaged urban 3.5$ Extreme rural JN ( 4.1$ Other 2S1 1.S) 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 14-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 Virginia FIGURE 9 LEVEL 300 State Adv. urban Disadv. urban Ext. rural Other Adv. urban D1sadv. urban Ext. rural Other Nation Adv. urban 134sadv. urban Ext. rural Other LEVEL 250 Stat. Adv. urban Disadv. urban Ext. rural Other Rigion Mv. urban Disadv. urban Ext. rural Other Nation My. urban Disadv, urban Ext. rural Other LEVEL 200 State Mv. urban Disadv. urban Ext. rural Other Region Adv. urban Dlsadv. urban Ext. rural Other Nation Mv. urban Disadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community TIE NATIOWS REPORT CARD 'TA 111111 1,.111,=.111.104 1-00,1*4 F".41"4 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by I-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! 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). 0.4014 100 34 28 THE 1990 NARP TRIAL STATE ASSESSMENT 30 ( 4.9) 4 ( 2.0)) ( 1,7) 12 ( 15) ( 444.) 4 ( 4.2)1 9 ( 1.9) ( 4.8)1 7 ( 2.1)! ( 2.3)1 12 ( 1.2) 113 ( 2.6) 40 ( 5-5)1 44 ( 2.8) 81 ( 2.3) **) ,tte 04 48 (17.4)1 63 ( 3.9) 93 ( 4.6)1 48 ( 5.0)' se ( 8.2)! ( 2.3) 103 ( 0.4) 96 ( 3.3)1 ( 1.9) 95 ( 0.5) 00) ...) 90 (13.5): 94 ( 22) 100 ( P.0) N ( 1.5)t 97 ( 2.8)1 97 ( 1.0) Virginia PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In Vvginia, the avenge mathematics proficiency of eighth-gade public-school students having at least one parent who graduated from college was approximately 40 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 Virginia (41 percent) and in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 10 percent for Virginia and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School Mathematics.Proficiency by Parents' Education NW 141alhonsatics Sca 0 200 225 250 275 300 500 1104 1.40-0011 1-1,41m4 COM Virginia HS non-graduate HS graduate Some college College graduate Southeast HS non-graduate HS graduate Some college College graduate Nation HS non-graduate HS graduate Some college College graduate Pmfidency 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 t4-I). If the confidence intervals for the populations do not owrlap, there is a statistically significant difference between the populauons. 35 THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Virginia ... THE ATION1 REPORT FIGURE 1 1 I Levels of Eighth-Grade Public-School CARO Mathematics Proficiency by Parents' Education LEVEL 300 State HS non-grad. HS graduate Some college College grad. Roction HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 230 State HS non-grad. ?IS graduate Some college College grad. Rogion HS non-grad. graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 Stat. MS non-grad. HS graduate Some college College grad. Region 115 non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors a;4 presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-1-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 400 3 6 30 THE 1990 NAEP TRIAL STATE ASSESSMENT 1 ( 0.9) 4 ( 0.7) 13 ( 1.8) 29 ( 2.9) 1 ( 0.0) 3 ( 1.7) ( 2.3) 19 ( 3.8) 1 ( 0.9) 6 ( 1.5) 12 ( 1.4) 21 ( 1.9) 36 ( 4.7) 50 ( 2.3) 71 ( 2.5) ID ( 1.7) 29 ( 8.9) 43 ( 5.4) SI ( 8.3) 72 ( 3.5) 37 ( 4.6) 86 ( 2.7) 71 ( 2.0) 79 ( 2.0) 94 ( 1.8) 97 ( 0.8) 99 ( 0.7) ( 0.4) 93 ( 3.5) 03 ( 2.4) 97 ( 25) 97 ( 2.0) 96 ( 1.9) 97 ( 0.8) 99 ( 0.7) 99 ( 0.7) fPMIOMMII.11...I..I GENDER Virginia As shown in Figure 12, there appears to be no diffezence in the average mathematics proficiency of eighth-grade males and females attending public schools in Virimia. Compared to the national results, females in Virginia performed no differently from females acloss the country; males in Virginia performed no differently from males across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender Virginia Male Female Soutfioast Male Female Nation 044 Mate 1.10 PIO Female The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by1-4-I). 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 Virginia who attained level 200. The percentage of females in Virginia who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in Virginia who attained level 200 was similar to the percentage of males in the nation who attained level 200. 3 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 31 Virginia FIGURE 13 LEVEL 300 State Male Female Region Male Female Nation Male Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female Levels of Eighth-Grade Public-School Mathematics Proficiency by Gender 0 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 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. 35 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 17 ( 2.0) 14 ( 1.5) 10 ( 1.9) ( 2.0) 14 ( 1.7) 10 ( 1.3) 64 ( 2.2) 93(1.7) 80 ( 3.6) 64 ( 3.8) 64 ( 2.0) 64 ( 1.8) OS ( 0.5) 97 ( 0.6) 93 ( 3.0) ( 1.9) 07 ( 0.9) 97 ( 0.8) Virginia In addition, there was no difference between the percentages of males and females in Virginia who attained level 300. The percentage of females in Virginia who attained level 300 was similar to the percentage of females in the nation who attained level 300. Also, the percentage of males in Virginia who attained level 300 was similar to the percentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. 3a THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Virginia TABLE 3 Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 19110 NAEP TRIAL STATE ASSESSMENT Numbers And Operation kballUraill.rd j Geomettlf Data Analysts, libtelltioo, and Probability Mgabra and FINICUOIS TOTAL State Region Nation RACE/ETHNICITY Whits State Region Nation Black State Region Nation Hispanic State Region Nation Asian State Region Nation TYPE Of COMMUNITY Advantaged urban State Region Nation Disadvantaged urban State Region Nation Extreme rural State Region Nation Other State Region Nation 261 210 20 fr$11410016! ( 1.4) (2A) 1A) %246 258 6$ 1.1 221 20 1 9 254 ( 11 gtss 250 3.31 254 211 0110 274 ( 211$ ( 1.7) 1.6) 273 ses ( 3.0 251 ( 42) 259 3.5) 263 3.4 273 ( 1.6 287 ( 2.0) 287 1.5) 272 1.8 244 ( 232 ( 2.1) 1.4) 242 ( 5.1 222 ( 5.4) 228 4.2i II; 1 111 244 ( 3.1 227 ( 3.8) 234 2A 231 3.8 248 i Lill 24141 24.5,( 4.0) 234 ( 43) 248 ( 2.7) 2311 ( 3.4) 243 ( 3:2) 229 ( 3.43 299 ( 3.3) 292 ( 5.5) 293 ( 4.0) 296 ( 4.8) ...1 di* ( * NON ( *IN) ;IS 1 .5:2)1278 1 NI 8.3)1 275 ( 5.9)1 282 ( 5.9)1 2811 ( 3.8) IhNo ( INN) 283 ( 3.2)1 252 ( 2.9)1 ( *dm) 255 ( 3.1)1 253 ( 2.3) 254 ( 9.8)1 258 ( 4.3)1 284 ( 1.7) 259 ( 3.3) 208 ( 1.9) 280 ( 4.3) ( 281 ( 34)1 238 ( 8.1)1 242 ( 4.9)1 241 ( 39) 241 (17.1)1 254 ( 4.2)1 258 ( 2.0) 244 ( 4.0) 257 ( 2.4) 281 ( 4.0) ( **el 277 ( 5.2)1 239 (52)1 248 ( 32)1 243 ( 3.1) 244 (18.4)1 253 ( 4.5)1 257 ( 1.9) 249 ( 2.7) 259 ( 1.7) 288 ( 4.1) y) 285 ( 4.8)1 243 ( 8.7)1 247 46)1 245 ( 3.8) 245 (132)1 257 ( 3.0)1 200 ( 2.1) 251 ( 3.8) 201 ( 2.2) 271 288 1.41 245 237 2.7) 243 ( 3.1) 4.51 218 ( 8.7)1 283 ( 3A) ( .41 277 ( 4.8)1 243 ( 4.8)1 247 ( 3.2)1 249 ( 3.2 251 (14.7 258 ( 4.8)! 202 ( 1.11) 25$ ( 3.0) 281 ( 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. 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). 4 0 34 THE 1990 NAEP TRIAL STATE ASSESSMENT rginia TABLE 3 I Eighth-Grade Public-School Mathematics (cmtinued) i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Meastretnent . Geometry Data Analysis Stalistks, and Probability _ Algebra and nincliam . yOTAL State Region Nation PARENTS' EDUCATION Prolkiency 268 ( 1.4) 256 ( 2.9) 266 ( 1.4) Preidioney 256(1.6 248 ( 256 ( 1.7 Praichocy 261 15 240 2.6 250 lA HS non-graduate State 245 ( 2.5) 232 ( 2.5) 240( 2.3) Region 243 ( 4.5) 227 ( 8.1) 237 ( 4.1) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) HS graduate State 256 ( 1.4) 246 ( 1.7) 247 ( 1.5 Region 252 ( 4.7) 235 ( 5.3) 242 ( 3.3 Nation 259 ( 1.6) 24111 ( 2.1) 252 ( 1.6 Some college State 270 ( 1.5) 265 f 2.5) 264 ( 1.8) Region 265 ( 34) 257 ( 6.3) 253 ( 4.2) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) CoNage graduate State 283 ( 2.0) 275 ( 2.4) 277 ( 21) Region 275 ( 39) 264 ( 4.6) 263 ( 3.6) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) GENDER Male State 260 ( 1.9) 264 ( 2.1) 263 ( 1.9) Region 257 ( 3.6) 249 ( 4.4) 249 ( 3.2) Nation 266 ( 2.0) 262 ( 2.3) 260 ( 1.7) Femal State 267 ( 1.3) 255 ( 1.9) 258 ( 1.5) Region 261 ( 2.9) 243 ( 4.0) 248 ( 2.4) Nation 266 ( 1.4) 253 ( 1.6) 248 ( 1.5) Prolkiancy Prandsocy A14 1.6 205 1.11) 3.3 254 2.7) , ( 1.6 200 13) 236 ( 2.5) 234 ( 4.7) 240 ( 3.1) 248 .9 1 242 5.4) 253 2.2) 2681 2.0) 200 ( 33) 200 ( 2.4) 263 ( 2.4) 207 4.6) 276 ( 2.2) 265 ( 2.2) 249 ( 3.9) 262 ( 2.1) 262 ( 1.7) 251 ( 3.7) 261 ( 1.9) 242 ( 2.6) 240 ( 3.5 242 ( an 251 ( 1.6) 247 ( 4.5) 253 ( 2.C) 2602% 524.71 263 ( 2.2i 281 ( 2.2) 210( 4.1) 273 ( 1.7) 264 ( 2.1) 253 ( 32) 260 ( 1.0) 266 ( 14) 255 ( 2.6) 260 ( 1.4) The standard errors of the estimated stAtifttiCS 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 eirors of the estimate for the sample. 41 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Virginia THE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics pmficiency I v2luab1e in and of itself, but it becomes more useful for improving instruction ar, 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 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 learnit.g and instruction -- fundamental aspects of the educational process in the country. THE 1990 NAEP TRIAL STATE ASSES; 'NT 4 2 Virginia Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an enormous impact on fidure academic achievement. Yet, as shown in Chapters 3 and 7, large proportions of students report having spent much more time each day watching television than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 38 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia 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 policymakershave recommended widespread reforms that are changing the dilution of mathematics education. Recent reports have called for fundamental revisions in cuniculum, a reexamination of tracking practices, Unproved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.3 This chapter focuses on curricular and instructional content issues in Virginia 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 Virginia (74 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. Curtis McKnight, et al., The Underachieving Curriculum: Assessing U.S. School Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign, IL: Stipes Publishing Company, 1987). Lynn Steen, Ed. Everybody 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 Virginia In Virginia, 97 percent of the students could take an algebra course in eieith grade for high school course placement or Qua Almost all of the students in Virginia (94 percent) were taught mathematics by teachers who teach only one subject. Many (80 percent) of the students in Virginia were typically taught mathematics in a class that was mimed by mathematics ability. Ability grouping was less prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in Virginia Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Vtrgkila Southeast Nation Percentage of eighth-grade students in public schools that identified mathematics as receiving special emphasis in school-wide goals and objectives, Instruction, in-service training, etc. Percentage of eighth-grade public-school students who are offered a course in affebra fOr high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who toady only mathematics Percentage of eighth-grade students in public schools who are assignod to a mathematics class by their ability in mathematics Percentage of eighth-grade students in public schools who receive bur or more hairs of mathematics instruction per week Parcontago Parcootogo Porventego 4 ( 44) 70 (10.6) 53 ( SS) 97 ( 1.7) 60 (101) 76 ( 4.6) 94 ( 1.6) 77 (11-.6) 91 ( 3.3) 80 ( 24) 63 ( 13.0) 63 ( 4.0) 32 ( 3.5) 51 (11.1) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eiglith graders in Virginia are taking mathematics courses. Based on their responses, shown in Table 5: About the same percentage of students in Virginia were taking eighth-grade mathematics (46 percent) as wen taking a course in pre-algebra or algebra (51 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in Virginia who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-gade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT I Virginia _ Southeast Nation Percentage and Pnalicianclf Percentage and ProfirJency Percentage and Proficiency What kind of matherrmtics class are you taking this year? Eighth-grade mathematics 46 ( 2.0) 64 ( 3.7) 82 ( 2.1) 244 ( 1.5) 241 ( 3.4) 251 ( 1.40 Pre-algeb, a 35 ( 1.8) 23 ( 4.4) 19 ( 1.9) 271 ( 1.5) 269 ( 4.8)1 272 ( 2.4) Algebra 16 ( 1.0) 11 ( 2.2) 15 ( 1.2) 305 ( 2.4) 290 ( 4.8)1 290 f 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 mterest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. I Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 4 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Virginia Further, from Table A5 in the Data Appendie A greater percentage of females (55 percent) than males (46 parent) in Vuginia were enrolled in pre-algebra or algebra courses. In Virginia, 55 percent of White students, 41 percent of Black students, 37 percent of Ifispanic students, and 61 percent of Arian students weir enrolled in pm-algebra or algebra courses. Similarly, 61 percent of students attending schools in advantaged urban areas, 48 percent in schools in disadvantaged urban areas, 43 percent in schools in extreme rural areas, and 49 percent in schools in areas classified as "other" were enrolled in pit-algebra or algebra 1:011230. 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, respettively. According to their teachers, the greatest percentage of eighth-grade students in public schools in Virginia 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 Virginia, 2 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 3 percent of the students in Virginia 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 4 2 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia The results by race/ethnicity show that 3 percent of White students, 4 percent of Black students, 2 percent of Hispanic students, and 4 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 2 percent of White students, 3 percent of Black students, 4 percent of Hispanic students, and 1 peseent of Asian students spent no time doing mathematics homework. In addition, 2 percent of students attending schools in advantaged urban areas, 16 percent in schools in disadvantaged urban areas, 3 percent in schools in extreme rural areas, and 3 percent in school's in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 1 percent of students attending schools in advantaged urban areas, 8 percent in schools in &advantaged urban areas, 1 percent in schools in extreme rural areas, and 2 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IIVO NAEP TRIALSTATE ASSESSMENT Virginia Southeast Nation About how much time do students spend on mathematics homework each day? 45 Wastes An how or mere .,11,, Paventaes and Prefidency 2 ( 0.5) 41 ( 2.7) 252 ( 2.2) 42 Penalties Percentsgs e nd end Proficiency Proficiency 1 ( 1.0) ( 44 ( 74) 245 ( 5.1)1 ( 0.3) ***) 43 ( 4.2) 256 ( 2.3) 43 ( 1.9) 268 ( 2.3) 11 ( 1.4) 285 ( 4.5) 3 ( 1.0) 278 ( 9.8)1 44 ( 1.6) 200 ( 5.4)1 ( 2.7) 3 ( 1.3) ( impel ( 4.3) 266 ( 2.8) 10 ( 1.9) 272 ( sly 4 ( 0.9) 278 ( sAy The standard errors of the estimated statistics appear in parentheses. It can be said vith 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). 48 THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Virginia TABLE 7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NW TRIAL STATE ASSESSMENT *Oat Southeast Nation About how much time do you usually spend each day on mathematics homework? None 15 minutes 30 minutes 46 minutes An how or more Patio lase Parcomiref Poraidapp ese Poilifleigy Widow 24/ f t:i :1 1 1. 1 1.;1 2 36 ( 1.1) 287 ( 12) 10 ( 01 14 ( 0.7) 20e ( 11) 11 ( 1 .9) CZ ( Sot) 25 ( 1.01 253 ( 13) 33 ( 2.5) 250 ( 340) 17 ( 2.2) 261 ( 2.5) 14 ( 1.4) 247 ( 4.8) 2Sti °it 31 ( 1.0) 2114 ( 1.11) 22 ( 13) 2113 ( 1A) 10 ( 1A) 21011 ( 13) 12 ( 1.1) 255 ( 3.1) Vm111 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 «ample. And, according to the students (Table 7 and Table A7 in the Data Appendix): In Virginia, relatively few of the students (6 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 11 percent of the students in Yuginia and 12 percent of students in the nation spent an hour or more each day on mathematics homework. The results by race/ethnicity show that 11 percent of White students, 11 percent of Black students, 13 percent of Hispanic students, and 15 percent of Asian students spent tin hour or more on mathematics homework each day. In comparison, 6 percent of White students, 7 percent of Black students, 9 percent of Hispanic students, and 2 percent of Asian students spent no time doing mathematics homework. 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia In addition, 12 percent of students attending schools in advantaged urban areas, 9 percent in schools in disadvantaged utban areas, 13 percent in schools in extreme rural areas, and 11 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 4 percent of students attending schools in advantaged urban areas, 4 percent in schools in disadvantaged urban areas, 10 percent in schools in extreme rural areas, and 7 percent in schools in areas classified as "other" spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement.' Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "Iravy," "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 theTrial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proponion, 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, Statistks, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. National Council of Teachers of Mathematics, Curricutwn and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teacherssf Mathematics, 1989), THE 1990 NAEP TRIAL STATE ASSESSMENT 45 Virginia 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 glheavy emphasis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numben and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 46 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE 8 I Teachers' Reports on the Emphasis Given to i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1100 NAEP TRIAL STATE ASSESSMENT vitsima Southaast Nation Teacher "emphasis" categories by content areas Numbers and Operations Heavy emphasis Little or no emphasis Illeasureenent Heavy emphasis Little or no emphasis Geometry Heavy emphasis Uttle or no emphasis Data Am Wats, Statistics, and Probability Heavy emphasis Little or no emphasis Algebra and Functions Heavy emphasis Uttle or no emphasis 111817:1011110 firslisSsow 2: VIZ 11 ( 2.1) 2111 ( 4.3) 12 ( 2.0) 245 ( AS) 41 ( 3.1) 272 ( 11.2) 2811( 3.5) 34 ( 2.4) 259 ( 23) 10 ( 1.6) 270 ( 5.0) so ( 2.9) 210 ( 2,2) 52 ( 2.3) 262 ( 2.3) 23 ( 2.0) 234 ( 2.2) Peslislowi ( 7.3) 59 258 ( 3.1)1 15 ( 4.8) 262 ( 7.7P .4410981110 sod 11,011thow 48( 8.0) 28) ( 1.8) 18 ( 2.1) *07(34) 13 ( OA) 17 ( 11.0) 242 ( 7.6)1 250 ( 5.8) 22 ( 0.1) 23 ( 4.0) 259 (10.7)1 272 ( 4.0) 22 ( 7.0) 24 ( 3.6) 253 ( 7.5)1 240 ( 3.2) 22 ( Le) 21 ( 3.3) 253 ( 1.7)1 264 ( 54 ) 19 ( 5.9) 14 ( 2.2) 274 ( Le) 261 ( 4.3) 54 (10.4) 53 ( 4.4) 246 ( 5.4)1 261 ( 2.11) 42 ( 8.0 44 341 277 ( 2 75 2 .5 21 ( 1.1) 20 ( 3.0) 238 ( 0.7)1 243 ( 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 t 2 standard errors ) of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasier 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 Virginia SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: About three-quarters of the eighth-grade students in Virginia (74 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Virginia, 97 t of the students could take an algebra course in eighth grade for school course placement or credit. About the same percentage of students in Virginia were taking eighth-grade mathematics (46 percent) as were taking a course in pre-algebra or algebra (51 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 Virenia 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 reportei either 15 or 30 minutes daily. In Virginia, relatively few of the students (6 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 11 percent of the students in Virginia and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Funcions. 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. th) 48 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia CHAPTER 4 yaxx BIM uui.ui BM 1111111111111111111111 IMMO 1111111M 111111111111111M111111 11111111k111M111111 SUM 11111111111 MUM, IMF OMB IMMO& SIP MIMI NOON Ir.Igig HIM 11111111 AMIN SOM. How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning orfor those who come from different cultural backgrounds is an important aspect of teaching.' An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. 6 National Council of Teachers of Mathematics, Pmfessional Standards for the Teaching of Mathematics (Reston, VA: National Cotmcil of Teachers of Mathematics, 1991). 5 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Virginia From Table 9 and Table A9 in the Data Appendix: In Virginia, 22 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 31 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 Virginia, 33 percent of students attending schools in advantaged urban areas, 0 percent in schools in disadvantaged urban areas, 25 percent in schools in extreme rural areas, and 18 percent in schools in areas classified as "other" had matbrmatics teach= who got all the resources they needed. By comparison, in Virginia, 21 percent of students attending schooLs in advantaged urban areas, 75 percent in schools in disadvantaged urban areas, 45 percent in schools in extreme rural areas, and 30 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had higher mathematics achievement levels than those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY I1990 NAEP TRIAL STATE ASSESSMENT Virginia Sougiesst Nation Which of the following statements is true about how well supplied you are by your school system with the instructional materials and other resources you need to teach your class? I get alI the resources I need list most of the maim need. I get some or none of the resources I need. porcenlate Percentage Perootege and and and Proficiency Proficiency Pro noiency 22 ( 2.5) 8 ( 4.0) 270 ( 3.1) 253 (12.2)1 47 ( 3.4) 11 ( 9.5) 267 ( 1.9) 255 ( 3.3)I 31 ( 3.1) 21 ( 9.7) 253 ( 3.4) 257 ( &O)1 56 ( 4.0) 265 ( 2.0) 31 ( 4.2) 261 ( 2.9) The standard errors of the estimated statistics uppear 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 dots not allow accurate determination of the variability of this estimated mean proficiency. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructionkl activities that facilitate students' mathematics learning. Increasing the 113C of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: About half of the students in Virginia (48 percent) worked mathematics problems in small groups at least once a week; some never worked mathematics problems in small groups ( II percent). The largest percentage of the students (66 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; some never used such objects (12 percent). In Virginia, 70 percent of the students were assigned problems from a mathematics textbook almost every day; 4 percent worked textbook problems about once a week or less. Less than half of the students (44 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (27 percent). ' Thomas Romberg, "A Common Curriculum for Mathematics," Individual Dyferences and the Common Currkulum. Eighty-second Yearbook of the National Societyfor the Study of Education (Chicago, IL: University of Chicago Press, 1983). 56 THE 1990 NAEP TRIAL STATE ASSESSMENT 51 Virginia TABLE 10 I Teachers' Reports on Patterns of Mathematics 1 Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1660 NAEP TRIAL. STATE ASSESSMENT About how oftlsn do students work problems in smell groups? At toast once a weak Lass than ones a meet About how often do students use objects like rulers, counting blocks, or geometric solids? At Matt We a %Mk Loss than once a wee4 Panonailia and Pralkiesay Paraantap tad PnIkAtiney Ilhaveltaga ant Preidenay 41( 2.5) 44 ( 12) 50 ( 4.4) 265 ( 2.4) 255( 4.7)? 200 ( 2.2) 41 ( 2.4) 41 ( 6.3) 43 ( 4.1) 263 ( 2.1) 255 ( WI 284 ( 2.3) 11 ( 1.9) 7 ( 4.1) ( 2.0) 251 ( 3.6) OM ( ***) 277 ( 5.4)I Pareantaga Parcontage and and Pliwalkianay Prallekonay 21 ( 2.8) 258 ( 2.9) OS ( 2.7) 264 ( 1.9) I 12 ( 1.7) 271 ( 4.5) Pan* :Imp Maloney 19 ( 82) 22 ( 3.7) 243 ( 4.3)1 254 ( 5.2) ISS (10.3) 60 ( 3.9) 257 ( 3.8)t 263 ( 1.9) iS ( 8.1) ....,* ( *41 9 ( 282 ( 2.6) 5.9)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 52 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE 11 I Teachers' Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT vIrginia Southeast Nation About how often do students do problems from textbooks? Nmost every day Several Nines a week About once a week or less About how often do students do problems on worksheets? At least several times a week About once a ~It Less than weekly Paraindage and Prat/dam Panandaga Paraanta. sad and Prollaitacy Priliklarna 70 ( 2.5) 75 ( 7.6) 62 ( 3.4 ) 247 ( 1.9) 259 ( 3.7) 267 ( 1.8) 26 ( 25) 22 ( 7.1) 31 ( 3.1) 254 ( 2.4) 246 ( 5.2)1 254 ( 2.9) 4 ( 1.1) 3 ( 2.6) ( 14) 252 (11.9)1 04* ( 260 ( 5.1)1 Parcardase and Prone:fancy 44 ( 3.4) 259 I 2.1) 29 23) Percantaga Percentage and and Proliclancy Pralkdancy 30 ( 66) 251 ( 3.4)1 44 34 ( 3.6) 256 ( 2.3) 33 ( 264 ( 2.8) 27 ( 3.2) 270 ( 3.4) ( 0.1) 256 ( 32)1 27 ( 8.8) 263 ( 6.0)1 ( 3.4) 260 ( 2.3) 32 ( 3.6) 274 ( 2.7) The standard errors of the estimated Aatistics 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 thi., sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). The next section presents the students' responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. 5S THE 1990 NAEP TRIAL STATE ASSESSMENT 53 Virghtla COLLABORATING IN SMALL GROUPS In Viretnia, 42 percent of the students reported never working mathematics problems in small groups (see Table 12); 29 percent of the students worked mathematics problcms 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 14100 NAEP TRIAL STATE ASSESSMENT VirRklia Southeast Nation How often do you work In small groups In your mathematics class? At least once a week Less than once a week New Parcaneasa and Prolickpacy 29 ( 2.1) 204 ( 2.9) 29 Powid$641 Olnieniage and Prallalimay tondligidneY 52 di 3 20 22) 29 ( 2.5) 259 ( 2.7) 2$ 1.4) ( 1.1) 271 ( 2.2) 42 ( 2.4) 259 ( 1.9) ( 259 ( 3.9) 49 ( 4.8) 252 ( 2.4) ( 2$7 ( 2.0) 44 ( 2.9) 2$1 ( 1.0) 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. Examining the subpopulations (Table Al2 in the Data Apnendix): In Virginia, 26 percent of students attending schools in advantaged urban areas, 31 percent in schools in disadvantaged urban areas, 30 percent in schools in extreme rural areas, and 30 percent in schools in areas classified as "other" worked in mall groups at least once a week. Further, 28 percent of White students, 31 percent of Black students, 33 percent of Hispanic students, and 26 percent of Asian students worked mathematics problems in small groups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (27 percent and 31 percent, respectively). 54 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia USNG MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: About half of the students in Virgiaia (47 percent) never used mathematical objects; 24 percent used these objects at least once a week. Mathematical objects were used at least once a week by 19 percent of students attending schools in advantaggd urban areas, 31 percent in schools in disadvantaged urban areas, 19 percent in schools in exiseme rural areas, and 26 pexcent in schools in areas classified as "other". Males were more likely than females to use mathematical objects in their mathematics classes at least once a week (28 percent and 20 percent, respectively). In addition, 22 percent of White students, 25 percent of Black students, 32 percent of Hispanic students, and 30 percent of Asian 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 MO NAEP TRIAL STATE ASSESSMENT 1111111 How often do you work with objects like rulers, counting blc...,ts, or geometr.: solids in your mathematics class? At least once a week Less than once a week Percentage Percentap Percentage Ind and and Prollidency Prolidency Prolichmey 24 ( 1.6) 261 ( 2.9) 29( 1.3) 269( 1.7) 47 ( 2.2) 262 ( 1.7) 23 ( 3.4) 242 ( 3.6) 29 ( 2.5) 261 ( 3.5) 46 ( 4.5) 254 ( 3.0) 28 ( 1.8) 258 ( 2.6) 31 ( 1.2) 269 ( 14) 41 ( 2.2) 259 ( 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. GO THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Virginia MATERIALS FOR MATHEMATICS INSTRUCTION Thz percentages of eighth-grade public-school students in Virginia who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teething and learning. Regarding the frequency of textbook usage (Table 14 and Table Al4 in the Data Appendix): About three-quarters of the students in Vtrginia (77 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of the students in the nation. Textbooks were used almost every day by 78 percent of students attending schools in advantaged urban areas, 64 percent in schools in disadvantaged urban areas, 78 percent in schools in extreme rural areas, and 77 percent in schools in airas classified as "other". TABLE 14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY .. 1990 MEP TRIAL STATE ASSESSMENT Virginia Southeast Nation - How often do you do mathematics problems from textbooks in your mathematics class? Percentage and Praticiency Percentage aerial Preldincy Percentage end PreactencY Almost every day 77 ( 1.8) 78 ( 2.4) 74 ( 1.9) 267 ( 1.5) 257 ( 2.8) 287 ( 1.2) Savant linos a two* 15 ( 1.1) 14 ( 1.9) 14 ( 0,6) 255 ( 2.4) 248 ( 4.4) 252 ( 1.7) About once a weak or lass 8 ( 1.0) ( 2.7) 12 ( 141) 248 ( 4.1) 222 ( 5.3)1 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 perornt 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 Virginia And, for the frequency of worksheet usage (Table 15 and Table A I S in the Data Appendix): Less than half of the students in Virginia (43 percent) used worksheets at least several times a week, compared to 38 percent in the nation. Worksheets were used at least several times a week by 49 percent of students attending schools in advantaged urban areas, 57 percent in schools in disadvantaged urban areas, 38 percent in schools in extreme rural areas, and 41 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 MO MEP TRIAL. STATE ASSESSMENT Southeast Nation How often do you do mathematics problems on worksheets in your mathematics class? Parcentage and ProSdancy Percentage and Prolickmoy Percentage and Povidericy At least several times a week 43 ( 1.8) 38 ( 4.3) $S ( 2.4) 258 ( 2.0) 245 ( 4.3) 253 ( 22) About once a week 29 ( 12) 32 ( 1.5) 2S ( 1.2) 263 ( 1.8) 254 ( 2.11) 261 ( 1.4) Lass than remedy 28 ( 1.7) 29 f 3.9) 37 ( 2.$) 274 ( 2.6) 263 t 3,3) 272 ( 1.9) 41 The standard errors of the estimated statistics appear in parentheses. It can be said with about clq vvroent certainty that, for each population of interest, thr; value for the entire population is within ± 2 standa.0 errors of the estimate for the sample. Table 16 compares students' and teachers' responses to questions about the patterns of claproom instruction and materials for mathematics instruction. 62 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS NAEP TRIAL STATE ASSESSMENT Patterns of classroom instruction Pentemise Sladmit Tsedwrs knintaile Illudmis Tudors Pert000110 Ilimisigs Tesclin Percentage of students Mt* ovArk mathemetics problems In small groups At least once a week 29 ( 2.1) 48 ( 2.8) 20 ( 3.0) 44 8.2) 25 ( 2.5) 50 ( 4.4 Less than once a week 29 ( 1.7) 41 ( 2.4) 28 ( 2.2) 48 8.3) 28 ( 1.4) 43 ( 4.1 NeVer Percentage of students tWto use objects Me nders, counting blocks, er geomettic solids At least once a week 24 ( 1.8) 21 ( 22) 23 ( 3.4) 19 ( 8.2) 25 ( 1.8) 22 ( 3.7) Lees than once a week 29 ( 1.3) 08 ( 2.7) 29 ( 2.5) 05 (10.3) 31 ( 1.2) 09 ( 32) Never 47 ( 2.2) 12 ( 1.7) 45 ( 4.5) 18 ( 8.1) 41 ( 3.2) 9 ( 2.8) Materials for mathematics Percentage Percentage Percentage instruction Students Teachers Students Teachers Students Teschars Percentage of students W110 Use a mathematics textbook Almost every day 77 ( 12) 70 ( 22) 78 ( 2.4) 75 ( 7.8) 74 (12) 62 ( 3.4) Several times a week 15 ( 1.1) 20 ( 2.5) 14 ( 1.9) 22 ( 72) 14 ( 0.8) 31 ( 3.1) About once a Week or less ( 1.0) 4 ( 1.1) 8 ( 2.7) 3 ( 2.8) 12 ( 1.8) 7 ( 12) Percentage of students who use a mathematics woltshest At least several times a week 43 ( 12) 44 ( 3.4) 38 ( 4.3) 30 ( 0.0) 38 ( 2.4) 34 ( 32) About once a week 29 ( 1.2) 29 ( 2.3) 32 ( 1.5) 44 ( 2.1) 25 ( 1.2) 33 ( 3.4) Less than weekly 26 ( 1.7) 27 ( 3.2) 29 ( 32) 27 ( 6.6) 37 ( 2.5) 32 ( 32) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 58 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia 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 mathanatics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachers: About half of the students in Virginia (48 percent) worked mathematics problems in small groups at least once a week; some never worked in small groups (11 percent). The largest percentage of the students (66 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and some never used such objects (12 percent). In Virginia, 70 percent of the students were assigned problems from a mathematics textbook almost every day; 4 percent worked textbook problems about once a week or less. Less than half of the students (44 pacent) 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 Virginia, 42 percent of the students never worked mathematics problems in small groups; 29 percent of the students worked mathematics problems in small groups at least once a week. About half of the students in Virginia (47 percent) never used mathematical objects; 24 percent used these objects at least once a week. About three-quarters of the students in Virginia (77 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. Less than half of the students in Virginia (43 percent) used worksheets at least several times a week, compared to 38 percent in the nation. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Virginia CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks!' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. 8 National Assessment of Educational Progress, Alathernaks Otrjectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 65 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Table 17 provides a profile of Virginia eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 27 percent of the students in Virginia had teachers who allowed calculators to be used for tests. About the same percentage of students in Virginia and in the nation had teachers who permitted unrestricted use of calculators (14 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of Virginia Policies on Calculator Use PERCENTAGE OF STUDENTS 1800 NAEP TRIAL STATE ASSESSMENT Virginia Southeast Nation Percentage of eighth-grade students In public schools whose teachers permit the unrestricted use of calculators Percentage of eighth-grade students in public schools whose teachers permit the use of cskadators tor tests Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned by the school Pareontmip Perametes Perconlage 14 ( 2.4) ( 3.1) 1$ ( 3.4) 27 ( 2.7) 15 ( 5.1) 33 ( 45) 72 ( 33) 56 (11.6) 55 ( 4$) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Vbrinia THE AVAILABILITY OF CALCULATORS 01111111111111= In Virginia, most students or their families (98 percent) owned calculators (Table 18); however, fewer students (44 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In Virginia, 43 percent of White students, 47 percent of Black students, 49 percent of Ifispanic students, and 37 pereent of Asian students had teachers who explained how to We them. Females were as likely as males to have the use of calculators explained to them (43 percent and 45 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1NO NAEP TRIAL STATE ASSESSMENT /lb Southeast Do you ar your family own a calculator? Yes No Porointa. Perowtage Peroontago and sad old Pro liciency Pfn Wawa Wu *hum 98 ( 0.3) ( 1.2) 20 ( 1.5) 254 I 24) 2 ( 0.3) 4 ( 1.2) 97 ( OA) 203 ( 1.3) 3 ( 0.4) 234 ( 3-8) Parcontage and Proachincy Parcentap and Proficiency Perearttow anti Prolidancy Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes 44 ( 2.0) 411 ( 5.9) 49 ( 2.3) 259 ( 1.6) 250 ( 10) 253 ( 1.7) No 56 ( 2.0) 54 ( 5.9) 51 ( 2.3) 26$ ( 1.6) 256 ( 2.5) 266 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 6" THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia THE USE OF CALCULATORS -11101M..t As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment, stud, -'s were asked how frequently (never, sometimes, almost always) they used calm, ..rs for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In Virginia, 27 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. Some of the students (16 percent) never used a calculator to work problems at home, compared to 31 percent who almost always used one. Less than half of the students (37 percent) never used a calculator to take quizzes or tests, while 26 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calcuistor 1 for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT Virginia Southeast Nation How often do you use a calculator for the Pareentalle and Percentage Percentage and and following tasks? Proficiency Proilcieney Proficient, Working problems in class Almost always 45 ( 1.2) 48 ( 3.0) 445 1.5) 253 ( 1.5) 243 ( 2.6) 254 ( 1.5) Never 27 ( 1.6) 26 ( 4.0) 23 ( 1.9) 273 ( 2.2) ( 3.1) 272 ( 1.4) Doing problems at home Almost always 31 ( 1.3) 29 ( 3.1) 30 ( 1.3) 264 ( 1.5) 252 ( 3.6) 261 ( 1.6) Never 16 ( 1.0) 16 ( 1.8) 19 ( 0.9) 270 ( 3.0) 256 ( 4.4) 263 ( 1.6) Taking quizzes or tests Almost always 26 ( 1.2) 31 ( 2.1) 27 ( 1.4) 251 ( 1.7) 240 ( 3.8) 253 ( 2.4) Never 37 ( 1.5) 35 ( 3.1) 30 ( 2.0) 275 ( 1.8) 270 ( 3.1) 274 ( 1.3) l The standard errors of the estimated stittistiCS 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 Virginia WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know when the WC 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 calculgor 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 did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of qudents 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 cat4orized 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 calctator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 6 !) 64 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in Virginia were in the High group than were in the Other group. About the same pexcentage of males and females were in the High group. In addition, 50 percent of White students, 43 percent of Black students, 37 percent of Hispanic students, and 67 percent of Asian students were in the High group. TABLE 20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVEPAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Inn Oka Southeast Nation 'Calculator-use" group P4MIlltige and Prefidency Permits. Pareardap and and Proficiency Proficiency 48 ( 1.0) 42 ( 24) 42 ( 1.3) 271 ( 2.0) 264 ( 2.9) 272 ( 1.6) 52 (1.0) 58 ( 2.4) 58 ( 1.3) 257 ( 1$) 247 ( 2.8) 255 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with abcut 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 194/0 NAEP TRIAL STATE ASSESSMENT 65 Virginia SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instnictional time to teaching dudents how to perfoim routine calnilations by hand. Using calculators to replace this time-consuming process would create more instnictional time for other mathematical skill topics, such 33 problem solving, to be emphasized. The data related to calculators and their U3C show that: In comparison to 33 percent across the nation, 27 percent of the students in Virginia had teachers who allowed calculators to be used for tests. About the same percentage of students in Virginia and in the nation had teachers who permitted unrestricted U3C of calculators (14 percent and 18 percent, respectively). In Virginia, most students or their families (98 percent) owned calculators; however, fewer students (44 percent) had teachers who explained the use of calculators to them. In Virginia, 27 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. Some of the students (16 percent) never used a calculator to work problems at home, compared to 31 percent who almost always used one. Less than half of the students (37 percent) never used a calculator to take quizzes or tests, while 26 percent almost always did. 71 66 ME 1990 NAEP TRIAL STATE ASSESSMENT Vitrinia CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? ln 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.' Many states have begun to raise teacher certification standards and strengthen teacher training proptins. As shown in Table 21: In Virginia, 32 percent of the students were being taught by mathematics teachers who reported having at kast a master's or education specialist's degree. This compares to 44 percent for students across the nation. More than half of the students (68 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. Almost all of the students (94 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 cf Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). 72 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 Virginia TABLE 21 I Profile of Eighth-Grade Public-School 1 Mathematics Teachers PERCENTAGE OF STUDENTS 1$00 NAP TRIAL STATE ASSESSMENT Virginia Southeast Nation Percentage of students Mem mathematics teachers reported having the following degrees Bachelor's degree Master's or specialist's degree Doctorate Or professional degree. Percentage of students whose mathematics teachen have the blowing types of teaching certificates that are recognized by Virginia No regular certification Regular certification but less than Me highest available Highest certification available (permanent or long-term) Percentage of students whom mathematics teachers have the following types of teaching certificates that are recognized by Virginia Mathematics (middle school or secondary) Education (elementary or middle school) Other Ammo. pffewsas SS (2.5) 50 ( 12) 50 ( 42) 31 (2.6) 39 ( $.4) 42 ( 42) * (0.2) 5 ( 53) 2 ( 14) ( 1.5 2.3) 1.2) 24 ( 53 10.4) 29 4.3) SS ( 3.4 42 10.1) OS 4.3) ( 1.5) 84 ( 5.1) $4 ( 2.2) 4 ( 1.4) 14 ( 4.6) 42 ( 2.6) 2 ( 01) 2 ( 1.5) 4 ( 1.3) 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. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. 68 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In Virginia, 48 percent of the eighth-grade public-school students were being taught mathematics by teachers who had 'an undergraduate major in mathematics. In compluison, 43 percent ofthe students across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school studems in Virginia (14 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 1 Graduate Fields of Study PERCENTAGE OF STUDENTS MO MEP TRIAL STATE ASSESSMENT Virginia Southeast Nation , What was your unaergraduate major? wawa& 4S ( 3.3) 34 ( 22) 15 ( 2.1) Pomace 44 ( 9.0) 43 ( 9.0) 14 ( 8.5) Pountage 43 (3.9) 35 (311) 22(33) Mathematics Education Other [What was your graduate major? Percentage Percentage Percentage Mathematics 14 ( 21) 15 ( 5.4) 22 ( 34) Education 32 ( 3.2) 43 ( LS) 3. ( 3.5) Other or no gracksate level study 53 ( 3.2) 41 ( SA) 40 ( 3,4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT 69 Virginia Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In Virginia, 31 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students bad teachers who spent at least that much time 011 Si Mika types of in-service training Some of the students in Virginia (13 percent) had mathematics teachers who spent no time on in-service education devoted to mathematicsor the teaching of mathemeics. Nationally, 11 percent of the students bad mathematics teachers who spent no time on similar in-service training. TABLE 23 f Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS NAEP TRIAL STATE ASSESSMENT virsolnia sc"msa_l During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? None One to 15 hour, 18 hours or more Percentage Percents. Percents. 13 ( 2.7) 11 ( 8.0) 11 ( Se ( 3.4) 48 (12.0) Si ( 4.4 31 ( 2.8) 43 (10.1) 39 ( 3.8 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE. ASSESSMENT Vitsinia SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement." Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and tenitmies are described, variations in teacher qualifications and piactices may point to arm worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers educational backgrounds and experience reveals that: . In Virginia, 32 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. More than half of the students (68 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 Virginia, 48 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in Virginia (14 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. s° Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Differences: An International Assessment of Mathematks and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). I' Ina V.S. Mullis. John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement: NAEP's 1990 Assessment of the Nation and the Thal Assessment of the States (Princeton, t J: National Assessment of Educational Progress, Educational Testing Service, 1991). 76 THE 1990 NAEP TRIAL STATE ASSESSMENT 71 Virginia In Virginia, 31 percent of the eigith-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time 011 similar types of in-service training. Some of the students in Virginia (13 percent) had mathematics teachers who spent no time on in-sesvice education devoted to mathematics or the teaching of mathematics. Nationally, 11 peroent of the students had mathematics teachers who spent no time on similar in-service training. 73 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia 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. 78 THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Virginia AMOUNT OF READING MAMRIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students participating in the Trial State Assessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Virginia Southeast Nation Does your family have, or receive on e regular basis, any of the following items: more than 25 books, an encycdopedla, newspapers, magazines? Zero to two typos Four typos ,-1 Pannoiase and 1$ ( OA) Parana. and anaCallier 25(2.3 ) 247 ( 1.7) 225 3.4) 31 ( 1.1) 29 ( 24) 233 ( 1.4) 248 ( 44) 51 ( 1.2) 48 ( 2.7) 273 ( 2.1) 208 ( 2.8) Ponnmenpn and The standard errors of the estimated statistics appe tr 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 Virginia reveal that: Students in Virginia 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 highei mathematics proficiency than did students who had zero to two types. 7 C.) 74 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia A smaller percentage of Black, Hispanic, and Asian students had all four types of these reading materials in their homes than did White students. A greater pFcentage of students attending schools in advantaged urban areas than in disadvantaged urban areas, extreme rural areas, or areas classified as "other" bad all four types of these reading materials in thcir homes. HOMS OF TELEVISION WATCFIED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFiCIENCY 19$0 MEP TRIAL STATE ASSESSMENT Virginia Southeast Nadu)i Viermmow How much televlsion do you usually watch each day? Parasites. anti Prelldonoy Percentme mg Preedincy Pententage and Prvadency One hotr ins 13 ( 0.8) 12 ( 1.3) 12 ( 0A) 270 ( 3.4) 262 ( 8.2) 289 ( 2.2) Two hours 21 ( 1.1) le ( 2.1) 21 ( 0.9) 272 ( 2.4) 258 ( 4.2) 288 ( 1.8) Three hours 21 ( 0.7) 22 ( 1.9) 22 ( 0.8) 289 ( 1A) 25$ ( 3.3) 285 ( 1.7) Fotw to eve hours 29( 1.1) 2$ ( 1.8) 28 ( 1.1) 257 ( 1.5) 251 ( 3.8) 280 ( 1.7) Six hours or more 18 ( 0.9) 18 ( 1.4) 48 ( 1.0) 247 ( 1.7) 238 ( 2.8) 245 ( 1.7) The standard errors of the estimated stitistiCS appear in parentheses. It can be said with about 95 percent certainty that, for each population of inttrest, 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 Virginia From Table 25 and Table A25 in the Data Appendix h. Virginia, 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 Virginia (13 percent) watched one hour or less of television each day; 16 percent watched six hours or more. About the same pementage of males and females tended to watch six or more hours of television daily. Similarly, about the same percentage of males and females watched one hour or less per day. In addition, 10 percent of White students, 33 percent of Black students, 21 percent of Hispanic students, and 8 percent of Asian students watched six hours or more of television each day. In comparison, 15 percent of White students, 6 percent of Black students, 15 percent of Irtspanic students, and 17 percent of Asian students tended t". watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix: In Virginia, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in Virginia (41 percent) did not miss any school days in the month prior to the assessment, while 24 percent missed three days or more. In addition, 25 percent of White students, 23 percent of Black students, 28 percent of Hispanic students, and 9 percent of Asian students missed three or more days of school. 6 I 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia Similarly, 23 percent of students attending schools in advantaged urban areas, 32 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" missed three or more days oi school. TABLE 26 1 Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1NO MEP TRIAL i I ',`"" VISESSMENT Peresela. Ind How many days of school did you miss last month? None 41 ( 1.1) 248 ( 1.?) Om or two days 3$ ( 0.5) 247 ( 2.0) Three days or more 24 ( 0.9) 252 ( 1.7) Poramises Parcergage awl PrallicOncy Praticfaavg 48 ( 1.4) 253 ( 3.4) 32 ( 1.7) n) ( 2.0) 22 ( 15) 242 ( 3.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 77 Virginia STUDENTS' PERCRTIONS 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.12 Students were asked if they agreed or disagreed with five statemeans 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: Hike mathematics; I am good in mathematics. Value of matheinatks, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people use mathematks in thek jobs; mathematics is not more for boys than for girls. The nature of mathethatics, including students' ability to identify the salient features of the discipline: Mathematics is useful for sohting everyday problems. A student "perception index" was developed to examine students' perceptions of and attitudes towArd mathematics. For each of the five statements, students who responded "strnngly 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 agret. with tile statements (an index (I I), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statements (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 Virginia: Average mathematics proficiency was lowest for students who were in the "undecided, disagree, strongly disagree" category. About one-quarter of the students (29 percent) were in the "strongly agree" category (perception index of I). This compares to 27 percent across the nation. About one-quarter of the students in Virginia (21 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. .-nrriculum and Evaluaaon Standards for School Mathematics (Reston, VA: National Council of Teachers ot .iwathematics, 1989). tm 0 78 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10110 NAEP TRIAL STATE ASSESSMENT WOO Sou Mead Ninon =1.11.1.=11.N [Student °perception index° groups Sten* Woo ("perception index" of 1) Agra, ("perception index" of 2) Unchwided, &wee, strongly disagror ("perception index" of 3) 45( 2.1) 261 ( SA) 2511 244 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. 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 Virginia who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of =Aerials showed higher mathematics proficiency than did students who had ztro to two types. 8 4 THE 1990 NAEP TRIAL. STATE ASSESSMENT 79 Virginia Some of the eighth-grade public-school students in Virginia (13 percent) watched one hour or less of television each day; 16 percent watched six hours or mote. Average mathematics pmficiency was lowest for students who spent six hours or more watching television each day. Less than half of the students in Virgjnia (41 percent) did not miss any school days in the month prior to the asseument, while 24 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. About one-quarter of the students (29 percent) wen in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was lowest for students who were in the "undecided, disagree, strongly disagree" category. 8 5 80 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia 1 THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon vthich the assessment was based, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Educational Testing Service. The development of the Trial State Assessment Program benefitted from the involvement of hundreds of representatives from State Education Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the program. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive 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. 66 THE 1990 NAEP TRIAL STATE ASSESSMENT 81 Virginia The blocks were then assembled into assessment booklets so that each booklet contained two background questionnairts -- the first consisting of general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required approximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets io that each block appeared in exactly three booklets and each block appeared with every other block in one booklet. Seven assessment booklets war used in the Trial State Assessment Program. The booklets were spYakd or interleaved in a systemgic sequence so that each booklet appeared an appropriate number of tiMe3 in the sample. The students within an assessment session wtre 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 repo& 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 A 1). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on stue :Ins' performance on the set of mathematics items they received. IRT provides a common scale on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This common scale makes it ptlssible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. National Assesmient of Educational Progress, Mathematics Objectives' 1990 Assessmen (Princeton, NJ: Educational Testing Service, 1988). 6" 82 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia FIGURE Al I Coated Areas Assessed [Numbers and Operations This content area focuses on students' understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-world situations, as well SS computational and estimation situations. Understanding numerical relationships as expressed in ratios, proportions, and percents Is emphasized. Students' abilities In estimation, mental computation, use of Calculators, generalization of numerical patterns, and verification of results I also included. Measurement Thls content area focuses on students' ability to describe real-world objects using numberS. Students are asked to Identify attributes, select appropriate units, apply meaSurement concepts, and communicate measurement-related Ideas to others. Questions are included that require an ability to read instruments using mdstric, customary, or nonstandard units, with emphasis on precision and accuracy. Questions requiring estimation, measurements, and applications of measurements of length, time, money, temperature, mass/weight, area, volume, capacity, and angles are also included in this content area, This content area focuses on students' knowledge of geometric figures and relationships and on their skills in working with this knowledge. These skills are important at all levels of schooilng as well as in pradical 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. 1 Algebra and Functions This content area is broad in scope, covering algebraic and functional concepts in more informal, exploratory ways for the eighth-grade Trial State Assessment. Proficiency in this concept area required; both manipulative facility and conceptual understanding: it involves the ability to use algebra as a means of representation and algebraic processing as a probiem-solving tool. FunCtions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. 88 THE 1990 NAEP TRIAL STATE ASSESSMENT 83 FIGURE A2 I Mathematical Abilities al I I I I I II I* I N. I I I The following three categories of mathematical abilities are not to be consti.od as hierarchical. For example, problem solving involves Interactions between conceptual knowledge and procedural skills, but what is considered complex problem solving at one grade level may be considerea conceptual understanding Of procedural knowledge at another. Conceptual1.1----7.-------vnderstandlng Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counlerexamples of concepts; can use and interrelate models, diagrams, and varied representations of concepts; can identify and apply principles; know and can apply facts and definitions; can compare, contrast, and integrate related concepts and principles; can recognize, interpret, and apply the signs, symbols, and terms used to represent concepts; riind can interpret the assumptions and relations involving concepts in mathematical settings. Such understandings are essential to performing procedures in a meaningful way and applying them in problem-solving situations. Procedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to select and apply appropriate procedures correctly, verify and justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors Inherent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have been created as tools to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce greens and tables, execute geometric constructions, and perform noncomputational skills such as rounding and ordering. Problem Solving I 1 1 I 1 1 I NM I I I NI MI 1 NI In problem solving, students are required to use their reasoning and a..alytic abilitieS 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, deouctive, statistical, and proportional); and judge the reasonableness and correctness of solutions. 84 TIIE 1990 NAEP TRIAL STATE ASSESSMENT Vitginia A scale ranging from 0 to 500 was created to report performance for each content area. Each content-area scale was based on the distribution of student performance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standani deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing that is, by comparing students at a particular scale level to other students. In contra:it, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define perforni ince at each of the four levels on the scale, NAEP analyzed sets of mathematics items from 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. 9 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students petforming 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 successlidly. 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.2 Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials even to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as acadonic degrees held, teaching certification, training in mathematics, and ability to get instru-tional 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 work ..leets were used, the instructional emphasis placed on different mathematical topics, Lnd the use of various instructional approaches. Because of the nature of the sarnplin .; for the Trial State Assessment, the responses to the mathematics teaches questionnaire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 91 86 THE 1990 NAEP TRIAL STATE ASSESSMENT FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 GeV Sob Git 0 MA* aft T. ugh MI bet isoo ben ail be sea air amil sins earls kmils of bib so Awe 466.6, X oh( fib use Ng utb the keg d bib *Sm. whish Ms *a hoe be Mime bob fa he 0 The lug wish ibe Norio balk 0 The biz sub OM *ISA 0 Mr bog wick Ow nabs bah * s creNtsil EXAMPLE 2 MIS OF Ma MOE= AT PAAAWAT FARM Mr Ma VW This timperSle WWI ClArsAWS V. Haw aro, boar of mew win picked as Tbstids0 O SS 0 60 70 O SO CD 10 0 ioal know. 110 92 Grade 4 Overall Percentage Correct: 73% Percentage Correct for Anchor Levels: Z2R 1§2 65 91 100 Grade 4 Overall Percentage CUrAlc 80% Percentage Correct for Anchor Levels: 222 ZO2 222 212 75 91 100 Grade Overs9 Percentile' Correct 69% Percentage Correct for Anchor Levels: 212 2§2 76 87 96 100 virginia FIGURE A3 f Example Items for Mathematics Proficiency Levels (continued) EXAMPLE 7. What is the value of v + S wInn n so 3 Answa: EXAMPLE 2 NAIR COLOR It/RVIY RIDLIn Cobvt9 Power Mir A The sable aim Atm dos Ws s I a army et logn mks. On do dodo Mew, sake tinte swpb ahownte dos docs is uso oak. /.4441 644 pot ol dm nods pose slob doe Immo WS sass. yOti vii ;31 colaiksoi so this qweatioot Yu 0 No EXAMPLE 3 6. Koala* n pecktog bowed& ioto boxes. loch bos hoicks 6 bombans. Slsc hoe 24 balk Which surbor masa will kip ha tioi out bow way boom she win Nava CD 24 (90 24 + w cD 24 + w 0 a. 24 x Eh 0 ED 1 tioal know. Grade 8 Mandl Parcentage Coma: 76% Parcetaao COMMA for Mahar Leonia: TSI2 262 321 28 09 96 96 Grads 8 Overall Poventatta Comet 73% Pstaontaaa Comet fix Mcbor Levels: MI nit 21/Q 1111 68 92 92 Grad. 8 Overall PINUNItagi Oxrect 77% Percentage Correct for Anchor Levels: 222 21X1 37' 71 95 100 C t.7 88 '11113 1990 NAM' TRIAL STATE Assessmorr FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) 0 Level 300: Reasoning and Problem Solving Involving Fractions, Psalms's, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE 1 II. Wbiela a am foam* aims doe soak al Moss the atm mimeo cam dm Ws it a) a) EXAMPU 2 Is tke marl Nava do a dm k bsadisi. is es 0 ka kin opassaa4 by a male said I Wks M. i As moo oak is 144 a imam teat rtyrsameal Ay a malt nodal few way lacks WO Dif yes su dm oak:Wass iguaniaat 0 1* 0 No BEST COPY AVAILABLE 9 4 Grade 8 OVOMII POroantal COMIC* CO% PWOINItiall COM* for Anchor Levels: 202 222 aea 1122 33 49 TT 90 Grade 12 OveraN Percentage COM* 75% Percentage Correct for Anchor Levs'e: 222 01S 222 46 79 96 Grade 8 °MOW Percentage Correct: fQ% Percentage Correct for Mcher Levels: 222 MO MI Mt 17 48 Se 99 FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 350: Reuoning and Problem Solving involving Geometric Relationships, Algebraic Equational and Beginning Statistics and Probability EXAMPLE 'I ON **ma 1647 mkt ea the klialriag puma al iat-lephabs. 111 1 2 2 4 16. U =sat 62aigars v mamas& haw way don will k m doe leo 00 100 4D 101 4112 199 4119 200 42201 EXAMPLE 2 17. tolaids haw you Wad yaa Nova so 'podia 16. Grade OveraN Percentage Correct 34% Percentage Correct for Mahar Levels: all2 13 19 53 88 Grade 12 Owali Pacentage Correct 49% Percentage Correct for Anchor Levels: 1%/ 2QQ MQ --- 22 48 90 Grade 8 Overall PKOOfItaile Correct 15% Percentage Correct for Anchor Levels: ZQQ 2110 aQQ 2B2 1 4 25 74 Grade 12 Overall Pecontage Correct 27% Percentage Correct fur Mchor Levels: 222 2:0 Sit 2§12 3 22 74 5 90 ME 1990 NAB' TRIAL STATE ASSESSMENT Virginia SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offesinp, 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. Althou0 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 mew or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAEP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like almost all estimates based on assessment measuxes, 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 particimed in the Trial State Assessment was administered a subset of questions from the total ;et 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 different estimates of total group and subgroup proficiency might have been obtained. Thus, a second source of uncertainty arises because each student was administered a subset of the total pool of questions. 96 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 Virginia In addition to reporting estimates of average proficiencies, proportions of studelis at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called stendard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a background question in a certain way or the proportion of students in certain racial/ethnic groups) reflect only sampling error. NAEP uses a methodology called the jackknife prooedure to estimate these standard errors. Drawing Inferences from the Results One of the goals of the Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the 'uncertainty associated with all samples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population , neans and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency * 2 standard errors npresents a 95 percent confidence interval for the corresponding population quantity. This means that with approximaLly 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within * 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. Si 7 92 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, racejethnicity, 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 doyou usually spend each day on mathematics homework? Still other subgroups are defmed by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As an example, one might be interested in answering the question: Do students who reported spending 45 minutes or more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is higher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in performance between the two groups in the population because of the uncertainty associated with the estimated average proLiciency of the groups in the sample. Remember that the intent is to make a statement about the entire population, not about the particular sample that was assessed. The data from the sample are used to make inferences about the population as a whole. As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore poseible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standaed error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the manner in which the standard error for an individual group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there ie insufficient evidence to claim a real difference between groups in the population. If the interval does not contain zero, the difference between groups is statistkally significant (different) at the .05 level. 98 TtiE '990 NAEP TRIAL STATE ASSESSMENT 93 Virginia As an example, suppose that one were interested in determining whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade 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 Average Proficiency Standard Error Female 259 2.0 Male 255 2.1 The difference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is V 2.0 + 2.1' = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero. and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing cor:clusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be -light may represent a statistically significant difference in the population because of ihe magniturle of the standard errors. Conversely, a difference that appears to be large may not be .tatistically 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. 6.7 94 THE 1990 NAEP TRIAL STATE ASStaMENT Virginia The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significance is being performed. However, in each chapter of this report, many different groups are being compared (i.e., multiple sets of confidence intervals are being analyzed). When one considers sets of confidence intervals, statistical theory indicates that the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. If one wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be mule to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol 41". 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 goups defined by race/ethnicity and type of school community, as well as by gender and parents' education level. NAFP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficientl ;. 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. 10 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 Virginia The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or tenitory, divided by the stzndard deviation of the proficiency in the total population. If the aue 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. DescAbing the Size of Percentages Some of the percentages reported in the text of the report art given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage . Description of Text In Report p = 0 1IMENIMMIMMdl , None 0 < p 5 10 Relatively few 10 < p 5. 20 Some 20 < p 5 30 About one-quarter 30 < p 5 44 Less than half 44 < p 5 55 About half 55 < p .5 69 More than half 69 < p 5 79 About three-quarters 79 < p 5 89 Many 89 < p < 100 Almost all p = 100 All 101 96 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia ME NATION'S REPORTITIV CARD DATA APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains corresponding data for each level of the four reporting subpopulations -- race/ethnicity, type of community, parents' education level, and gender. 102 THE 1990 NAEP TRIAL STATE ASSESSMENT 97 Virginia TABLE AS I Students' Reports on the Mathematics ClaSS They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pre-algebra Algebra TOTAL and Proficiency Peroentage and Proliciency Petventage and Pralicklancy State 40 ( 2.0) 35 ( 1.8) 10 ( 1.0) 244 ( 1.5) 271 ( 1.5) 305 ( 2A) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 298 ( 2A) RACE/ET1NICITY Whits State 42 ( 2.1) 36 ( 2.2) 19 ( 1.3) 251 ( 1.9) 277 ( 1.3) 307 ( 2.`, Nation 59 ( 2.5) 21 ( 2.4) 17 ( 1.5) sack 259 ( 1.8) 277 ( 2.2) 300 ( 2.3) State 57 ( 3.2) 32 ( 2.9) 9 ( 1.4) 22$ ( 1.3) 252 ( 2.4) Nation 72 ( 232 ( 4.7) 3.4) 16 ( 248 ( 3.0) 6.4) 9 ( 2.2) ***) Hispanic State 61 ( 232 ( 5.4) 3.7) 30 ( 5.0) 4) 8 ( 3.5) ( .") Nation 75 ( 240 ( 4.4) 2.4) 13 ( *** 3.9) ***) ( 1.5) 4) Asian State 28 ( 5.0) 35 ( 4.1) 27 ( 43) .") Nation 32 ( 0.0* 6.5) 21 ( -- 6.5) 41 4,4,* ( 7.4) ( TYPE Of COMMUNITY Advantaged urban State 35 ( 3.9) 40 ( 42) 21 ( 2.2) 280 ( 3.9) 282 ( 2.8)1 322 ( 3.7)f Nation 55 ( 269 ( 9.4) 2.5)1 22 ( 7.9) 44..) 21 ( 4.4) *"..) Disadvantaged urban State 48 (12.1) *** ) 32 (12.5) 17 4*. ( 3.7) Nation 85 ( 6.0) 14 ( 3.3) 240 ( 4.0)4 287 ( 4.2)1 Extreme rural State 58 ( 233 ( 5.8) 3.4) 27 ( 254 ( 3.7) 5.9)1 15 44* ( 3.0) ( *4.1 Nation 74 ( 249 ( 4.5) 3.1)1 14 ( 5.0) 411 4i* ( 2,2) ( *Of ) Other State 48 ( 2.1) 34 ( 2.3) 15 ( 1.2) 242 ( 2.3) 269 ( 1.8) 301 ( 3.0) Nation 61 ( 2.2) 20 ( 2.1) 16 ( 1.4) 251 ( 2.0) 272 ( 2.8) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. Interpret with caution - the nature of the sample does not allow accurate determination of the variabiLty of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 r 3 98 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A5 I Students' Reports on the Mathematics Clan (continued) They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Eighth-grade Mathematics Pre-algebra 1 Algebra TOTAL and Proffoisam Percentage and Proficiency Percentage and Proficiency State 48 ( 2.0) 35 ( 11) 18 ( 1.0) 244 ( is) 271 ( 1.5) 305 ( 2.4) Nation 82 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 298 ( 2.4) PARENTS EDUCATION HS non-graduate State 84 ( 4.2) 28 ( 4.1) 232 ( 2.2) 2.54 ( 4.5) **. Nation 77 ( 241 ( :3.7) 2.1) 13 ( ( 3.4) 41 3 ( IP** 1.1) HS graduate state 55 ( 2.8) 34 ( 2.6) 9 ( 0.8) 238 ( 1.3) 283 ( 1.8) 287 ( 3.8) Nation 70 ( 2.8) 18 ( 2.4) 8 ( 1.1) 249 ( 1.9) 286 ( 3.5) 277 ( 5.2) Some coflege State 43 ( 3.0) 38 ( 3.3) IR ( 1.8) 249 ( 2.2) 275 ( 22) 301 ( 3.0) Nation 80 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 276 ( 2.8) 295 ( 3.2) College graduate State 34 ( 2.7) 38 ( 2.5) 26 ( 1.7) 25$ ( 2.5) 280 ( 1.6) 311 ( 2.6) Nation 53 ( 2.7) 21 ( 2.3) 24 ( 1.7) 259 ( 1.5) 27$ ( 2.8) 303 ( 2.3) GENDER Male state 50 ( 2.5) 31 ( 2.2) 15 ( 1.3) 246 ( 1.9) 274 ( 1.7) 313 ( 2.6) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 2.5) Female State 42 ( 2.0) 38 ( 2.0) 18 ( 1.3) 241 ( 1.8) 269 ( 1.6) 299 ( 2.5) Nation 61 ( 2.6) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within I 2 standard errors of the estimate for the sample. The percentages may not total WO percent because a small number of students reported taking other mathematics courses. *** San size is insufficient to permit a reliable estimate (fewer than 62 students), I 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Virginia TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STArE ASSESSMENT 15 Minutes 30 Minutes 45 lilinutas An Hour or More TOTAL. Percentage and Proficiency 0.3) m 2 ( 0.6) ( ( 0.3) 44, ...) 3 ( 1.0) *** ( 1 ( 0.7) *** ( "") 1 ( 0.8) 4 ( ***) *** ( ***) 1 ( 0.4) ( 1 ( 0.9) ...) 8 ( 4.6)( ( 0.0) *** ( ***) ( 0.8) ...) 0 ( 0.0) ..) 2 ( 0.8) 1 ( 0.4) ...) Perventap and Proficiency 41 ( 2.7) 262 ( 2.2) 43 ( 4.2) 268 ( 2.3) 41 ( 2.9) 259 ( 2.5) 39 4.5) 286 ( 2.2) 43 ( 4.5) 231 ( 2.0) 55 ( 7.8) 232 ( 3.1) ( 46 ( 7.8) 245 ( 3.0)1 36 ( 6.9) ( 29 ( 7.8) 04* ( *41 41 ( 5.6) 269 ( 4.1)1 61 (11.3) 273 ( 3.1)1 38 (15.0) 41 (12.6) 236 ( 2.1)1 50 ( 8.1) 237 ( 3.4)) 68 (14.9) 253 ( 5.4)1 41 ( 3.5) 250 ( 2.5) 37 ( 4.3) 256 ( 3.1) Peeventege and Pro Oolong, 42 ( 1.0) 288 ( 23) 43 ( 4.3) 288 ( 2.6) 41 ( 2.2) 278 ( 2.2) 46 ( 5.1) 270 ( 2.7) 42 ( 3.1) 247 ( 2.8) 40 ( 6.7) 248 ( 5.3) 45 ( 8.3) 34 ( 6.8) 251 ( 4.2)1 33 ( 5.9) ( *Mt ) 37 ( 8.8) ..) 40 ( 3.8) 288 ( 5.3)1 32 ( 8.6) 4.* **1 31 ( 8.2) 44.) 38 ( 9.4) 253 ( 9.0)1 44 ( 6.8) 255 ( 5.1) 14 (10.9) ...) 42 ( 2.7) 264 ( 2.7) 49 ( 5.1) 265 ( 2.5) Peroentage acW Proficiency 14 ( 1.4) 285 ( 4.5) 10 ( 1.0) 272 ( 5.7)1 12 ( 1.5) 292 ( 4.2) 11 ( 2.4) 277 ( 7.8)1 8 ( 2.7) ( 3 ( 1.2) ( 4") 11 ( 3.2) *** ( ***) 13 ( 2.9) *4* ( **4) 25 ( 6.5) ( m) 10 ( 5.4) 17 ( 3.0) 303 ( 7.3)1 5 ( 3.4) ...) 7 ( 7.8) *44(4*4) 1 2 ( 5.9) 'Pe* 4-41,1 11 ( 1,9) 276 ( 3.9) 10 ( 2.4) 276 ( 8.6)1 Percentage and Pfxdidency 3 ( 1.0) 278 ( 9.8)1 4 ( 0.9) 278 ( 5.1)1 3 ( 1.4) 944 ( 4 ( 0.9) 279 ( 5.8)1 4 ( 1.1) ( ****) 2 ( 0.8) 2 ( 1.7) ( "4) 7 ( 2.1) ( ( ***) 24 (10.2) Ft* itiMt 2 ( 1.1) *44(4*4) 0 ( 0.0) 4.. 16 ( 5.1) ) ( ***) 3 ( 2.6) 10 ( 7.3) 4.4 4 ( 1,1) 282 (11.6)1 State Nation RACE/ETHNICITY WM. State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantagod urban State Nation Disadvantaged urban State Nation Extrarna rural State Nation Mbar State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 interpret with caution - the nature of the sample does not allow accurate determination of the variabibty of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A6 Teachers' Reports on the Amount of Time (continued) Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT I None 15 Minutes - - 30 Minutes 45 Minutes An Haw or More TOTAL Peroentage and Prancioncy 2 ( as) ...) ( 0,3) ( 4 ( 1.8) ( 0.6) .4, 2 ( 0.7) 4..11 1 ( 0.5) ( 2 ( 0.6) ( 0.9) *** *e.) 1 ( 0.4) *** *** ( ***) 1 ( 0.3) ( ( "e) Percentage and Proficiency 41 ( 2.7) 252 ( 2.2) 43 ( 4.2) 250 ( 2.3) 49 ( 4.5) 233 ( 2.7) 49 ( 6.3) 240 ( 2.8) 47 ( 3.6) 244 ( 1.9) 43 ( 52) 249 ( 3.1) 41 ( 3.7) 260 ( 2.8) 44 ( 5.4) 265 ( 2.8) 35 ( 3.1) 266 ( 3.2) 40 ( 4.7) 265 ( 2.5) 42 ( 2.8) 253 ( 2.6) 44 ( 4.4) 257 ( 2.9) 41 ( 2.9) 252 ( 2.3) 41 ( 4.4) 255 ( 2.3) Percentage and Prolidency 42 ( 1.9) 266 ( 2.3) 43 ( 4.3) 200 ( 2.8) 39 ( 4.3) 245 ( 2.Z) 40 ( 0.1) 246 ( 3.7) 40 ( 2.9) 256 ( 2.2) 44 ( 5.8) 258 ( 2.7) 44 ( 3.1) 272 ( 2.9) 43 ( 5.e) 270 ( 3.8) 44 ( 2.4) 282 ( 3.0) 44 ( 4.1) 277 ( 3.0) 40 ( 2.1) 272 ( 2.8) 43 ( 4.3) 268 ( 2.9) 43 ( 2.2) 264 ( 2.2) 43 ( 4.7) 264 ( 2.8) Percentage and Proeciency 11 ( 1.4) 285 ( 4.5) id ( 1.9) 272 ( 5.7)1 6 ( 1.8) *gm. 6 ( 1.7) «14 7 ( 1.7) ( ( .") 10 ( 2.2) 414* 41 7 ( 2.1) 16 ( 1.9) 298 ( 4.2) 11 ( 2.3) 287 ( 8.1)1 11 ( 1.6) 286 ( 5.4) 9 ( 1.9) 273 ( 7.3)1 12 ( 1.4) 284 ( 4.9) 11 ( 2.0) 272 ( 5.7)1 Parcentage and Prodding 3 ( 1.0) 27$ ( 94)1 4 ( 0.9) 278 ( 5.1)1 3 ( 1.4) ewe ***) 4 ( 1 .3) ( 41 3 ( 1.3) 3 ( 1.0),) 4 ( 1.3) ( ".) 4 ( 1.0) **) *** ( ***) 5 ( 1.3) ** ( "*.) 5 ( 1.31 279 ( 7.7)1 3 ( 1.1) State Nation PARENTS EDUCATION 113 non-graduate State Nation KS graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statistics ;appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, tilt: value for the entire population is within 2 standard errors of the estimate for the sample. Interpret 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 101 Virginia TABLE A7 1 Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT - None 15 Minutes 30 Minutes _ 45 Minutes - An Hour or More TOTAL favoring* and Proi icianay ( 0.7) 247 ( 2.3) ( 0.8) 251 ( 2.8) 6 ( 0.2) 252 ( 2.4) 10 ( 1.0) 258 ( 3.4) 7 ( 1.0) 11,1111. .41 ( 1.5) ..) 9 ( 2.6) .41 12 ( 1.8) 2 ( `") 4 ( 2.0) t ...) 8 ( 2.5) 4 t 2.9) 12 ( 3.7) *-- 10 ( 3.0) ( 444 ) 8 ( 2.3) ...) 7 ( 0.9) 246 ( 2.8) 9 ( 1.0) 250 ( 3.8) Parontaga and Proficiency 31 ( 1.1) 281 ( 1.7) 31 ( 2.0) 284 ( 1.9) 32 ( 1.3) 289 ( 1.9) 33 ( 2.4) 270 ( 1.9) 31 ( 1.4) 239 ( 2.3) 26 ( 2$) 241 ( 3.8) 28 ( 4.2) *44 ( *41 27 ( 3.n) 248 ( 3.6, 17 ( 4.5) 4.. ) 22 ( 4.8) 0.** ** 29 ( 2.5) 277 ( 3.7) 41 (12.5) 278 ( 3.0)1 24 ( 3.3) 253 ( 4.9)1 27 ( 1.9) 248 ( 5.8) ( 4.6) 260 ( 3.5)1 32 ( 1.3) 258 ( 2.0) 30 ( 1.8) 263 ( 2.3) Poontaga and Proliciancy 35 ( 1.1) 287 ( 1.9) 32 ( 12) 263 ( 1.9) 35 ( 1.4) 274 ( 2.2) 32 ( 1.3) 270 ( 2.4) 35 ( 1.8) 243 ( 1.9) 33 ( 2.7) 237 ( 3$) 32 ( 4.8) 444 ( 444 ) 30 ( 2.6) 248 ( 3.4) 47 ( 7.4) ...) 31 ( 5.6) 38 ( 2.7) 288 3.6) 31 ( 6.6) 280 ( 4.8)t 33 ( 3.6) t IMP* 31 ( 3.0) 247 ( 4.7)1 33 ( 2.3) 248 ( 2.8) 31 ( 2.9) 255 ( 5.1)1 35 ( 1.4) 262 ( 2.2) 32 ( 1.3) 264 ( 2.3) Perontage and Pro Ociency 18 ( 0.8) 269 ( 2.7) 18 ( 1.0) 268 ( 1.9) 18 ( 1.0) 277 ( 2.2) 15 ( 0.9) 277 ( 2.2) 15 ( 1.3) 242 ( 3.6) 18 ( 2.3) 240 ( 3.8) 18 ( 3.7) ...) 17 ( 2.1) 241 ( 4.3) *44 18 ( 2.0) 287 ( 6.8)1 12 ( 3.3) ...) 20 ( 1.9) 250 ( 4.8)1 17 ( 2.2) ( 444 ) 18 ( 3.8) 14 ( 1.1) 268 ( 2.6) 15 ( 1.1) 267 ( 2.1) Partantaga and Proficiency 11 ( 0.7) 289 ( 3.1) 12 ( 1.1) 25$ ( 3.1) 11 ( 1.0) 276 ( 3.8) 11 ( 1.3) 268 ( 3.3) 11 ( 1.4) 247 ( 4.4) 18 ( 1.9) 232 ( 3.7) 13 ( 3.3) ...) 14 ( 1.7) ( ".) 15 ( 3.7) ...) 25 ( 6.2) t 4.4) 12 ( 1.7) 286 t 6.6)1 7 ( 3.4) ( 444 9 ( 2.4) .... I .4.) 14 ( 2.2) ...) 13 ( 1.4) .4. ( 2.7) ( *44 ) 1 1 ( 0.9) 267 ( 3.5) 13 ( 1.1) 25$ ( 3.6) State Nation RACEFETRNICITY Whits State Nation Slack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sampIr: 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). 102 .1.1- 7 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia 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 1990 MEP TRIAL STATE ASSESSMENT None _ 15 Minutes . 30 Minutes 45 NIkestes , An Hour or More TOTAL Percentage and Prodder/my Perventage Proficiency Percentage and Proficiency Percentage and Proficiency Perceatap and Proficiency State 0.7) 31 ( 1.1) 35 ( 1.1) 18 ( 0.6) 11 ( 0.7) 247 ( 2.3) 281 ( 1.7) 267 ( 1.9) 269 ( 2.7) 266 ( 3.1) Nation 0 ( 0.8) 31 ( 2.0) 32 ( 1.2) 16( to) 12 ( 1.1) 251 ( 2.8) 284 ( 1.9) 283 ( 1.9) 2.0( 1,9) 258 ( 3.1) PARENTS EDUCATION 143 non-graduate State 12- ( *AIM ) 32 ( 238 ( 3.0) 3.1) 30 ( 244 ( 2.9) 4.2) 15 ( 1.9) ( «no) 11 ( ( 1.9) Nation 26 ( 3.3) 34 ( 4.4) 246 ( 4.0) 245 ( 2.6) 411-* *MI ( 041 HS graduate State ( 1.2) 34 ( 1.8) 36 ( 2.0) 13 ( 1.3) 10 ( 1.2) Mr* ( ) 253 ( 2.3) 251 ( 2.1) 252 ( 32) 247 ( 3.7) Nation 10 ( 1.7) 33 ( 2.2) 31 ( 1.9) 16 ( 1.4) 11 ( 1.5) 248 ( 4.2) 259 ( 3.2) 254 ( 2.4) 25$ ( 2.b) 244 ( 3.4) Son* college State 34 ( 2.3) 37 ( 2.3) 267 ( 2.4) 269 ( 2.7) ( 4111 Nation 9 ( 1.2) 30 ( 2.7) 36 ( 2.1) 14 ( 1.8) 11 ( 1 .5) 266 ( 3.0) 266 ( 2.6) 274 ( 3.5) College graduate State 4 ( 0.7) 27 ( 1.5) 36 ( 1.7) 19 ( 1.4) 13 ( 1.5) 273 ( 2.5) 283 ( 2.5) 288 ( 4.1) 286 ( 3.6) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 285 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Male State 8 ( 1.0) 35 ( 1.7) 33 ( 1.6) 14 ( 1.2) 0 ( 0.8) 248 ( 2.8) 263 ( 2.2) 271 ( 2.4) 273 ( 4.4) 268 ( 3.7) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 266 ( 2.4) 265 ( 3.0) 258 ( 4.1) Female State 5 ( 0.7) 27 ( 1.1) 37 ( 1.4) 18 ( 1.0) 13 ( 1.1) 245 ( 3.7) 258 ( 1.8) 264 ( 2.1) 268 ( 2.7) 271 ( 3.5) Nation 7 ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 246 ( 4.1) 263 ( 1.5) 280 ( 2.0) 267 ( 2.4) 256 ( 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 within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). s THE 1990 tiAEP TRIAL STATE ASSESSMENT 103 Virginia TABLE AS I Teachers' Reports on the Emphasis Given To I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT tiumben and Operations M.amsd Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis -, Little or No Emphasis TOTAL Percentage Percentage Percentage Percent Percentage Parcentage and d and and and and Pro Wow Preficiency Prefickncy Proficiency Proficiency Pre Wain 46 ( 2.4) 18 ( 2.1) 12 ( 2.0) 41 ( 3.1) 16 ( 2.1) 34 ( 2.4) 256 ( 1.8) 297 ( 4.3) 245 ( 3.9) 272 ( 3.2) 266 ( 34) 259 ( 2.7) 49 ( 3.8) 15 ( 2.1) 17 ( 3.0) ( 4.0) 26 ( 3.8) 21 ( 3-3) 200 ( 1.8) 237 ( 3.4) 250 ( 5.6) 277. 4.0) 260(3.2) 264 ( 5.4) 44 ( 2.4) 21 ( 2.4) 12 ( 2.2) 45 ( 3.0) 20 ( 2.4) 33 ( 2.5) 263 ( 2.0) 299 ( 4.1) 255 ( 4.5) 27$ ( 2.9) 272 ( 3.8) 267 ( 2.6) 48 ( 3.7) 161 2.4) 14 ( 34) 36 ( 4.7) 27 ( 4.4) 22 ( 3.4) 287 ( 2.2) 3.5) 259 ( 6.9)1 277 4.3) 265 ( 3.3) 273 ( 5.6) 57 ( 4.8) ( 2.1) 14 ( 3.0) 28 ( 3.8) 13 ( 2.0) 30 ( 4.5) **a 1,4111 243 ( 1.8) 222 ( 4.3)1 239 ( 4.7) 235 ( 4.1)1 233 ( 2.4) 54 ( 7.9) 1 1 ( 3.3) 25 ( 7.4) 23 ( 5.7) 33 ( 7.9) 24 ( 7.3) 243 ( 4.3) 228 ( 2.8)1 238 ( 8.1)1 242 ( 5.6)1 233 ( 4.7)1 45 ( 5.4) 16 ( 4.6) 11 ( 3.3) 15 ( 3.7) 34 ( 5.8) *41 Kelt ( qt111 ) INFO ( ***) 444 ( **el 47 ( 8.7) 6 ( 2.2) 23 ( 4.1) 34 ( 5.8) 16 ( 5.5) 248 ( 4.6) ( *41 255 ( 4.4)1 ( ***) ,.**) Ii ( 4.2) 55 ( 6.7) 28 ( 5.7) 33 ( 4.7) 5 * ) 32 ( 9.6) 27 ( 5.2) 44 ( 8.9) 34 ( 9.2) 14 ( 6.8) *.p.) ..**) 44 **.) ( *a.) 37 ( 4.6) 27 ( 5.1) ( 3.4) 52 ( 5.7) 24 3.6) 34 ( 4.0) 271 ( 3.1)1 315 ( 4.8)1 .41 288 ( 5.9)1 280 ( 4.0)1 288 ( 8.4)1 28 (13.0) 16 ( 4.2) 9 ( 7.0) 40 ( 8.5) 38 ( 9.4) 13 ( 3.2) *Mt) iv* ( 267 ( 4.9)1 ( 56 (10.3) 4 ( 3.8) 1 ( 1.3) 2 ( 2.4) 31 ( 9.4) ( 6441 48 (12.1) 9 ( 4.0) 39 (10.3) 21 ( 63) 33 (11.8) 18 ( 7.6) 255 ( 6.3)1 ( *a.) 238 ( 8.4)! 248 ( 8.2)1 44-) 59 ( 7.3) 16 ( LO) 21 ( 8.8) 24 ( 5.9) 13 ( 4.9) 32 ( 7.2) 249 ( 4.2) ( 229 ( 8.4)t 251 ( 7.4)1 236 ( 4.5)1 53 (12.4) 8 ( 3.6) 6 ( 4.9) 32 (11.7) 9 ( 6.1) 16 ( 7.9) 257 ( 7.1)! 4.0.) 555(55*) 265 ( 9.1)1 *) 0.**) 47 ( 3.3) 16 ( 2.4) 13 ( 2.7) 38 ( 4.1) 19 ( 3.3) 34 ( 3.3) 254 ( 2.5) 293 ( 4.8) 246 ( 5.2)1 287 ( 3.7) 261 ( 5.1) 252 ( 2.4) 52 ( 4.1) 16 ( 2.7) 16 ( 3.9) 34 ( 5.3) 28 ( 4.8) 24 ( 4.3) 260 ( 2.3) 286 ( 3.6) 253 ( 7.1)1 270 ( 4.6) 260 ( 3.9) 265 ( 5.1) State Nation RACE/ETHNICITY Mite State Nation Slack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Diudvantaged urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the 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. i Interpm 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). .11 ;) 104 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE AS I Teachers' Reports on the Emphasis Given to (c°ntinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measuremert Geometry J Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage and Welchem Percentage and Proildency Pecentags and Proileken Pervsnbgpe and Proficiency Percentage and Preliclenw Percentage and Proficiency State 48 ( 2.4) 18 ( 2.1) 12 ( 2.0) 41 ( 3.1) 18 ( 2.1) 34 2.4) 256 ( 1.8) 297 ( 4.3) 246 ( 3.9) 272 ( 3.2) 266 ( 3.5) 250 2.7) Nation 49 ( 3.8) 15( 2.1) 17 ( 3.0) 33( 4.0) 29 ( 3.8) 21 3.3) 260 ( Le) 287 ( 3.4) 250 ( 5.6) 272 ( 4.0) 260 ( 3.2) 264 ( 5.4) PARENTS' EDUCATION NS non-graduate State 55 ( 243 ( 4.8) 3.5) 44.) 16 ( 3.0) ( *el 32 ( 230 ( 4.8) 6.0) 19( 3.8) ***) 34 ( 231 ( 4.5) 2.2) Nation 60 ( 251 ( 6.9) 3.4) ( *al ***) 32 (( 6.3) 1111 20 ( *ft* ( 6.7) 41111 NS graduate State 51 ( 2.8) 11 ( 2.1) 14 ( 2.6) 37 ( 3.0) 16 ( 2.3) 35( 2.9) 250 ( 1.8) 275 ( 8.1) 240 ( 5.6) 254 ( 3.5) 250 ( 3.7) 242 ( 2.4) Nation 55 ( 259 ( 4.8) 2.9) 11 ( 2.8) 0, 17 ( 251 ( 3.9) 6.1)1 27 ( 253 ( 5.0) 4.7)1 27 255 4.5) 4.2) 24 ( 24$3 ( 5.1) 4.8)1 Some college State 46 ( 3.5) 18 ( 2.5) 12 ( 2.5) 40 ( 4.1) 16 ( 2.4) 34 ( 3.2) 260 ( 2.8) 291 ( 5.7) 276 ( 3.7) 270 ( 5.0) 284 ( 3.8) Nation 47 ( 265 ( 4.4) 2.6) 17 ( 284 ( 3.3) 4.1)1 12 ( 2.7) *se) 39 ( 279 ( 5.5) 4.5) 27 ( 262 ( 5.0) 4.8)1 23 ( 270 ( 4.1) 4.7) College graduate State 40 ( 2.9) 27 ( 3.0) 10 ( 2.2) 47 ( 3.4) 22 ( 2.8) 31 ( 2.7) 266 ( 2.5) 310 ( 2.9) 253 ( 5.4)1 289 ( 3.8) 27$ ( 3.0) 279 ( 4.1) Nation 44 ( 4.1) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 269 ( 2.6) 296 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 260 ( 6.4) GENDER Male State 48 ( 2.8) 18 ( 2.2) 13 ( 2.3) 39 ( 3.3) 18 ( 2.3) 36 ( 2.8) 258 ( 2.3) 305 ( 5.0) 24$ ( 5.3) 277 ( 4.1) 270 ( 4.3) 280 ( 3.2) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 281 ( 2.5) 287 ( 4.4) 25$ ( 6.7) 275 ( 4.8) 263 ( 3.5) 268 ( 6.8) Female State 44 ( 2.8) 19 ( 2.3) 12 ( 2.0) 42 ( 3.1) 19 ( 2.2) 32(23) 255 ( 1.6) 291 ( 4.2) 242 ( 4.8) 267 ( 3.2) 262 ( 3.6) 258 ( 3.0) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 260 ( 2.0) 266 ( 3.3) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 283 ( 5.0) The standard errors of the estimated stAllstics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. 1 Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Virginia TABLE AS I Teachers' Reports on the Emphasis Given To (cmtinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra and FUnctions Heavy E phasls _ , Little or No Emphasis Heavy Emphasis Little or No . Emphasis TOTAL Pimento. and Proecioncy Porcontage and Proaciony P11111:411111119 and Proficiency Posconfafle and Proficiency State 10 ( 1.8) CO ( 2.9) 52 ( 2.3) 23 ( 2.0) 270 ( 5.0) 200 ( 2.2) 282 ( 2.3) 234 ( 2.2) Nation 14 ( 2.2) 53 ( 4.4) 46 ( 3.8) 20 ( 3.0) 260 4.3) 281 ( 2.9) 275 ( 2.5) 243( 3.0) RACE/ETHNICITY *bite State 10 ( 1.9) 80 ( 3.3) 57 ( 2.4) 20 ( 2.3) 278 ( 5.5) 271 ( 2.3) 286 ( 2.0) 240 ( 2.5) Nation 14 ( 2.4) 53 ( 5.0) 48 ( 4.2) 18 ( 2.8) 278 ( 4.1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) Slack State 85 ( 4.4) 39 ( 3.8) 35 ( 3.1) 233 ( 2.0) 262 ( 3.8) 228 ( 2.9) Nation 14 ( 3.4) 53 ( 82) 39 ( 7.1) 27 ( 8.9) 225 ( 4.3) 253 ( 8.3) 226 ( 2.2)1 Hispanic State 9 ( 3.3) 61 ( 5.7) 44 ( 8.5) 29 ( 5.4) IHr* eGe) 226 ( 6.2) ( Nation 15 ( 4.1) 56 246 ( 6.3) ( 4.4) 48 257 ( 5.9) ( 4.0)1 id ( 4.2) (*444*4) Asian State 20 ( 6.0) 84 ( 5.7) -.) 10 ( ( 3.3) ***) Nation 34 04* ( 8.7) ( 441 61 ( 8.1) ( 444 ) 9 ( *** ( 4.9) "4) TYPE OF COMMUNITY Advantaged urban State 15 ( 4.2) 60 ( 5.8) 81 ( 4.6) 15 ( 3.8) 288 ( 5.8)1 284 ( 4.8)1 298 ( 4.0) 245 ( 4.2)1 Nation 4** ( **IP) 65 284 (10.4) ( 7.4)1 41 286 ( 8.9) ( 7.9)1 18 ( ( 5.3) 4.) Disadvantaged urban State 4 ( 2.3) 67 (11.6) 40 (10.5) 240 ( 6.1)1 Nation 34 (11.4) 53 (11.8) 20 ( 9.4) 238 ( 8.2)1 254 ( 6.3)1 *4* ( 444) Wren* rural State 7 ( 4.4) 68 ( 9.0) 57 (10.5) 20 ( 94) **1 ) 236 ( 3.2)1 258 ( 5.2)1 Nation 5 ( 5.4) 65 254 (16.9) ( 6.7)1 33 ( 8.1) *411 42 (16.0) 241 ( 5.9)1 Otter State 10 ( 2.3) 58 ( 3.8) ( 2.8) 27 ( 2.8) 263 ( 7.1)1 256 ( 2.4) 280 ( (.8) 235 ( 2.7) Nation 15 ( 2.9) 53 ( 5.2) 47 ( 4.3) 17 ( 3.3) 287 ( 4.7) 260 ( 3.4) 276 ( 2.8) 245 ( 4.4)3 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate 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). 1.6. 106 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A8 I Teachers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT - Data Analysis, Statistics, and Probability Algebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No _ Emphasis TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Pf Onda State 40 ( 1.8) 60 ( 2.9) 52 ( 2.3) 23 ( 2.0) 270 ( 5.0) 260 ( 2.2) 282 ( 2.3) 234 ( 2.2) Nation 14 ( 22) 53 ( 4.4) 46 ( 3.6) 20 ( 3.0) 269 ( 4.3) 281 ( 2.9) 275 ( 2,5) 243 ( 3.0) PARENTS' EDUCATION HS no*graduat State 82 ( 4.9) 39 ( 4.9) 31 ( 4.3) ( 230 ( 3.6) 255 ( 5.0) 225 ( 5.1) Nation 9 ( 3.0) 53 ( 7.7) 28 ( 5.2) 29 ( 8.9) 240 ( 8.2) *Ire) HS graduate State 9 ( 22) 64 ( 3.6) 45 ( 2.8) 30 ( 32) 256 ( 13.0)1 244 ( 2.4) 287 ( 2.8) 232 ( 2.8) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) ammo college 261 ( 8.0)1 247 ( 2,9) 265 ( 3.5) 239 ( 3.4) State 10 ( 2.0) 63 ( 3.9) 56 ( 3.8) 19 ( 2.4) 266 ( 2.9) 282 ( 2.7) 240 ( 4.3) Nation 57 ( 5.8) 48 ( 4.8) *Hi* ( 11-- 270 ( 3.7) 278 ( 3.0) College graduate State 11 ( 2.5) 56 ( 3.4) 61 ( 3.0) 17 ( 1,9) 287 ( 6.0)1 281 ( 3.2) 295 ( 2.7) 241 ( 33) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 18 ( 2.4) 282 ( 4.5) 275 ( 3.8) 288 ( 3.0) 249 ( 4.0) G "NDER Male State 11 ( 2.0) 61 ( 3.1) 49 ( 2.6) 27 ( 2,4) 277 ( 6.0) 260 ( 2$) 283 ( 2.7) 235 ( 2.6) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.6) 275 ( 5.8) 260 ( 3.5) 278 ( 3.2) 243 ( 3.0) Female State 10 ( 1.8) 60 ( 3.0) 56 ( 2.5) 20 ( 2.1) 262 ( 6.0) 259 ( 2.4) 281 ( 2.2) 234 ( 2.8) Nation 16 ( 2.4) 53 ( 4.5) 48 ( 3.6) 18 ( 2.9) 263 ( 4.4) 262 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ** Sample size is insuffic ent to permit a reliable estimate (fewer than 62 students). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT 107 Virginia TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL I Get AO the Resources I I Get Most of the I Oei Some or Hone of STATE ASSESSMENT Need Resources I Need the Resources I Need TOTAL Percentage and Pnalkiency Percentage and Proliciency Percentage and PreAciency State 22 ( 2.5) 47 ( 34) 31 ( 3.1) 270 ( 3.1) 267 ( 1.9) 253 ( 34) Nation 13 ( 2.4) 58 ( 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 261 ( 2.9) RACE/ETHNICITY *Mite State 23 ( 3.1) 51 ( 3.9) 25 ( 3.4) 274 ( 3.0) 273 ( 2.0) 285 ( 4.0) Nation 11 ( 2.5) 5$ ( 4.8) 30 ( 4.8) 275 ( 3.5)1 270 ( 2.3) 267 ( 3.3) Slack State 17 ( 2.5) 35 ( 3.5) 4$ ( 4.1) 246 ( 3.4) 243 ( 2.5) 237 ( 2.0) Nation 15 ( 4.2) 52 ( 8.8) 33 ( 7 2) 241 ( 5.3)1 242 ( 2.4) 236 ( 4.9) Hispanic Siate 17 ( 4.5) vs.) SO ( 6.9) ( .41 33 ( 8.8) ( .41 Nation 23 ( 7.6) 44 ( 4.9) 34(7.7) 246 ( 7.7)1 250 ( 2.9) 244 t 3.0)1 Asian State 28 ( 62) *** ( 40 ( 7,7) 44* 23 ( 7,6) Nation 19 ( 8.6) ( ***) 37 7.7) ( .41 44 (12.7) ( *91 TYPE OF COMMUNITY Advantaged urban State 33 ( 6.9) 48 ( 8.7) 21 ( 7.7) 283 ( 6.3)1 284 ( 4.0)1 281 (12.2)1 Nation 35 9.2) 59 ( 6.9) 272 ( 85)1 286 ( 1.3)! ( 41.411 Disadvantaged urban State 0 ( 0.0) ***) 25 (10.1) «N. ( 75 (10.1) 240 ( 3.2)1 Nation 10 ( 6.8) ( *4.) 40 (13.1) 251 ( 5.4)1 50 (14.5) 253 ( 5.5)1 Extreme rural State 25 (10.0) 30 ( 8.4) 45 (10.4) 263 ( 6.6)1 249 ( 5.9)1 236 ( 2.2)1 Nation 54 (10.4) 43 (10.3) (other 200 ( 8.8)1 257 ( 5.0)1 State 18 ( 2.6) 52 ( 4.5) 30 ( 4.3) 262 ( 2.5) 264 ( 2.5) 252 ( 3.2) Nation 11 ( 2.9) 58 ( 5.4) 31 ( 5.6) 265 ( 3,9)1 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear m parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 st-indard 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). 108 113 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A9 I Teachers' Reports on the Availability of (continued) 1 Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRIAL I Get NI the Resources I I Get Most of the 1 Oet Some or None of STATE ASSESSMENT Need Resources I Need the lissome* I Need TOTAL floweentaes and Pralidency Peraeltept en6 Pralkienny PerCenteme MI6 Prolkisnqr State 22 ( 2.5) 47 ( 3.4) 31 ( 3.1) 270 ( 3.1) 201 ( 1.9) 253 ( 34) Nation 13 ( 2.4) 56 ( 4.0) 31 ( 42) 265 ( 42) 265 ( 2.0) 261 ( 2.9) PARENTS' EDUCATtON NS non-graduate State 20 ( 4.2) ***) 3$ ( 244 ( 4.9) 2.9) 42 ( 235 ( 5.0) 2.9) Nation 8 ( 2.6) 54 ( 5.7) 35 ( 0.3) 444 ( 244 ( 2.7) 243 ( 3.5)1 NS graduate State 20 ( 2.9) 46 1 3.7) 35 ( 3.6) 252 ( 2.2) 255 ( 1.9) 243 ( 2.6) Nation 10 ( 2.5) $4 ( 4.9) 35 ( 4.9) 253 ( 4.8)1 256 ( 1.9) 256 ( 2.8) Some coNege State 21 ( 3.3) 43 ( 4.2) 31 ( 3.6) 274 ( 3.6) 209 ( 24) 259 ( 3.0) Nation 13 ( 3.3) *-11 02 ( 209 ( 4.3) 2.5) 25 ( 267 ( 4.1) 3.6) College graduate State 24 ( 2,9) 50 ( 4.2) 25 ( 4.0) 264 ( 4.3) 281 ( 2.2) 271 ( 0.2) Nation 15 ( 2,9) 56 ( 4,9) 30 ( 5.1) 270 ( 5,4)1 276 ( 2.2) 273 ( 3.7) GENDER Male State 21 ( 2.6) 49 ( 3.4) 30 ( 3.1) 273 ( 3.5) 266 ( 2.4) 254 ( 4.0) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4.0) 264 ( 5.0)1 285 ( 2.6) 264 ( 3.3) Female State 22 ( 2.6) 4$ ( 3.0) 32 ( 3.4) 266 ( 3.3) 206 ( 1.9) 253 ( 3.3) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 266 ( 3.9) 264 ( 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 estimate for the sample Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 Virginia TABLE AIN I Teachers' Reports on the Frequency of Small i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASS AT EIPMF Al Least Once a Week Wes Than Owe a Week Never TOTAL State Nation RACFIETHNICITY Mite State Nation Blade State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation Penolass aid Prolldsoly 4$ ( 205 ( 24 30 ( 260 ( 22) 48 ( 3.3) 274 ( 2.6) 49 ( 4.6) 266 ( 2.7) 48 ( 3.5) 238 ( 1.9) 47 ( 8.1) 240 3.4) 64 5.5) 243 ( 5.7) 64 ( 72) 248 ( 2.5) SS ( 7.4) CIO ( 8.2) Veit ( 11,911r) 40 288 39 68 70 24$ 4.5 247 35 255 47 282 50 260 INI114441161. Arid fireilitlensy 41 f 2.4) 2.1) 43 4.1) 264 22) 42 ( 2.8) 12 ( 2.1) 289 ( 288 ( 32) 43 ( 4.5 $ ( 2.3) 271 ( 2.2 ( 4.9)I 40 ( 3.8) 12 ( 2.8) 244 1.9) 23$ 4.8)I 45 7.0) 9 ( 4.1) 238 4.0) ( 9 ( 3.2) 32 ( $.9) 4 ( 1.4) 247 ( 8.3)! 39 ( its* 7.2) 44.1 4 ( 4445, 2.2) 44,) 4 2.7) ( 8.3) 40 ( 4.9) 14 ( 3.9) ( 5.1)! 285 ( 3.6)! 271 ( 4.5)1 (22.9) :es) 41 (17.9) 273 ( 6.0)1 20 (i2.2) 0+4 ***) ( 5.5) 20.( 9.5) 14 ( 9.5) 0** ( 41141* *el (11.7) ( 4.8)t 21 ( 9.0) 249 ( 8.7)! 9 ( 8.5) o ( 6.5) 47 ( 8.1) 8 ( 3.2) ( 4.4)! 248 ( 3.7) (14.8) ( 5.5)1 58 (17.1) 258 ( 5.9)1 9 ( 9.8) a4. ( ( 4.0) 42 ( 3.4) 11 ( 2.4) ( 2.7) 258 ( 2.8) 250 ( 4.7)1 ( 4.4) 44 ( 4.5) 8 ( 1.8) ( 2.4) 284 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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). 110 THE 1990 NAEP 1 121AL STATE ASSESSMENT Virginia TABLE Al Oa I Teachers' Reports on the Frequency of Small (cmitinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT AI Least Once a Week Lass Than Orme a Week M yer TOTAL PIWOONDMIS and Pndkdancy fiemintspo and PollIdancy Perasnla. old landoianay State 44 2.8) 41 ( 2.4) 11 1 205 2A) 263 ( 2.1) 258 Nation 50 4.4) 43 ( 4.1) 2.0 260 ( 22) 264 ( 2.3) 277 54)1 PARENTS EDUCATION MS nen-graduate State 45 237 ( 5.9) ( 3.3) 42 ( 241 ( 5.4) 3.5) 13 ( 3.6) ego* ( Nation 00 244 ( 6.4) ( 2.2) 30 ( 244 ( 6.5) 3.2)1 ( 1.4) *44 .) MS graduate t:tate 43 ( 3.6) 44 ( 3.5) 13 ( 2.4) 249 ( 1.9) 251 ( 2.1) 250 ( 5.1) Nation 49 252 ( 4.8) ( 2.8) 45 ( 257 ( 5.1) 2.7) ( 2.5) «a* ( *44) Same coNegs State 46 ( 3.8) 41 ( 3.8) 12 ( 2.6) 266 ( 2.6) 267 ( 2.4) *Mit ( 041 Nation coNdge graduate 51 ( 200 5.2) ( 3.1) 42 ( 268 ( 5.1) 3.2) ( 2.3) es* ***) State 53 3.0) 38 ( 2.6) 9 ( 1.8) 290 ( 2.9) 279 ( 2.9) 276 ( 4.4)4 Nation 48 5.2) 43 ( 4.4) 11 ( 2.7) 271 2.6) 276 ( 3,0) 285 ( 44)1 GENDER State 49 ( 2.9) 41 ( 2.5) 10 ( 1.7) 267 ( 2.8) 265 ( 2.6) 256 ( 4.7) Nation 50 ( 4.5) 42 ( 4.0) ( 2.1) 261 ( 3.0) 265 ( 3.1) 278 ( 5.3)1 Female State 47 ( 3.0) 41 ( 2.6) 12 ( 2.2) 262 ( 2.3) 261 ( 2.2) 260 ( 3.7) Nation SO ( 4.7) 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE AlOb I Teachers' Reports on the Use of Mathematical 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Al Least Once a Week Lass Than Ones a Weak , TOTAL Perowslage an0 Prelldency 21 ( 25$ 2.9 22 S. 254 32) 21 ( 2.9) 264 ( 24) 17 ( 4.0) 261 ( 3.8)1 20 ( 4.0) 238 ( 3.5)1 22 ( 5.9) 233 ( 5.9)t fiNP iMhe 39 7.5) 247 ( 3.8) 18 ( 5.7) 42 ( 8.5) ..**) 14 ( 2.3) 255 ( 5.1) 23 (14.4) .44,) 19 (19.7) 39 (11.4) 247 ( 7.5)1 15 ( 6.3) #44) 27 (14.9) *at ( 441 20 ( 3.8) 259 ( 3.9) 19 ( 4.3) 253 ( 3.9)1 Pensiestaw and ihrseolancy $33 ( 21) 284 ( 1.9) GO ( 3.9) 283 ( 1.9) 86 ( 3.0) 271 ( 2.0) 72 ( 42) 289 ( 2.1) 70 ( 3.4) 240 ( 1.7) TO ( 83) 241 ( 2.9) 56 ( 5.9) 240 ( 5.8) 55 ( 7.3) 245 ( 3.8)1 ( 5.8) «it ( 041 52 ( 5.7) 71 ( 4.1) 285 ( 3.7) 63 (11.5) 278 ( 5.6)1 70 (16.6) 237 ( 21)1 59 (121) 253 ( 7.0)1 74 ( 6.0) 248 ( 3.1) 65 (14.6) 282 ( 2.8)1 62 ( 19) 259 ( 1.8) 72 ( 5.0) 263 ( 22) Perosniags am, 12 1.7) 271 4.5) 9 2.6) 282 ( 5.9)1 13 ( 22) 279 ( 4.1) 10 ( 2.7) 268 ( 62)1 11 2.3) 1140 fihIP ) S ( 3.9) $4* ( 110.1 9 ( 2.6) 1114* *a* ( 12 ( 3.4) 11** ( 6 ( 4.2) to.fr 41.) 15 ( 3.8) 293 ( 0.8)1 15 ( 9.3) 11 ( 5.5) 4.4 2 ( 1.8) 14 ( 4.8) 8 ( 3.9) 44. ( 11 ( 22) 265 ( 5.6)1 9 ( 3.3) 281 ( 7.1)1 State Nation RACE/ETHNICITY White State Nation sack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged trban State Nation Disadvartaged urban State Nation Extreme rural Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent 6-vrta1nty 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 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE AlOb I Teachers' Reports on the Use of Mathematical (continued) i Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Om* a Week Less Than Once a Week New TOTAL State Nation PARENTS' EDUCATION NS non-graduate State Nation NS graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation lianandage and rmlictimy 21 ( 2.8) 258 ( 2.9) 22 ( 32) 254 ( 3.2) 28 ( 4.3) 230 ( 3.8) 26 5.8) "fre 21 ( 2.8) 247 ( 2.8) 23 ( 4.8) 240 ( 4.0)I 21 ( 3.4) 262 ( 3.4) 18 ( 4.0) 201 ( 4.4)1 20 ( 32) 272 ( 3.8) 20 ( 3.9) 266 ( 3.5)1 22 ( 2.9) 263 ( 3.4) 22 ( 4.1) 255 ( 4.1) 20 ( 2.8) 253 ( 3.0) 21 ( 3.8) 254 ( 3.3) Parvannap and Prellaiangr Pansodasa and Pratkimay 82 2.7 12 11) 254 1,1 271 4.5) Oki 3.9 9 2.8) 283 ( 1.9 262 SAN 64 ( 241 ( 4.4) 241) 9 (2.1) lee en 00 ( 243 ( 7.2) 2.2) 9 ( et* ( 0.5) 00 ( 2.5 13 ( 1.9) 250 ( 1.7) 255 ( 5.4) TO ( 255 ( 5.3) 2.2) 7 ( eee 2.8) 66 ( 267 ( 3.8) 2.3) 13 ( eee 2.7) 73 ( 4.3) 9 ( 2.4) 269 ( 2.3) see 4.4s4) 67 ( 3.5) 13 ( 2.0) 279 ( 2.5 292 ( 5.0) 89 ( 3.7) 11 ( 23) 274 ( 2.2) 297 ( 4.2)! 65 ( 3.0) 13 ( 2.0) 265 ( 2.5) 272 ( 6.0) 89( 4.1) 8 ( 2.0) 265 ( 2.1) 287 ( 7.2)1 68 ( 2.8) 12 ( 1.8) 283 ( 1.7) 271 ( 4.1) 69 ( 4.2) 10 ( 3.3) 262 ( 1.9) 278 ( 8.0)I 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). 118 THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Virginia TABLE Al la I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Almost airy Day Several Times a Week About Om, a week or Less TOTAL lald Pradallenty 70 ( 2.5) 207 ( 1.9) 02 ( 34 ) 207 ( 1i) 75 ( 2.7) 273 ( 1.9) 64 ( 3.7) 272 ( 1.0) 58 ( 4.7) 244 ( 2.1) 56 ( 7.7) 244 ( 4.0) 68 ( 6.0) 247 ( 4.5) 61 ( 8.8) 251 ( 3.1) 60 ( 6.9) 83 ( 6.9) 284 ( 74)1 77 ( 4.8) 286 ( 3.5) 03115.9) 283 7.3)1 42 (18.4) .4. ( ea (10.7) 252 ( 4.7)1 60 ( 8.3) 255 ( 3.8)1 50 (10.6) 268 ( 4.0)1 72 ( 2.9) 261 ( 2.1) 03 ( 3.9) 267 ( 2.3) lismoodai. and Pralkdanay 25 ( 24) 254 ( 2.4) 81 ( 3.1) 254 ( 2.11) 22 ( 2.6) 263 ( 2.7) 26 ( 32) 264 ( 3.4) 35 ( 5.0) 225 ( 2.1) 41 ( TA) 233 ( 3.9)! 30 ( 13.1) 32 ( 5.3) 240 ( 4.3)! 32 ( 6.9) 10 ( 32) ( *41 17 ( 3.2) 271 ( 5.7) 23 ( 5.2) 50 (20.3) .44 31 (11.1) 243 ( 8.0)1 32 ( 5.3) 236 ( 2.9)1 40 (10.0) 247 ( 7.6)1 26 ( 3.1) 257 ( 3.4) 31 ( 34) 25$ ( 3.1) Ponandape and Pradancy 4 ( 1.1 252 (11.911 7 ( 1.6 200 ( 5.1)1 3 ( 1.1) 111141 ( 2.3) 234 ( 5.4)1 5 ( 1.4) gm* ( 2 ( 1.4) ( *in 2 ( 12) ( 441 8 ( 2,3) ( 8 ( 5.0) ...) 7 ( 5.4) ( .41 8 ( 3.3) 14 (14.8) 44. 441 7 ( 6.4) .4. ( 4 ( 2.2) ***) ( 1.2) ( .41 10 ( 7.3) .44 ( 2 ( 1.2) ( ( 1.9) 257 ( 5.8)1 State Nation NACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme neat State Nation Otiusr State Nation The standard errors of the estimated statisfics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 114 THE 1990 NABP TRIAL STATE ASSESSMENT Virginia TABLE Alla I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT\ Almost Every Day Several Times a Week About Once a Week or Len TOTAL State Nation PAR_ENTS' Enucknow NS non-graduate State Nation NS graduate State Nation Some - State Nation Collage graduate State Nation GENDER Male State Nation Female State Nation lionnutage mad 0086.14860, Portuslaga and Prilidenay 70 ( 2.5) 26 (24) 267 ( 2$4 ( 2.4) 02 ( 3.4 $1 ( 3.1) 207 ( 1.8 254 ( 2,9) Pereentage Wel Prelkinseg 252 1111 iA1 200 ( 5.1 68 ( 4.5) 28 ( 4.4) 4 (1.7) 241 ( 2.5) 233 ( 34) IMO ~I 811 ( 5.5) 3.2) 27 ( 4k11* 5.2) 8 ( or. ( 2.1) 71 ( 32) 25 ( 3.1) 4 ( 1.13) 253 ( 1.7) 244 ( 2.3) 61 ( 4.4) 34 ( 33) ( 1.5) 257 ( 2.5) 250 ( 2.9) 72 ( 3.1) 251 3.1) ( 1.1) 271 ( 1.8) 257 ( 3.7) ( 88 ( 4.2) 26 ( 3.7) 8 ( 1.9) 272 ( 2,7) 256 ( 5.2) 71 ( 3.3) 25 ( 3.0) 4 ( 1.7) 283 ( 2.4) 289 ( 32) 61 ( 281 ( 4.0) 22) 31 ( 265 ( 3.9) 3.1) 3 ( 3,4) ***/ 69 ( 270 ( 2.6) 2.4) 27 ( 256 ( 2.7) 2.6) 4 ( 13) .+0) 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 209 ( 2.1) 258 ( 3.6) 261 ( 8.7)1 72 ( 2.7) 25 ( 2.6) 3 ( 1.1) 26C ( 1.7) 252 ( 2.0) ". OS ( 36) 23 ( 3.3) ( 2.2) 266 ( 1.8) 253 ( 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. 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 perniit a reliable estimate (fewer than 62 students). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT 115 Virginia TABLE Al lb I Teachers' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIE'sICY MO NAEP TRIAL STATE ASSESSMENT AS Least Several Times a Week About Once a Week Lass than %Noddy TOTAL State Nation MOLOSSLTY. White State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation add Ordidesigf 2:12 41 .11 250 2.3 43 ( 3.9) 200 ( 2.3) 32 ( 4.1) 264 ( 2.7) 44 ( 4.7) 235 ( 2.1) 45 ( 7.5) 232 ( 3.1)1 62 ( 8.3) «4. ( 41 41 ( 7.7) 242 ( 32)1 49 ( 8.1) 37 ( 6.3) V") 40( 5.6) 278 ( 3.7) 59 (13.9) 273 ( 3.4)1 1 3 .144 ( 441 50 (13.9) 237 ( 2.4)1 54 (10.8) 239 ( 41)1 27 (14.3) 41 ( 4.8) 255 ( 2.9) 30 ( 4.4) 256 ( 3.3) Paradiria us4 Padkirry 2:1 2.01 33 3.4) 200 2.3) 2$ ( 2.4) 272 ( 2.8) 33 ( 3.5) 264 ( 2.7) 33 ( 4.5) 242 ( 2.0) 31 ( 7.8) 243 ( 2.3)1 31 ( 5.1) 4144 ( 1 2e ( 5.3) 244 ( 5.1)1 22 ( 4.1) imp* 35 ( 9.7) **ft ( *I») rsd linareacy 270 3.4 S2 SA 274 2. 29 ( 4.0) 270 ( 35( 3.0 279 ( 2A 24 ( 3.4) 247 ( al) 23 ( 0.3) 244 ( 7.0)1 17 ( SA) 33 ( 7.5) 257 ( 2.3)1 30 ( 5.7) .41 27 (10.4) *IV ( *OM) 25 ( 4.5) 20 ( 7 .1) 284 ( 8.3)1 293 ( 5.5)1 20 ( ILO) ( 041 21 ( 8.2) 51 (20.8) ( 044) 18 ( 8.3) *Olt ( *ivy 22 (11.2) 28 (10.7) 258 ( 8.3)1 2613 ( 4.1)1 24 ( 6.4) 21 ( 7 .7) 254 ( 7.0)1 256 ( 3.4)1 49 (12.7) 24 (10.1) 258 ( 6.7)1 30j 3.3) 29 ( 4.4) 260 ( 3.3) 285 ( 3.8) 35 ( 4.3) 36 ( 41) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 116 121. THE 1990 NAEP TRIAL STATE ASSESSMENT Vftinia TABLE Al lb I Teachers' Reports on the Frequency of (continued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAP TRIAL At Laast Several Times STATE ASSESSMENT a Week About Once a Week Lau than Wieldy TOTAL OM Prolkisicy poramiew and firsesioncy Peto~ -W ProlidencY State 44 29 23) 27 $.2) 259 2.1 2541 2.8) 270 $.4) Nauon 34 3.8 33 (3A) $2 SA) 256 (2.3) 280 ( 2.3) 274 ( 2.7) PARENTS' EDUCATION NS non-graduat State 39 ( 6.0) 32 ( 4.5) 29 ( 5.2) 230 ( 33) 238 ( 3.1) 242 ( 3.7)4 Nation 35 ( GA) 239 ( 3.5) 29 onk ( 63) Mel 36 ( 250 ( 8.9) 4.5)1 KS graduate State ( 4.0) 28 ( 2.8) 30 ( 3.8) 244 ( 1.8) 252 ( 2.0) 256 ( 2.7) Nation 35 ( 5.3) 30 ( 4.5) 30 ( 4.3) 250 ( 3.6) 250 ( 2.7) 263 ( 3A) Soma cottage State 43 ( 3.7) 32 ( 3-3) 25 ( 3.9) 260 ( 2.5) 272 ( 3.6) 272 ( 4.0) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 23) 206 ( 4.2) 276 ( 2.8) Co Sego graduate State 48 ( 3.6) 26 ( 2.3) 26 ( 3.3) 275 ( 2.7) 278 ( 4.0) 288 ( 3.6) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 204 ( 2.8) 271 ( 24) 289 ( 2.9) GENDER Male State 45 ( 3.5) 26 ( 2.4) 27 ( 3.2) 280 ( 2.2) 267 ( 3.9) 271 ( 4.2) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 281 ( 2.8) 275 ( 3.2) Female State 42 ( 3.8) 30 ( 2.6) 28 ( 3.4) 257 ( 2.4) 261 ( 2.4) 26a ( 3.1) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 254 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT 117 Virginia TABLE Al2 I Students' Reports on the Frequency of Small 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 MEP TRIAL STATE ASSESSMENT At Least Once a Weft Lass Than Once a Wash Now TOTAL State Nation EMUS:MIMI White State Nation Mack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNiTY Advantaged urban State Nation Disadvantaged urban State Nation &tram rural State Ws:ion Other State Nation ferentalle and Praidency 29 2.1) 264 2.0) 28 24) 258 2.7) 28 ( 2.3) 274 ( 32) 27 ( 2.9) 288 ( 3.1) 31 238 2.2 28 3.0 234 ( 3.0) S3 ( 42) *gm) 31 ( 52) 242 ( 3.9) 28 ( 8.8) ( 044) 2$ ( 0.4) .hp.) 20 ( 4.0) 227 ( 8.5)1 27 (13.9) 31 ( 5.8) 21 ( 5.7) 245 ( 4.0)1 30 ( 7.1) 243 ( 3.1 )1 34 (10.8) 249 ( 5.2)1 30 ( 2.9) 262 ( 2.9) 27 ( 2.6) 260 ( 3.3) 1411181411110 and PraliddinT 29 ( 1.7) 271 22) 28 (1.4) 207 (2.0) 31 ( 2.0) 270 ( 2.2) 29 ( 1.7) 272 ( 14) 24 ( 22) 24924 343.(4 245 ( 4.0) 27 ( 4.0) 22 ( 3.8) 250 ( 3.4) 39 ( 8.7) *v. ( 32 C 4.0) ( *In 31 ( 4.2) 292 ( 4.0)1 33 ( 4.5) 220 ( 54)1 25 ( 8.8) 20 ( 2.8) 207 ( 64)1 24 ( 3.5) 257 ( )1 27 ( 3.8) 264 ( 3.5)1 30 ( 2 265 ( 28 ( 1 264 ( 2.1) nomodese and ItrallsOonf 24:11 261 1.0 41 ( 2.8 28744 34) 270 1..7) 48 461 4.7) 234 ( 3.1) 30(4.8) oe 41 ( 5.0) 240 1 2.8) 35 (82) 40 ( 02) .4* ( 43 ( 0.3) 27$ ( 32)1 40 (13.4) 279 ( 3.5)1 44 (11.6) 49 ( 0.3) 245 ( 3.7)l 46 ( 6.7) 24$ ( 3.4) 39 (11.6) ase ( 0.2)1 40 ( 2A) 257 ( 2.4) 45 ( 3.3) 202 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -. the nature of the sample does not allow accurate determination of the variability of this estimated ;man proficiency. *6* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 " 118 THE 1990 NAEP TRIAL. STATE ASSESSMENT Virginia TABLE Al2 I Students' Reports on the Frequency of Small (c°11tinued) i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1690 NAEP TRIAL STATE ASSESSMENT At Least Once a Weak Lad Than Ones a Meek Never TOTAL peromesse and PraiekteCy Potosolage sod Preadiemy Perdarialp and Pretialeneg State 29 (2.1) 29 ( 1.7) 42 ( 2.4) 264 (2.8) 27! ( 2.2) 250 1.9) Nation 26 2.5) 28 ( 1.4) 44 2.9) 256 ( 2.7) 287 ( 2.0) 281 1.8) PARENTS' El:mom* 143 non-graduate State 27 ( 4.3) 27 ( 3.1) 48 234 ( 2.11) 248 ( 3.9) 242 2.8 Nation 20 ( 4.5) 29 ( 3.0) 42 4.5 242 ( 3.4) 244 ( 3.0) 242 ( 2.7) N$ graduate State 23 ( 2.4) 25 ( 2.4) 48 ( 3.0) 247 ( 2.5) 258 ( 2.4) 250 ( 2.1) Nation 26 ( 3.0) 26 ( 1.6) 43 ( 3A) 251 ( 3.f) 281 ( 2.8) 252 ( 1.7) Some college State 27 ( 3.0) 33 ( 2.5) 40 ( 3.2) 264 ( 3.4) 275 ( 2.6) 264 ( 2.5) Nation 27 ( 3.9) 27 ( 2.4) 46 ( 3.8) 265 ( 3.6) 258 ( 3.3) ( 2.1) WW1* graduate State 32 ( 2.8) 32 ( 2.3) 96 ( 2.9) 262 ( 3.9) 284 ( 2.8) 275 ( ".3) Nation 2$ ( 3.0) 28 ( 1.9) 44 ( 3.6) 270 ( 2.7) 276 ( 24) 275 ( 2.2) GENDER Mato State 31 ( 2.2) 29 ( 1.8) 44 ( 2.3) 264 ( 3.5) 275 ( 2.9) 260 ( 2.2) Nation 31 ( 2.9) 25 ( 1.7) 41 ( 2.9) 258 ( 3.3) 20$ ( 2.0) 202 ( 1.6) Femme State 27 ( 2.3) 30 ( 2.0) 43 ( 2.8) 264 ( 2.6) 257 ( 2.4) 259 ( 2.2) Nation 26 ( 24) 27 ( 1.8) 47 ( 32) 257 ( 2.8) 208 ( 1.7) 250 ( 1.8) The standard errors of the estimated statisfics 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. 124 THE 1990 NABP TRIAL STATE ASSESSMENT 119 Virginia TABLE A13 I Studente Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT . At Least Once a week - Lass Than Once a weak Never . TOTAL tententies and Pnes Maw Ilkodantly and Pralkaleacy State 24 ( 1.8) 29 ( 2e1 ( 2.9) ( 1.7 Nation 28 ( 1.8) ( 1.2 238 ( 2.6) 20$ ( 1.5) RACEMIldNICITY White State 22 ( 1.9) 20 ( 1.4) 270 ( 3.2) 275( 1.9) Nation 27 ( 1.9) 33 ( 14) 288 ( 2.6) 275 ( 1.8) Ma& State 2$ ( 2.7) 28 ( 2.3) 2341 ( 3.0) 246 ( 2.4) Nation 27 ( 3.3) 27 ( 3.2) 234 ( 3.7) 248 ( 4.5) Hispanic State 32 ( 4.9) 2$ ( 4.0) 114* ( ) Nation 38 ( 42) 23 ( 2.0) 241 ( 4,6) 253 ( 4,3) Asian State fIl. in 33 ( 4.7) ( *61 Nation 32 ( 3.7) 30 ( 3.2) ( TYPE OF COMMUNITY Advantaged urban State 19 ( 3.7) 30 ( 2.8) 283 ( 8.3)1 286 ( 3.7) Nation 36 (10.3) 33 ( 48) 278 ( 6.1)1 284 ( 3.2)1 Disadvantaged tartan State 31 (12.0) 20 ( 7.2) *44 ( I** ) Nation 35 ( 8.6) 19 ( 2.1) 249 ( 5.3)1 256 ( 5.7)1 Extreme rural State 19 ( 2.5) 23 ( 3.1) 252 ( 3.8)1 Nation 21 ( 3.1) ***) 37 ( 4.7) 262 ( 4.7)1 Other State 26 ( 1.8) 31 ( iS) 259 ( 3.3) 267 ( 2.3) Nation 27 ( 2.0) 31 ( 1.4) 256 ( 2.9) 270 ( 1.8) persomio and Prtialmay 47 ( 2.2) 262 11) 41 2.2) 1.8) 47 ( 2.4) 270 ( 1.8) 40t 2.5) 288 ( 1A) 49 ( 3.2) 240 ( 2.0) 46 ( 45) 232 ( 2A) 39 ( 5.0) 40 ( 4.0) 240 ( !A) 38 ( 4.7) 38 ( 4.7) 52 ( 5.1) 282 ( 3.9)1 32 (11.1) 261 ( 5.9)1 50 ( 6.9) «. 48 ( 6.4) 248 ( 4.6)1 56 ( 4.6) 245 ( 3.9) 43 ( 5.0) 251 ( 5.2,1 43 ( 2.5) 257 ( 1.6) 41 ( 24) 200 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be saki 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: 5 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A 13 I Students' Reports on the Use of Mathematics (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 15110 NAEP TRIAL STATE ASSESSMENT At Lust Once a Week Lass Than One a Week Never , TOTAL liercentage and Preachingly Percentapp Proilkiancy Parcessisse and Proliskracy State 24 ( 1.8) 29( 1.3) 47 ( 281 ( 2.9) 200 ( 1.7) 282 ( 1. Nation 2$ ( 1.8) ( 1.2) 41 ( 2.2 258 ( 2.8) 209 ( 14) 258 ( 1.6) PARENTS' EDUCATION NS nangraduato State 23 ( 2.8) .4.4) 32 ( 247 ( 2.6) 3.6) 45 ( 238 ( 3.2) 3.1) Nation 27 t 4.2) 20 ( 2.7) 47 ( 5.0) 247 ( 3.0) 253 ( 34) 240 ( 2.3) KS graduate State 28 ( 2.3) 27 ( 1.9) 47 ( 2.7) 248 ( 2.3) 257 ( 2.1) 250 ( 1.9) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some collage State 20 ( 2.3) 31 ( 2.2) 49 ( 2.9) 2U2 ( 3.6) 270 ( 2.5) 288 ( 24) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.8) 261 ( 34) 274 ( 2.2) 283 ( 2.1) College graduate State 24 ( 1.9) 30 ( 1.8) 48 ( 2.8) 278 ( 4.5) 285 ( 2.6) 278 ( 2.0) Nation 30 ( 24) 32 ( 2.0) 38 ( 2.8) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Male State 28 ( 1.9) 29 ( 1.4) 43 ( 2.3) 262 ( 3.3) 270 ( 2.1) 25$ ( 2.4) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 12) Fens** State 20 ( 1.6) 29 ( 1.8) SI ( 2.4) 259 ( 3.3) 268 ( 1.9) 260 ( 1.7) 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 statistier apcear in parentheses. It can be said with about 95 percent certainty that, for each population of Mterest, 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). 126 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Virginia TABLE A14 I Students' Reports on the Frequency of i Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT Ntnost Every Day - Sawa Times a Weak About Once a Weak or Loss TOTAL Perosrdap aml Prelliciency 77 ( 1.8) 247 ( 1.5) 74 ( 1.9) 247 ( 1.2) 80 ( 1.8) 274 ( 1.5) 76 ( 24) 274 ( 1.3) 70 ( 3.3) 244 ( 1.8) 71 ( 2.8) 240 ( 2.9) 69 ( 4.0) 251 ( 4.3) 61 ( 3.7) 249 ( 2.3) 72 ( 5.5) 302 ( 4.5) 79 ( 4.9) 269 ( 5.0)1 76 ( 4.6) 266 ( 3.7) 73(11.1) 286 ( 4.6)1 64 (11.0) 246 ( 6.5)1 09 ( 2.8) 253 ( 3.7)1 78 ( 3.5) 251 ( 2.9) 6$ (11.3) 263 ( 4.2)1 77 ( 1.9) 264 ( 1.8) 75 ( 2.2) 267 ( 1.6) Pormitarp Praciency 15 ( 255 ( 2.4 14 ( OS 252 ( 1.7 13 ( 12) 264 ( 3.4) 13 0.6) 258 ( 2.2) 20 ( 2.1) 237 ( 2.4) 15 ( 1.7) 232 ( 3.1) 21 ( 3.7) ( 21 ( 2.9) 242 ( 5.1) 13 ( 3.4) ( 16 ( 3.0) 271 ( 5.8)1 13 ( 1.7) «Hi 2$ ( 5.6) *el 15 ( 2.5) 243 ( 4.4)1 14 ( 3.3) 4k.4) 15 ( 3.6) 15 ( 12) 252 ( 2.13) 14 ( 1.0) 252 ( 2.8) Pars8.4.80 aid .841801614/ $ 1.0) 24$ 4.1) 12 1.11) 242 ( 4.5) ( 1.0) 25$ ( 4.7) 11 ( 2.2) 252 ( 5.1)1 10 ( 1.9) IN* 44) 14 ( 3.2) 223 ( 61)1 10 2.9) ***) 17 ( 2.7) 224 ( 3.4) $ ( 4.3) ihMt itIN) a ( 2.6) OS* ( V111 7 ( 2.1) 4,4. 14 (104) 10 ( 5.6) 15 ( 2.2) 235 ( 8.5)1 ( 2.5) 17 ( 8.2) ( 1.4) 243 ( 3.9) 10 ( 1.9) 239 ( 4.3)1 State Nation RACEIETNNICITY %Wt. State Nation State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Dfudvantagad urban State Nation Extrom rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r0 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A14 Students' Reports on the Frequency of (continued) i Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 NAEP TRIAL STATE ASSESSMENT Mmost Every Day Several Times a Week About Once a Week or Less TOTAL POssoldgill old Praliciency 000.90418 Prall#499% "alig State 77 ( 14) 1$ ( 1.1) 1.0) 287 ( 255 ( 268 4.1) Nation 74 ( 1.9 14 ( 041 12 14) 287 ( 1.2 252 ( 1.7 242 4$) PARENTS' EDUCATION 113 non-graduate State 72 ( 3.7) 244 ( 2.3) 18 ( 2.6) 11 ( 2.5) ( *el Nation 64 ( 3.4) 245 ( 2.3) 1, ( 2.0) iptva 18 11) as* 61 HS graduate State 75 ( 2.1) 17 ( 1.6) 1.0) 253 ( 1.4) 244 ( 2.8) Nation 71 ( 3.8) 16 ( 1.8) 13 ( 2.8) 256 ( 1.8) 249 ( 3.2) 239 ( 3.4)I Some college State 83 ( 1.9) 270 ( 1.5) 12 ( 1.6) ( owe) 5 ( 1.4) Nation 80 ( 2.0) 270 ( 1.9) ***) 9 ( 1.7) iht ( owe) College graduate State 78 ( 2.7) 15 ( 1.7) 7 ( 1.4) 284 ( 2.0) 270 ( 4.3) 263 ( 5.5)1 Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 260 ( 2.6) 257 ( 6.4)! GENDER Male State 74 ( 2.1) 17 ( 1.5) 9 ( 1.3) 269 ( 1.9) 258 ( 3.1) 248 ( 3.8) Nation 72 ( 2.4) 16 ( 1.2) 12 ( 2.1) 268 ( 1.6) 252 ( 2.5) 242 ( 6.1) Female State 79 ( 1.8) 14 ( 1.3) ( 1.2) 206 ( 1.5) 251 ( 2.7) 248 ( 5.8) Nation 76 ( 1.8) 13 ( 1.0) 411 ( 1.6) 255 ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of intereiit, 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* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 128 THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Virginia TABLE A 15 I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT . At Least Semi Times a %Wok _ Ilbot41 Once a Week Less Than Weekly TOTAL PeseentIll mei Praaahling Pargentana Prallialemay Paranatain and Prelbaktnq State 43 ( 11 29( 211. 258 ( 211 293( 1.11 274 2 Nation 38 ( 2.4 29( 11 97 2.5 253 ( 2.2) 2111 ( 14) 272( 1.9) ItACEMTNNICITY Whits State 41 2.0) 2812 (, 31 ( 2.1) 290 2.4) 271 ( 1.9 279 ( 24) Nation 35 2.9) 24 ( 1.3 41 ( 3.0) 282 ( 2.5) 269 ( 14) 217 ( 2.0) Black State 48 ( 12) 31 ( 3.0) 20 ( 238 ( 1.9) 244 ( 2.1) 249 ( 3.7 Nation 4 ( 3.8) 32 ( 2.7) 20 ( 3.1 232 ( 4.3) 241 ( 2.9) 241 f 4.4) Hispanic State 57 ( 4.5) 242 ( 4.2) 22 ( 3.8) *** 21 ( 3.7) 0.4 Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 23$ ( 32) 247 ( 3.3) 24$ ( 3.3) Asian State 41 ( 4.3) 30 ( 4.3) 29 ( 4.1) *44 ( *MI 1111. *21 Nation 32 ( 5.1) ( 17 ( 3.5) *04 ( **a) 51 ( 5.9) *dm ( TYPE OF COMMUNITY Advantaged titan State 49 ( 4.5) 23 ( 2.3) 28 ( 44) 277 ( 4.2)1 261 ( 3.4) 296 ( tip Nation 50 ( 9.0) 19 ( 4.9) 31 ( 9.3) 271 ( 3.3)1 290 ( 5.3)1 Disadvantaged urban State 57 ( 9.1) 27 ( 7.0) 18 ( 4.8) 241 ( 4.7)1 ( *IP* ( din Nation 37 ( 5.6) 23 ( 3.6) 41 ( 8.7) 240 ( 42)1 253 ( 4.1)1 255 ( 4.2)1 Extrema rural State 38 ( 6.4) 35 ( 5.2) 27 ( 5.5) 235 ( 2.4)1 256 ( 4.8) 254 ( 4.1)1 Nation 42 (10.1) 30 ( 4.4) 28 ( 74) 249 ( 4.0)1 256 ( 3.4)1 267 ( 7.3)1 Other State 41 ( 24) 90 ( 1A) 29 ( 2.2) 254 ( 24) 261 ( 2.6) 270 ( 2.8) Nation 36 ( 22) 28 ( 1.2) 38 ( 2.9) 252 ( 3.0) 261 ( 2.1) 272 ( 14) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *0* Sample size is insufScient to permit a reliable estimate (fewer than 62 students). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A 15 I Students' Reports on the Frequency of ("ntinued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT At Utast Sawa Times a Week About Once a !AWN Less Than Weekly TOTAL State Nation natlyrinAmt NS nan-graduate State Nation NS radiate State Nation Same college State Nation Catiege graduat State Nation GENDER Yale State Nation Female State Nation 43 ( 25$ ( 2,0 SS ( 4 253( ...2) 37 ( 4.2) 235 ( 3.3) 41 ( 4.5) 235 ( 3.1) 44 ( 24) 244 ( 1.6) 40 ( 3.2) 247 ( 2.7) 41 ( 3.1) 262 ( 2.6) 34 ( 3.4) 259 ( 2.3) 44 ( 2.4) 274 ( 2.6) 36 ( 2.6) 264 ( 2.6) 44 ( 2.0) 259 ( 2.4) 39 ( 2.7) 263 ( 2.7) 43 ( 2.1) 256 ( 2.1) 37 ( 2.5) 253 ( 2.1) 32 ( 240 8.2 30 2.7 243 2.7) 30 ( 1.8) 251 ( 29 ( 22 250 ( 2.5 28 ( 271 ( 2.9 20 ( 22 209 ( 2.8) 28 ( 1.8) 277 ( 2.4) 22 ( 1.8) 273 ( :c.5) 29 ( 1.8) 268 2.5) 25 1.6) 263 2.3) 2$ ( 1.3) 261 ( 1.9) 25 ( 1.5) 259 ( 1.8) 30 3 348 20 4.0 253 2.8 27 ( 2.2) 261 ( 2.5) 21122 21 31 ( 2.9) 272 ( 2.9) 40 ( 3.6) 271 ( 2.11) 29 ( 1.9) 292 ( 3.1) 41 1 2.0) 285 ( 2.3) 27 ( 1.6) 275 ( 3.3) 33 ( 2.7) 274 ( 2.4) 29 ( 2.1) 274 ( 2.8) 38 ( 2.8) 208 ( 22) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 Vfrginia TABLE A18 S*maents' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 18110 MEP TRIAL !TATE ASSESSMENT Own a Calculator Teacher lb/stains Calculator Use Yes No Yes No 1 State Nation RACE/ETHNICITY Iblilte State Nation Black State Nation Plipanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvwdagad urban State Nation Extreme rurai State Nation Other State Nation PerssiOses Peroaltage lel Pnliolow Prallokete air04094911 an. 0"144411"Y Pw09010. aid PrallOknoy $S AS) 2 44 50 2.0) 203 259 1 12 203 97 04 3 0.4 40 2.3 51 2.3 203 LS 294 01 351 1 393 1 2:2 I 11 270 1.5 93 ( 237 ( 93 ( 240 ( 92 ( 24$ ( 98 ( 290 ( 99 ( 282 ( 99 ( 283 ( 99 ( 281 ( 97 ( 244 ( 94 ( 250 ( 98 ( 249 ( 98 ( 257 ( 96 ( 281 ( 97 ( 283 ( 1.5) 2.8) 2.4) 3.8) 1.2) 2.7) 1.4) 3.9) 0.9) 5.3)1 0.3) 3.8) 1.0) 3.8)1 1.5) 4.0)1 1.2) 34)1 1.8) 2.9) 1..3) 32)1 0.4) 1.7) 0.5) 1.7) 7 i 1.5) 7 ( 2.4) 8 ( 1.2) 44.) ( 0.9) ***) 1 ( 0.3) 4.44) 1 ( 1.0) ( 441 3 ( 1.5) ow* ( 8 ( 1.2) *** t *") 4 ( 1.8) don ***) 2 ( 0.4) 3 ( e).5) 233 ( 6.4) 43 ( 22) 207 ( 1.5) 44 ( 2.0) 205 ( 1.8) 47 ( 238 ( 2.0 53 ( 4.9 235 ( 32) 49 ( 5.4) 63 ( 4.3) 243 ( 3.4) 37 ( 62) 52 ( 44) ,6* 44) 38 3.8) 278 42) 45 122) 278 2.5)4 40 5.1) ( 53 ( 7.5) 247 ( 4.1)1 48 ( 72) 243 ( 5,5)1 42 ( 8.7) 251 ( 4.8)1 47 ( 2.1) 258 ( 2.0) 50 ( 2.7) 258 ( 2.1) 57 ( 22 275 ( 2,01 54 ( 2.8 273 ( 1.6 53 ( 3.5) 244 ( 14) 47 ( 4.9) 239 ( 2.7) 51 ( 5.4) *kb ( *el ( 4.3) 245 ( 2.9) ( 82) 48 ( 4.8) *** «91 84 ( 3.8) 287 ( 32)1 55 (122) 285 ( 8.4)4 80 ( 6.1) ( 2.2)1 47 ( 7.5) 251 ( 34)1 54 72) 262 (24) Ss (8.7) 281 ( 4,4)4 53 ( 2.1) 263 ( 2.3) 50 ( 2.7) 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 Virginia TABLE Alti Students' Reports on Whether They Own a (continued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT Gall a Calculator Teacher Eop Wino Calculator Use Yin No Yes No TOTAI. State Nation fv_mumnsm KS non-erackhat State Nation 14$ graduate State Nation Some college State Nation College graduate State Nation GENDER Paresteap and Pre lioleacy 98(0.3) 205 ( 1.5) 07(04) 283 ( 1.3) 33 ( 1.6) 242 ( 2.1) 92 ( 1.8) 243 ( 2.0) 98 ( 0.8) 251 ( 1.3) 97 ( 0.6) 255 ( 1.5) 98 ( 0.8) 217 ( 14) 90 ( 0.9) 260 ( 1.8) 90 ( 0.3) 280 ( 2.1) 99 ( 0.2) 275 ( 1.6) 98 ( 0.4) 206 ( 1.9) 97 ( 0.5) 264 ( 1.7) 98 ( 0.4) 203 ( 1.4) 97 ( 0.5) 262 ( 1.3) Noramtags sod Prfationcy 3 234 7 4,04 $ 40. 2 3 2 4 ea* 1 2 4,84. 3 2 3 t'.2) 0.41 ( 34 ( 1 .6) 0.64.) ( ( 0.6) ( 0.6) we) ( 0.8) ( 441 ( 0.9) ( ( 0.3) ( 0.2) 4.4,1 ( 0.4) ( «on 0.5) ( OA) ( ( 0.5) "sevembos arid Prolkioncy 44 ( 2.0) 234 ( 1.8 40(2.31 258 ( 1.7 41 ( 3.7) 236 ( 2.7) 53 ( 4.6) 242 ( 2.9) 47 ( 2.7) 248 ( 1.9) 54 ( 3.0) 252 ( 1.0) 41 ( 3.1) 264 ( 24) 48 ( 32) 265 ( 2.4) 43 ( 2.4) 275 ( 2.3) 48 ( 2.6) ( 22) 45 ( 22) 282 ( 51 ( 2.6) 258 ( 2.1) 43 ( 2.3) 258 ( 1.7) 47 ( 2.5) 258 ( 1.7) Peromeass and Parikkacy Se ( 1.11 51 2.3 288 1,5) 52 ( 3.7 245 2.8 47 ( 4.61 243 ( 2.5) 33 ( 2.7) 253 ( 2.1) 48 ( 3.0) 258 ( 2.0) 59 ( 3.1) 270 ( 2.0) 52 ( 3.2) ( 2.2) 57 ( 2.4) 284 ( 2.4) 54 ( 2.8) 280 ( 1.9) 55 ( 2.2) 209 ( 2.4) 49 ( 2.8) 200 ( 2.1) 57 ( 2.3) 267 ( 1.8) 53 ( 2,5) 283 ( 1.8) Maki State Nation Female State Nation The standard errors of the estirnated 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 46 ( 1.2) 4$ IA) 254 1.5) 27 1 273 21 23 13 272 1.4 2:14 30 1181 11 in kg X 11 .15 13 19 27 IA , 30 1.2 203 1.8 SU (,2.4 274 , 42 13) 20) 31 13) 18 ( 1.2 Zt IA 40 IA 261 1.8) 277 271 1.4) 2.9 291 41.0 219 13 48 12) 24 2.2 Si 13) 111 1.2 U te it 10 2e2 1.7) 274 ( 13 270 1.7) se 2.3 283 2.6 210 1,2 55 ( 2.4) 24 2.1 31 ( 2.2 10 ( 1.4) U 2.7 14 1 234 ( 254 2.4 238 ( 22 252 ( 3.1) 233 2.1 245 24 57 ( 3.2 20 SA 31 ( 2.9 16 ( 1.9) 36 $.3 24 2.1 232 ( 2.4 249 ( 4.0 233 ( 33 248 ( 5.5) 230 3.8 ) 251 ( 4.1 55 ( 4.3) 15 1 34) 23 ( 3.9) 12 ( 2.6) 30 } 4.0) Z i !..$4 240 ( 31 Imp. ..... 1.0. ( ..) . ( ....) 239 ( 2.8) 252 ( 3.3 238 ( 4.8) 244 ( 3.1) 237 ( 3.2 238 ( 4.2) 51 ( 2.9 16 ( 3.511 20 ( 3.2) 21 ( 2.1) ge ( 221 22 i 3.1) 98 ( 4,5) 23 1 5.3) 38 ( 4.11 21 5.2) 21 ( 33) etif 1 f2/ *6. ( .4) .....1 .... i .04. I** ton *** ( 1 35 ( 6.3) 29 ( 5.8) 30 ( 3.3) 23 ( 4.4) 23 ( 5.8) 46 ( 8.4) wel, ( ,....) ... i .H..) ..... ( *...) 0,9* ( *el 444. t *el 1.3 272 ( 3.11) 51 ( 5.4) 23 (10.7) 32 ( 6.1) 15 2.4) 31 33 287 ( 5.0r 280 ( 23) 291 7.2p 272 3.4 200 iS I 11) .: ii 40 ( 2.7) 0 ( 4.4) 39 ( 3.0) 18 23) 23 2.5 270 ( 4.7)1 *** ( ***) 274 ( 4.9)1 *** ( ***) 281 7.8 245 4.2 50 ( 6.0) 29 ( 23) 19 ( 5,5) 22 ( 2.4) 30 ( 5.3) 34 all 0** ( INin 4111. ( *an MIMI ( In OR* ( Ra) 44* ( *0) $2 ( 3.1) 22 ( 4.5) 90 ( 3.3) 24 ( 2.3) 27 ( 2.9) 27 4.8) 241 ( 3.8)1 259 ( 5.4)1 248 ( 5.2$ 254 ( 4.ey 240 ( 4.9P 203 ( 5.0y 47 ( 1.9) 27 ( 3.4) 27 ( 3.2) 14 ( 2.2) 27 ( 36 2.3) P37 ( 3.1) 200 ( 3.4)f 245 ( 3.2) *** ( '4) 235 ( 3.4 261 46 ( 74) 29 ( 8.5) 20 ( 2.5) 23 ( 3.9) 24 ( OA 37 3.3 kV ( 4.3p 266 ( till -- ( -1 263 ( 4.4)I ( "") 270 ( 4.0 45 ( 1.4) 26 ( 1.7) 30 ( 1.8) 17 ( 1.1) 27 ( 1.8) 37 ( 251 ( 1.8) 270 ( 2.1) 200 ( 2.0) 265 ( 2.7) 249 ( 2.1) 272 ( 22 48 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1.8) 29( 2.1 254 ( 2.1) 272 ( 1.8) 263 ( 2.3) 263 ( 2.8) 253 ( 22) 275 ( 1.9) Virginia TABLE A19 I Students' Reports on the Use of a Calcuiator for Problem Solving or Tests PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAV TRIAL STATE ASSESSMENT - War Idng Problem in Class Doing Problems at Hems Takkvg guinea or Tests , Aimee Always Never Almost Always Never I Almost Always Never I Ar1.1111111. Percentage ParesOko. Ihevenie. ,Paripiesso ,i618818118 fIliFOOMM. OM 688 848 111111 IMO Ilt1091imm 1,110068,11 M11114111M0 ,!./.4*41NR1 IFY4,0110 PRI14000180 TOTAL State Nation RegaThusod Wife State Nation Mack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged sorban State Nation Wrestle rind State Nation Ottor State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 128 1.33 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A19 I Students' Reports on the Use of a Calculator (continued) i for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Working Problems In Class Doing Prabloms Taking Wins or Testi Almost Always Never Almost { Never Always Almost Always Never TOTAL Pareadaga and Pnalclowsy Parasnhap aid Prenciency State 45 ( 27 ( 1.6 ) 253 ( 1.5 273 ( 2.2 Nation 4$ ( 1.5 23 ( 1.9 254 ( 1.5) 272 ( 14 PARENTS' EDUCATION naniraduat State 51 ( 2.8) 24 ( 2.7) 233 ( 2.5) 251 ( 3.4) Nation 54 ( 3.3) 19 ( 3.8) 240 ( 2.3) ( ***) 14$ graduato Slate 50 ( 1.7) 25 ( 1.8) 244 ( 1.9) 259 ( 2.1) Nation 52 ( 2.5) 20 ( 2.4) 249 ( 1.4) 265 ( 2.7) Sw COMM* State 44 ( 2.2) 31 ( 2.5) 257 ( 2.0) 279 ( 2.4) Nation 48 ( 2.8) 26 ( 2.8) 258 ( 2.1) 272 ( 2.5) Collago gliduat. State 40 ( 1.8) 28 ( 2.4) 268 ( 2.3) 284 ( 3.2) Nation 45 ( 1.9) 25 ( 2.4) 285 ( 1.7) 244 ( 1.8) GENDER Male State 48 ( 1.7) 24 ( 12) 254 ( 2.0) 278 ( 3.3) Nation 50 ( 1.7) 20 ( 2.0) 255 ( 1.9) 275 ( 2.2) State 43 ( 1.4) 30 ( 1.7) 251 ( 1.8) 270 ( 1.8) Nation 48 ( 2.0) 26 ( 2.1) 252 ( 1.7) 289 ( 1.8) Paraentage Pam*. Parnardello Percentaat and and and and Pflaciency Proliciency Proficiency Proficiency 31 ( 1.3 264 ( 1.5 30 ( 1.3 261 ( 1.8 31 ( 3.3) 242 ( 3.4) 28 ( 3.1) 244 ( 3.8) 30 ( 2.1) 251 ( 2.2) 29 ( 1.9) 250 ( 24) 32 ( 2.1) 264 ( 2,4) 28 ( 2.0) 287 ( 3.0) 33 ( 1.7) 276 ( 2.1) 33 ( 2.0) 274 ( 2.2) 30 ( 1.4) 2437 ( 2.4) 20 ( 1.8) 264 ( 2.8) 33 ( 1.7) 261 ( 1.6) 32 ( 1.5) 259 ( 1.7) 18 ( 1.0) 1.2) 37 ( 1.5) 270 ( 3.0) 251 1.7) 27$ ( 1.5) 19 ( 0.9) 27 1.4) 30 ( 2.0) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) 14 ( 1.9) 31 ( 3.8) 28 ( 22) ( ) 232 ( 3.2) 255 ( 34) 22 ( 2.6) 32 ( 3.6) 24 ( 3.2) 244 ( 4.2) 237 ( 2.3) 251 ( 4.8) 18 1.5) 30 ( 1.8) 34 ( 1.8) 259 ( 2.7) 241 ( 2.1) 261 ( 1.8) 18 ( 1.5) 26 ( 1.8) 27 ( 2.2) 256 ( 2.4) 246 ( 2.8) 265 ( 2.0) 17 ( 1.8) 25 ( 1A) 42 ( 2.4) 260 ( 2.9) 254 ( 2.7) 279 ( 2.0) 20 ( 1.9) 26 ( 2.4) 35 ( 2.5) 293 ( 3.2) 255 ( 3.6) 275 ( 2,0) 17 ( 1.9) 23 ( 1.7) 40 ( 2.5) 285 ( 4.6) 267 ( 2.4) 288 ( 2,5) 18 ( 1.4) 28 ( 1.8) 33 ( 2.7) 278 ( 2.8) 268 ( 2.0) 285 ( 2.0) 18 ( 12) 27 ( 1.0) 33 ( 1.7) 272 ( 3.9) 252 ( 2.3) 279 ( 2.8) 19 ( 1.3) 27 ( 1.5) 26 ( 2.1) 263 ( 2.5) 256 ( 3.0) 277 ( 1.9) 16 ( 1.2) 26 ( 1.4) 41 ( 1.7) 267 ( 2.9) 250 ( 1.9) 271 ( 1.5) 18 ( 1.2) 27 ( 1.8) 33 ( 2.I) 283 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest., the value for the entire population is within * 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 Virghila TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11130 NAEP TRIAL STATE ASSESSMENT MO "Calculator-Use Group I Oilier 'Talculator-Use Grow 41111MINIUNIOW TOTAL Paroollois MO "'flaw 4$ ( 271 ( 42( 13 272 ( 1.6 and Setikkagy 52 ( 1.0) 237 1.6) 50 13) 235 14) State Nation RACE/ETNNICITY Mite State 50 ( 13) 50 ( 1.3) 27S ( 1.9) 266 ( 1.7) Nation 44 ( 14) 56 ( 1.4) 277 ( 1.7) 263 ( 1.7) Stade S ate 43(2.2) 57 ( 2.2) 248 ( 2.0) 23e ( 14) Nation 37 ( 3.4) 63 ( 3A) 243 ( 3.9) 231 ( 10) Hispanic State 37 ( 5.7) ( won ( 5.1) *** ( Nation 38 ( 4.2) 64 ( 4.2) 254 ( 44) 238 ( 3.0) Asian State 87 4.3) ***) 33 4.3) Nation 50 ( 4.6) ( owe) SO ( 4.6) ( 441 TYPE Of COMMUNITY Advantaged urban State 52 ( 24) 48 ( 2.8) 292 ( 3.9) 273 ( 4.1) Nation 50 ( 3.8) SO ( 3.8) 286 ( 4.9)1 275 ( 44)1 Disadvantaged urban State 42 ( 1.9) *** ( 56 ( 1.9) IRV* ( fel Nation 38 ( 4.2) 82 ( 4.2) 262 ( $.6)1 244 ( 3.9)! Extreme rural State 44 ( 3.2) 58 ( 3.2) 280 ( 4.7) 230 ( 2.4) Nation 39 ( $4) 61 ( 59) 289 ( 4.4)1 248 ( 4.3)1 Other State 48 ( 1.4) 52 ( 1.4) 288 ( 2.2) 255 ( 1.8) Nation 42 ( 1.4) 58 1.4) 271 ( 1.9) 255 ( 0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variajility of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r4 130 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 MEP TRIAL "Caw STATE ASSESSMENT Nigh Valcsdator-Use Grow Other later-Usew Group . _ TOTAL Pagoda.. and ativaantage aid Prolakinoi State 48 tO) 52 1.0 271 2.0) 257 131 Nation 42 13) 58 13 272 ( 1.6) 255 ( 1.5 PARENTS' EDUCATION ItS non-graduate State 28 ( 3.2) 82 ( 3.2) 247 ( 3.6) 238 ( 3.0) Nation 34 ( 3.3) 08 ( 3.3) 248 ( 4.4) 242 ( 2.4) NS graduate State 44 ( 58 ( 2.1) 259 ( 1.9 245 ( 2.2) Nation 40 ( 2.2 BO ( 2.2) 263 ( 2.0 249 ( 1.8) Some college State 49 ( 2.8) 51 ( 2.8) 273 ( 2.8) 262 ( 2.4) Nation 4S ( 2.2) 52 ( 2.2) 277 ( 2.6) 258 ( 2.5) College graduate State 53 ( 1.7) 47 ( 1.7) 258 ( 2.6) 273 ( 2.6) Nation 48 ( 2.0) 54 ( 2.0) 282 ( 2.1) 266 ( 1.9) GENpfR M. State 48 ( 1.5) 54 ( 1.5) 274 ( 2.8) 257 ( 1.9) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Fanlike State 50 ( 1.5) 50 ( 1.5) 259 ( 1.9) 257 ( 1.8) Nation 45 ( 1.8) 55 ( 1.8) 259 ( 1.7) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 Virginia TABLE A24 1 Students' Reports oh a of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ WOO NAEA TRIAL STATE ASSESSMENT Zero to TWO Typos Throe Typos For Typos TOTAL Pima lap add Ilralkieday Pandidalle and Priadancy State 1$ ( 0.9) 111 1.1) 247 1.7) 258 14) Nation 21 1.0) 30 1.0) 244 2.0) 25$ ( 1.7) RUE/ETHNICITY *bite State 14 ( 1.1) 29 ( 1.3) 252 ( 1.9) 2811( 1.8) Nation 18( 1.1) 29 ( 1.3) 251 (.2.2) Zee ( 1.5) Mack State 25 ( 1.7) 39 ( 2.2) 235 ( 2.1) 240 ( 1,5) Nation 31 ( 1.9) 38 ( 2.2) 232 ( 3.2) 233 ( 32) Hispanic State 31 ( 3.7) 29 ( 4.0) IPIP* 44k) Nation 44 ( 3.0) ( 2.4) 237 ( 3.4) 244 ( 4.3) Asian State 27 ( 5.3) 37 ( 5.2) ( Nation 28 ( 8.0) ow.) 33 ( 5.8) TYPE Of COMMUNITY Advantaged Mon State 13 ( 2.0) 27 ( 1.8) 288 ( 4.3)1 274 ( 3.1) Nation 13 ( 3.8) 144 ( 26( 2.1) Disadvantaged urban State 20 ( 4.2) 43 ( 1.8) ***) Nation 32 ( 3.9) 31 ( 2.3) 243 ( 2.9)1 247 ( 3.7)1 Extreme rural State 25( 2.3) 31 ( 3.8) 234 ( 3.9) 245 ( 2.5) Nation 17 ( 4.9) 33 ( 3.2) 253 ( 4.3)1 Mot State 18 ( 1.2) 33 ( 1.4) 244 ( 2.1) 257 ( 2.1) Nation 22 ( 1.5) 30 ( 1.3) 144 ( 2.6) 259 ( 2.2) Pareadage and PriaidencY 51 272 2.1 4 1.3 272 1.5 ( 1.5) 210 ( 2.1) 50 ( 1.5) 278 ( 1.7) 30 ( 2.4) 240 ( 2.1) 33 ( 2.4) 245 ( 3.3) 40 ( 3.5) 44+ ( 28 ( 2.3) 253 ( 2.4) 38 ( 52) Lin 38 ( 42) *is* ( 00 ( 2.2) 291 ( 4.9) 81 ( 4.9) 287 ( 3.8)1 *01 37 ( 3.8) 257 ( 4.9)1 44 ( 32) 250 ( 4.5) 50 ( 5.1) 283 ( 5.8)1 49 ( 1.7) 289 ( 1.9) 48 ( 1.5) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent ,at, 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 3 7 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A24 I Students' Reports on Types of Reading (continued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Far Typos TOTAL Pim lobos snit Wok asnoy 18 ( 0.0) 24? 1 ) 21 1.0) 244 2.0) State Nation NS non-graduate State 35 ( 3.0) 237 ( 2.7 Nation 4? ( 4.01 240 ( 3.4 KS graduate State 22 ( 1.7) 244 ( 2.8) Nation 20 ( 22) 248 ( 2.2) 5onw eoNsge State 15 ( 1.7) 258 ( 3.4) Nation 17 ( 1.5) 251 ( 4.0) Co Sege graduate State 10( 1.1) 260 ( 3.6) Nation 10 ( 0.8) 254 ( 2.8) GENDER Male State 18 ( 1.1) 247 ( 2.4) Nation 21 ( 1.5) 244 ( 2.3) Female State 1$ ( 1.2) 248 ( 2.1) Nation 22 ( 12) 244 ( 2.2) ireiresdare aid "aking, .4011411", U3I dps I ;II 30 ( 19 ( 1.3i 251 ( ( 19) 90 ( 3.1) 240 3 ( 2$ ( 31 243 ( 3.9 33 ( 1.9) 250 ( 2.1) 33 ( 19) 253 ( 2.7) 38 ( 2.4) 261 ( 2.2) 32 ( 1.7) 262 ( 2.6) 27 ( 1.4) 271 ( 2.4) 28 ( 1.8) 269 ( 2.5) c 4) 4 31 ( 1.5) 259 ( 2.1) 32 ( 1.8) 258 ( 1.7) 29 ( 1.4) 2501 ( 19) 29 ( 3A) 244 ( 3.3) 25 ( 2.8) 248 ( 3.3) 45( 2.0) 254 ( 2.0) 40 ( 1.7) 200 ( 2.1) 50 ( 2.7) 275 ( 2.1) 51 ( 2.0) 274 ( 1.9) 83 ( 1.8) 287 ( 2.8) 62 ( 2.0) 200 ( 1.8) 51 ( 1.7) 275 ( 2.7) 4$ ( IA) 273 ( 2.0) 50 ( 1.6) 271 ( 1.9) 49 ( 19) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of mterest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 3 S THE 1990 NAEP TRIAL STATE ASSESSMENT 133 Virginia TABLE A25 I Students' Reports on the Amount of Time Spent 1 Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT , One HMV or Less Two Hours Three Hours For to Five Hours Six Hours or More TOTAL 104waratlei and Prolicksey 13 ( 04) 279 ( SA) 12 ( 0.8) 209 ( 2.2) 15 ( 1.0) 284 ( 3.3) 13 ( 1.0) 276 ( 2.5) 6 ( 12) 04. ( .) 6 ( 0.8) 15 ( 4.0) 14 ( 2.4) 444.) 17 ( 3.11) ( .41 1$ ( 5.0) ( 17 ( 2.2) 301 ( 5.2)1 18 ( 1.4) , «81 ¶4 ( 4.5) 9 ( 1.2) 444 ( 444 ) 10 ( 1.5) 4** ( 14 ( 3.3) 12 ( 1.1) 273 ( 4.3) 12 ( 1.0) 258 ( 2.6) Polvddidoe Madam 21 ( 1.1 272 ( 2.4 21 ( 0.91 208 (14) 25 ( 275 ( 2 23 ( 1.2 27$ ( 2.2) 11 ( 1.3) 244 ( 4.3) 13 ( 1.7) 239 ( 7.0) 19 ( 3.3) 20 ( 2.5) 245 ( 3.2) 25 ( 4.1) 24 ( 4.2) din 27 ( 1.9) 289 ( 4.9) 25 ( 4.3) ( *41 19 ( 2.9) 17 ( 3.1) 250 ( 4.0)1 19 ( 3.0) 19 ( 2.5) *el 20 ( 1.3) 268 ( 3.0) 21 ( 1.0) 269 ( 2.3) Parosatags Preikimeat 21 Q7) 259 14) 22 OS) 265 ( 1.7) 24 ( 1.0) 272 ( 1.8) 24 ( 1.1) 272 ( 14) 13 ( 1.4) 244 ( 2.9) 17 ( 2.1) 239 ( 5.0) 15 ( 3.0) 444 ( 441 19 ( 2.4) 242 ( 5.6) 25 ( 4.6) ( *el 22 ( 3.1) 23 ( 1.7) 281 ( 4.2) 21 ( 1.8) 044 ( 13 ( 1.4) 19 ( 2.1) 255 ( 5.0)1 18 ( 24) ( 4401 23 ( 2.0) 22 ( 1.0) 267 ( 2.2) 23 ( 1.2) 255 ( 2.1) Parromedge and PnikildecY 29 ( 1.1) 257 ( 14) 28 ( 1.1) MO (1.7) 26 ( 1.4) 265 ( 14) 27 ( 1.4) 267 ( 1.7) 37 ( 2.0) 241 ( 1.9) 32 ( 1.8) 239 ( 4.0) 28 ( 42) **V 444) 31 ( 3.1) 247 ( 3.5) 2$ ( 4.0) .44 uk...1 23 ( 4.7) 44.) 23 ( 1.8) 273 ( 3.8) 30 ( 4.3) 441 23 ( 24) orip) 34 ( 2.4) 251 ( 4.7)1 32 ( 4,2) 246 4.5)1 26 (2.7) 256 ( 3.6)1 30 ( 1A) 255 ( 1.8) 27 ( 1.2) 259 ( 2.2) Paraddass and Priadkagt 0.9) 247 in 16 tO) 245 13) 10 ( 250 ( 2.5 12 ( 1.2 2S3 ( 24) 33 2.3) 240 2.4) 32 22) 233 ( 2.5) 21 ( 3.4) es* 17 ( 1.7) 236 ( 3.8) 8 ( 2.8) *** 13 ( 4.0) .11,0 *al 9 ( 1.3) 44* ( ***) ( 2.0) 31 ( 5.7) *I* ( 20 ( 3.2) 238 ( 4.5)1 22 ( 14) 241 ( 3.9) 17 ( 1.3) 248 ( 1.7) 17 ( 1.4) 246 ( 2.5) State Nation 24CE1fTHNICITY vo to :Antes Nation Black State Nation Hispanic State Nation Asian State Nation TYPE_OF COMMUNITY Advantaged urban State Nation Disadvantaged State Nation Extrema rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the 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 n 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A23 I Students' Reports on the Amount of Time Spent (ctintinued) I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11060 NAEP TRIAL STATE ASSESSMENT - Ono Hoar or Lass Two Hours Throe Hors FPur t° El" Hours _ 5131 limn' clr Moro TOTAL and Poilichsow Paressimp a an apd Iui Pralidency flarauSsis one PralkOmiar Sogralmesp awl Wallidany State OM 21 1.1 02) 1.1) let 279 3.4) 272 2.4 200 ill) 257 1.5) .247 ( 1.7 Nation 12 OA) 21 0.01 2204 ) 23 1.1) 10 ( 1.0 203 ( 2.2) 203 ( 14) 205 ( 1.7) 200 ( 1.7) 245 ( 1.7) PARENTS' goucsnes HS eon-graduate State 9 ( 1.4) ( .41 18 ( 3.1) *lb* ( -*) 20 (3.3) 32 ( 3.0) 239 ( 2.9) 20( 2.5) 4,41 Nation 12 ( 2.2) es. *** 11M1 21 ( 2.1) ***) 28 ( 24) 244 ( 3.2) 20 2.4)*) HS graduate State ( 1.1) 19 ( 22 ( 1.5) 34 ( 17 24$ ( 44 ) 255 ( 2.7) 257 2.4) 247 ( 2.0 245 2.0 Nation 8 ( 1.0) 17 ( 1.4) 23 2.0) 32 ( 2.3 10 1.0 249 ( 4.7) 257 ( 2.8) 259 ( 3.2) 253 ( 2.5) 243 ( 3.0) Sem censor State 11 ( 1.8) et,* ( Ipen 21 ( 2.1) 271 ( 3.4) 21 ( 1.9) 271 ( 3.1) 30 ( 2.5) 257 ( 3.2) 17 ( 2.1) 2$2 ( 3.1) Nation 10 ( 1.4) 44, 25 ( 2.4) 275 ( 2.7) 23 ( 2.8) 269 ( 3.5) 2$ ( 2.2) 207 ( 2.5) 14 ( 1.5) 242 ( 3.4) College graduate State 17 ( 1.5) 25 ( 1.5) 22 ( 1.3) 24 ( 1.2) 12 ( 1.2) 297 ( 3.6) 288 ( 3.0) 281 ( 2.3) 269 ( 22) 258 ( 3.1) Nation 17 ( 1.3) 22 ( 1.8) 23 ( 1.1) 25 ( 1.5) 12 ( 1.1) 282 ( 2.8) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 32) OENDER Male State 12 ( 1.0) 21 ( 1.4) 22 ( 1.3) 29 ( 1.3) 17 ( 1.5) 282 ( 4.8) 274 ( 3.4) 269 ( 2.3) 259 ( 2.2) 250 ( 2.7) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 28 ( 1.3) 17 ( 1.5) 269 ( 3.3) 287 ( 2.8) 267 ( 2.2) 262 ( 2.1) 248 ( 2.5) Amato State 14 ( 1.0) 22 ( 1.3) 21 ( 1.0) 28 ( 1,3) 15 ( 1.0) 276 ( 3.7) 270 ( 2.4) 268 ( 2.1) 256 ( 1.6) 244 ( 2.3) Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 14) 15 ( 1.2) 2119 ( 2.8) 289 ( 2.2) 264 ( 1.8) 258 ( 1.9) 241 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 140 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Virginia TABLE A26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 RAEP TRIAL STATE ASSESSMEXT , None Ons or Two Oars Three Days or More 12Thi. State Nation Bffegggffti_Cill White State Nation Mack Stets Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural' State Nation Other State Nation Peramtap and Proficiency 41 20 45 285 3$ ( 278 ( 43 ( 273 ( 4$ ( 247 ( 58 ( 240 ( 42 ( 41 ( 245 ( 85 ( 1111.* 82 ( 287 ( 40 ( 287 ( 47 ( 284 ( 44 ( ( 42 ( 254 ( 38 ( 251 ( 43 ( 257 ( 42 ( 288 ( 45 ( 265 ( Peternlep and Iftlidency Pecesidaye and Proficiency 1.1) 35 ( 24 ( 12) 287 ( 2.0 252 12 1.1) 32 ( 0.9 23 1.1 1.$) 200 ( 1.5 250 1.9) 1.8) 38 ( 1.1) 25 ( 1.2) 1.7) 274 ( 2.3) 201 ( 2.0) 1.2) 34 ( 1.2) 23 ( 12) 1.5) 272 ( 1.7) 25$ ( 2.1) 2.1) 281 1.8) 23 ( 2.0) 1.5) 241 2.4) 229 ( 2.3) 3.1) 21 1i 23 ( 2.5) 32) 240 C 4.1 224 ( 3.5) 52) 30 ( 414141. 4.2) 4141 23 ( ( 42) 0.1 3.3) 32 ( 22) 27 ( 2.8) 4.6) 250 ( 3.3) 235 ( 3.1) 4.1) 28 ( 3.8) 9 ( 2.6) Mir ( 5.8) 4.7)1 27 ( 5.3) hi 4.9) 04..) 1.8) 37 ( 2.2) 23 ( 1.9) 3.6) 288 ( 4.5) 274 ( 5.2) 2.3) 4.4)1 38 ( 279 ( 2.6) 4.5)1 15 1 ( 3.7) .44) 2.7) 24 ( .44 ( 1.6) 32 ( fid ( 4.1) GIN ) 3.3) 26 ( 1.8) 32 ( 2.7) 3.7)1 256 ( 4.2)1 238 ( 6.3)1 3.3) 381 2.2) 26 ( 2.0) 3.2) 252 ( 4.4) 237 ( 2.8) 44) 4.1)1 32 ( 264 ( 4.2) 5.8)1 25 ( 04* ( 3.9) 44 1.5) 35 ( 1.1) 23 ( 1.2) 2.1) 263 ( 2.3) 245 ( 2.0) 1.3) 32 ( 1.1) 23 ( 1.1) 2.2) 268 ( 1.9) 251 ( 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. ! 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). 141 136 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A26 I Students' Reports on the Number of Days of (cmitinued) I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY UM NAEP TRIAL None One or Two Days Throe Days or More , STATE ASSESSMENT 1 TOTAL Pagilmild and ProNcisoty 41 ( 1.1) 268 ( 1.7) 45 ( 1.1) 205 ( 1.6) 27 ( 3.2) 249 ( 3.9) 36 ( 32) 245 ( 3.0) 39 ( 2.0) 254 ( IA) 43 ( 2.1) 255 ( 2.0) 42 ( 2.4) 289 ( 2.4) 40 ( 1.8) 270 ( 3.0) 45 ( 1.8) 282 ( 2.2) 51 ( 1.6) 275 ( 2.1) 42 ( 1.3) 271 ( 2.3) 47 ( 1.6) 206 ( 2.0) 40 ( 1.6) 266 ( 1.7) 43 ( 1.4) 264 ( 2.3) 4,1. sod Polk:km 25 ( 0.8) 207 ( 2.0 32 ( 0.2 208 ( 1.5) 35 ( 3.1) 245 ( 3.3) 26 ( 3.1) 249 ( 3.3) 34 ( 2.0) 252 ( 1.8) 31 ( 1.9) 257 ( 2.6) 35 ( 2.4) 269 ( 2.6) 37 ( 1.6) 271 ( 2.5) 36 ( 1.9) 282 ( 3.3) 33 ( 1.2) 277 ( 1.7) 32 ( 1.3) 269 ( 2.4) 31 ( 1.4) 267 ( 2.1) 38 ( 1.1) 206 ( 2.2) 32 ( 1.1) 206 ( 1.7) Parandapi mod Prvidency 24 252 23( 250 38 231 237 27 245 27 249 23 261 23 253 ( 19 270 16 ( 265 ( 26 ( 253 ( 22 ( 250 ( 22 ( 251 ( 25 ( 250 ( ( 0.9) ( 1.7) 1.1) ( 1.9) ( 3.9) ( ( 33 ( 3.1 ( 1.9) 2.4) 1.9) 2.4) 2.1) 3.2) 1.6) 3.1) 1.3) 3.3) 1.3) 3.1) 1.1) 2.5) 1.4) 2.6) 1.3) 1.6) 1.3) 1.8) State Nation PANDITS' EDUCATION HS noniracksata State Nation NS graduate State Nation Sonia collega State Nation Collect* graduate State Nation GENDER Male State Nation Femal State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample, 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 13'r Virginia TABLE A27 I Students' Perception of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Shull* AWN Agree , IANNKMad. Disarm, amen, oisagrse , TOTAL State Nation WEEMCiCITY Witte State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advalleagsd urban State Nation Disadvantaged urban State Nation Wrung neat State Nation Other State Nation Sad Perventaim NW PreikesoCy 28 (1.1) 52 ( 13) 22 ( 13) 277 2.0) 273 ( 2.0) 292 ( 11 28 1.6) 48 ( 1.3) 28 ( 13 279 2.0) . 272 ( 1.6) 257 ( 2.01 30 ( 1.1) 48 ( 13) 18 247 ( 2.6) 240 ( 1.7) 232 23 32 ( 23) 52 ( 2.3) 16 1.9 247 ( 4.1) 233 ( 3.3) 227 42) 30 ( 4.5) 45 4.7) 21 it!? ... ( ...) ... ...) 24 ( 2.5) 48 2.6) 23 ( 2.1) 07 ( 5.5) 244 ( 2.2) 238 ( 3.3) 37 ( 5.6) 55 ( 5.8) ( 2.9) ( 29 ( 5.5) 53 ( 5.8) 17 ( 4.9) Oa* 11411 1110* 25 ( 1.8) 289 ( 4.7) 17 ( 3.2) .4» ( ***) 40 ( 2.9) ( 26 ( 2.9) 280 ( 5.6)1 34 ( 3.0) 250 ( 3.1) 34 ( 23) 270 ( 3.9)1 29 ( 1.0) 289 ( 2.2) 27 ('+.4) .?71 ( 2.4) 54 285 55 280 47 IMMO 48 249 48 248 49 252 50 261 46 263 ( 0111* ( 2.0) 21 ( 4.8) 272 ( 2.4) ( 4.1)1 26 am. 5.1) 13 * ) ( 2.9) 28 ( 4.8)1 240 ( 3.4) 21 ( 3.5) 247 ( 2.2) ( 4.1)1 17 ( 12) 21 ( 1.9) 251 ( 12) 25 ( 2.2) 250 ( 1.7) ( 32) ( 4.2) 3.3) ( 32) ( 45)1 ( 3.3) ( 3.1)1 ( 1A) ( 1.2) ( 1.8) ( 1A) ( 1.9) , The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. **$ Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 138 143 THE 1990 NAEP TRIAL STATE ASSESSMENT Virginia TABLE A27 I Students' Perceptions of Mathematics (continued) PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL STATE Allik$SMENT , Stroll* AOrste *Oros 1 Unnacidad, Diu9141*, Stroll* Disagree TOTAL State Nation Eammaginat HS non-graduate State Nation RS graduate State Nation Same college State Nation College graduate State Nation RENDER Male State Nation Femal State Nation Paramtage fad Onestancy 20 ( 2A) 243 ( 5.2) 20 ( 2.8) ( *01 24 ( 1.3) 254 ( 2.4) 27 ( 2.1) 262 ( 2.7) 32 ( 2.4) 270 ( 2.7) 25 ( 2.5) 274 ( 3.1) 29 ( 1.5) 250 ( 2.4) 30( 2.3) 280 ( 2.4) 30 ( 1.3) 270 ( 2.2) 28 ( 1.5) 273 ( 2.3) 28 ( 1.0) 267 ( 1.8) 26 ( 1.7) 26a ( 2.1) Percalltais at441 arelkasow 50( 1.0 1.9} 49 tO 202 1.7) 51 ( 3.4) 243 ( 2.5) 50 ( 3.3) 243 ( 2.0) 52 2.0) 251 47 2.3 2$5 ( 2.3 48 ( 2.4) 271 ( 47 ( 2.4 2e7 (1.2) 51 ( 1.7 281 ( 3.0 51 ( 1.8 274 ( 2.2 50 ( 1.7) 267 ( 2.5) 4e ( 1.2) 263 ( 2.0) 51 ( 1.4) 264 ( 1.7) 50 1.7) 262 ( 1.8) 21 0.9 295 14 24 1.2 251 1.8 23 (3.2) 30 ( 3.0) 234 ( 43) 20 ( 247 ( 1.9 20 ( 20 245 ( 2.4) 22 ( 2.3 25$ 3.4) 24 ( 1.6) 254 ( 3.2) 20 1.4) 249 2.8) 19 1.8) 240 ( 2.5) 21 ( 1.3) 254 ( 2.5) 24 ( 1.4) 251 ( 2A) 21 ( 1.2) 252 ( 2.1) 25 ( 1.9) 252 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). /44 THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing Service (Fn), Westat, and National Computer Systems (NCS). The program benefitted from the contributions of hundreds of inclividuals at the state and local levels Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Finally, and most importantly, NAEP is fgateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (C(SSO) for its considerable contributions to the program, especially its management of the National Assessment Plana* Project. That project resulted in the mathematics framework and objectives for the auessment and recommendations about reporting the results of the program. In particular, we note the significant contributions of Ramsay Selden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Phinning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza worked closely and collegially with EIS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people from school districts, colleges and universities, and State Education Agencies worked tirelessly to help EFS staff develop the assessment and a framework for interpreting the results. Under the NAEP contract to ETS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mazzeo, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspeets; and Stephen Koffier, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printin& distrthution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zaback. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the iesults of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koffier wrote the text for the report. Kent Ashworth was responsthle for coordinating the cover design and final printing of this report. Special thanks are also due to many individuals for their invaluable assistance in reviewing the reports, especially the editors who improved the text and the analysts who checked the data. US. GOVERNMENT PRINTING OFFICE : 1991 0 - 293-273 QL 3 (DK. 37) 146