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DOCUMENT RESUME ED 330 554 SE 052 064 TITLE The State of Mathematics Achievement in the District of Columbia: 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 146r.; 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 SL 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior 7igh 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 *District of Columbia; National Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (ISA); for tha first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. Trie 1990 ISA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In the District of Columbia, 2,135 students in 36 public schools were assessed. This report describes the mathematics proficiency of District of Columbia eighth-graders, compares their overall performance to students in the Northeast region of the United States and the nation (using data from the NAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopalations (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, District of Columbia students had an average proficiency of 231 compared to 2E1 nationwide. Many fewer students (District of Columbia-2%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS 11.1.11M1011.6 The STATE of Mathematics Aeleeve e t in the DISTRICT of COLUMBIA The Trial State Assessment at Grade Light THE NATION'S REPORT CARD KST COPY AVAIABLE 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 a what America's students know and can do in vanous subject areas. Since 1469. assessments have been conducted periodically in reading, mathematics. science, writing. history/geography, and other fields. By making objective information on student performance available to policymakers at the national, state, and local levels. NAEP is an integral 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 guarani:vs the privacy of individual students and their families. NAEP is a congressionally mandated projext of the National C'enter for Education Statistics, the U.S. Department of Education. The Commissioner of Education Statistics is responsible. by law, for carrying out the NAEP project through competitive awards to qualified organiutions. NAEP repons directly to the Commissioner. who is also responsible for providing continuing reviews, including validation studies and solicitation of public comment. on NAEP's conduct and usefulness. In 1988. Congress created the National Assessmen: Governing Board (NAGB) to formulate policy guidelines for NAEP. The hoard is responsible for selecting the Ribject areas to be assessed. which may include adding to those specified by Congress; identifying appropriate achievement goals for each age and grade; developing assessment objectives; developing test specifications; designing the assessment methodology; developing guidelines and suaidards for data analysis and for irporting and disseminating results; developing standards and proceaures for interstate, regional. and national comparisons; improving the form and use of thc National Assessment; and ensuring that all item.s selected for use in the National Assessment arc 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-Wari-en B.O.C.E.S. Saratoga Springs. New York Frantic Alexander Associate Superintendent California Departnient ot' Education Sacr.unento. California David P. Battini High School History Teacher Cairo-Durham High School Cain% New York Parris C. Battle Teacher Horace Mann Elementary Schooi Elonda Mary R. Blanton Attorney Cromwell, Porter. Blanton & Blanton Salisbury. North Carolina Boyd W. Boehljt Attorney Gaass. Klyn. & Bochlje Pella. Iowa Linda R. Bryant Teacher Greenway Middle School Teacher Center Pittsburgh. Pennsylvania Honorable Michael N. Castle Governor of Delaware Carvel State Office Building Wilniington, 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 S. Glode Wyoming State Board of Education Saratoga. Wyoming Christine Johnson Principal Abraham Lincoln High School Denver, Colorado John Lindley Principal South Colby ; lernentary School Pon Orchard. Washington Carl J. Maser r ;rector of Schools The Lutheran Chutch Missouri Synod International Center St. Louis. Missoun Maric D. Moskk President Southern Regional Education Board Atlanta. Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith. Arkansas Matthew W. Prophet, Jr. Superintendent Portland Oregon School District Portland, Oregon Honorable William T. Randall Commissioner of Education State Department of Education Denver. Colorado Dorothy K. Rich President Home and School Institute Special Projeets Office Washington, D.C. Honorable Richard W. Riley Attorney Nelson. Mullir.s. Riley and Scarborough Columbia, South Carolina Thomas Topuzes /wormy Law (aces of Frank Rogozienski Coronado, California Herbert J. Walberg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and Improvement (Ex-Officio) U.S. Department of Education Washington. D.C. Roy Truby Executive Director. NAGB Washington. NATIONAL CENTER FOR EDUCATION STATISTICS 1,1W The STATE of Mathematics Achievement in the DISTRICT of COLUMBIA The Trial State Assessment at grade Els lit 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 U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. Mott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports rut available directly from the pardcipating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Congress, Catalog Card Number: 91-61478 ISBN: 0-88685-14-9 The work upon which this publication is based was performed for the National Center for Education Statistics, Office of Educational &march and Improvement, by Educational Testing Service. Educational Thsting Servicz is an equal opportunity/affirmative action employer. Educational Testing Service, ETS, and are registered tradernarks of Educational Testing &MCC. Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of the District of Columbia 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in District of Columbia Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 1.evels of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 23 Race /Ethnicity 24 Type of Community 27 Parents' Education Level 29 Gender 31 Content Area Performance 13 (-; TUE 1990 NAEP TRIAL STATE ASSESSMENT In PART TWO Finding a Context fm. Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students 'faught in Mathematics? 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How is Mathematics Instruction Delivered/ 49 Availability of Rmlurces 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 U:dng 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 Summar). 66 Chapter 6. %Vito Is Teaching Eighth-Grade Mathematics' 67 Educational Backgound 68 Summary 71 Chapter 7. The Conditions &yowl School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the I lome 74 Ilours of Television Watched per Da) 75 Student Absenteeism 76 Students Perceptions of Mathematics 78 Sunman 79 PROCEDURAL APPENDIX DATA APPENDIX 97 Iv THE 3990 NAEP TRIAL STATE ASSESSMENT- District of Columbia .11=.Im.......14.101101Pne. 411M1=11IM THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congress passed new legislation fin the National Assessment of FAii..ational Progress (NAYP), which included for the first time in the project's history -- a provision authorizing voluntary state-by-state ass,: !;ments on a trial basis, in addition to continuing its primary mission, the national ass,.'...7inents that NMI/ has conducted since its inception. As a result of the legislation, the 1')90 NAFP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simuhaneously in 1990 at grades four, eight, and t welve. Fur 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 randornly 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 District of Columbia In the District of Columbia, 36 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-pude students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in the District of Columbia. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample. 1 percent of the eighth-grade publie-school population was classified as Limited English Proficient (LEP). while 5 percent had an Individualized Education Plan (1E1'). 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 aoivities and/or related services necessary to achieve the goals and objectives. Schools were pes mined 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 wid (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, 2,135 eighth-grade District of Columbia public-school students were assessed. The weighted student participation rate was 88 percent. This means that the sample of students who took part in the assessment was representative of 88 percent of the eligible eighth-grade public-school student population in the District of Columbia. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from the District of Columbia on the NAEP mathematics scale is 231. This proficiency is lower than that of students across the nation (261). Average proficiency on the NAP!' 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, \AFT used the results from the 1990 national assessments of fo,irth-, 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 NAFP scale. 9 2 THE 1990 NAEP TRIAL STA1 E. ASSESSMENT District of Columbia In the District of Columbia, 8f, percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired *ills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in the District of Columbia (2 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 arid Functions. Students in the District of Columbia performed lower than students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the District of Columbia eighth-grade student population defmed by race/ethnicity, type of community, parents' education level, end gender. In the District of Columbia: Black students had higher average mathematics proficiency than did Hispanic students. Further, about the same percentage of Black students as I lispanic students attained level 300. The results by type of community indicate that the average mathematics performance of the District of Columbia students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas or areas classified as "other". In the District of Columbia, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 13 points higher than that of students whose parents did not graduate from high school. The results by gender show that eighth-grade males in the District of Columbia had a lower ..Aerage mathematics proficiency than did eighth-grade females in the District of Columbia. In addition, there was no difference between the percentages of males and females in the District of Columbia who attained level 300. Compared to the national results, females in the District of Columbia performed lower than females across the country; males in the District of Columbia performed lower than males across the country. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 3 District of Columbia 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 the District of Columbia are as follows: Many of the students in the District of Columbia (83 percent) were in schools where mathematics was identified as a special priority. This is a greater percentage than that for the nation (63 percent). In the District of Columbia, 86 percent of the students could take an algebra COUTNC in eighth grade for high-school course placement or credit. A greater percentage of students in the District of Columbia were taking eighth-giade mathematics (57 percent) than were taking a course in pre-algebra or algebra (41 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a Mune in pre-algebra or algebra. According to their teachers. the greatest pementage of eighth-gsade students in public schools in the District of Columbia spent 15 minutes doing matheniatics 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 whon teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations, Measurement, Geometry, and Data Analysis, Statistics, and Probability had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 11 4 '11-1E 1990 NAEP TRIAL SLATE ASSESSMENT District of Columbia In the District of Columbia, 4 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 58 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 the District of Columbia, 14 percent of the students never used a calculator to work problems in class, while 55 percent almost always did. In the District of Columbia, 60 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (71 percent) had teachers who had the highest level of teaching certification available. This is similar to the figure for the natian, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in the District of Columbia 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 UT° 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 7.era to two types. Relatively few of the eighth-grade public-school students in the INstrict of Columbia (8 percent) watched one hour or less of television each day; 33 percent watched six hours or more. Average mathematics proficiency was similar for students in the District of Columbia regardless of which amount of time they spent watching television each day. 12 THE 1990 NAEP TRIAL STATE ASSESSMEN 1 5 District of Columbia THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon Califinnia Marykuid Pennsylvania Colorado Michipn Fthode Wand Connecticut Wfumesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands 13 THE 1990 NAEP TRIAL STATE ASSESSM EN T District of Columbia This report riescribes the performance of the eighth-grade public-school students in the District of Columbia 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 the District of Columbia. Part One describes the mathematics performance of the eighth-grade public-school students in the District of Columbia, the Northeast region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in the District of Columbia, the Northeast region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Eclucational 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 sun,ey instrument for the eighth grade and shall conduct a demonstration of the instrument in 1990 in States which wish to participate, with the purpose of detemining whether such an assessment yields valid, reliable State representative data. (Section 406 (i)( 2 )(C)( i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(0(2)(0W)) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance progam designed to ensure that the sessions were being conducted uniformly. Th.: results of the monitoring indicated a high degree of quality and uniformity across sessions. 4 8 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patterned after the consensus pro=ss described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that author d the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council of Chief State School Officers in mid-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,' the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national prop-am, 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 p-ade eight. An overview of the mathematics objectives is provi.ied in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-p-ade public-school students in the District of Columbia, in the Northeast region, and for the nation. Results also are provided for groups of students defined by shared characteristics raceiethnicity, type of community, parents education level, and gender. Defmitions*of the subpopulations referred to in this report are presented below. The results for the District of Columbia are based only on the students included in the Trial State Assessment Prop-am. However, the results for the nation and the region of the country arc based :sn the nationally and regionally representative samples of public-school students who were assessed in Januaiy or February as part of the 1990 national NAEP prop-am. Use of the mgional and national results from the 1990 national NAEP prop-am was necessary because the voluntary nature of the Trial State Assessment Prop-am did not guarantee representative national or retOonal results, since not every state participated in the program. National Council of Teachers of Mathematics, Curriculum and Evaluation Standardsfor School Mathrma:ic.s (Reston, VA: National Council of '1 eachers of Mathematics, 1989). 15 THE 1990 INAEP TRIAL Si ATE ASSESSMENT 9 District of Columbia 11,111,111=1".111,111% RACE/ETHNICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Prooxlural Appendix, there mus: be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, result! for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for the District of Columbia. TYPE OF COMMUNITY Results are provided for four mutually exclusive community types -- advantaged urban, disadvantaged urban, extreme rural, and other -- as defined below: Advantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are in professional or managerial positions. Disadvantaged Urban: Students in this goup live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are on welfare or are not regularly employed. Extreme Rural: Students in this group live outside metropolitan statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents 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. Thg reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDIXATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not fmish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. J6 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Colwnbia 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 Fig= 1. All 50 states and the District of Columbia are listed, with the participants in the Thal State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Wuhington, DC, metropolitan statistical a= is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURE 1 I Regions of the Country NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Mebane Minot' Alaska Delaware Arkansas Indiana Arizona District al Columbia Florida Ian Caliendo Maine Oeargla Kansas Cobrado Maryland Kesiacky Mbhigan Hawaii Massschusetts Leablamt ilkiassole Idaho New Nampehlre Mississippi Missouri Madam New Jersey North CaroUrta Nebraska Nevada New York South Carolina axe Dakota New Meiko Pennsylvania Tennessee Ohio Oklahoma abode Island Webb South Dakota Oregon Vermont West Yirgiala Wiscomin Tame Utah Washington Wyoming J. 17 THE 1990 NAEP TRIAL STATE ASSESSMENT 11 District of Columbia 4.10.01.=V Guidelines for Analysis This report &scribes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specifie 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 arc based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported arc 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 arc based on statistkal tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistically significant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) -- regardless of whether the sample means or sample proportions appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the difference is not statistically significant). the means or proportions are described as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the amirent magnitude of the difference between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular goup had higher ( or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups. the confidence interval included zero, and thus no difference could be assumed between the groups. When three or more groups arc being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendix. is 12 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 perevnt 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 stmistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statisticahy 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 pm-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 arc 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 difer 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 bc 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). 19 THE 1990 NAEP TRIAL STATE ASSESSMENT 13 District of Colombia Profile of the District of Columbia EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in the District of Columbia, the Northeast region, and the nation. This profile is based on data coDected from the students and schools participating in the Trial State Assessment. TABLE 1 I Profile of District of Columbia Eighth-Gnide I Public-School Students PERCENTAGE OF STUDENTS 1090 NAV TRIAL STATE ASSESSMENT Dhtrict ot Columbia Norlhaest , Nation DEMOGRAPHIC SUBGROUPS Raearehnieity White Black Hispanic Asian American Indian S ( OA) 94 ( tO) 10 ( OA) ( 0,2) 2 ( 30 ( 4.2) 12 4.2) 5 3 1.1 1 0.3 04) 46 0.3) 10 OA) 2 ( 05) 2 ( 0.7) T. al Community Advantaged urban 17 ( 02) 23 7.3) 10 3.3) Disadvantaged urban 97 ( 02) I 5.7) 10 ( 22) Eadreme rural 0 ( 0.0) 14 10.3) 10 ( 3.0) Other 17 ( OA) 55 11.2) 70 ( 4.4) Parents' Education Did not finish high school Graduated high school Some education after high school Graduated college Gondar Male Femait ( 0.7) 31 ( to) 17 ( 0..) 34 ( 1.2) 47 ( 0.9) 53 ( 02) 7 ( 2.2) 23 ( 3.3) 15 ( 5,0) 49 ( 5.8) 50 ( 2.1) 50 ( 2.1) 51 ( 1.1) 42 ( 1.1) The standard errors of the estimated statistics appear in parentheses. It can be said with shout 95 percent certainty that,, for wilt population of interest, the value for the entire population it 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 he true of Parents' Education, for which same students responded "I don't know.'"Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 2 0 THE 1990 NAEP TRIAL STATE ASSESSMENT Distrkt of Columbia SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile susnmatizing participation data for Distlict of Columbia schools and studgnts sampled for the 1990 Trial State Assessment. In the District of Columbia, 36 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in the District of Columbia. TABLE 2 I Profile of the Population Assessed in the I District of Columbia EkOHTWORADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution EIGHTH-GRADE PUBLIC-SCHOOL STUDENT PARTICIPATION Weighted school participation rate after substitution 1001* Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number ot substitute schools participating Total number of participating schools 315 Weighted studera participation rate after make-ups Number of students selected to participate in the assessment Number of students withdrawn from the asseesment Percentage of students who Were el Limited English Proficiency Percentage of students excluded from the assessment due to Limited English Proficiency Percentage of students who had an Individualized Education Plan Percentage of students excluded from the assessment due to Individualized Education Plan status Number of students to be assessed Number of students assessed 811% 2,SW 237 1% 4% 5% 5% 2A37 2,135 In the District of Columbia, the Triai State Assessment was based on all eligible schools. There was no sampling of schools. , 21 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 District of Columbia 0 In each saool, a random sample of students was selected to participate in the assessment. As estimated by the sample, 1 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 5 percent had an IndMdualized Education Plan (IEP). An 1EP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and 'or related services necessary to achieve the goals and objectives. Schools were permitted to exciude 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, 2,135 eighth-grade District of Columbia public-school students were assessed. The weighted student participation rate was 88 percent. This means that the sample of students who took part in the assessment was representative of 88 percent of the eligible eighth-grade public-school student population in the District of Columbia. 22 lo THE 1990 NAEP TRIAL, STATE ASSESSMLN1 District of Columbia THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in District of Columbia 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 the District of Columbia. Chapter I compares the overall mathematics performance of the students in the District of Columbia to students in the Northeast 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. 23 THE 1990 NAEP TRIAL STATE ASSESSMENT 17 Marna of Columbia CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from the District of Columbia on the NAEP mathematics scale is 231. This proficiency is lower than that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency The standard errors are presented in psrentheses. 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 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 24 13 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia .=.1.1.14Inn LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the 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. 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 Aimmarized the kinds of abilities needed to answer each ,iet 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 th2se levels are based solely on student performance on the 1990 mathematics assessment. The levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In the District of Columbia, g6 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 the District of Columbia (2 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, end 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 District of Columbia, Northeast region, and national results for each content area. Students in the District of Columbia performed lower than students in the nation in all of these five content areas. 25 THE 1990 NAEP TRIAL STATE ASSESSMENT 19 District of Columbia FIGURE 3 I Levels of Mathematics Proficiency LEVEL 200 1 Simple Additive Reasoning and Problem Solving with 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, these students can read a ruler as well as common weight and graduated scaleS. They alSo can make volume comparisons baSed on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these Students can recognize translations of word problems to numerical sentences and extend simple pattern sequences. FETE:7510 Simple Multiplicative Reasoning and Two-Step Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders ana two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to other elementary two-Step word problems. In these basic problem-solving situations, they can identify missing or extraneous information and have some knowledge of when to use computational estimation. They have a rudimentary understanding of such concepts as whole number place value, "even," "factor." and "multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis. they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and 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 District of Columbia FIGURE 3 I Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasoning and Problem Solving involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations Students at this level are able to represent, interpret, and perform simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, and recognize the equivalence between common fractions and decimals, including pictorial representations. They can interpret the meaning of percents I3ss than and greater than 100 and apply the concepts of percentages to solve simple problems. The Se 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 exponer.ts. They can recognize scientific notation on a calculator and make the trInsition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles to solve problems. They can find the circumferences of circles and the surface areas of solid figures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirect measurement. These students also can apply their knowledge of the properties of geometric figures to problems, such as determining the slope of a line. In data analysis, these students can compute means fron. 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. 27 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 District of Columbia FIGURE 4 I Levels of Eighth-Grade Public-School I Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation 0 20 40 80 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-1-1). 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 0 ( 0.1) 0 ( 0.5) 0 ( 0.2) 2 ( 0.5) 18 ( 2.7) 12 ( 1.2) 23 ( 1.0) 72 ( 4.8) 54 ( 1.6) Be ( 0,8) 99 ( 0.6) 97 ( 0.7) t. I ! ). $ IS 1 I I I I I II I .:- ; =r" 44.. , ".;;;T,` 4.104,, 4 SI . sat . Z .4 , I I. I 5 4 il ....f 4 4 4 11.1..11 4 0.1.1.1.111- CHAPTER 2 District of Columbia Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, typc of community, parents' education level, and gender. RACEfETHNICITY The Trial State Assessment results can bc compared according to the different racial/ethnic goups 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 Black and Hispanic students from the District of Columbia are presented in Figure 6. As shown in Figure 6, Black students demonstrated higher average mathematics proficiency than did Hispanic students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that about the same percentage of Black students as Hispanic students attained level 300. a 0 24 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia FIGURE 6 I Average Eighth-Grade Public-School Mathematics Proficiency by Race/Ethnicity The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by )44). 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). BEST COPY AVAILABLE e 31 THE 1990 NAEP TRIAL STATE ASSESSMENT 25 P I '.0_11. JAIL_ - 111 r 1 4 -4 41 442. t! I/1 `I' I I .,4 1 11 t4_/ I*41 NI _4 4 a 4 44 .4 .A4 a. I .11!.'1 . 41R. 1 4 44 I I 111". gi II -1 4 4IaI I 4 I -!11/4 4- -4 ii1/14, District of Colmnbia TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, disadvantaged urban arms, and areas damnified as "other". (These are the "type of commtmity" groups in the District of Columbia with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the District of Columbia shidents attending schools in advantaged urban areas was higha than that of students attending schools in disadvantaged urban areas or areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community NAEP Mathematics Scale 0 200 225 250 275 300 500 'District of Columbia Advantaged urban Disadvantaged urban Other !fa* <, - 1;;;.5. , 11=4,11:0101,.. P'",hime P-1114 . " Northeast Advantaged urban Disadvantaged urban Other Nation Advantaged urban Disadvantaged urban Other The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant &Terence between the populations. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 . , - Tr-TT a. I - i . - i- , .. IF- 4 .r r , 'IP` Immli 1 milmEn. 1 P I 0 i 4 , -111ji iTr: f 4 4 a r--.' r 4 t District of Columbia PARENTS' EDUCATION LEVEL Previous NAEP fmdings have shown that students whose parents are better educated tend to have higher mathematics proficiene3r (see Figures 10 and 11). In the District of Columbia, the average mathematics proficiency of eighth-grade public-school students having at lest one parent who graduated from college was appmximarely 13 points higher than that of stucknts who reported that neither parent graduated from high school. As shown ha Table 1 in the Introduction, a smaller percentage of students in the District of Columbia (34 percent) than in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 8 percent for the District of Columbia and 10 percent for the nation. FIGURE 10 1 Average Eighth-Grade Public-School I Mathematics Proficiency by Parents' Education District of Columbia HS non-graduate HS graduate Some college College graduate Northeast HS non-graduate HS graduate Some college College graduate Nation HS non-graduate HS graduate Some college College graduate z,74 The standard errors are prevented in parentheses. With about 95 percent certainty, the swage mathematics proficiency for each population of interest is within * 2 standard errors of the estimated mean 515 percent confidence interval, denoted by s+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. *** Stannic Mze Is insufficient to permit a reliabk estimate (fewer than 62 students). 35 THE 1990 NAEP TRIAL STATE ASSESSMENT 29 I I ,,. t , tt $ 11 I 1-1( WIELIMP 10 ILO I *tort ivol= . 1,1 4 4 VI. t-r- . a 4 a I 44 .4 1 . 1.1 IS t._11.../ 1 ' 4 ' _ . ,.. a ,,.. I J I 4 44 I ,a 1 ". . I -/ItIl.."- -11-149 ' -4 $ ?Ili -.If ..... . . 4 14 SS .4 t.,-.11# 4 4 Jo I - " a District of Columbia GENDER vliMm As shown in Figure 12, eighth-grade males in the District of Columbia had a lower average mathematics proficiency than did eighth-grade &Maks in the District of Columbia. Compared to the national =sults, females in the District of Columbia performed lower than females across the country; males in the District of Columbia performed lower than mates across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender The staadard 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 S-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in the District of Columbia who attained level 200. The percentage of females in the District of Columbia who attained level 200 was smaller than the percentage of females in the dation who attained level 200. Also, the percentage of males in the District of Columbia who attainmi level 200 was smaller than the percentage of males in the nation who attained level 200. 37 THE 1990 NAEP TRIAL STATE ASSESSMENT 31 District of Columbia FIGURE 13 I Levels of Eieitik-Grade Public-School I Mathematics Proficiency by Gender LEVEL XIO Nate Male Female Regkos Male Female Nation Male Female LEVEL 250 Slate Male Female Region Male Female Ration Mate Female LEVEL 200 Stale Male Female Region Male Female Ration Male Female 2 ( 0.7) 3 ( 0.5) 19 ( 3.3) 13 ( 3.8) 14 ( 1.7) 10 ( 1.3) 22 ( 1.6) 25 ( 1.7) 72 ( 5.8) 72 ( 4.5) 64 ( 2.0) 64 ( 1.8) 0 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percem certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1+4). If the confidence intervals for the populations do not overlap, there is statistically significant"' difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia In addition, there VMS no difference between the percentages of males and females in the District of Columbia who attained level 300. The percentage of females in the District of Columbia who attained level 300 was smaller than the percentage of females in the nation who attained level 300. Also, the percentage of males in the District of Columbia who attained level 300 was smaller than the percentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. THE 3990 NAEP TRIAL STATE ASSESSMENT 33 District of Columbia TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT , Numbers and Opera:bin 44111/1"8"1" allognift Data Anityds, Sististial, AM Probability ilifiabra and Rvittiona TOTAL Pra &kw 0.8 271 20 1.4 22107 1 0311 244 Mc lirollaioncy 11 Se 1 210 ( 0.1) 233 ( 94)1 227 ( 3S) State Region Nation MeEM.11-MX Black State Region Nation Hispanic State Region 227 2.11 221 2.47 Nation 241( 23) 231( 34) TYPE OF OOMMLEIrrY Advantaged urban State 282 ( 248 ( 3.8) Region 232 ( 4.5 1 279 ( 0.8)1 Nation 223 ( 3.2 1 241 ( 3.2)1 Disadvantaged State 233 0.8) 214 1.0) Region 251 7.2$ 238 (13.8)1 Nation 258 3.1)1 242 ( 4.9)1 Other State 240 ( 2.2) 224 ( 2.4) Region 274 ( 3.7) 26$ ( 8.5) Nation 208 ( 1.9) 257 ( 2.4) Pre Wow Pro 0414no 1,11/440*/ ne to 1 7.74 22$ 234 2.8) 215 ( 2:9) ) 243 ( 3.2) 221:41 1.2 2o2 Fif 220 ( 1.1) 244 ( 4.2)1 231 ( 3.3) 200 13 234 I It 237 s7.77 222 ( ~It *4 41r 243 3.1 257 ( 14) 258 ( 4.0) 202 275 ( 2.01, 282 ( 8.5)1 273 10.1 277 ( 5.2)1 21115 ( 4.4)1 277 48 222 ( 1.1) 213 12) 2211 ( 1.4) 242 (13,5)1 245 11.11$ 243 (128)1 248 ( 3.7)1 247 46)1 247 ( 3.2$ 230 ( 2.5) 225 ( 2.9) 237 9.1) 272 ( 3.3) 277 ( 3.9) 271 3.4) 250 ( 1.7) 261 ( 22) 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. ! 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 () 34 THE 1990 NAEP TRIAL STATE ASSESSMENT DI 'via of Columbia TABLE 3 I Eighth-Grade Public-School Mathematics (continued) Contest Area Performance hy Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 111110 MEP TRIAL STATE ASSESSIIERT , Slumbers and Opandiane Ileaaramant Onianstry Data Analysis, Stalin lea, and MOM Idly Algebra and ToTAI State Region Nation ESSEMESATM naniraiduata State Region Nation HS graduate State Region Nation Sam =Naga State Region Nation eallega wants State Region Nation frIsis State Region Nation Female State Region Nation tit es 1 34 2.21 1V4 247 ( 2.4) 237 ( 34) 242 ( 2.2) 240 ( $.1) 213( ( 3.1 241( 2.1 *211571 231 ( 2231 270 1 204 ( 23 a 22$ ( 2 2751 7.4 2277.22 2311( 1.1) 272 ( SS) 2100 ( 2.0) 270 3.1) 1.1) 200 1.4) 222 14) 271 tp 202 2.3) 220 ( 1A) 281 ( 4.3) 2531 1.49 224 205 203 1 222 2.0j 213 ( 1.1) ( 3.9) 270( 1.11) 226 ( 1.3) 280(40) 203 ( LT) t 233 27$ 3.:1 203 2.4 233 ( 207 ( SA 278 ( 2.2 221 1.7) 2274 421.1i 231 ( 1.0) 200 ( 4.1) 235 ( 1.6) :2732 I ;,,A 201 1.9) tlit74 263 ( :32 111, 2.21 24g 2731 17 232 1.1 203 4.1 .00 1A1 237 ( 1.3) 208 ( 3.7) 200 ( 1.4) The standkrd 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. mr* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 District of Columbia NE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, an( ..ndents. To gather such information, the students p sticipating 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 progams. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information on student achievement. It is important to note that the NAEP data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. 4 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 37 District of Columbia 4=11li,, Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and , classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an enormous impact on future academic achievement. Yet, as shown in Chapters 3 and 7, .ge proportions of students report having spent much more time each day watching :...evision than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instrwtional 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. 43 38 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of informatior. about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.' Ilfis chapter focuses on curricular and instructional content issues in District of Columbia 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: Many of the eighth-grade students in the District of Columbia (83 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curtis McKnight, et al., The Underachieving Curriculum. Assessing U.S. .School Mathematics from an International Perspective, A Nauonal Report on the Second International Mathematics Study (Champaign, IL Supes 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 District of Columbia ln the District of Columbia, 86 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Almost all of the students in the District of Columbia (96 percent) were taught mathematics by teachers who teach only one subject. About half (51 percent) of the students in the District of Columbia were typically taught mathonatics in a class that was grouped by mathematics ability. Ability grouping was more prevalent across the nation (63 percent). TABLE 4 Mathematics Policies and Practices in District of Columbia Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 19110 NAEP TRIAL STATE ASSESSMENT District of Columbia Northeast Nation _ Percentage of elghth-grade students in pubhc schools that identified mathematics ss receiving special emphasis In school-wide goals end objectives, Instruction, in-service training, etc. Percentage of eighth-grade public-school students who are offered 'a course in algebra for high sCh001 course placement or Credit Percentage of eighth-grade students in public schools who are taught by leachers who teach only mathematics Percentage of eighth-grade students in pubi,c schools who are assigned to a mathematics class by their ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hews of mathematics insbuction per week Percanta. PUOINellp Peresnia. 83 ( 0.3) 43 (183) 63 ( 5.0) 86 ( 0.3) 90 ( 7.3) 78 ( 4.11) 90 ( 0.1) 100 ( 0.0) 91 ( 63) 51 ( 'I.1) 71 (10.1) 63 ( 4.0) 38 ( 02) 14 ( 54) 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 populution is within * 2 standard errors of the estimate for the sample. 4 5 40 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Coismbia CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in the District of Columbia are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in the District of Cohunbia were taking eigith mathematics (57 percent) than welt taking a course in Fe-algebra or algebra (41 percent). Across she nation, 62 percent were eighth-grade mathematics and 34 percent were taking a course in pie-algebra or algebra. Students in the District of Columbia who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficitiwy than did those who woe in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pit-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Clan 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY HMO NAEP TRIAL STATE ASSESSMENT Dialect of Columbia floremat Nation What kind of mathematics class are you thing this year? Eioldh-grafie malliontatics Pro-afgabra Algebra 111110111110. and Prolklencv Paroweaso wd inalkianot 57(1.0) 2:11 217 ( 0.8) 2141 101 83.111 253(14) 411 113 Parnadage and Pralidonty 62 ( 2.1) 251 ( 14) 19 ( 1.9) 212 ( 24) 15 ( 1.2) 206 ( 24) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. I Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 46 THE 1990 NAEP TRIAL STATE ASS District of Columbia Further, from Table A5 in the Data Appendix:4 A greater percentage of females (45 percent) than males (37 percent) in the District of Columbia were enrolled in pre-algebra or algebra courses. In the District of Columbia, 41 percent of Black students and 30 percent of Hispanic students were enrolled in pre-algebra or algebra courses. Similarly, 58 percent of students attending schools in advantaged urban areas, 40 percent in schools in disadvantaged urban areas, and 34 percent in schools in areas classified as "other" were enrolled in pre-algebra or algebra courses. MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in the District of Columbia spent 15 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 1)ata Appendix): In the District of Columbia, 3 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 6 percent of the students in the District of Columbia 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 leport 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 42 THE 1990 NAEP TRIAL STATE ASSESSMENT District of COltanbia The results by race/ethnicity show that 7 parent of Black students and 1 percent of Hispanic students spent an hour or more on marthernatics homework each day. In comparison, 3 percent of Black students and 4 percent of Hispanic students !pant no time doing mathematics homework. In addition, 4 percent of students attending schools in Fidvautaged urban areas, 8 percent in schools in disadvantaged urban areas, and 5 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 0 percent of students attending schools in advantaged urban areas, 4 percent in schools in disadvantaged urban areas, and 0 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports OD the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSEDSMEXT District of CARO la northeast Nation1i About how much time do students spend on mathematics homework each day? 15 mleartos 30 minutes 45 agnates An hour sr mars Pawnee. Praildemay 3 ( OA) 44* ( «tin 44 ( 221 ( 0.1) 15 0.7) 242 ( 2.3) 0 ( 0.4) 245 ( 1.8) Perantie Perawitspr and and Pallaissey PnOdincy so.) 0 0.0) 54 (13.2) 264 ( 4.7)1 35 (12.5) 270 ( 4,1y pe 2.71 St0011) 0.e) } 43 1 24.24 2: tt 10 ( la) 272 ( 5.7)1 2/1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certaimy 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 netermination of the variability of this estimated mean proficiency. It" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 48 THE 1990 NAEP TRIAL STATE ASSESSMENT 43 District of Colombia .111.1111MIN.1.111=1....M. TABLE 7 I Students' Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIEMCY IMO NAEP TRIAL STATE ASSESSMENT District of Csiumbis Nottheast Natlan 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 ± 1 standard errors of the estimate for the sample. m Sample Size is insufficient to permit a reliable estimate (fewer than 62 students). And, avoiding to the students (Table 7 and Table A7 in the Data Appendix): In the District of Columbia, relatively few of the students (7 percent) reported thal they spent no time Nich day on mathematics homework, compared to 9 t for the nation. Moreover, 16 percent of the students in the of Columbia and 12 percent of students in the nation spent an hour or more each day on mathematics homework. The results by racejethnicity show that 16 percent of Black students and 16 peivent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 8 parent of Black students and 4 percent of Hispanic students spent no time doing mathematizs homework. 4 9 44 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia In addition, 16 percent of students attending schools in advantaged urban areas, 15 percent in srliools in disadvantaged urban areas, and :8 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 2 percent of students attending schools in advantaged urban areas, 8 percent in schools in disadvantaged urban areas, and 8 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 measurements Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. 5 National Couni:$1 of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, A: National Council of Teachers of Mathematics, 1989). 5 THE 1990 NAEP TRIAL STA1 E. ASS ESSM ENT 45 District of Columbia The responses of the assessed students' teachers to the topic emphasis questions for each content area were combined to create a new variable. For each question in a particular content area, a value of 3 was given to "heavy emphasis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content axea. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations, Measurement, Geometry, and Data Analysis, Statistics, and Probability 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 District of Columbia TABLE 8 I Teachers' Reports on the Emphasis Given to Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 18110 NAEP TRIAL STATE ASSESSMENT District et Columbia Nation Teacher "emphasis' categories by content areas PeRNMININIS IMO 4? 41 231 ( 1A) 211 8.5) '24:1= 041 Numbers and Operations Heavy eMPhesis Little or no emptunis Measurement Heavy emphasis 15(01) 32 (11.0) 1.0) 257 (114 Little or no emphasis 20 ( 01) 34 ( 5.3) 230 ( 2,S) 212 ( 4 4)1 Geometry Heavy emphasis 25 ( 0,9) 40 (11.0) 229 ( 1.9) 264 ( Little or no emphasis 10 ( 10) 240 ( SA) ( tin 01 Data Analysts, Statistii.e, and Probability Heavy emphesis 31 ( 0.1) 12 1.11 220 ( 13) } Little or no emphasis 20 ( 1.0) 238 ( 1.8) 40 (10.1) 2ni sAy Alpine and Functions Heavy emphasis 4e ( 1.0) 52 (11.5) 251 ( 1.4) 273 ( &S); Little or no emphasis 10 ( 0.15) 14 ( 0.0) 220 ( 2.0) ( 2:081 IS( 2.11 217 24) Sh3 1 44.1 14 ( 22) ( 43) 28153 44 275 ( 23) 24320 S.05.01 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 perceat certainty that, for each population of interest, the value for the entity 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 docs not allow accurate determination of the variability of this estimated mean proficiency. "0 Sample tize is insufficient to permit a reliable estimate (fewer than 62 students). 52 THE 1990 NAEP TRIAL STATE ASSESSMENT 47 District of Columbia 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: Many of the eighth-grade students in the District of Columbia (83 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In the District of Columbia, 86 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in the District of Columbia were taking eighth-grade mathematics (57 percent) than were taking a course in pre-algebra or algebra (41 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 the District of Columbia spent 15 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 cach day, while students reported either 15 or 30 minutes daily. In the District of Columbia, rrlatively few of the students (7 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 16 percent of the students in the District of Columbia and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations, Measurement, Geometry and Data Analysis, Statistics, and Probability had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 53 48 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia CHAPTER 4 vex -42C...3 EM uieisai 11111111$11111111118 SUR 1111-1011-1111 1111111MI R f 1111R11111111111111 11111111 EM 1.11011/.111111 mnessollINR11111 1811111 MOWN UNN 111BORS 11111116111111111211111 How Is Mathematics Instruction Delivered? Teachers facilitate learnin 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 or for those who come from different cultural backgrounds is an important aspect of teaching.' An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learnin activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. ° National Council of Teachers of Mathematics, Professional Standards for the Thaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991), 54 THE 1990 NAEP TRIAL STATE ASSESSMENT 49 District of Columlia From Table 9 and Table A9 in the Data Appendix: In the District of Columbia, 4 percent of the eigith-rade students had mathematics teachers who reported getting ii of the reSOUtaCts they needed, while 58 percent of the students were taught by teachers who got only mole or Nose of the resources they needed. Across the naiion, thew figuits were 13 percent and 31 percent, respectively. In the District of Columbia, 0 percent of students attending schools in advantaged urban areas, 7 percent in schools in disadvantaged urban areas, and 0 percent in schools m areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in the District of Columbia, 66 percent of students attending schools in advantaged urban areas, 58 percent in schools in disadvantaged urban aim, and 42 peivent in schools in aseas classified as "other" were in classrooms where only some or no TCSOWVC3 were available. Students whose teachers got all the resources they needed had higher =lunatics achievement levelr than those whom teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ISIS MAEP TRIAL STATE ASSESSMENT District of Columbia Northeast Nation Which of the following statements is true about how well supplied you are by your school system with the instructional Poroolop Porvadep and materials and other resources you need to teach your class? 4 Arslisimsy 227111 fa get ell the resources I need. 1 get most of the mamas most 3$t 1,21 Se (IV) #34 1.1) 212 ( 2,9)1 I get some or none of the Memos I need. 1.1) 30 (11.11 1.1) svAr. 2,1311 :..1; 450 33241 a The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent ceridanty that, for each population of interest, the value for the entim population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow aexurate determination of the variability of this estimated mew proficiency. 5 5 50 THE 1990 NAM TRIAL STATE ASSESSMENT District of Columbia P41TERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: Many of the students in the District of Columbia (82 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics problems in small groups (2 percent). The largest percentage of the students (52 percent) used objects like rulers, counting blocks, or geometric shapes less than once a wek; relatively few' never used such objects (5 percent). In the District of Columbia, 39 percent of the students were assigned problems from a mathematics textbook almost every day; 19 percent worked textbook problems about once a week or less. About half of the students (51 percent) did problems from worksheets at least several times a week; some did worksheet problems less than weekly (20 percent). Thomas Romberg, "A Common Curriculum for Mathematics." individual Differences and the Conirrwn Curriculum Eighty-xcond Yearbook ol the National Society for the Study of Education (Chicago, II.: University of Chicago Press, 1983). 5 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 51 District of Colsoftbia ,INW.=111111111/.M...110m.m. TABLE 10 I Teachers' Reports on Patterns of Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT District of Colum bia Northeast Nation About how often dO students work problems in small groups? At least once a week Less than once a weak Never About how often do students use objects like rulers, counting blocks, or geometric solids? At least once a week Less than once a week New $2 ( 03) 229 ( 0.7) 7 ( 0.8) 247 ( 3.1) 2 ( OA) ege) 44 1.4 $O ( 2110 ( 4.4) 22) 11.21 43 ( 4.1) 2:79 294 ( 23) 17 ( 63) $ ( 2.0) ".) 277 ( 544)4 Peramilage Poimmts. Powsidee aol sae Prelldsecy Prolkiancy inedwicv 43 ( 0.8) 231 ( OA) 52 ( tO) 230 ( 1.0) 275s "721 14 ( 5.5) *Mt ( 4141 714 ( RS) 200 ( 1.0) 9 ( 2.5) ( "e) 22 PZ4 ao 203 9 282 ( 3.7) (34) ( ( IA) ( 2.9) ( 5.911 The standard errors of the estimated statistics appear M parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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). 5 7 52 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Colombia TABLE 11 1 Teachers' Reports on Materials for Mathanatics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT District of Columbia Northeast Nation The standard errors of the estimated statistics appear in parentheses. lt can bt said with about 95 percent certainty that, for each population of interest, the value for tbe entire population is within ± 2 standard errors of the estimate for the sample. I interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). The 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 gudents to those of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT 53 District of Columbia COLLABORA11NG IN SMALL GROUPS In the District of Columbia, 34 percent of the students reported never working mathematics problems in small groups (see Table 12); 47 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 I Students' Reports on the Frequency of Small l Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT District et Columbia Northeast Nation Parton haps sad lasicisnag Psecsatass and Pivadancte Parcealagra sad Prailaisacv How often do you work In small groups in your mathematics class? At least once a week 47 ( 1.1) 27 ( 8.7) 29 ( 2.5) 228( 1.0) 200( 4.8), 259 ( 2.7) Less than once a week 19 ( 0.7) 22( 2.8) 28 ( 1.4) 243 ( 1.5) 271 ( 5.0) 267 ( 2.0) Never " 34 ( 12) ( 7.9) 44 ( 2A) 230 ( 0.9) '273 ( 4.6 201 ( 1A) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 perlent 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. Examining the subpopulations (Table A 12 in the Data Appendix): In the District of Columbia, 32 percent of students attending schools in advantaged urban areas, 48 percent in schools in disadvantaged urban areas, and 61 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 47 percent of Black students and 56 percent of Hispanic students worked mathematics problems in small groups at least once a week. Females were less likely than males to work mathematics problems in small groups at least once a week (45 percent and 51 percent, respectively). 59 54 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: Less than half of the students in the District of Columbia (42 percent) news used mathematical objects; 37 percent used these objects at least once a week. Mathematical objects wen used at least once a week by 40 percent of students attending schools in advantaged urban areas, 37 percent in schools in disadvantaged urban areas, and 40 percent in schools in arms classified as "other". Males were more likely than females to Use mathematical objects in their mathematics classes at least once a week (41 percent and 34 percent, respectively). In addition, 37 percent of Black students and 44 percent of Hispanic students used mghematical 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 10S9 NW TRIAL STATE ASSESSMENT District of Columbia Northeast Latian How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Paramins and lirelkiknav fentants0 and illnaciency ParoxNage and Preidancy At least once a wash 37 ( 02) 30 ( 4.3) 20 ( 1.3) 227 ( 1.1) ass ( &a) 288 ( 2.15) Lau than ones a weak 21 1.1) 30( 9.2) 31 ( 12) 2311( 22) 211 ( 3.9) 2e2 ( 1.5) 42 ( 0.2) 40 ( 4.8) 41 ( 22) 230 ( 1.0) 250 ( 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 pupulation is within ± 2 standard errors of the estimate for the sample. 6 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 55 District of Columbia MATERIALS FOR MATHEMATICS INSTRUCITON The percentagn of eighth-grade public-school students in the District of Columbia who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequercy of textbook usage (Table 14 and Table Al4 in the Data Appendix): About half of the students in the District of Columbia (53 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 46 percent of students attending schools in advantaged urban areas, 55 percent in schools in disadvantaged urban areas, and 58 percept in schools in areas classified as "other". TABLE 14 I Students' Reports on the Frequency of I Mathemslics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MAEP TRIAL STATE ASSESSMENT IMaio! ot Columbia Northeast How often do you do mathematics problems from textbooks in your mathematics class? Penceniege end Presidency and Prelicioncy Paromilay and Preildinsy Atmool ovary day 53 ( 1.1) 72 ( 5.3) 74 ( 1.9) 233 ( 1.3) 275 ( 3.7) 207 ( 12) Several limos a mak 27 ( 1.0) 14 ( 1.6) 14 ( 0.0) 232 ( 1.2) 281 ( 4.5) 252 ( 1.7) About once a *took or loss 20 ( 0.3) 14 ( 4.3) 12 ( 1.5) 222 ( 1.1) 242 ( 7.4)4 242 ( 4.5) The standard errors of the estimated statistics appear in pxrentheses. 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 variahlity of this estimated mean proficiency. 56 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia And, for the frequency of worksbeet usage (Table 15 and Table A15 in the Data Appendix): More than half of the students in the District of Columbia (58 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 53 percent of students attending schools in advantaged urban areas, 60 percent in schools in disadvantaged urban areas, and 53 percent in schools in areas classified as "other". TABLE 15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTF AND AVERAGE MATHEMATICS PROFICIENCY 1NO *AEA TRIAL STATE ASSESSMENT [ District of Columbia Mothball Nation How often do you do mathematics problems on worksheets in your mathematics class? Pontonlaso and ProNeloney Plloanlap Prolleioney Paroonlago and Proieloney At Wall users' times a week 58 ( 1.1) 44 ( 5.9) 3$ ( 2.4) 225 ( 01) 2151 ( 3.8) 253 ( 22) About axe a week 24 ( 1.1) 22 ( 1.8) 25 ( 1.2) 236 ( 1.5) 258 ( 3.6) 281 ( iA) Loss than moldy 18 ( 0.7) 34 ( 8.5) 37 ( 2.5) 241 ( 1.9) 282 ( 4.3)1 272 ( 1.9) I11111W 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 stendar 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. Table 16 compares students' and teachers' responses to questions about the patterns of clas&room instruction and materials for mathematics instruction. 62 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 District of Colombia TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS -.1I1I 1210 MEP TRIAL STATE ASSESSMENT ON Arid of Columbia Northeast7 mown 1 Patterns of classroom instruction Peresntage of students she work mathemalks problems in swell groups , At least once a week Less than once a week NOW Percentage of atudento mho dee oblects Ms Mem, counting blocks, or geometric solids At least once a week Materials for mathematics instruction Percentage of students oho use a mathemetics texthook Almost every day Several times a week About once a week or less Percentage of students vfilo uee a mathematics worksheet At least several times a week About once a week Less than weekly Perslatito 11.0010. Taselers . . Ne Vet Less than once a week 21 1.1) 0.9) 42 (0.9) 0.8) ( 0.1) ( 0.4) 4$ ( 52 ( 1.0 5 ( CS 47 ( 1.1) 112 11 ( 0.7) 17 34 ( 13) 2 21 44 f 21 ( 22 ( 2.11 30 ( 1 24 4 51 ( 79 17 f SA 44( 30 30 3.2 40 4.8 14 (5.5) 21 ( 71 (SE) 31 ( 35) 41 ( 2.5) 50 ( 4.4 144) ( 4.1 29) 8 ( 2.0} 22 1.2 EN 3.8 2.2 ( 2.1 Percentage Percenlogo Percentega Teachers thadecte Teschers Itheames Teachers 53 ( 1.1) 30 ( 1.2) 72 ( $7 9.3) 74 ( 1.9) 62 ( 3.4) 27 ( 1.0) 42 ( 1,0) 14 1.$ 31 ( 8.3) 14 ( 0.8) 31 ( 3.1) 20 ( OA) 19 ( 0.9) 14 ( 4.3 13 ( 2.8) 12 ( 1.8) 7 1.8) 58 ( 1.1) 51 ( 1.3) 44 ( 5.9) 53 (11.3) 3$ ( 2.4) 34 ( 3.8) 24 ( 1.1) 29 ( 1.1) 22 1.8) 32 ( 8.2) 25 ( 1.2) 33 ( 3.4) 18 ( 0.7) 20 ( 0.0) 34 ( 8.5) 15 ( 4.8) 37 ( 2.5) 32 ( 3.6) The standard errors of the estimated statistics appear th parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the earire population is within ± 2 standard errors of the estimate for the sample. 63 58 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible 113e of what is known about effective instructional delivery practices and resources. It appears that mathematic:, textbooks and worksheets continue to play a major role in mathematics 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: Many of the students in the District of Columbia (82 percent) worked mathematics problems in small groups at least once a week; relatively few never worked in small groups (2 percent). The largest percentage of the students (52 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (5 percent). In the District of Columbia, 39 percent of the students were assigned problems from a mathematics textbook almost every day; 19 percent worked textbook problems about once a week or less. About half of the students (51 percent) did problems from worksheets at least several times a week; some did worksheet problems less than weekly (20 percent). And, according to the students: In the District of Columbia, 34 percent of the students never worked mathematics problems in small groups; 47 percent of the students worked mathematics problems in small groups at-least once a week. less than half of the students in the District of Columbia (42 percent) never used mathematical objects; 37 percent used these objects at least once a week. About half of the students in the District of Columbia (53 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. More than half of the students in the District of Columbia (58 percent) used worksheets at least sever..1 times a week, compared to 38 percent in the nation. 6 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 District of Columbia CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks.8 The increasing availability of affordable calculators should make it more likely and atiractive 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 ProgressVathernatks Obfralves 1990 Assessment (Princeton, NJ: 1.clucauonal Testing Servia, 1988). National Council 9f Teachers of Mathematics, Curriculum and Evaluation Siandara.4 for School Mathemati(.4 (Reston, VA: National Council of Teacners of Mathematics, 1989). 65 60 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Colombia Table 17 provides a profile of District of Columbia eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 49 percent of the students in the District of Columbia had teachers who allowed calculators to be used for teats. A rata percentage of students in the District of Columbia than in the nabon had teachers who permitted unrestricted use of calculators (38 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of District of Columbia I Policies on Calculator Use PERCENTAGE OF STUDENTS 1005 NAEP TRIAL STATE ASSESSMENT District of Colonels Northeast Percentage ot eighth-grade students in public schools whose teachers permit the unresbicted ups of calculators Percentage of eighth-grade students in schools whose teachers permit the use of calculators lir tests Percentage o1 eighth-grade students In public schools whoso teachers report that studerts have access to calculators owned by the school florOMPise Peramdap ( 1.1) 20 (11.3) 1$ ( 3.4) 40 ( 0.8) 14 ( 9.2) $3 ( 44) 75 ( 0.3) 25 ( $2) ( 4.5) The standard errors of the eitintated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 ctaNiard snort of the estimate for the sample. cc THE 1990 NAEP TRIAL STATE ASSESSMENT 61 District of Columbia ME AVAILABILITY OF CALCULATORS In the District of Columbia, most students or their families (96 percent) owned calculators (Table 18); however, fewer students (74 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In the District of Columbia, 73 percent of Black students and 79 percent of Hispanic students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (72 percent and 76 percent, respectively). TABLE 18 Students' Repofts on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Dfstrict of Cohan!) la Northeast Nation Permodote and Pniacianey 231" "0.7i 4 ( 0.4) 218 ( 2.7) Permeate end Proficiency Percentote and Prolidency 98 ( 0.7) 209 ( 3.3) 2 ( 0.7) Percenteep and Madam Parma. Ond Proficiency 7 ( 04) 263 ( 1.3) 3 ( 04) 234 ( 3.8) Pcroentor end PmlicilemY Do you or your family own a calculator? Yes No Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes 74 ( 0.8) 30 ( 4.0) 49 ( 2.3) 230 ( 1.0) 258 ( 4.3) 258 ( 1.7) No 28 ( 0.8) 70 ( 4.0) 51 ( 2.3) 234 ( 1.2) 274 ( 3.8) 288 ( 1$) .1=,rmi 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 esfimate for the sample. "" Sample size is insufficient to permit a rehable estimate (fewer than 62 students). 67 62 THE 1990 NAM' TRIAL STATE ASSESSMENT District of Columbia ME USE OF CALCULATORS As previously noted, calculators cau free students from tedious computations and allow them to concentrate instead on problem solving and other important alas and content. As part of the Trial State Msessment, studeno t-ese asked how frequently (never, sometimes, almost always) they used calculatt. ar working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In the District of Columbia, 14 percent of the students never used a calculator to work problems in class, while 55 percent almost always did. Some of the students (15 percent) never used a calculator to work problems at home, compared to 32 percent who almost always used one. About one-quarter of the students (26 percent) never used a calculator to take quizzes or tests, while 32 percent almost always did. TABLE 19 I Students' Reports OD the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT District of Columbia Nation 1 How often do you use a calculator for the following tasks? 1 I Wetting problems In class Almost always Never Doing problems at home Almost always Never Tains witzss or tests Almost always Nevef Paninisol and itralkiency Parenntage Illanunispo and and Pralicidncy Prolidanay 55 ( 0.9) 40 ( 4.0) 48 ( 1.5) 224 ( 0.9) 255 ( 3.9) 254 ( 1.5) 14 ( 0.8) 39 ( 8.0) 23 ( 11) 246 ( 12) 252 ( 22) 272 ( 1.4) 32 ( 0.9) 30 ( 3.3) 30 ( 13) 22$ ( 1.3) 264 ( Le) 21 ( 1.8) 15 ( 0.8) 22 ( 2.5) 19 (..0.9) 239 ( 1.8) 275 ( 2.3) 263 ( 1.8) 32 ( tO) 23 ( 3.3) 27 ( 1.4) 225 ( 1.1) 256 ( 5.8) 253 ( 2A) 26 ( 1.0) 45 ( 5.1) 30 ( 2.0) 24$ ( 1.5) 204 ( 2.1) 274 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. Cs THE 1990 NAEP TRIAL. STATE ASSESSMENT 63 District of Columbia WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were cateporized into two groups: 9 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 R5 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. G 64 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in the Distict of Columbia were in the High group than were in the Other group. A smaller percentage of males than females were in the High group. In addition, 39 percent of Black students and 34 percent of Hispanic students were in the High group. TABLE 20 J Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL STATE ASSESSMENT District of Columbia Northeast - halloo "Calculalor-use" group High liareintags ParauddiP and and and Orsikianay Andidancy Praidsmay 39 ( 14) 240 ( 2.1) 81 ( 1.4) 228 ( DS) 44 ( 2.5) 279 ( 3.6) 58 ( 24) 283 ( 2.9) 42 ( 1.3) 272 1.8) 56 ( 1.3) 255 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE i990 NAEP TRIAL STATE ASSESSMENT 65 District of Columbia SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instructional time to teaching students how to perform routine calculations by hand. Using calculators to replace this time-consuming process would create more instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 49 percent of the students in the District of Columbia had teachers who allowed calculators to be used for tests. A greater percentage of students in the District of Columbia than in the nation had teachers who permitted unrestricted use of calculators (38 percent and 18 percent, respectively). In the District of Columbia, most students or their families (96 percent) owned calculators; however, fewer students (74 percent) had teachers who explained the use of calculators to them. In the District of Columbia, 14 percent of the students never used a calculator to work problems in class, while 55 peret-nt almost always did. Some of the students (15 percent) never used a calculator to work problems at home, compared to 32 percent who almost always used one. About one-quarter of the students (26 percent) never used a calculator to take quizzes or tests, while 32 percent almost always did. 7 1 66 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In re zent years, accountability for educational outcomes has become an issue of increasing importance to federal, state, and local governments. As part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.9 Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In the District of Columbia, 60 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of' the students (71 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 pement of the students were taught by mathematics teachers who were certified at the highest level available in their states. Almost all of the students (92 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, i991), 72 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 District of Columbia TABLE 21 I Profile of Eighth-Grade Public-School i Mathematics Teachers PERCENTAGE OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT Didrkt of Columb ia Northeast Nation Percentage of sWelaists io.. mailmmatics teachers reported having the following degrees Bachelor's degree Master's or specialist's degree Doctorate or professional degree Percentage of students shine mathematics teachers have the blowing types of leaching cartlecates that are recognized by the District of Columbia No regular certification Regular bertiticatiOn but less than the highest available Highest certitcation available (permanent or long-term) Percentage of students whose mathematics teachers have the following types of teaching certificates that are receilnisud by the District of Columbia Mathematics (middle school or secondary) Education (elementary or middle school) Other ilvrantigs Peroistaip lierceible 42 4 4.2 :11 1131 " 4.4) 2 ( 1.4) di 3:13i 1: ((All 2: I 1411 71 ( 0.7j 01 (11.5) 88 ( 4.3) 92 ( 0.7) 89 ( 3J) 84 ( 22) 8 ( 0.7) ( 3.8) 12 ( 2.8) ( 0.2) 4 ( 2.7) 4 ( 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. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instmction 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. 73 68 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia Teachers' resporses to questions concerning their undergraduate sad graduate fields of study (Table 22) show that: In the District of Columbia, 64 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergnicluate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers will the same major. Less than half of the eighth-grade public-school students in the District of Columbia (36 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 i Teachers' Reports on Their Undergraduate and I Graduate Fields of Study PERCENTAGE OF STUDENTS MO NAEP TRIM. STATE ASSESSMENT District el Columiga Northeast nation 0111111101, 1 What was your undergraduate major? Mathematics Education Other [-What was your graduate major? Mathenuitics Education Ottur or no racked* Wei study Parcentege Percentage Percentage 64 ( 1.0) 44 ( 9.2) 43 ( 3.9) 20 ( 0.6) 34 ( SA) 35 ( 3.6) 171 0.9) 22 ( 63) 22 ( 3.3) Peramtage Percentage Persentage 36 ( 1.2) 22 ( 9.7) 22 SA) 35 ( 1.3) 42 ( 92) 36 3.5) 29 ( 0.9) 37 ( 4.5) 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 District of Columbia Teachers' responses to questions concerning their in-service training for the year up to the Thal State Assessment (Table 23) show that: In the District of Columbia, 53 percent of the eighth-grade public-schoo: 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 id least that much time on similar types of in-service trainin& Relatively few of the students in the District of Columbia (5 percent) had mathematics teachers who Tent no time on in-service education devoted to mathematics or the teachmg of mathematics. Nztionally, 11 pement of the students bad mathematics teachers who spent no time on similar in-service training. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS 1000 KW MAL STATE ASSESSMENT District of Co tumble northeast Nation During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? NOM OOP to 15 hews 1$ hours or more 4451 5.3 ( "1.01 0.0) 25 ( 37 ( 36 ( 7.0) 4.1) 6.4) 11 51 IIS 2.1 4.1) 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 75 70 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with 3tudents 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 requiting special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In the District of Columbia, 60 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (71 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 the District of Columbia, 64 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Less than half of the eighth-grade public-school students in the District of Columbia (36 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Differences An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Philhps, The State of Mathematics Achievement NA EP's 1990 Assessment of the Nation and the 7).1a1 Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 7991). '7 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 71 District of Columbia .MIMMINIP1=111111. In the District of Columbia, 53 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had leachers who spent at least that much time on similar types of in-service i raining. Relatively few of the students in the District of Columbia (5 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. 77 72 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia 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 0,11 District of Columbia AMOUNT OF READING MATERIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling Students participating in the Trial State Assessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11110 NAEP TRIAL STATE ASSESSMENT District of Columbia Northeast Nation Does your family have, or receive on a regular basis, any of Me following items: more than 25 books, an encyclopedia, nestspapers, magazines? Zero to two types Tina types 34 ( 1.2) 227 ( 12) Far types 2:2S 1) .1) rarawdse Walloimity 224 111MIIMIIM Peramtige 1S 1 2.01 252 (3.11) Awswalese anatimwr ( 1.0) 244 ( 2.0) 31 ( 2.7) SO ( 10) 254 ( ZS) 25$ ( 1.7) 50 ( 3.7) 4 ( 1.3) 275 ( 4.3) 272 ( 15) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The data for the District of Columbia reveal that: Students in the District of Columbia 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 imilar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia A smaller percentage of Hispanic students had all four types of these reading materials in their homes than did Black students. A greater percentage of =dents attending schools in advantaged ur:)an areas than in disadvantaged urban areas or areas classified as "other" had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watchin8 is generally seen as detracting from time spad 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 MO KAEP TRIAL STATE ASSESSMENT Mgr lot of Cohanista Northeast j Mahon Poraestaga add Prididency Pergola. and Proficiency Percantage and PrefIdeNcy How much television do you usually watch each day? Om hour or less 12 ( 1.3) 12 ( 0.6) 238 ( 11.2) 277 ( 4A) ( 2.2) Two hours 12 ( 0.8) 21 ( 2.3) 21 ( 232 ( 2.0) 278 ( 3.1) 2ed ( 1.8) Three hews 18 ( 0.7) 23 ( 12) 22 ( 0.8) 2250 ( 1.7) 271 ( 3.5) 265 ( 1.7) Four to Rye hours 311 1.2) 2$ ( 2.0) 20 ( 1.1) 233 ( 1.2) 2OO ( 4.1) 200 ( 1.7) Slx hours or more 33 ( 1.1) 15 33) 10 ( 1.0) W ( 1.2) 2S4 ( 5.5)1 245 ( i.?) The standard errors of the estimated statistics appear in parentheses, It can be said with atwut 95 perce:it certainty that, for each population of interest., the value for the entire population is within ± 2 standard errors of the estimate for the sample. 0. ".nterpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 75 District of Columbia From Table 25 and Table A25 in the Data Appendix: In the District of Columbia, average mathematics proficiency was similar for students in the District of Columbia regardless of which amount of time they spent watching television each day. Relatively few of the eighth-grade public-school students in the District of Columbia (8 percent) watched one hour or less of television each day; 33 percent watched six hours or more. A smaller percentage of males than females tended to watch six or more hours of television daily. However, about the same percentage of males and females watched one hour or less per day. In addition, 34 percent of Black students and 26 percent of Hispanic students watched six hours or more of television each day, In comparison, 7 percent of Black students and 10 percent of Hispanic students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student 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 the District of Columbia, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in the District of Columbia (33 percent) did not miss any school days in the month prior to the assessment, while 37 percent missed three days or more. In addition, 38 percent of Black students and 37 percent of Hispanic students missed three or more days of school. S 1 76 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Cohunbio Similarly, 26 gement of students attending schools in advantaged urban areas, 40 percent in schools in disadvantaged urban areas, and 36 percent in schools in areas classified as "other" mived three or more days of school. TABLE 26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL $TA r st .:NIESSMENT Maid of Columbia Northeast Ration 33 ( 1.1) VS( 1.1) 544iNt44. Pralleliwy 43 ( 33) 273( 10) 45 ( 1.1) ( to) How many days of school did you miss last month? One or two days 30 ( 1.3) 37 ( Si) 235 ( 1.5) 271 ( 2.1) 2: 1 Throe days or more 37 ( 1.2) 21 ( 3.0) 23 ( 1.1) 224 ( 1.2) 255 ( 5.5) 250 ( 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 arors of the estimate for the sample. 82 THE 1990 NAEP TRIAL STATE ASSESSMENT 77 District of Columbia SP ;c.NTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not only to master essential skills and concepts but also to develop confidence in their mathematical abilities and to value mathematics as a discipline. 12 Students were asked if they agreed or disagreed with five statements designed to elicit their perceptions of mathematics. These included statements about: Personal experience with mathematics, including students' enjoyment of mathematics and level of confidence in their mathematics abilities: I like mathematics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for solving everyday problems. A student "pemption index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "Arongly 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 "undecides.1," "disagme," or "strongly disagree" were given a valce of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception indcx according to whether they tended to strongly agree with the statements (an index of 1), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statements (an index of 3). Table 27 provides the data for the students' attitudes toward mathematics as defined by their perception index. The following results were observed for the Distr;ct of Columbia: Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided. disagree, strongly disagree" category. Less than half of the students (38 percent) were in the "strongly agree" category (perception index of 1). This compares to 27 percent across the nation. Some of the students in the District of Columbia (14 percent), compared :o 24 percent across the nation, were in fir "undecided. disagree, or strongly disagee category (perception index of 3). " National Council of leachers of Mathematics, Curriculum and Evaluation .Standards for School Mathematics (Reston, V A: National Council of Teachers of Mathematics, 1989). 83 78 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AWRAGE MATHEMATICS PROFICIENCY MO NisEP TRIAL STATE ASSESSMENT IMAM of Columbia Northeast Nation The standard errors of the estimated statistics appear in parentheses. It can be raid 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. SUMMARY Some out-of-school factors cannot be changed, but othess 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 the District of Columbia who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency thin did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. 84 THE 1990 NAEP TRIAL STATE ASSESSMENT 79 District of Columbia Relatively few of the eighth-grade public-school students in the District of Columbia (8 percent) watched one hour or less of television each day; 33 percent watched six hours or more. Average mathematics proficiency was similar for students in the District of Columbia regardless of which amount of time they spent watching television each day. Less than half of the students in the District of Columbia (33 percent) did not miss any school days in the month prior to the assessment, while 37 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students (38 percent) were in the "strongly agree" category relating to students' perceptions of mathematics, Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. 85 80 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia ME NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, thL, mathematics framework and objectives upon which the assessment was based, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Educamal 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. 86 ME 1990 NAEP TRIAL STATE ASSESSMENT 81 District of Columbia =1=411.1....... The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first comisting of general background questions and the second consisting of mathematics background questions .- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required approximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets were spiraled or interleaved in a systematic sequence so that each booldet appeared an appropriate number of times in the sample. The students within an assessment sesion were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based conser Ais process, as described in the introduction to this report.' The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure Al). The three mathematical ability areas assessed were Conceptual Understanding, Prom:11.1ra] Knowledge, and Problem Solving (see Figure A2). Data Analy:iis and Scaks 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 students' performance on the set of mathematics items they received. IRT provides a common scale on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This conimon scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). 57 82 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia FIGURE Al I Content 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 as computational and estimation situations. Understanding numerical relationships as expressed in ratios, proportions, and percents is emphasized. Students' abilities in estimation, mental computation, use of calculators, generalization of numerical patterns, and verification of retults are alSo included. 1111=11111Ell, Measurement This content area focuses on students' ability to describe real-world objects using numbers. Students are asked to Identify attributes, Select appropriate units, apply measurement concepts, and communicate measurement-related Ideas to others. Questions are included that require an ability to read instruments using metric, customary, or nonstandard units, with emphasis on precision and arztracy. Questions requiring estimation, measurements, arid 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 schooling as well as in practical apphcations. 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. Algebra and Functions This content area is broad in scope, covering algebraic and functional concepts in more informal, exploratory ways for the eighth-grade Trial State Assessment. Proficiency in this concept area requires both manipulative facility and conceptual understanding: it involves the ability to use algebra as a means of representation and algebraic processing as a problem-solving tool. Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. BS THE 1990 NAEP TRIAL STATE ASSESSMENT 83 District of Columbia FIGURE A2 J Mathematical Abilifies The following three categories of mathematical abilities are not to be construed hierarchical. For example, problem solving involves interactions between conceptual knowledge ant. rocedural Skills, but what is considered complex problem solving at One grade level may be considered conceptual understanding or procedural knowledge at another. IConceptual Understanding Students demonstrate conCeptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts: can use and interrelate models, diagrams, and varied representations of concepts; can identify and aPPly principles: know and can apply faCts and definitions: can compare, contrast, and integrate related concepts and principles: can recognize, interpret, and apply the signs, symbols, and terms used to represent concepts: and can interpret the assumptions and relations involvinu 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 mherent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have been created as toots to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncomputational skills such as rounding and ordering. Li_koblem Solving In problem solving, students are required to use their reasoning and analytic abilities when they encounter new situations. Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, data, models, and relevant mathematics: generate, extend, and modify procedures: use reasoning (i.e., spatial, inductive, deductive, statistical, anci proportional): and judge the reasonableness and correctness of Solutions. S9 84 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia A scale ranging from 0 to 500 was created to report performance for each content area. Each content-area scale was based on the distribution of student performance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In contrast, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection Jf four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics itemr '-om the 1990 assessment that discriminated well between adjacent levels. The criteri3 selecting these "benchmark" items were as follows: To deme performance at level 200, items were chosen that werc 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. L DO THE 1990 NAEP TRIAL STATE ASSESSMENT 85 District of Columbia Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 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: cumculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Proram. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and the use of various instructional approaches. Because of the nature of the sampling for the Trial State Assessment, the responses to the mathematics teacher questionnaire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. 'Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fuul th-grade national assessment ind.ione exemplifying level 350 is from the twelfth-grade national assessment, .1. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT Dinda of Columbia FIGURE M I Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 Timis Geri/ lab e Intik Oitf J ib fflibdlibir 0 lebett 11611 7. Liles lad dem imp haws a Ow isms Was oaf thin &tome louis of balli is shown aleve. the Us swab Owe with the beg of bens thews. wtoob baa will hove the fewest balls in CD ne boo with the mots bogs CD The box with die gull M. eD The hue with tho Mien W You can't wilt EXAMPLE 2 1 MCP 01' MIT MUD AT FARAWAY MOO Um tow Wad lbws Dip 01111. tams=QupiReii 9. How away haus al mem were pidad ort Thwasisyl CD 55 CV 60 Cd 70 SO CV 90 ir+ 1 deal Lwow. Grade 4 Overall Peroentaa. Correct 73% Percentage Coifed for Anchor Level& 122 ZS) 22Q 65 91 100 Grade 4 Overall Porcontage COMIC' Percentage Correct for Anch. 212 2gg 75 91 100 Grade 8 Overall PitfeenSa. Correct 89% Percentage Correct for Anchor Levels: 222 ag 2QQ Mt 76 87 96 100 92 ME 1990 NAEP TRIAL STATE ASSESSMENT 87 District of Columbia FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 250: Simple Multiplicative Reasoning and Two-Step Problem EXAMPLE 1 7. What is the vahic of n + 5 whcn a 3 ? Answer: EXAMPLE 2 ma we Bkd Bow Ni-1111 .11'7W sbass shows dos woks 81 a mac y bab cabs. Oa atm slick Wow, asks tisk re* se &arm dm dm is the Wis. Label oak pan el dis sisal pope wish mos bait saw Did psi so the minium se Ibis *NNW 011ss 01.4 EXAMPLE 3 4. latklato *w)am b000boilo logo boon. Ex* bos holis 6 baseballs She bao 24 balk Which risasiss MilUtiCe wtU kip has hi+S out how Jassy hone ski wili ass& CD 24 CD 24 4. 4 "' 4,24+60 4124x610 CD idan't Mow . ES Grade 8 Onorall Percentege Percentage Coma MI 29 all Grade 8 Overall Percentage Percentage Correct Correct 784% for Anchor Levels: 221 OS 98 Correct 73% for Mellor toads: 242 ZtiQ 201 411Q 21 63 92 92 Grade 8 Overati Percentage Percentage Correct 262 37 71 n3 COITect 77% for Anchor Levels: 392 95 100 11113 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) 1 Loyal 300: Reasoning and Prcb lam Solving involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE 1 116. IFAieis of At foiiowies slows die Nook of 404 tm aavs ufas417 com tie Lae EXAMPLE 2 1cbs.4d MVO dm a elese bui4lisb. s ow 3 fees him is avpotsensei by s auk sadaJ i Wises how IJ the seise soda sled, boos IS fea, b4b inlaid be reswaseolad &y a i. 4041 Iwo =my Sodas kW Grade 8 Overall Percentiles Correct 80% Percentage Correct for Archar Levels: 242 2211 244 222 33 49 77 90 Grade 12 Overall Percentees Cornet 75% Percentage Correct for Anchor Levels; 224 224 224 48 79 95 Grade 8 Overall Percentage Percentage Correct Cornet 59% for Anchor Levels: & CD s ID 7 cc 242 17 224 48 222 88 222 59 MI sou ow the eatessleon ea ibia ipmeileist 0 Yes 0 14a District of Columbia FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability EXAMPLE 1 1110 Qua liar 16-17 Wet to dot Winw la pawl dol-hgotr, I. 11 AU cellar ci dot-fautts is took000d. Low ago, doa wiak a eke 100dt CD 100 CD 101 0199 0 100 40101 EXAMPLE 2 17, Evian bow you fatal yaw wawa to Noma. 16. Grade 8 Overall Percentage Correct 34% Percentige Coned for Moho; Levels: 2Q2 2211 QQ2 11Q 13 19 53 88 Grade 12 Overall Percentage Conant 49% Percentage Correct for Anchor Lewis: 222 212 Ng 2/2 22 48 90 Grade 8 Overall Percentsge Correa 15% Percentage Coned for Anchor Levels: a92 QQQ 4 28 74 Grade 12 01/117111 Pfirdinika COM& 27% Pmentage Correct for Anchor Levels: a2g 22Q QM Afil 3 22 74 90 THE 1990 MEP TRIAL STATE Ascragmbwr District of Columbia SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teathers or from a sample of schools, it is consistent with NAEP's goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state 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 measures, '.`:AEP's total gr-oup and subgroup proficiency estimates are subject to a second source of un,..ertainty, in addition to sampling error. As previously noted, each student who participated in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropriate, set of the assessment questions -- or the entire set of questions -- somewhat different estimates of total group and subgroup proficiency might have been obtained. Thus, a second source of uncertainty arises because each student was administered a subset of the total pool of questions. n 0 TIIE 1990 NAEP TRIAL STATE ASSESSMENT 91 District of Columbia In addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a background question in a certain way Or the proportion of students in certain racialiethnic groups) reflect only sampling error. NAEP uses a methodology called the jackknife procedure to estimate these standard errors. Drawing Inferences from the Results One of th- 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 ass Iciated 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 means and proportions in a manner that reflects the unczrtainty associated with ttle sample estimates. An estimated sample mean proficiency 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within 2 standard errors of the sample mean. As an example, suppose that tE average mathematics proficiency of the students in a particular state's sample were -56 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 251.6 and 258.4. Similax 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 constnicted in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. D7 92 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgxoups are defined by students' responses to background questions such as About haw much time do you usual& 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 proficiency of the gyoups 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 whok. As discussed in the previous section. each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a differeet 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 degsee of uncertainty called the standard error of the difference between the gsoups -- 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 goup mean or proportion is used, the standard error of the difference can be used to help determine whether differences between gyoups 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 thak there is insufficient evidence to claim a real difference between poups in the population. If the interval does not contain zero, the difference between groups is statistically significant (different) at the .05 level. fl THE 1990 NAEP TRIAL STATE ASSESSMENT 93 District of Columbia 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 + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference 4 ± 2 (2.9) 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' 'Throughout this report. when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower ) average proficiency than a second group. the 95 percent confidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups. the confidence interval included zero, and thus no difference could he assumed between the gmups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to he slight may represent a statistically siimificant difference in the population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. ihe procedure described above (especially the estimation of the standard error of the difference) is, in a strict sense, only appropriate when the statisties being compared come from independent samples. 1-or certain comparisons in the report, the groups wer'e not independent. In those cases, a different (and more appropriate) estimate of the sla,rdard cm -r diffcrvm was used, 94 THE 1990 ti AEP TRIAL STATE ASSESSM District of Columbia 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 made to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subjecl to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol "!". In such cases, the standard errors -- and aiiy 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 Assessmeot technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defmed by raceethnicity and type of school community, as well as by gender and parents education level. NAFP collects data for five racialiethnic subgoups (White, Black, Hispanic, Asian' Pacific Islander, and American Indian/Alaskan Native) and four types of communitiei (Advantaged Urban, Disadvantaged I :rban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency ancEor 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 .g or geater. 1 00 E 1990 \AEI) TRIAL STATE NSSESSMENT 95 District of Columbia The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or territory, divided by the standard deviation of the proficiency in the total population. If the tnte 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. Der:ribing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage Description of Text in Report , p --= 0 None 0 < p s 10 Relatively few 10 < p s 20 Some 20 < p s 30 About one-quarter 30 < p s 44 Less than half 44 < p s 55 About half 55 < p s 69 More than half 69 < p s 79 About three-quarters 79 < p s 89 Many 89 < p < 100 Almost all p = 100 All , THE 1990 NAEP TRIAL &TATE ASSESSMIAT District of Columbia THE NATION'S REPORT CARO 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. z 1r2 'DIE I 99O NAEP TRIAL STATE ASSESSMENT 97 District of Columbia TABLE A5 I Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL EOM-grads STATE ASSESSMENT Mathematics Pre-algebra Algsbra TOTAL ftwoullage Pre *law Perventage aml Proficiency Ilerseigie and Prilkienco State ( 1.0) 10( 04) 32 ( 0.9) 217 ( 0.8) 241 ( 1.7) 2$3 ( 1.4) Nation 82 ( 251 ( 2.1) 14) 19 ( 1.9) 272 C 2.4) 15( 298 ( 1.2) 2.4) RACE/ETHNICITY Slack State 57 ( 1.0) 9 ( 09) 32 ( 10) 217 ( 0.7) 237 ( 2.3) 249 ( 1.0) Nation 72 ( 4.7) 16 ( 3.0) 9 ( 2.2) 232 ( 3.4) 248 ( 8.4) IHM ( 441 Hispank State 89 ( 4.0) 11 ( 3.2) 19 ( 3.1) 210 ( 2.1) ( Nation 75 ( 4.4) 13 ( 3.9) 6 ( 14) 240 ( 2.4) TYPE OF COMMUNITY Advantaged urban State 40 ( 1.8) 20 ( 2.1) 38 ( 2.8) 235 ( 2.5) *Aro ( orin 282 ( 4.7) Nation 55 ( 269 ( 9.4) 2.5)1 22 ( 7.9) *el ( 4 el Disadvantaged titan State 58 ( 1.2) ( 0.8) 31 ( 1.1) 212 ( 0.8) 228 ( 2.0) 245 ( 1.1) Nation 6$ ( 240 ( 8.0) 4.0)1 16 ( ( 4.1) *41 14 ( 287 ( 3.3) 4.2)1 Other State 85 ( 3.0) 29 ( 24) 223 ( 1.5) 255 ( 3.2) Nation 81 ( 2.2) 20 ( 2.1) 18 ( 1.4) 251 ( 2.0) 272 ( 2.8) 294 ( 2.7) The standard errors of the enimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1C3 913 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A5 I Students' Reports on the Mathematics Class ("mtinued) i They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Eighth-grade Mathematics _ Pre-algebra de' 1 Mos MALL Peaveddslis loradalarnoll Panatella avd Prollatacy Pereadies Prolialency State 57( tO) 10 ( 0.13) °S1.4i 217 ( 0.8 ) 241 ( 1.7) 211332 Nation 62 ( 2.1) 19 ( 12) 15 ( 12) 251 ( 1.4) 272 ( 2.4) 296 ( 2A) PARENTS' EDUCATION NS nortiracktate State 88 ( 3.9) ( 22) 24 ( 3.7) 216 ( 2.3) 0114. ( Nation 77 ( 3.7) 241 ( 2.1) 13 ( 3.4) ( pi 3 ( 1.1) KS racked State 81 ( 2.4) 214 ( 1.1) 7 ( 1.1) w- ( .41 30 ( 2.0) 243 ( 1.7) Nation 70 ( 2.6) 18 ( 2.4) 8 ( 1.1) 249 ( 1.9) 280 ( 3.5) 277 ( 5.2) Some college State 53 ( 2.3) 12 ( 1.4) 34 ( 22) 224 ( 1.7) 258 ( 2.9) Nation 80 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 278 ( 2.6) 205 ( 3.2) Maori graduate State 47 ( I 9) 11 ( 12) 38 ( 1.9) Pro , 1.1) 247 ( 3.0) 281 ( 3.0) Nation ( 2.7) 21 ( 2.3) 24 ( 1.7) 29(1.5) 278 ( 2.8) 303 ( 2.3) GENDER M. State 61 ( 1.4) 9 ( 0.9) 2$ ( 1.4) 217 ( 0.9) 240 ( 3.4) 252 ( 2.4) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 25) Female State 53 ( 1,3) 10 ( 1.0) 35 ( 15) 216 ( 0.9) 241 ( 2.4) 254 ( 1.6) Nation 01 ( 2.8) 20 ( 2.3) 15 ( 1.7) 251 ( 15) 269 ( 3.0) 292 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that., for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics COMO' s" SaMple siZe is insufficient to permit a reliable estimate (fewer than 62 students). BEST COPY AVAILABLE THE 1990 NAEP TRIAL STATE ASSESSMENT 99 District of Columbia TABLE A6 Teachers' Reports on the Amount of Time Strxients Spent on Mathematics Homeworit Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT . - Nene _ 15 Minutes 30 Minutes 45 Minutes - AR NOW Of Mere TOTAL Illaraankie and Predidenty 3 ( 0.4) MIR ( ***) 03) OPP0 4.1 3 ( 0.5) .4,$) I ( 0.7) &a* aloa) 4 ( 1.1) .44 ( .41 1 ( 0.8) 0 0.0) Mit In ( 0.9) ( **) 4 ( 0.6) 0 ( 0.0) 4.* ( **4 *44 ) 1 ( 04) ( Poraintaga and Paa lidancy 44 0.9) 221 OA) 43 42) 250 ( 23) 45 ( 1.1) 222 ( 0.9) 55 ! 7.5) 232 ( 3.1) 49 ( 3.6) 213 ( 2.7) 48 ( 7.8) 245 ( 3.0)1 23 ( 0.7) 243 ( 2.7) 61 (11.3) 273 ( 47 ( 1.1) 217 ( 1.0) 41 (12.6) 236 ( 2.1)1 47 ( 3.3) 225 ( 2.5) 37 ( 4.3) 256 ( 3.1) State Nation RACEMTHNHITY Mack State Nation Hispanic State Nation TYPE OF COMMUNITy Advantaged urban State Nation Disadvantaged State Nation Other State Nation 32 OA) 2$ 11 1.7) 43 43) 200 2.0) 31 ( OA) 234 ( 13) 40 ( 5.7) 240 ( 5.3) 35 ( 3.7) 34 ( 6.8) 251 ( 4.2)1 57 ( 2.6) 267 ( 3.6) 32 ( 8.6) *441 26 ( 0.7) 228 ( 1.7) 36 ( 9.4) 23 ( 9.0)1 30 ( 2.4) 237 ( 1.3) 4. ( 5.1) 255 ( 2.5) and PraRcbaney 15 ( 0.7) 242 ( 2.3) 10 ( 11) 272 ( 5.7)I 15 ( 0.7) 240 ( 2.3) 3 ( 1-2) 4.11 10 ( 2.2) Imp* ( 13 ( 2.9) 16 ( 2.1) es* ( 5 ( 34) «pp) 15 ( 0.6) 235 ( 2.7) 12 ( 59) 16 ( 2.6) iNnit ( *ft ) 1 0 ( 2.4) 270 ( 03)1 and PrallakincY 245 f 14) vs4 5.0.14 T ( 05) 245 ( 1.9) 2 ( 0.8) ( 0.7) *es 7 ( 2.1) ( *en 4 ( 0.1 ) ( INN) 0 ( 0.0) 8 ( 0.6) 241 ( 2,4) 10 ( 6.2) 4 ( 1.1) 262 (11.6)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. 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). 100 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A6 Teachers' Reports on the Amount of Time (cmitinued) StudeLts Spent on Mathematics Homework Each My PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1STATE ASSESSME91110 SABI TRIAL NT None 15 Minutes 30 Minutes 46 Mafia An Hour or Mora TOTAL Peradaps Prididacy 3 ( 0.4) is* «on 1 03) oft. «pi 1 ( 12) 0.41 ( *kb) ( OA) woo ( 3 ( 0.7) «Imp 1 ( 0.5) *4,4 3 ( 1.2) ( 0.9) 3 ( 0.6) 4.44) 0 ( 0.3) I** 0**) 3 ( 0.5) 44 ) ( 0.3) 111** *el 2 ( OA) *** ( .") 1 ( 0.4) Peauddige "Maw 44 0.9) 221 OA 43 4.2 250 2.31 50 (4.0) 219 2.6) 49 53) 240 ( 2.6) 46 ( 13) 219 ( 14) 43 ( 52) 249 (3.1) 30 ( 23) 229 ( 22) 44 ( 5.4) 296 ( 23) 39 ( 1.6) 224 ( 1.6) 40 ( 4.7) 296 ( 23) 46 ( 1.3) 220 ( 1.0) 44 ( 44) 257 ( 2.9) 43 ( 1.3) 222 ( 1.0) 41 ( 4.4) 255 ( 2.3) lioniaboo and *Adam 3202) 236 1.7) 43 4.3) 209 2.5) 23 ( 3.9) ye, ( 40 ( 9.1) 245 ( 3.7) 30 ( 13) 227 ( 2.4) 44 ( 5.6) 259 ( 2.7) 34 ( 2.4) 240 ( 2.4) 43 ( 5.6) 270 ( 3.6) 36 ( 2.0) 251 ( 3.5) 44 ( 4.1) 277 ( 3.0) 31 ( 14) 239 ( 23) 43 ( 43) 266 ( 2.9) 93 ( 1.2) 239 ( 1.9) 43 ( 4.7) 264 ( 2,6) Pomodage Prielkancy 13 (0.7) 242 10 1.9 272 ( 6.7 18 3.2) ( 1.7) +4* ( 13 ( 1.4) 235 ( 3.0) 9 ( 3.1) ***) 17 ( 2.0) *ow ( 7 1 2.1) .44 10 ( 1.4) 247 ( 2.6) 11 ( 2.3) 287 ( 6,1)1 15 ( 0.9) 240 ( 2.9) 9 ( 1.9) 273 ( 7.3)1 15 ( 1.1) 244 33) 11 2.0) 272 5.7)1 State Nation PARENTS' EDUCATION 116 non-graduate State Nation Ns graduate State Nation Some college State Nation COMP,* graduate State Nation GENDER Male State Nation Female State Nation lismage ad linaciandfi 24:1 1.411 2711 5 ( 0.5) .41 5 ( 1.3) 279 ( 7.1), 7 0.7) 248 3.0) 4 0.9) The standard errors of the estimated stAtistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, ,he 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). 106 THE 1990 NAEP TRIAL STATE ASSESSMENT 101 District of Columbia TABLE A7 I Students' Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT 13 Min 30 MInutas 46 Mutes ade: An Noir or More TOTAL. Paccionsp and Pralicianny Peroantage Paroamtaga and and Prolkinniy Prendancy Parcentags and Pralkdoney Perosninp and lindidency State ( 0.8) 25 ( 33 ( 1.0) 10 ( 0.7) 18 ( 0.7) 220 ( 2.2) 232 ( 1.6 235t 1.3) 231 ( 1A) 227 ( 1.8) Nation 0 ( 0.8) 31 ( 2.0 12 ( 1.2) IS ( 1.0) 12 ( 1.1) 251 ( 2.8) 264 ( 1.0) 203 ( 1.9) 280 ( 1A) 258 ( 9.1) MOIMUNS_ITY Black State 3 0.8) 24 ( 1.1) 33 ( 1.1) 19 ( 0.7) 18 ( OA 220 ( 2.3) 230 ( 1.4) 233 ( 1.2) 230 ( 1.3) 228 ( 1.8 Nation 7 ( 1.5) so. 26 ( 2.5) 241 ( 3.8) 33 ( 2.7) 237 ( 3.5) 18 ( 2.3) 240 ( 3.0) 18 ( 1.9 232 ( 3.7) Hispanic State 4 ( 1.8) 444 ( 25 ( 2.8) 444 ( 44) 92 ( 3.4) 23 ( 2.7) op* ( *el 18 ( 2A Nation 12 ( 1.8) 27 ( 3.0) 30 ( 2.8) 17 ( 2.1) 14 ( 1.7) *41t 44.) 248 ( 3.8) 248 ( 3.4) 241 ( 4.3) TYPE OF COMMUNITY Advantaged urban State 2 ( 1.5) 444 ( *MI 23 ( 2.1) 283 ( 0.7) 37 ( 2.7) 264 ( 3.3) 22 ( 1.5) 250 ( 3.4) 10 ( 2.0) ( .41 Nation 8 ( 2.5) et. ( *) 41 (12.5) 278 ( 3.0)l 31 ( SA) 280 ( 4.8)1 12 ( 3.3) ( 3.4) Dioadvantagad urban state 8 ( 0.7) 25 ( 1.1) 83 ( 1.1) 20 ( 0.9) 15 ( 1.0) 219 ( 2.5) 224 ( 1 A) 227 ( 1.4) 225 ( 1.7) 221 ( 2.2) Nation 12 ( 3.7) 24 ( 3.3) 31 ( 3.0) 20 ( 1.9) 14 ( 2.2) 253 ( 4.9)I 247 ( 4.7)1 250 ( 4.8)I Other State 8 ( 1.3) 28 ( 3.0) 31 ( 3.2) 18 ( 1.?) 18 ( 1.5) 444 ( 441 235 ( 2.6) 236 ( 3.2) ( irom. Nation ( 1.0) 30 ( 1.$) 32 ( 1.3) 15 ( 1.1) 13 ( 1.1) 250 ( 3.3) 203 ( 2.3) 204 ( 2.3) 267 ( 2.1) 258 ( 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 t 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficier.cy. *** Sample size is insufficient topermit a reliable estimate (fewer than 62 students). 102 TtlE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia 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 MO NAEP TRIAL STATE ASSESSMENT None - 15 Minutes 30 II limas* 45 Mimi*" An I4our or More TOTAL Slate Nation PARENTS' pUCATION KS non-graduate State Nation HS graduate State Nation Some coNege State Nation Malawi graduate State Nation GENDER Maio State Nation Fmale State Nation Parseakap Nom lap Pweentspa Ponied.. listamlap imd NW ant mod and 1100111dency linliklincy Pry alum Prelidem loralkasecw 22U / 211 $ ( 06) 251(24) 11 ( 2.8) dis .41 17 ( 3.0) 9 ( 1.1) 4.**) 10 ( 1.7) 246 ( 4.2) 5 ( 11) ( .41 *** ( 15 ( 1.0) ( *el 7 ( 0.9) 285 ( 35) 9 ( 1.0) 221 ( 2.9) 11 ( 1.1) I2$5 ( 3.9) 4 ( 0.7) 220 ( 3.7) 7 ( 0,9) 248 ( 4.1) 251 S3 ( 1.0) 19 ( 0.7) 10 ( 07) 232 235 ( 1.3) 231 ( 1.5) 227 ( 1.11) 31 ( 2.0) 32 ( 12) 10 ( 41.0) 12 ( 1.1) 264 ( 1.6) 205 ( 1.9) 200 ( 1.9) 25$ ( 6.1) 21 ( 3.6) eird. 3.4) 17 ( 22) 17 ( el* ( 3.1) 0011) 20 ( 3.3) 34 ( 4.4) 12 2.5) 10 ( 22) 246 ( 4.0) 248 ( 25) **IP ( del 27 ( 14) 35 ( 1.9) 16 ( 1.7) 13 ( 14) 225 ( 22) 22$ ( 1.7) 223 ( 3.1) 218 ( 34) 33 ( 2.2) 31 ( 1.9) 115 ( 1.4) 11 ( 1.5) 259 ( 3.2) 254 ( 2.4) 250 ( 2,8) 244 ( 3.4) 27 ( 2.4) 34 ( 3.2) 20 ( 2.3) 15 ( 2.2) 237 ( 3.1) 240 ( 3.2) 235 ( 3.4) 30 ( 2.7) 30 ( 2.1) 14 ( 1.8) 11 ( 15) 200 ( 3.0) 208 ( 2.8) 274 ( 3.5) ( 20 ( 1.5) 33 ( 15) 22 ( 1.4) 19 ( 14) 241 ( 3.9) 245 ( 2.4) 238 ( 3.0) 231 ( 2.7) 31 ( 3.4) 31 ( 2.0) 10 ( 12) 14 ( 14) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 25) 20 ( 1,3) 33( 1.7) 19 ( 1.3) 14 ( 12) 232 ( 1.9) 233 ( 1.9) 227 ( 2.2) 224 ( 25) 34 ( 24) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 204 ( 25) 263 ( 2.4) 205 ( 3.0) 258 ( 4,1) 24 ( 1.3) 33 ( 14) 20 ( 1.0) 17 ( 1.1) 231 ( 2.5) 230 ( 1.8) 235 ( 1.9) 229 ( 2.5) 28 ( 2-0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 263 ( 1.5) 200 ( 2.0) 2e1 ( 24) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 103 District of Columbia TABLE A8 I Teachers' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Nutters and Operations M.aswums Geometry Heavy Emphasis Late or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation RACE/ETHNICITY Black State Nation Hispanic State Nation TYPE Of COMMUNITY Advmtaged urban State Nation Disadvantaged irban State Nation Other State Nation Parouniese Pereentese Perantase Peromitese Permits. Pommies, and and and and and and Prolicionay Preiciency Pralkienlf Mildew draildenoy Preikeeney 471 1.0) 231 ( 1.4 264 2 217 1.8 236 2 229 1.8 246 49( 3.8 15 2.i 17 5.0 33 4.0 28 3.8 21 3.3 260 ( 1.8 287 ( 3.4 250 ( 5.6 V9 ( 4.0) MO ( 3.2 164 ( 54 48 ( 1.1) 231 ( 1.8) 54 ( 7.9) 243 ( 4.3) 48 ( 4.2) 223 ( 3.7) 47 ( 8.7) 248 ( 4.8) 27 ( 1.0) 260 ( 3.3) 28 (13.0) 52 ( 1.2) 228 ( 1.6) 48 (12.1) 255 ( 8.3$ 59 ( 2.4) 238 ( 3.3) 52 ( 4.1) 280 ( 2.3) 14 ( 0.8) 254 ( 2.1) 11 ( 3.3) 13 ( 2.3) . 8 ( 2.2) /pr. ( **al 35 ( 2.9) 285 ( 5.0) 16 ( 4.2) ( 444) 9 ( 0.7) 252 ( 2.9) ***) 10 ( 14) 18 ( 2.7) 288 ( 3.8) 25 ( 1.0) 216 ( 2.0) 25 ( 7.4) 228 ( 2.8)I 31 4.0) ( eel 23 ( 4.1) *M ( *el 34 ( 2.0) 242 ( 3.6) ( 7.0) 24 ( 1.0) 206 ( 2.3) 39 (10.3) 238 ( 8.4$ 16 ( 1.8) *IN ( 16 ( 3.9) 253 ( 7.1)4 13 ( 1.0) 226 ( 3.0) 23 ( 5.7) ( 16 ( 2.6) 414., 34 ( 5.8) 255 ( 4.4)1 22 ( 3.1) 40 ( 8.5)) 21 ( 1.0) 220 ( 2.3) 21 ( 8.5) ( r* ) 17 ( 3.0) *al 34 ( 5.3) 270 ( 44) 25 ( 1.2) 229 ( 2.4) 33 ( 79) 242 ( 27 3.6) 27 ( 6.8) 100* 111141) 40 ( 2.0) 256 ( 3.2) 38 ( 9.4) 267 ( 4.9)i 22 ( 1.3) 221 ( 2.2) 33 (11.8) 248 ( 8.2)! 24 ( 2.0) 226 ( 3.7) 28 ( 4.8) 260 ( 3.9) 18 ( 1.1) 238 ( 2.0) 24 ( 7.3) 233 ( 4.7$ 12 ( 1.9) 4pon 16 ( 5.5) *on 19 ( 3.0) *0* ( 13 ( 3.2) 22 ( 1A) 232 ( 2.3) 16 ( 7.8) is ( 2.8) ( 441 24 ( 4.3) 285 ( 5.7) The standard errors of the eFtimated 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 litcause the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). .1 c c . ) t 104 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE AS I Teachers' Reports on the Emphasis Given to (continued) i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT limbers and Operations M.atsms Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Pareintimp ime Prolkiency neramemp End Pro Waxy Pumentage and Profit Ism Perosedapp and Praciency Persembes and Proildwat Ponmniap and Pro Mow State 47 ( 0.3) 0.6) 20( 25( 1.0) 231 ( 1.4 264 2.9) 217 1.8) 236 ( 2.0 229 1.0 244 3.4) Nation 49 ( 3.3 15 2.1) 17 3.0) 33( 4.0 2$ 3.3 21 3.3) 240 ( 1.3 237 ( 3.4) 250 ( 5.6) 272 ( 4.0 240 3.2 264 5.4) PARENTS' EDUCATION NS non-gracktate State 44 4.7) v.* ( 23 ( 3-3) 4.4.) 21 (( 42) 28 ( 9.7) 17 ( 2.8) 20 ( 3.4) Nation OD ( 6.9) 251 ( 14) 7 ( 2.3) *el «F. ( 25 ( ( 5.3) 32 (( 6.3) 141 20 ( 8.7) ( *el HS graduate State 49 ( 1.7) 11 ( 0.9) 25 ( 1.7) 17 ( 1.4) 23 ( 1.7) le ( 1.5) 226 ( 1.6) 253 ( 3.7) 213 ( 3.2) 223 ( 4.9) 227 ( 4.4) 232 ( 3.5) Nation 55 ( 4.8) 259 ( 2.9) 11 ( 2.8) 0*i 17 ( 251 ( 3.9) 8.1)1 27 ( 253 ( 5.0) 4.7)1 27 ( 255 ( 4.5) 4.2) 24 ( 248 ( 5.1) 4.8)1 Santa coftge State 42 ( 2.5) 240 ( 2.5) 18 ( 259 ( 2.3) 4.3) 24 ( 221 ( 24) 5.0) 20 ( 235 ( 2.0) 6.9) 28 ( 232 ( 2.1) 42) 18 ( 2.0) ( *dm ) Nation 47 ( 4.4) 265 ( 2.8) 17 ( 264 ( 13) 4.1)1 12 ( *v. 2.7) 39 ( 279 ( 5,5) 4.5) 27 ( 262 ( 5.0) 4.8)1 23 ( 4.1) 270 ( 4.7) College graduat State 49 ( 2.5) 20 ( 2.0) 28 ( 1.9) 21 ( 2.2) 28 ( 1.9) 23 ( 2.3) 234 ( 2.2) 276 ( 4.8) 223 ( 2.5) 253 ( 7.0) 235 ( 3.0) 281 ( 6.2) Nation 44 ( 4.1) 19 ( 2.4) 18 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 289 ( 2.8) 298 ( 3.4) 284 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 6.4) GENDER Maga State 50 ( 1.7) 13( 1.1) 26 ( 1.4) 18 ( 1.4) 25 ( 1.4) 18 ( 1.5) 229 ( 1.9) 263 ( 4.8) 218 ( 2.8) 239 ( 4.4) 226 ( 2.4) 241 ( 4.8) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( D.9) 29 ( 4.1) 20 ( 3.3) 261 ( 2.5) 287 ( 44) 258 ( 8.7) 275 ( 4.8) 203 ( 3.8) 206 ( 6.5) Female State 45 ( 1.2) 18 ( 1.0) 24 ( 1.3) 21 ( 1.1) 26 ( 1.4) 20 ( 1.2) 233 ( 1.8) 264 ( 3.0) 218 ( 3.1) 234 ( 3.9) 233 ( 2.8) 249 ( 3.5) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 293 ( 2.0) 286 ( 3.3) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 263 ( 5.0) The shandard 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 reliable estimate (fewer than 62 students). 1! 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 105 District of Columbia TABLE As Teachers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11Ie0 NAEP TRIAL STATE ASSESSMENT Data Analysts, Statistics, and Probability Algobra and Rinctkes F Little or Het No , Emphasis Emphasis Heavy Emphasis Little or No Emphasis TOTAL Pornostago and Proilcion-y 31 ( 0,8) 220 ( 12) 14 ( 22) 209 ( 4.3) 33 ( 0.8) 221 ( 2.0) 14 ( 3.4) 44,) 23 ( 3.3) 414. ***) 15 ( 4.1) ( ***) 31 ( 1.6) 250 ( 34) 37 ( 0.9) 214 ( 2.1) 19 ( 9.4) 44* 18 ( 2.3) *.t. 4-**) 15 ( 22) 267 ( 4.7) 1Porocalap and Prolidoncy 28 ( 286 53 261 28 ( 233 ( 53 225 26 (( 56 ( 248 37 ( 200 65 (19.4) 284 ( 27 ( 228 ( 34 (11.4) 236 ( 23 ( ( 260 ( 1.0) ( 1.6) ( 4.4) ( 22) 1.2) 1.9) ( 6.2) ( 4.3) 3.3) *al 6.3) ( 4.4) 24) ( 3.1) 7,4)1 1,4) 2.3) 8.2)! 22)) 5.2) 3.4) Panconap and Prolifleacy 48 ( 1.0) 251 ( 14) 49 ( 3.8) 2T5 ( 2.5) 48 ( 1.2) 249 ( 1.3) 39 ( 7.1) 253 ( 6.3) 30 ( 4.3) 644 ( «fry) 48 ( 5.9) 257 ( 4.0)1 57 ( 2.3) 278 ( 3.7) 41 ( 8.9) aS ( 7.9)1 43 ( 1.3) 244 ( 1.6) 53 (11.8) 254 ( 6.3)1 45 ( 3.5) 249 ( 4.1) 47 ( 4.3) 270 ( 2.8) Parconicgo and Prolifioacy 10 ( 0.5) 220 ( 2.0) 20 ( 3.0) 243 ( 3.0) 10 ( 0.7) 221 ( 2.0) 27 ( 6.9) 226 ( 2.2)1 11 ( 2.6) «iv ( 18 ( 4.2) (..4) 0 ( 0.0) ( «HI 18 ( 5.3) .4.9) 12 ( 0.7) 217 ( 2.4) 20 ( 9.4) 6.4 ( 7 ( 3.0) RIM *4.1 17 ( S.3) 245 ( 4.4)1 State Nation RACEIETH N !CITY Black State Nation H spanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation D I udvanta god urban 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_ Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 i 106 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE AS I Teachers' Reports on the Emphasis Given To (wiltinued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Data Analysts, Statistics, and Probability Ngebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Plinnallas and Poilkionly " 1.7"i2$ 220 14 ( 2.2) 202 ( 4.3) 28 ( 4.9) Poosida and firalkdowy ( 1.0) 233 ( 1.8) 53 ( 44) 211 ( 2.9) 33 (3.9) *gm del loaraindala and Ondiakacy 46 ( 1.0) 23i ( 14) 46 ( L5) 275 ( 2.5) 39 ( 3.8)) Perandais and Prallialancy 10 ( 22o f 2.0 20 243 ( 3.0) 12 ( 2.2) State Nation PARENTS' EDUCATION noniraduato State Nation 404 ( 53 ( 7.1) 240 ( 8.2) 2Sf 52) «E 29 .4. 8.9) +.1 NS graduate State 36 ( 2.0) 24 ( 1.7) ( 2.2) 11 ( 0.9) 213 ( 3.7) 221 ( 4.0) 241 ( 2.4) 215 ( 2.7) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 281 ( 3.0)1 247 ( 2.9) ( 3.5) 239 ( 3.4) Sarno caliege State 29 ( 231 ( 2.0) 4.2) 31 ( 250 ( 2.8) 5.5) 53 ( 254 ( 2.5) 2.1) 9 (( 1.9) *41 Nation 13 ( 2.5) 57 ( 5.3) 48 ( 4.8) 17 ( 3.1) 270 ( 3.7) 278 ( 3.0) *** Wiese graduat State 30 ( 229 ( 1.9) 3.3) 30 ( 240 ( 2,0) 3.1) 50 ( 2.0) 200(2.9) 7 ( .44 1.3) Nation 15 ( 2.4) 53 ( 4A) 50 ( 3.9) 18 ( 2.4) 282 ( 4.5) 275 ( 3.8) 288 ( 3.0) 249 ( 4.0) GENDER Mak, State 31 ( 1.4) 20 ( 1.5) 42 ( 1.8) 11 ( 1.0) 219 ( 2.4) 238 ( 3.7) 247 ( 2.5) 218 ( 2.8) Nation 13 ( 22) 54 ( 4.7) 44 ( 4.1) 22 ( 3.8) 275 ( 5.8) 200 (3.5) 278 ( 3.2) 243 ( 3.0) Female State 30( 1.1) 30 12) 49 ( 1.3) 9 ( 1.0) 220 ( 2.0) 237 ( 2.7) 254 ( 1.7) 221 ( 3.0) Nation 10 ( 2.4) 53 ( 4.5) 4$ ( 3.8) 1$ ( 2.9) 283 ( 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. 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). 112 THE 1990 NALP TRIAL STATE ASSESSMENT 107 District of Columbia TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL I Get Ail the Resources I 1 Oat Most of th I I Get Some or None of STATE ASSESSUENT Need Resources I Need the Resources I Need TOTAL end Prolkieng, lorallekincy Pereeidass ass. State 033.11 Se ( 1.2) 56 i.i) 2444 234 ( 1.1) 226 1.1} Nation 13 ( 2.4) 50 ( 4A) 31 ( 42) 265 ( 4.2) 205 ( 2.0) 261 ( 2.0) RAM/ETHNICITY Black State S ( 0.4) S7 ( 1.4) 58 ( 13) 243 ( 3.2) 233 ( 1.0) 227 (0.8) Nation 15 ( 4.2) S2 ( 6.6) 33 (72) 241 ( 5.3)1 242 ( 2.4) 230 (4.9) Hispanic State ( .44 ( 0.6) 461 39 ( 3.4) 229 ( 4.0) 80 ( 3.5) 213 ( 2.7) Nation 23 ( 7.6) 44 ( 4.9) 34 ( 7,7) 246 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 TYPE Of CONDADM Advantaged urban Mate 0 ( .4. ( 0.0) ...) 34 ( 1.7) 254 ( 11) 86 ( 1.7) 282 ( 3.5) Nation 36 ( 272 ( 9.2) 6.5)1 59 ( 6.9) 266 ( 1.3)1 3 ( 3.1) ( tin Disadvantaged urban State 7 ( 0.5) 35 ( 14) 58 ( 1.3) 244 ( 3.1) 228 ( 1.2) 219 ( 1.0) Nation 10 ( ( 64) 4.1 40 (13.1) 251 ( 5.4)1 SO (14.5) 253 ( 5.5)1 Other State 0 ( 44. ( 0.0) 4rfri 58 ( 4.3) 237 ( 3.2) 42 ( 4.3) 228 ( 2.3) Nation 11 ( 2.9) 56 ( SA) 31 ( 5.8) 265 ( 3.9)1 254 ( 2.1) 283 ( 42) 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). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A9 I Teachers' Reports on the Availability of (continued) i Resources PERCENTAGE OF STUUENTS AND AVERAGE MATHEMATICS PROFICIENCY 1160 SNP TRIAL I O. AM the Mssourars I Mat Wog of the I Oet Some or None of STATE ASIESSUEST Need Reesurcee I Need the Idesurces I Need W-M State Nation LAffiffuggsess NI nonieuktate State Nation ItS graduate t: 1.5 4 $ t!,41) 211 2$4 '11* 31 4.0) 36 4.0) 34 iq 244 2. State .2 I 41°4 39 231 ( 2.1 Nation 54 4.9 21503 / 43 255 15 Some college State Sc 40 ( 2.0) 241 ( 3.0) Nation #3 3.3) 4..) 62 299 ( 43) ( 25) College graduat State ( 0.7) 37 ( 1.8) 236 ( 2.1) Nation 15 ( 25) 56 ( 4.9) 270 ( 5.4)4 27$ ( 2.2) MOM Male State 3 ( *ea ( 0.5) 37 232 ( 1.5) ( 1A) Nation 13 ( 25) 57 ( 4.0) 264 ( 5.0)1 Female State 5 ( ( 0.4) *41 38 2313 ( 1.4) ( 1.8) Nation 13 ( 24) 55 ( 4.4) 266 ( 3.9) 284 ( 2.0) Pi 225 21) 36 140 243 &Of 59 ( 23) 219( 1.1) 35 ( 4.9) Vie ( 2.6) 51 ( 223 ( 15 25 ( 4.1 267 ( 38 58 ( 1.8) 239 ( 25) 30 ( 5.1) 273 ( 3.7) eo ( 1,4) 221 1.7) $0 4.0) 264 3.3) 57 ( 1.4) 229 ( 1.2) $2 ( 4.7) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. 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 District of Columbia TABLE AlOa I Teachers' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , ism MEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Ones a Week New , TOTAL State Nation RACEMINNICITY Illadt State Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Other State Nation 84 ( 0.0) 229( e) 47 ( $.1) 240 ( 34) 78 ( 219 2.3 84 72 240 25) 253 t 1.31 39 jag 68 ( 1.9 Oar* It) 82 ( 1,1) 223 ( 0.9) 70(11.7) 248 ( AS)! $3 ( 2.0) 235 ( 24) 50 ( 44) 200 ( 24) IS ( 41 t 1 O 23$ 4.0 I: I ti 32 ( 8.9) 247 ( 03)1 27 ( 33) 288 ( 53) 41 (VA 273 ( 0.0)I 10 ( 1.0) 234 ( 2.0) 21 ( 9.0) 249 ( $.7)1 17 ( 2.0) 44,9 44 ( 4.5) 264 ( 23) 5 14) 20 122? j Eti 9 8.5) 444 ( .41 0 ( 0.0) 24 )131 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 inandard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 115 110 THE 1990 NAE TRIAL STATE ASSEMMENT District of Columbia TABLE MO& I Teachers' Repoits on the Frequency of Small (c°11thlued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY raTareseisaaTRIALirr At Lust Once a Week Lass Than Once a Week New TOTAL State Nation tfinfilLAMM 1111 naniradisato State Nation HS graduate State Nation Sante maws State Nation College araduste State Nation OIERE Maio State Nation Female State Nation 417 ( U) ( 2.4) SO SI ( 1.0) 224 ( 13) 49 ( 4,$) 252 ( 2.8) 937 la 200 3.1 $1 51 52 77 ( 234 ( 1.2 4S ( 52 271 ( 25) SO ( 1.2) 227 ( 1.1) 2:11 i 31 03 1.0) .2 231 50 4.7 250 ( 2 14 ( 233 4.0 45 5.1 257 2.7 17 ( 2.3) 400., evoi 1 0.8) ... ...) 9 2.5) 2 ( 0.7) IMP on 42 ( 5.15 2S0 ( 32) 7 2.3) 0,6* 1 .44.) 21 ( 15) 1 ( 02) 2.82 6.1) 43 (4.4) 11 ( 2.7) 270 ( 3.0) 205 ( 4.9)1 10 ( 1.4) 2 ( 0.0) 245 ( 4.5) 42 ( 45) ( 2.1) 205 ( 3.1) 276 ( 5.3)1 10 ( 245 ( 1.0) 3.5) 1 0.3) in* 43 ( 4.7) 7 1 2.1 283 ( 2.1) 275 ( 11.1111 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 1 1 District of Columbia TABLE AlOb I Teachers' Reports on the Use of Mathematical I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSMISMENT At Last Owe a Week Lees Than Once a Weak 11~ TOTAL liwomplara and Po *Wm State 43 ( 1111) 231 Nation 22 ( 3.? 214 ( 32 WM DAM Mack State 45 ( 1.1) 230 1.0) Nation 22 ( 52) 233 ( 5.9)I Hispank State 41 3.5) 222 32) Nation 39 (7.5) 247 3.8) TYPE OF COMMUNITY AA/waged urban State 44 ( 1.0) 2eo ( 2.1) Nation 23 (14.4) *** Mal Disadvantaged urban State 42 ( 1.2) 223 ( 0.9) Nation 39 (11.4) 247 ( 7.5)1 Other State 42 ( 2.5) 231 ( 1.8) Nation 10 ( 4.3) 253 ( 3.9)1 lkarcsatep and 50 ( 230 (1.0 2133 ( 1.11 52 ( 1.1) 2341 LSI 241 ( 2.9) 54 ( 4.0) 217 ( 3.7) 55 ( 7.3) 245 ( 3.5)1 41 ( 3.4) 246 ( 2.8) 83 (11.5) 278 ( 5.6)I be ( 1.1) 225 ( 1.2) 59 (12.1) 253 ( 7.0)I 56 ( 2.8) 238 ( 3.8) 72 ( 5.0) 263 ( 22) OMANIelage 3 ( 0.6) 2759 2 262 5.9 3 ( 0.4) ( 441 8 ( 3.9) ( 5 ( 1.1) elk* ( 441 7 ( 2.6) .44 ( 0.1 15 ( 3.5) ( 15 ( 9.3) 2 ( 0.4) ***) 2 ( 1.8) ( 0 ( 0.3) ( 9 ( 3.3) 2134 ( 7.1)1 Igwwwww.awm... 9 1.1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 1 7 112 THE 1990 NABS' TRIAL STATE ASSESSMENT District of Columbia TABLE AlOb Teachers' Reports on the Use of Mathematical (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1010 NAEP TRIAL STATE ASSESSMENT At Least Once a Wasik Less Than Once a Week Never TOTAL Poomptaga and **alimony 430.$) 231 (06) 22 (3.7) 264 ($.2) Yeamolasa Parmanlags and and findioisoig 0,40111111105 230 1.0) 275 ( 7.7 1.0) 5 ( MO SA) ( 2 203 1.9) 282 ( SA State Nation PARENTS' EDUCATION nonograduate State 43 42) 55 ( 4.4) 2 ( 12) *Mt iI41 229 ( 2.8) Nation 25 5.6) 06 ( 72) ( 6.5) 243 ( 2.2 NS graduate State 46 ( 1.9) 82 ( 2.0) 3 ( 04) 226 ( 1.4) 224 2.0) ( Nation 23 ( 246 ( 4.5) 4.0)4 70 20 5.3) 2.2) 7 ( ipeir 2,8) Some collage State 40 ( 2.9) 51 ( 2.9) 3 ( 1.0) 238 ( 2.1) 239 ( 2 4) Nation gra0sate 18 ( 251 ( 4.0) 4.4)1 73 ( 209 ( 4.3) 2.3) ( ( 2.4) 041 %tee 41 ( 2.3) 51 ( 1.9) ( 1.7) 238 ( 1.9) 233 ( 1.5) Nation 20 ( 3.9) 69( 3.7) 11 2.5) 200 ( 15)1 274 ( 2.2) 297 ( 4.2)1 OaDen M. State 43 ( 229 ( 1.7) 1.4) 54 ( 227 ( 15) 1.3) 4 ( 1.0) vim) Nation 22 ( 4.1) 00(4.1) 8 ( 2.0) 255 ( 4.1) 205 ( 2.1) 267 ( 7.2)1 Fonale State 44 ( 232 ( 1.2) 1.0) 51 ( 232 ( 1,3) 1.6) 5 ( 44. 0.6) $.0.1 Nation 21 ( 3.8) 09 ( 42) 10 ( 32) 254 ( 3.3) 262 ( 1.9) 278 ( 0.0)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 11" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 1 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 113 District of Columbia TABLE A l la I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - . 1900 NAEP TRIAL Aimed Every Day Several About Once a Week or STATE ASSESSMENT Times a Week Leas yam State Nation RACVETHNICITY Mack State Nation Niapank State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Othiw State Nation Portmata. and Ihrolldmicy SS 2211 92 207 30 ( 2$ 8 58 244 .15 01 251 ( Parma. mod Pvadency 12) 42 1.5) 220 3.4) 31 1.2) 254 12) 42 1.2) 230 7.7) 41 4.0) 233 33)*) 43 220 8.8) 22 3.1) 240 31 ( 3.2) 282 ( 54 al (15.91 263 ( 7.31 37 ( 1.4) 2)3 ( 1,3) 1110 (10.7) 252 ( 4.7)1 47 ( 5.1) 244 ( 3.1) 83 ( 3.0) 287 ( 23) 110110001111018111 and Pralliftsoy 1 19 01 222 t41 3.1 7 14 IS 5.1 ( 12) 1.0) TA 3.1P ( 4.5) ( 34) ( 53) ( 4,3)1 52 ( 14) 253 ( !A) 23 (52) *41 43 1.4) 226 ( 1.3) 31 11.1) 243 ( 8.0)1 31 ( 2.3) 224 ( 2.8) 31 ( 3.5) 255 ( 3.1) 20 1.0) 222 1.0) 2 1.4) ... ( ) 18 ( 3.0) 8 ( 2.3i a ( *el 17 ( 2.0) Ito 14 (14.8) ( eel 20 ( 12) 215 ( 19) 4 ( 2.2) wk.) 22 ( 3.1) 228 ( 3.4) ( 19) 257 ( 5.8)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 stsndard errors of the estimate for the sample. ! interpret with caution - the nature of the sample does not allow accurate determination of the vs.:lability 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 District of Colmmbio TABLE Alla Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY I1980 MEP TRIAL Almost Every Day Several About Ones a Weak or STATE ASSESSMENT i Times a Week LOSS TOTAL State Nation EfigrAjnag NI nonlyeduale State Nation le grubs!. State Nation Sam college State Nation College graduate State Nation GENDER US% State Nation Female State Nation .223: ;LA 62 (3,4) (1.1) 34 (34) $7 5.51 345 ( 32) 41 ( 2.3) 230 ( 2.1) 61 ( 4.4) 257 ( 2.5) 39 ( 2.9) 244 ( 2.9) 81 ( 42) 272 ( 2.7) 30 ( 2.0) 249 ( 3.8) 81 ( 4.0) 261 ( 2.2) 38 ( 1.7) 237 ( 2.4) 00 ( 3.7) 289 ( 2,1) 42 ( 1.5) 240 ( 1.6) $5 ( 3.8) 288 ( 1.8) lrn 2$042 31 3.1 256 ( 2.113 22345 3241 27 52 OIND «in 40 ( 22) 222 1.7) 34 32) 250 2.9) 42 ( 2.7) 240 ( 2.1) 26 ( 3.7) 258 ( 5.2) 42 ( 1.8) 236 ( 1.8) 31 ( 3.9) 265 ( 341) 45 ( 1.5) 228 ( 1.5) 33 ( 3.4) 256 ( 3,6) SO ( 1.2) 232 ( 1.2) 28 ( 33) 253 ( 2.5) ttailkiler 20 ( 3.6) eon 9 2.1) 04, 19 ( 1.7) 221 ( ( 15) .41 19 ( 2.2) 226 ( 2.9) ( 1.9) ( 19 ( 1.5) 227 ( 2.4) ( 3.1) elm ( 19 ( 1.3) 223 ( 2.0) ( 1.9) 261 ( 6.7)1 19 ( 1.1) 222 ( 1.8) ( 22) *el 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). 12 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 115 District of Columbia TABLE Al lb I Teachers' Reports on the Frequency of 1 Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAP TRIAL STATE ASSESSMENT AI Lind !Wend Times a Week About Once a Week Lass than Windily VIAL Poraratip kiventig rid add Prollolency Prdledincy State 51 ( 13) 25 1.1 228 ( 0.6) 240 2.1 Nation 34 ( 3.41) $3 341 2501( 23) 200 2.3 RACEJETNNICITY Black State 53 ( 1.3) 25 ( 1.1) 22$ ( 0.8 235 1.5) Nation 45 ( 7.5 31 7.0) 232 ( 3,1)1 243 23)1 NIspank State 4$ ( 4.1) 37 ( 4.1) 210 ( 3.6) ( 441 Nation 41 ( 7.7) 26 ( 5.3) 242 ( 3.2)1 244 ( 5.1)1 TYPE OF COMMUNITY Advantaged urban State 35 ( 2.8) 57 ( 2.6) 251 ( 2.2) 270 ( 3.7) Nation 50 (13.9) 20 ( 0.0) 273 ( 3.4)1 Disadvantaged urban State 50 ( 1.4) 21 ( 1.4) 225 ( 1.0) 221 ( 1.9) Nation 50 (13.9) 22 (11.2) 237 ( 2.4)1 258 ( 8.3)1 Other State 4$ ( 4.1) 32 ( 2.4) 224 ( 1.7) 239 ( 3.6) Nation 30 I 4.4) 35 ( 4.3) 256 ( 3.3) 259 ( 2.5) ditionefe del PridliciNKT 233 20 32 274 ( 2.7) 21 ( 1.0) 232 ( 13) 23 ( 03) 243 ( 7.0)1 of* ( 1141 33 ( 73) 257 2.3)1 7 ( 0.2) 21 ( $2) ike.) 23 ( 12) 228 ( 1.5) 28 (10.7) 283 ( 4.1)1 19 ( 2.7) 250 ( 5.8) 38 ( 4.2) 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. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 21 116 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE Al lb I Teachers' RepOrts OD the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10110 NAEP TRIAL Al Least Several Times STATE ASSESSMENT a Week AM* Once a Week Less num Moldy , TOTAL awl Prilkinny lorsedwily Pargaisp PrelWalml State 29 ( 1.1) 20 ( 2211 OA 240 ( 2.1) 233 ( 1.5 Nation 34 2sa 2.3 $3 ( 3,4) 290 ( 2.3) 32 274 ( 3.0 ( 2.7) PANDITS' EDUCATION NS non-graduate State Nation 48 ( 4.4) 222 ( 13) 35 ( ILO) 23 ( 4.0) *el 11449 29 (4.4) es (el) 239 ( SS) 250 ( 4.5)I 149 gnaw!, State 53 1.9) 20 1.0) 21 ( 1.9) 222 1.6) 227 2.7) 230 ( 2.8) Nation 35 5.3) 30 (4.5) 30 ( 4.8) Some college 250 ( 3.8) 250 ( 2.7) 203 ( 3.4) State 50 ( 2.4) 29 ( 2.1) 21 ( 2.0) 239 ( 2.3) 240 ( 2.2) 240 ( 4.4) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 206 ( 4.2) 27$ ( 2.0) College graduate State 41 ( 2.3) 34 ( 2.3 10 ( 12) 233 ( 1.4) 2S3 ( 4.1 233 ( 2.4) Nation 35 ( 3.8) 32 ( 3.4 33 ( 33) 264 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Male State 54 ( 1.5) 22e ( 1.3) 27 ( 1.4) 239 ( 2.7) 19 ( 230 ( 0.9) 1.0) Nation 35 ( 4.1) 35 ( 3.0) 31 ( 3.5) 257 ( 3.2) 231 ( 2.8) 275 ( 3.2) Fernald State 48 ( 1.7) 30 ( 1.3) 21 ( 1.4) 230 ( 0.9) 240 ( 2.2) 235 ( 2.0) Nlticn 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with &Wit 9$ percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! 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 District of Columbia TABLE Al2 I Students' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAP TRIAL STATE ASSESSMENT At Wad Once a Wok Loss Than Ones a asek New I TOTAL 8110 fteelidsmar SRA aid 1109010acy Prielklem State 47 1.1) 22e 1.0) 18 ( 243 ( 0.7) 1.5) 34 220 0.1! Nation 241 25) 20 ( 14) 44 2.9 258 ( 2.7) 297 ( 2.0) 261 ( 1 RACE/EIHNICITY Bieck State 47 ( 1.0) 18 ( 0.8 35 ( 227 0.9) 240 ( 1.3 229 ( 1.0 Nation 21 3.0) 24 ( 3.6 48 ( 4. 234 3.0) 245 ( 43) 238 ( 3.1) Hispanic State 56 216 4.1) 2.4) 17 ( .410 3.6) 27 ( SS) oil Nation 37 5.2) 22 ( 3.61 41 5.0) 242 ( 3.9) 250 ( 34 240 2.8) TYPE OF COMMUNITY Advantaged urban State 32 ( 2.4) 33 ( 1.5) 35 ( 2.3) 249 ( 3.9) 208 ( 3.6) 258 ( 3.4) Nation 27 (13.9) gel .) 33 ( 288 ( 4.5) 5.4)1 40 (13.4) 279 ( 3.5)1 Disadvantaged urban State 48 ( 1.3) 16 ( 1.0) 36 ( 1.6) 122 ( 1.1) 233 ( 1.7) 224 ( 1.2) Nation 31 ( 5.7) 20 ( 23) 49 ( 03) 245 ( 4.0)1 267 ( 0.4)1 245 ( 3.7)1 Other State 01 230 2.7 14 ( eve ( 1.3) 24 ( SS) 234 ( 2.1) Nation 27 2.6 20 ( 1.7) 45 ( 13) 2130 3.3 254 ( 2.1) 292 ( 2.2) The standard errors of the enimated 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). 123 1 IS THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE Al2 1 Students' Reports on the Frequency of Small (continued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11110 NAEP TRIAL STATE ASSESSMENT At Lard Once a Weak Lass Than Onto a Weak Never 410, «Ds 20 29 (3.5) 29 42 242 ( 242 121 11 2$ 2s1 231 ( 2611 21 3 ( 11 13 ( 224 1 252 13 NI( 43 3.4 27 { 3.9 265 46 ( 24$ ( 2.91 268 ( 3.3 27 ( 2.4 20( 2.3 237 206 2.1 41 31 2: 1 10.1)) 20 ( 1.1 32 ( 1.7) 270 2.7) e 3.0) 256 ( 2.$ 27$ ( 2.$ 20 ( 11 23$ 2.5) s 275 2.2) 44 3.0) 250 33 223 1.1 1.2 31 211 22$ ( tO 45 ( 26 ( 257 ( 21) 18 ( 1.2) 31 21) 241 30) 2$ 1.7) 20( 1.1) 245 2.0) 27 ( 11) 200 ( 1.7) 33 ( 1.5) 230 ( 14 262 ( 11 41 ( 2.9} 35 ( 1.7) 231 ( 1.3) 47 ( 2.2) 200( IA) 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 sin is insufficient to pexmit a reliable estimate (fewer than 62 students). /24 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Maria of Columbia TABLE A13 I Students' Reports on the Use of Mathematics Objecft PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSE8SAIENT At Lead Ones a Week Lau Thin Once a Wolk Maw TOTAL 37 ( State 2 27( 1.1) Nation 22 ( 1.6) 255 ( 2.8) geersgaLmoc Stack State 37 ( 1.0) 227 ( 1.1) Nation 27 ( 3.3) 234 ( 3.7) Hispanic State 44 ( 214 ( 3.1 Nation 311 ( 42 241 ( 4.8) TypE OF COMMUNITY Advantaged urban State 40 ( 13) 250 ( 33) Nation 36 (10.3) 276 ( 0.1)1 Disadvantaged urban State 37 1.1) 219 ( 1.2) Nation 36 ( 6.6) 249 ( 5.3)1 Other State 40 3.0) 227 1.3) Nation 27 2.0) 258 2.9) 21 (1.1) 42 236 2.21 to 31 1 1.2i 41 Z2 RI 15 25$ 1 19 ( 1.0) 235 ( 1.7) 27 ( 3.2) 248 ( 4.5) 1123 re12.0i 2S3 ( 4.3) 27 4.1) 208 02) 33 43) 2114 32)1 16 1.1) 228 1.3) 19 2.1) 256 5.7)1 22 ( 84) 228 ( 4.4) S1 ( 1.4) 270 ( 13) 44 1.1) 230 OM 22 44 35 ( 3.0) 210 ( 3.5 40 ( 4.0 240 ( 1.9) 33 ( 3.0) 27321 115.9341i 45 ( 1.2) 228 ( 1.2) 48 ( OA) 240 ( 43)I Se 2.4) 234 3.3) 41 2.4) 200 4 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 cf 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). Ir 4.. 0 120 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A13 I Students' Reports on the Use of Mathematics (xintinued) I Objects PERCEN1AGE OF STUDENTS AND AVERAGE MATHELSATiCS PROFICIENCY .P.......1......M...... MO NAP TRIAL STATE ASSESSMENT At Least Ones a Week Lees TIM O. a Welk Never TOTat Stabs Nation gaggmwraym HS non-graduate State Nation PM graduate State Nation Some college State Nation College pacluatt State Nation II 211) ( 241 1:11 1,2 SS 4 10 30 i 4.11 owl , out le 11 27) 223; i 342i X ( 2.T) 24 t as) 3$ I i 20 ( 15) 221 ( 1,111 231 (20) 27 ( 21 31 ( 2,4.) 250 ( 2.4) 259 ( 2,7) 3$ 2.0) 21 ( 23) 233 25) 243 I( 34) 20 2.0) X 03) 261 3.5) 214 ( 22) 38 ( 2.2) 72 ( 25) 233 ( 2.4) 24 ( 4,7) 30 ( 2.5) 32 ( 25) 200 ( 3.0) 212 ( 20) ' 4$ 5.1 225 2.01 47 5.0 240 ( 2.3) 42 ( 2.3) 224 ( 43 ( 3.3 253 ( 41 ( 2.3) 230 ( 2.5) 35 ( 25) 2e3 ( 2.1) 30 ( 1.7) 238 ( 2.5) 3$ ( 2.0) 275 ( 2.0) GENDER M. State 2.2 227 41 1.2) 21 ( 15) 39 ( 1.0) 234 ( 21) Nation 25. 25 32 20 30 ( 1 5) 2/1 t 2.1) 228 1.9) 200 15) 3$ ) Female State 34 1.2) 21 ( 13) 45 ( 1.4) 220 242 ( 3.2) 31 ( 15) 232 ( 1.1) NaVon 25 2.0 44 2.0) 257 ( 3.0 2N ( 1,5) 257 ( 1.9) ........ ..-.. The standard errors of the estimated statistics appear in parentheses. 1 t can be said with about 95 percent certainty that, for each population of interest, the value for the nitre population is within * 2 standard errors of the estimate for the sample. *** Sample size is insufncient to remit a reliable estimate (fewer than 62 students). 12 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 District of Colombia TABLE A14 I Students' Reports 011 the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Soma Tinos a Weak About Once a Mask or Liss TOTAL State 267 1.2) 233 13) 1.1) 74 .1A) RACE/ETHNICITY Slack State Nation DIsadvartnad urban State Nation Other State Nation 54 ( 1.2) 231 ( 05) 11 ( 25) 240( 2.9) 217 ( 4.1 41 ( ( 3.7 249 ( 2.3 209 55) 40 2.4) 73 11.1) 258 ( 45)4 55 ( 1.5) 220 ( 1.2) 09 ( 25) 253 ( 3.7)1 23$ 58 3.3) 75 2.2 207 15 20( 1:1) 231 ( 1.2) 15 ( 1.7) 232 ( 3.1) 3.( 33) 21 /4.:1 242 (6.1) 31 3.1) 2.2) 258 13 1.7) 26 ( 14) 228 ( 1.6) 15 ( 2.5) 243 ( 4.4)1 252 25 221 2.1 24 14 IA 2231 14 3.2) 1.3) 20 OA 223 41.1), 32(42 17 2.7) 224 SA) 237 2.2 23 ... en 14 104 217 1.7) 235 65)1 1$ 2.2) 1.0) 111 ( 2.1) ritt ( 4.3 10 i i.ii; 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 =Watt determination of the variability of this estimated mean proficiency. *4" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 ' 122 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A 14 Students' Reports on the Frequency of (continued) i Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . , 1SSO NAEP TRIAL About Once a Moak or STATE ASSESSMENT Aiwa Every Day amoral Times a Weak Lioas TOTAL; State Nation fERMLOBra-MI NS nonirackiato State Nation HS graduate State Nation Some college State Nation College graduate State Nation cseNDEA Male State Nation Fonedo State Nation 2211 64 ( SA) 245 ( 2.3) 54 1.11) 225 13) 71 S.M 258 ( 14) 50 ( 2.7) 240 2 110 2.01 270 1.9 SS ( 12) 243 ( 3.1) 77 ( 2.7) 279 ( 13) 52 232 1.11 72 24 261 ( 1 54 235 1.9 78 1.8 285 1.3) 28 ( 31 20 ( SA) 11 2.0$ *FR ( 11 01141 18 ( 3.1) *I 041 1110* ( on 25 ( 14) 225 ( 1.9) 211.1.5) 219 ( 2.8) 10 ( IA) 13 ( 2.8) 249 ( 3.2) 239 ( 3.4)I 30 ( 24 21 2.1) 237 2.9) 233 3.5 11 1.2) 9 1.7 28 ( 1.7) 17 ( 1.1) 237 ( 24) 224 2.4) 13 ( 0.9) 10 2.3) 280 ( 23) 257 15.4)1 31 ( 14) 229 14) 18 1.2) 282 24) 24 ( 1.3) 235 ( 2.1) 13 ( 1.0) 250 ( 2.5) 17 ( 1.2' 221 ( 141 12 ( 2.1) 242 ( 0,1) 22 ( 1.1) 223 ( 1.7) 11 ( 1.8) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. Interpret with coution - 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 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 123 District of Columbia TABLE A15 I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT I At Least Several Tinos a Weak _ Pima Onc* a Week Lass Than Wieldy , TOTAL State :24'44/411CV Nation 253 2.2 2 0.11 511 1.4 25 311 244 24 ( 1.1) 2S t5) 25 WM 1.4) 1.2) NigigniEM Raft State 59 ( 12) 24 ( 1.1) 17 0.9) 226 ( 1.0) 43 I 3.9) 234 ( 1.2) 234 1.4) Nation 32 ( 2.7) 20 3.1) 232 ( 43) 241 ( 2.9) .241 ( 4.4) nlaPinic Stets 63 ( 3.3) Nation 215 ( 2.8) 23*, , 3.9) 4t ( 4.1) 247 ( 3.3) 251 3.4) 32 4 241 3.3).3 19 2) 21 ( .5 Typg OF COMMUNITY Advantaged urban State 53 ( 3.4) Nation 271 ( 3.3)1 SO ( 9.0) 4 to. ( ..4.) 24 ( .9 19 ( 4J 31 279 7.0 22 9.3 1 248 ( 1.7) 203 ( 4. 299 5.311 Disadvantaged urban State 03 ( 14) 24 ( 14) 18 ( 0.9) 221 ( 1.1) 22$ ( 14 22$ ( 2.1) Nation 37 ( 54) 23 ( 3.6) 41 ( 6.7) 240 ( 44)1 253 ( 4.1)I 255 ( 4.2)1 Other State 53 ( 2.4) 28 ( 3.4 t2e ( 1.8) 237 ( 3.4 19 ( 'IA) 245 ( 5.1) Nation 38 ( 2.9) 28 ( 1.2 39 ( 29) 252 ( 3.0) 261 ( 2.1) 272 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *6* Sample size is insufficient to permit a reliable estimate (fewer than 02 students). 129 124 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A15 Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 MAD TRIAL . Al Least Seem Moss STATE ASSESSAIEWT a Week About Once a Weak Less Man Weakly Sate 19 3.3 , . 211 2.0 3,1 243 212iIii 1 1...401 Nation ? 20 2 It$ gradumbe ,-, Nation SI NI 29 22 17 i 1.51 34 1 State 230 ( 2,5 202 ( 2.2) Same ceiMge State ta 31 20 ( 1.9) 244 ( 23) 12 ( 1,0) Nation 34 34 34 ( 2.2) 40 1 34 240 13 RIO ( 23) 271 ( 23) &lege graduate State 330 1.2) 27 2.3) 242 39) 25 ( 2.0) 19 ( 12) Nation , 30 21) 224 746) 273 24) 22 1.4) 2: I till) MS 2.3) 21Efffa Male State SO ( 13 ) 20 ( 1.1) 1.1) 254 13 234 3.0) 240 2.3) Nation ' 39 2.7 ZS 1.6) SS 2.7) 253 2. 203 2,$) 274 24) Female State SI 14) 23 1.3) 20 1.2) 227 1.0) 237 2.0) 243 2.9) Nation 37 24) ZS 1.5) $1 2.0) 253 2.1) 2313 1.1) 209 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 stvdents). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 District of Columbia TABLE Al8 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICJENCY NM NAEP TRIAL STATE ASSESSMENT Own a Caladater Teacher EAplaine Cakdater Use Yes No I Yes I , No - TOTAL State Nation RACE/ETHNICITY Mack State Nation NIspante State Nation TYPE OF COMMUNITY Advantaged urban State Nation INsachwtaged urban State Nation Other State Nation logrontig and Prelialany 231 ( 0. 6 00 DT ( 0.4 23 ( 00 ( 03) 230 ( 237 ( 246 03 ( Z2.1 94 ( 1.7) 219 ( 2.2) 92 ( 1.2) 215 ( 2.7) 99 ( 0.7) 259 ( 24) 99 ( 1.0) 201 ( 34)1 95 ( 0.6) 224 ( 0.6) 94 ( 12) 250 ( 34)1 00 ( 1.2) 233 ( 2.1) 26397 "1.7i 21: 2.71 241 0.4 211 2.91 7 1.5 ( 0.5 04 n ( 1.7) ( 12) *** 01) IP** 091 $ 0.6) 216 ( 3.0) 6 ( 1.2) 041 900 All 4 1.2) 3 04) 233 ( 5.4) 27 ( $S 22$ INS 235 2344? 44 230 216 ( 23 243 ( 3A 70( 21 ( X2) 2175 114 256 ( 31 257 4.1 45 (12.2 ) 19 14) 51 ( 1 55 12.2) 276 ( 2,5)1 265 ( 64 66 ( 1.1) 32 ( 1.1) 221 ( 1.1) 231 ( 1.3) 53 ( 7.5) 47 ( TA) 247 ( 4.1)1 251 ( 1.6)1 $6 ( 2.3) 14 ( 2.3) 231 ( 24) ...) 251 ( 2.1) 50 ( 23) lei 1.:(3i The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each ropulation of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 131 126 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Colwnbia TABLE A18 Students' Reports on Whether They Ow. a (ccnItillued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Ono a Calculator Teacher Maks Calculator Use MO NAEP TRIAL STATE ASSESSMENT Yes 1 No Yes No TOTAL State Nation manumsansm INI non-graduate State Nation N3 gradude State Nation Senn Meg* State Nation Coll4110 radiate State Nation 9.2121a U. State Nation Female State Nation 24:1 11) 041 253( 09( 1.2) 2311( 1.6) 92( 0.9) ( 14) 2E91 11 27$ 113 00 ( 233 ( 0.9 97 ( 0,5 282 ( 1.3) 9 ( 2.2) .41 3 ( 4 ( 1.2) eop) dt. *of 4 ( 3 ;..51 11911* 41.017 4 ( 0.7) a.* 04648160404 operawy itargoilsop sod Otrolidem 230 11 74 0.6 2:44 49 2.3 51 ( 2.3 291 1.7 2011( 1 81 ( 35) 224 ( 3.4 53 ( 242 ( 74 ( 2.1) 223 ( 1.1) 54 3.0) 252 ( 1.9) 230 2.2) CM 2.8) 48 (32) 283 ( 2A) 73 ( 1.0) 290 ( 2.3) 48 ( 2.6) 208 ( 22) 76 ( 1.4) 224 1.3) 51 2.0) 254 2.1) 72 ( 1.4) 231 ( 13) 47 ( 2.5) 251 ( 1.7) 10 ( 34) 4143 ( .471 243 ( 2.5 28 ( 2.1 22e ( 241 40 ( 250 ( 2.0) 32 ( 2.8) 242 ( 24) 52 ( 12) 284 ( 2.2) 24 ( IS) 243 ( 2.2) 54 ( 2.0) 280 ( 1.0) 24 ( 1.4) 233 ( 2.4) 40 ( 24) 200 ( 2.1) 24 1.4) 238 ( 2.1) 53 ( 24) 203 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 District of Columbia TABLE A19 I Students' Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY'. MO NAEP TRIAL STATE ASSESSMENT Workkvg Problems in Class Doing Predicts' at Nome Taking Quizzes or Tuts Alln0St Atways Never Almost Ahvays Never Aimee Atways t4ever TOTAL State Nation RACE/ETHNICITY Black State Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State 41 ( 1.2) 244 ( 2.1) Nation 51 ( 5.4) 270 ( 4.7)1 Disadvanta9ad State 57 ( 1.3) Nation 52 ( 3.1) 241 ( 3.8)1 Paradiga Parade, Paradigm Paw*. ana Praildsney *deism, PrOiolinoy Pii.01868y 56 ( 0.9) 14 ( 0.8 32 I 15 ,0.8 224 ( OA) 246 1.8 220 ( 1.3 239 14 48 i 1.5) 23 1.9 30 ( 1.3 19 0.9 254 ( 1.5) 272 1.4 281 ( 1.8 263 1.9) 58 ( 1.0) 14 ( 0.8) 33 ( 0.9 ) 15 (' . 32 225 ( 1.0) 243 ( 226 1.4 .237 f '2.0 ,.225 57 ( 3.2) 20 ( 3.9 31 2.9 18 1 1 SI 232 ( 2.4) 249 ( 4.0 233 3.3 248 ( SA sip L 63 ( 3.7) 10 ( 2.8) 30 ( 3.2) 10 ( 2.1) .. 614A t.11 214 ( ZS) "" ( m) ( ) *** ***) '21? ( 51 ( 2.9) 10 ( 3.5) 26 ( 3.2) 21 2.1) ( 2.7 1 as 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 3.1) 237 ( Other state 81 ( 2.1) 228 2.1 Nation ) 46 1.9) 254 2.1) 10 ( 1.8) 23 (10.7) ( 18 ( 0.9) 238 ( 2.0) 22 ( 4.5) 2S9 ( 5.4)! 253 ( 32 32 ( 8.1 15 ( 2.4) 31 ( 3.8) .. 28 ( 3.8 30 ( -2 1 E.I4 2411 41 . ';'1131:1 274 ( 4.9 ' ( ") ,231 ( 7.8)1 ass ( 4.2 2;33 (( 11.1)) 2g 1 it 2VO I 11:t .22 .11:41 li 243: (i 3.1 24 (( 2.11 27 1.2.9 ' 2r$ it! 141 1.9) 431 322.2 214: 422 21811 VII 2:1;1 4 ' 2L9 1.1i 1 22 272 ( 9.1 2.0) 1.8) 34 ( 230 ( 2:3 (( 3.0) 2.6) 1;)) The standard errors of the estimated statirtics appear in parentheses. It can be said '.vith about 95 percent certainty that, for each population cf interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. 1. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a relialle estimate (fewer than 62 students). 133 128 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A 19 I Students' Reports on the Use of a Calculator (continued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11190 NAEP 1R1AL. STATE ASSESSMENT Working Problem in Class Doing Problems at Nome Taking Quizzes or Tests Almost 1. AiWay5 I Never Almost I Mays , . Never Almost I Always NOM TOTAL, State Nation BITS' EDUCATION KS noes-graduate State Nation NS grackatte State Nation some college State Nation College graduate State Nation Emma Make State Nation Fenssie State Nation PoriONS. plevamtise PIMMONIM Pir0101/0 Peresnlado lierantallel and tord and anti end and dimdkeing, predekno Prelloisndif Posidation Pradeassv Pilelktialed 454 ra 314 112 2412, 1..131 2:131 4(3 2:23 ;..i? 324: 3 48 t5 23 i SO tS 19 0.9 2? 1.4 30 10 254 1.5 212 IA 281 1.1 ZS 1.8 253 2.4 274 1.3 OD ( 4.2 12 ( 2.6) 301 .3;45 18 1 3.2) 33 ( SA 23 ( 3.4) 22 ""' ( *** "1 ow, on .4., ( 1,81 54 131 19 ( 3.8) 24( 3.1) 22 ( 21 321 16 241 3.2) 240 2.3 ( ) 244 ( 3.8) 244 ( 42 227 ( 2.3 251 4151 57( 1.5) 1.1) 14) 15 ( 14) 33( 211 1.5) 221 ( 1.5 233 224 2.3) 220 ( 3.0) 221 1. 235 ( 24) 52 ( 2.51 20 2A 29 12) 18 ( 1.5) 28 1.8 27 ( 22) 242 ( 1.4 265 ( 2.7 250 ( 24) 258 ( 2,4) 246 2.8) 205 ( 2.0) 52 ( 3.0) 1? ( 1.9) 27 ( 3.0) 15 ( 2.0) 34 ( 2.5) 32 ( 24) 230 ( 1-2) ... ( '6") 233 ( 2-8) "e .") 232 ( 2.8) 250 ( 3.0) 48 ( 2.11) 20 ( 24) 25 ( 2.0) 20 1.9) 26 ( 2A) 35 ( 2.5) 256 ( 2.1) 272 ( 2.5) 207 ( 3.0) 265 3.2) 255 ( 34) 275 ( 2.0) 54 ( 14 ( 1.2) 35 ( 14) 14 ( 1.8) 31 ( 2.2) 26 ( 1.8) 227 ( 1.9 260 ( 14) 235 ( 2.8) 254 ( 3.2) 227 ( 2.0) 261 ( 23) 45 ( 14 25 ( 2.4) 33 ( 2.0) 18 ( 14) 26 ( 1.8) 33 ( 2.7) 285 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 288 ( 2.8) 285 ( 2.0) 57 1.1 12 1.1 15 ( 1.1) 13 ( 22 ( ' .3) 229 1.4 247 3.1 227 1.9 239 ( 2.8) 224 ( 1.3 248 ( s) $) 1.7 20 2.0 29 1.6 19 ( 13) 2? ( 1.5 26 ( ...1) 255 12 275 2.2 284 ( 24) 263 ( 2,5) 258 ( 10) 277 ( 1.9) 53 ( 1.4) 18 ( 1.1) 35 ( 1.4) 15 ( 0.9) 31 ( 1.4) 29 ( 1.5) 225 ( 13) 246 ( 3.3 229 ( 1.8) 239 ( 2.4) 225 ( 1.8) 247 ( 2.2) 48 ( 2.0) 28 ( 2.1 32 ( 1.8) 18 ( 12) 27 ( 1.8) 33 ( 2.1) 252 ( 1.7) OW( 14 250 ( 1.7) 263 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errori 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 reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 District of Columbia TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11M0 NAEP TRIAL STATE ASSESSMENT Nigh "Calculator-Use Group Other Vaku laUw4koo" Grow TOTAL Perm lap and Mao boar Pomade. ant PrOktirriv State 38 ( 1.4) 240 ( 2.1) 81 ( lA 22. 0.01 Nation 42 ( 1.3) 511 ( 1.3 272 ( 1.6) 265 ( 1.5) RACE/ETHNICITY INN* State 30 ( 1.3) 131 ( 1.3) 230 ( 1.3) 226 ( 1.0) Nation 37 ( 3.4) 62(3.4 ) fg,48 ( 3.9) 231 ( 3.0) Hispanic. State 34 4.7) 06 ( 4.7) 214 ( 3.7) Nation 30 ( 64 ( 4.2) 254 ( 4.6) 238 ( 3.0) TYPE OF COMMUNITY Advantaged urban State 47 ( 4.4) 53 ( 4.4) 274 ( 7.0) 249 ( 2.7) Nation 50 ( 3.8) 50 ( 3.8) 288 ( 4.9)1 275 ( 4.4)1 Disadvantaged urban State 30 ( 1.7) 233 ( 1.8) 64 ( 1.7) 219 ( 1.3) Nation 38 ( 4.2) 62 ( 4.2) 262 ( 5.8)1 244 ( 3.9)1 Other State 47 ( 34) 53 ( 3.5) 233 ( 3.1) 231 ( 1.9) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent oertainty 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). 133 130 THE 1990 NAEP TRIAL STATE AZSESSMENT District of Coismthia TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 NAEP TRIAL STATE ASSESSMEAT High "Cakadatar-Use" Group 1 Other "Catradater-Uatr Group TOTAL State Nation le non-graduate State Nation 03-It. State Nation Some college State NatiOn Cottage graduat State Nation GENDER Male State Nation Finish State Nation fam$19$9 4019 1401.91wM 42 1.3 V2 1 38 4.7) 4.111 241 4.1 34 23) 229 23) 40 22) 263 ( 2.0) 49 ( 3.1) 243 ( 3.3) 44 ( 22) 277 ( 24) 40 ( 15) 251 ( 4.5) 45 ( 2.0) 252 ( 2.1) 36 2.1) 2311 2.9) 39 2.0) 274 2.0) 42 ( 11) 240 ( 2.1) 45 ( 14) 209 ( 12) 91wassIsis aid Mariam $1 ( 1.4) 220 ( 0.9) 541( 1.3) 235 ( 1.5) $2 ( 43) 221 ( 31) OD ( 3.3) 242 (, 2.4) 28 ( 2.5) 221 ( 60(2.2 249 ( 14 51 ( 3.1) 232 ( 2.1) 52 ( 22) 258 ( 2.5) 60 ( 14) 231 ( 1.7) 54 ( 2.0) 268 ( 1.9) 64 ( 2.1) 224 ( 1.4) 61 ( 2.0) 255 ( 2.3) 58 ( 11) 227 ( 12) 55 ( 14) 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. '1** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 District of Columbia TABLE A24 I Students' Reports rpes of Reading 1 Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAE'P TRIAL STATE ASSESSMENT Zen to llvo Types Digo Typos Far Typos 1 I TOTAL State Nation RACE/ETNNtgITY Stack State Nation tilsipanie State Nation TYPE OF COMMUNITY Actsantapd urban State Nation Disadvantaged urban State Nation Other State Nation , 24( 2241 2.0 1.1 21 tO 244 223 ( 1.0 23 ( 31 ( 1.9 232 ( 32) is 99 237 ( 3.4) $0 1 12 254 227 1,2 35 ( 13) 227 ( 13) 35 ( 2.2) 233( 3.9) ,*.< *** 29 ( 30 ( 2.4 244 ( 4.3) 2$ 4,2) 253 ( 2$) 28 (2.1) 28 ( 1.1) 34 ( 1.5) 220 ( 0.9) 222 ( 1.5) 32 ( 3.9) 31 ( 2.3) 243 ( 2.9)1 247 ( 3.7)1 21 3.1) 35 ( 2.5 228 4.7 22Sf 34 22 $ 11 30 ( 1.3) 244 ( 2.8 250 (2.2) 235 1.01 1.1 33 2.4 245 33 22533 1 4.03.2i 28 ( 2.3) 253 ( 2A) 5111( 23) 257 3.611 264 3.8 81 4.9 22$ ( 1.2 38 ( 37 ( 3.8 257 ( 4.9)1 44 ( 11) 240 ( 2.4) 48 ( 1.5) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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). 137 132 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A24 I Students' Reports on Types of Reading (millinued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11100 MEP TRIAL STATE ASSESOMENT Zero to Two Toss Three Noss Four Types TOTAL State Nation EABErs....IENIUM 1111nonlcatkiate State Nation NS graduate State Nation Sento college State Nation Collage graduate State Nation OENOER Maks State Nation FORMS State Nation -2,17 1 *I 1 $0 1 2441 2.0 SSO 1 11401304111:2 42 ( Iss 272 ( 1.5) 27 4.0) *111 47 4.0) 29 i 5.0 oe. ( ...01 23 ( 3.9) $40 ( 3.4) 243 ( 3.3 24 1( 3.01 25 ( 23) 24$ ( 3.3) 940 ( 22 221 ( 2.! 20 ( 2 222 ( 1141 33 ( 1.9 229 1.4) 40 1.7) '27 ( 1 30 ( 1. , 37 1.7) 253 ( 2.7) 200 ( 2.1) 23 ( 14) 31 ( 2.7) 17 1 233 ( 2.3) 1 251 ( 4,0 202 ( 2.6) 32 ( 1.7) 2445481 I 2224°41 274 1.9) 10 ( 1.1) 32 ( 2.3) 62 ( 2.1) 224 ( 2.5) 231 ( 14) 246 ( 2.6) 10 ( 04) 28 ( 1.8) 82 ( 2.0) 254 ( 24) 289 ( 2.5) 210 ( 14) 25 ( 14) 222 1.8) 21 1.5) 244 2.3) 2$ 12) 225 1.8) 22 12) 244 22) ( 1.5) 00,0 I (14 259 ( 2.1 1.7) Vatt 1.5) 29 14) 2513 ( 1.9) 30 ( 1.5) 237 ( 2.0) 48 ( 14) 273 ( 2.0) 44 14) 220 1.5) 49 14) 270 1.7) The nandard 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). 138 THE 1990 NAEP TRIAL STATE ASSESSMENT 133 District of Columbia TABLE A25 I Students' Reports on the Amount of Time Spent 1 Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRIAL STATE ASSESSMENT One How or Lass Two Hows Throe Hours Four to Five Howe Six Howe or More TOTAL State Nation RACE/ETHNIcITY Inadc State Nation Hispanic State Nation TYPE of COMMUNITY Advantaged listen State Nation Disadvantaged urban State Nation Other State Nation pervalego femsraiso 11411403104 itimmlap Paivaidee aml and aid Prsidency Panslancy Prildesso PrOdency Prildisney ( 0.7) 236( 52) 12 ( 0.6) 240( 22) 7 ( 0.6) 225 ( 2.7) 8 ( OA) 44* ( ***) 10 ( 2.5) 12 ( 222 ( 21 ( 0.6) 2.0) 0.9) 16 ( 220( 22( 0.1) 1.7) 02) 266 (12) 205 ( 1.7) 11 ( 4.8) 18 ( 0.6) 229 ( 1.6) 229 ( 12) 13 ( 1.7) 17 ( 2.1) 239 ( 7.0) 230 ( 0.0) is ( 2.5) 19 ( 3.1) 31 ( 1.2) SS (1.1) 233( 12) 227 ( 12) 24 ( 1.1) 16 ( 1.0) MO( 1.7) 245 ( 1.7) 32 ( 1.1) $4 1.1) 233 ( 1.1) 223 12) 32 ( 12) 32 22) 239 ( 4.0) 223 ( 22) 31 3.9) i 3.5) 2 . ( ...1 Mir! ( In OA* i *In ali* 140) 14 ( 2.4) 20 ( 2.5) 19 i 2.1) 31 3.1) 17 i 1.7 *** ( "") 245 ( 3.2) 13 ( 3.2) i11111. 1141/ 18 ( 14) omp. 7 ( 0.7) 219 ( 2.5) ( «4) 7 ( .0) 12 ( 1.0) 268 ( 2.6) 18 ( 2.1) ftel 25 ( 4.3) IN* ( 11 ( 0,8) 220 ( 22) 17 ( 3.1) 250 ( 4.0)1 12 ( 1.2) 'et 21 ( 1.0) 269 ( 23) 242 ( 5.6) 247 ( 3.5) 236 ( 3.6) 14 ( 1.7) 34 ( 4.5) 23 ( 4.9) 253 ( 3.6) 242 ( 2.7)I 21 ( 1.8) 30 ( 4.3) 2.0) 041.6 ( din 10 ( 0.9) 30 ( 11.3) 38 ( 1.1) 222 ( 14) 228 ( 1.1) 224 ( 1.5) 19 ( 2.1) 34 ( 2.4) 20 ( 31) 255 ( 50)1 251 ( 4.7)1 228 ( 46)1 18 ( 2.2) 33 ( 1.6) 30 ( 22) 1111, ( 236 ( 2.9) 232 ( 3.6) 23 ( 1.2) 27 ( 12) 17 ( 1A) 206 ( 2.1) 209 ( 2 2) 245 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample FiZe is insufficient to permit a reliable estimate (fewer than 62 students). 3 ;4 134 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A2$ I Students' Reports on the Amount of Time Spent (cntinucci) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1980 NAEP TRIAL STATE ASSESSMENT OM HOW Or Less Two Houn Throe MOWS Four to Flyo Hours Six Hours or Moro TOTAL State Nation 126/101.1egann HS non-graduate State Nation PM graduate State Nation Some college State Nation Wisp graduate State Nation OM U. State 8 ( 00 12 ( 09) 17 ( 1.1) 34 ( 1.8 30 ( 1.5) 227 ( 3.5) 226 ( 2.0 233 ( 1.8 226 ( 1.7) Nation 11 ( 0.9 22 ( 1.2) 22 ( 1.0 23 ( 12) ) 2S3 ( 8.1 17 ( 1.5) Ye ( &3 287 ( 2.6) 267 ( 2,2 202 ( 2.1) 248 ( 2.5) Flange State $ ( 0.9) 1 12 OA) 18 ( 0.8) 29 ( 1.4) 85 .5) 230 ( 5.8) 236 24) 232 ( 2.5) 234 ( 11) 228 14) Nation 14 ( 1.1) 20 1.3) 23 ( 1.4) 28 ( 1.8) 15 ( 1.2) 209 ( 2.8) 200 2.2) 264 ( 11) 250 ( 10) 241 ( 21) 12 0.8 a.t 22 O. 229 1 22 OA 2554 1/) 233.11 2$ 1.1) swo 1.7) Of 14 2271121 111 1.0 245 1.7) 7 (2.1) 2 ( 1.6) 17 21 211 ( 3.4) 17 (W) ,040 i 12 1 It 201 .$...11 21 21 20 1 2.9 20 2.4 op, ...) . ( ...) . .) 344 ( 32) , ( en 8 1 11 ( 1.2) 224 ( &O) 1$ ( 11) 27 1.8) 21$ 24 30( 1.0) 228 19) 222 1.8) $ f 1 17 ( 1.4) 231 2.0) 32 2.3) 19 1.6) 249 ( 4.7 257 ( 29) 250 3.2) 253 ( 2.5) 248 3.0) S ( 1 14 I !al 14 ( 1.8) 39 ( 26) 27 ( ...«. i 449 ( ft) 240 ( 2.6) CM ( 2A 10 ( 1.4 25 ( 24) 23 ( 2.45) 28 ( 2.2) 14 ( 1.5 275 ( 2,7) 260 ( 3.5) 281 ( 2.5) 242 ( 5.4) 10 ( 110 13 ( 12) 15 ( 1.5) 34 ( 2.1) 28 ( 2.3 253 (110) 241 ( 238 4.1) 230 ( 2.5) 230 ( 1A 1? ( 1.3) 22 ( 1.6 23 1.1) 25 ( 1.5) 12( 1.1) 202 ( 2.6) 200 ( 2.5 277 2.2) 270 ( 2.4) 255 ( 3.2 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 4 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 District of Columbia TABLE A26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Nona Ono or nvo Days Um Days or Moro - TOTAL Pwciadaga and Praliclancy Pnvantass and PIWON611.11 and Proadancy State 3$ ( 30 ( 1.3) 37 ( 12) 230 ( 1.t) 234 ( 1.5) 224 ( 1.2) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 205 ( 14) 266 ( 1.5) 250 ( 1.9) RACEJETHNIC TY Black State 33 ( 12) 29 ( 14) 38 ( 1.3) 234 ( 1.1) 233 ( 1.4) 223 ( 1.1) Nation 58 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 30 ( 3.1) 33 ( 3.4) 37 ( 3.1) 111** ( 001 224 ( 2.8) 213 ( 3.7) Nation 41 ( 3.3) 32 ( 22) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) TYPE OF COMMUNILY Advantaged urban State 41 ( 3.15) 33 ( 2.4) 26 ( 3.0) 280 ( 3.0) 262 ( 8.1) 251 ( 4.1) Nation 47 ( 2.3) 36 ( 2.6) 15 ( 3.7) 284 ( 44)1 279 ( 44)1 Disadvantaged urban State 32 ( 1.2) 28 ( 1.9) 40 ( 1.6) 228 ( 1.6) 227 ( 1.5) 219 ( 1.2) Nation 42 ( 3,3) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 266 ( 42)1 238 ( 6.3)1 Other State 34 ( 2.4) 90 ( 2.1) 36 ( 1.3) 241 ( 3.4) 234 ( 2,8) 225 ( 2.6) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 266 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of mterest, 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 4 1. 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 7 District of Columbia TABLE A26 (continued) .t ..'-:#4.4.eits Reports on the Number of Days of ,Missed : PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ipso Makilliii STATE Asui...marF., Ono or Two Days Throe Days or Moro MAE Maio State 'Nation FOOD . Pg.. NOW and Prillidency 90 2$4 1.5 32 0.91 266 ( 115 33 ( 3.6) 4111 26 ( 3.1) 249 ( $.3) 227 2.2) 27 1.7) 31 1.9) 257 ( 2.6) 27 ( 2.6) 241 ( 2.7) ( 1.6) 271 ( 2.5) 33 ( 22) 241 ( 3.3) 33 ( 12) 277 ( 1.7) and Prallakery 37(1.2 ) 12) 23 1.1) 250 1.9) 224 3.4) 41 4.6) 31 (3.5) 237 ( 3.1) 40 ( 216 ( 1.8 27 ( 1.9 249 ( 2.4) 42 ( 2,4) 233 (2.6) 23 ( 1.6) 253 ( 3.1) 31 ( 2.1) 230 ( 2.6) 16 ( 1.3) 265 ( 3.1) 13 ( .13) 30 ( ill) 37 ( 1.9) '220 ( 1.0) 232 ( 1.8) 221 ( 1.7) 47 ( I.6) 31 ( 1.4) 22 ( 1.4) ,k*,'-lei k 2A) 267 ( 2.1) 250 ( 2.8) ), SS 1.4) .::'. 237 15) ' 41 14) 202 2.3) 22 ( 1.8) 37 ( 1.3) 238 ( 2.4) 226 ( 1.4) 32 ( 1.1) 25 ( 1.3) 288 ( 1.7) 250 ( 1.8) The standsra errors of the eistimatted Statistics appear in parentheses. It can be said with about 95 percent certainty that, for each popuIatitta of lamest, the value for the entire population is within ± 2 standard errors of the artanale for the UM*, Mal Sample size is insufficiem to permit a reliable estimate (fewer than 62 EtUdeatiN 4 2 BEST COPY AVAILABLE THE 090 NAEP TRIAL STAT4 ASSESSMENT 13' District of Columbia TABLE A27 1 Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AtP AVERAGE MATHEMATICS PROFICIENCY 1980 MAD TRIAL STATE AMISINENT straw* Alm Arse . Wedded, DIsairse, giro* Mom TOTAL State Nation RACE/ETHNICITY Black State Nation Hispanic State Nation TYPE OF EOMMUNITY AtiVantaged urban State Nation Disadvantaged urban State Nation Other State . Nation 230 tO) 1.1) 32 2.5) 4/ 227 ZO 52 267 4.1) 33 ( 3.7 as 225 ( 4.4 24 ( 2 212 23 4$ ( 2 257 ( 5.5) 244 ( 2.2 44 ( t5) 203 ( 1.6) 17 ( 3.2) ( 341( 1.1) 231 ( 1.1) 26 ( 2.9) 260 ( 5.0)i 30 ( 2.5) 243 ( 3.9) 27 ( 14) 271 ( 2.4) 4.1 257 SS 2.4 223 1.1 49 2.9 249 ( 4.6)I 230 1.7) 203 22) 40 1.2) 48 a.ej 141 1.43) 6E0 1101 0 IL2) 214 2.7 24 3.2 13 0.6 240 ( 4511 14 11) 250 ( 1A 25 1 1.41 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 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. *** Sample size is insufficient to pesmit a reliable estimate (fewer than 62 students). .143 138 THE 1990 NAEP TRIAL STATE ASSESSMENT District of Columbia TABLE A27 I Students' Perceptions of Mathematics (continued) PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY t 1180 RAO TRIAL MATE .918IEISMEIIT Wrongly Agree Rego . Undo* bd. Disagree, elm* Diaarmt TOTAL State Nation 27 1.3 271 P.aiglinjEraM RS nowaclualo State 38 ( 4.9) f Nation 4,0* .41 20 ( 21) 4. i en NS graduate State 35 ( 1.7) Nation 27 ( 2.1) 232 ( 1.8) tome - State 39 ( 2.4) 243 ( 2.8) Nation 28 ( 2.5) 274 ( 3.1) College graduate State 44 ( 14) 24$ ( 1.7) Nation 30 ( 2.3) 200 ( 2.4) PERDER Male State 36 15) 2311( 1.7) Nation 211 ( 1.5) 273 ( 2.3) Female State 41 ( 1A) 239 ( 1.8) Nation 28 ( 1.7) 209 ( 2.1) 1.0 IA , 49 48 ( SI 1.7 14 ( 0. ft21 24 ( 1 251 ( 1.8 80 ( 5.0) 12 ( 3.0) 223 ( 24) 50 ( 3.3) 30 ( 3.0) 243 ( 2.6) 231 ( . 4.3) 49 ( 1.7) 10 ( 1.6) 223 47 ( ( 2.3 214 ( 28 ( 24) 2.0) 255 ( 2.3 245 ( 2.4) 47 ( 24 15 ( 2.3) 234 ( 2.4 et* ( 0111 47 ( 2.4) 25 ( 1.8) 287 ( 1.9) 258 ( 3.2) 45 ( 14) 11 ( 1.1) 238 ( 3.0) 229 ( 4.0) 51 ( 1.8) 19( 14) 274 ( 2.2) 288 ( 24) 49 ( 1.2) 16 ( 1.0) 227 ( 1.4) 221 ( 2.3) 44 ( 1.2) 24 ( 1.4) 283 ( 2.0) 251 ( 2.4) 47 ( 1.5) 12 ( 1.0) 230 ( 1.4) 222 ( 3.4) 50 ( 1.7) 25 ( 14) 282 ( 14) 252 ( 1.9) . The standard error: of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 144 THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Edncatioo Statistics (NCES), Educational Testing Service (ETS), Westat, and National Computer Systems (NCS). The program bcnefitted from the contriltutions of hundreds of individuals at the date and local lents Governors, Chief State School Officers, State and District Ted Directors, State Coortlinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Finally, and most importantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment Special recognition is due the Council of Chief State School Officeis (CCSSO) for its considerable contnlutioos to the program, especially its management of the National Assessment Planning Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In particular, we note the tignificant contrIntions of Ramsay Selden, Director of the State Education Auessment Center for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza worked closely and collegially with ETS, Westat, and NCI 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 Ednation Agencies worked tirelessly to help ETS staff develop the assessment and a framework for interpret* 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 Memo, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffler, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing distribution, and processing of the materials were the responsi$ility of NCS, under the direction of John O'Neill and Lynn Zaback. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-genereted data with high resolution test and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Memo oversaw the analyses fcr 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 responsible 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. UR GOVERNMENT MINTING OFFICE : 1991 0 - 523-875 QL. 8 MK 7) 146