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ae ea ee ED 330 586 SE 052 096 mrnr Mw - ~ 7 > > = 4 TITLE The State of Mathematics Achievement in Virgin Te? c TH -_ o Ace ~ Islands: The Trial State Assessment at Grade Tse ane mm Jsiue peace aaicat ag Lape eer eee Pee pair INSTITUTIO} Educational Testing Service, Princeton, N.J.; Wa 2 s72 Reeanen -¢ ZA 7~ | ~ ce Vational Assessment of cucationa. Progress, Princeten, Nd. a tok Sten) wa < 5 ~ € oy =+ Ces ate < ta Sel SPONS AGENCY Vational Center for Education Statistics (ED), ~ = ner an rere WA DSiimsiy eWiie awe © ee ONE 94a SHahDs Tehtehoacee—i 4. REPORT NO ETS-21-ST-02; ISBN-0-886385-14-9 eae RE PUSS VALS vUN Bo NOTE 146p.; The entire Report consists of a composite ~ - « Fe el - — ary ° ~ re an executive summary, and 40 separate reports eas. ERS PR ee oT ze for 3 states, DC, Guam, and the Virgin Islands, a Ee: 3 IS ae aaa SES respectively; see SE 052 055-095. se dsor ai Waeak a allem eae Sah 4 f s AVAILABLE FROM Individual state reports are available directly from “ho ecacemene aA n of +h poropriate State & assessmen > Givawaw Of 1@ appropriate osotate Devartment of Education. At ao eA " z ni ye ae = 7 PUB TYPE Statistical Data (110) -- Reporss - = a5 oo m _- | Research/Technical (143) Ee ee a Fa Soe a EDRS PRICE MFO1/PCO6 Plus Postage. noenr a ms ~ é o 7 7 @ ra ~~ . DESCRIPTORS Academic Achievement; Calculators; *Educational a a aes > Assessment; Family Environment; *Grade 8; Homework; Tas Ly ¢ 7 . Junior High Schools; *Mathematics Achievement; T < oC} . Mathematics Instruction; Mathematics Skil , Mathematics Tests; National Programs; Prob lving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing : IDENTIFIERS National Assessment of Educational Progress; xNumeracy; State Mathematics Assessments; Trial State Assessment (NAEP); *Virgin Islands ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In Virgin Islands, 1,326 students in 6 public schools were assessed. This report describes the mathematics proficiency of Virgin Islands eighth-graders, compares their overall performance to students in the nation (using data from the NAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, parents' educational level, and gender). To provide a context for the assessment data, participating students, their mathematics teachers, and principals completed questionnaires which focused on: instructional content (curriculum coverage, amount of homework) ; delivery of math instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, Virgin Islands students had an average proficiency of 218 compared to 261 nationwide. Many fewer students (Virgin Islands-0%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of e Mathematics | Achievement in the VIRGIN {SLANDS The Trial State Assessment at Grade Eight THE NATION’S REPORT — SS — . SST COPY AVAILABLE Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement « U.S. Department of Education ~~ SEOSA2AO09 What is The Nation’s Report Card? NATION’S REPORT (¢ what ARD. 1 Amer in reading, mathematics, THE continuing assessment ol penodically performance avaiabdle to policymake m and progress of education Students a 1Gud of Education Statistics 1 NAEP reports directly thor oO ress created the Nat selecting the subject areas to goals ft h or eac developing guidelines tale, regional ise in the The National Assessme an National he Natior (NAI ica S§ Sudents know science, writing and other fields rs al the nationa late. and a vels, NAEP 1s ar Only jucation Statistics » out the NAEP project sponsiD { pre } a a | *AEP’s conduct and u Ness > Commission g Board which n lal Assessment Governin be assessed age and grade: developing assessment and standards for data analysis d¢ id national compansons: improving Se | Assessment are free from racial, cult nt Governing Board Richard A. Boyd, Chairman Executive Director Martha Holden Jennings Four Cleveland, Ohio Phyllis Wiliiamson Aldrich Curnculum Coordinator Saratoga-Warren B.O.C.E.S Saratoga Springs, New York Francie Alexander Associate Superintendent California Department of Educ Sacramento, California David P. Battini High School History Teacher Cairo-Durham High School Cairo, New York Parris C. Battle Teacher Horace Mann Elementary Miami hoo yy Florida Mary R. Blanton Attorney Porter, Blanton & North Carolina Cromwell Salisbury Boyd W. Boehlje Attorney Klyn, & Boehlje lowa Giaass Pella Linda R. Bryant Teacher Greenway Middle Schoo! Pittsburgh, Pennsylvania Blanton Honorable Michael N. Castle Governor of Delaware Carvel State Office Building Wilmington, Delaware Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hartford, Connecticut Chester E. Finn, Jr. Protessor of Education Vanderbilt University Washington, D.¢ Michael S. Glode Wyoming State Board of Education Saratoga, Wyoming Christine Johnson Principal Abraham Lincoln High School Denver, Colorado John Lindley Principal South Colby Port Orchard Elementary School Washington Carl J. Moser Director of Schools The Lutheran Church Missouri: Synod International Center St. Louis, Missouri Mark D. Musick President Southern Regional Education Board Atlanta, Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith, Arkansas various subject area P Ss SINCE By cr dir specified by Congres i] of the making Tal st specifications sseminating he only nationally representatl 1969. assessments have beer objective information on st par of ot ation s aluation ol NAI re NAEP. The identutying hoard designing the assessment sults, developing standards Nationa Ass ment ind il yt Matthew W. Prophet, Jr Superintendent Portland Oregon Schoo! D Portland, Oregon Honorable William T. Randall Commissioner of Education State Department of Educatior Denver, Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington, D.¢ Honorable Richard W. Riley Attomey Nelson, Mullins Scarborough Riley and Columbia, South Carolina Thomas Topuzes Attomey Law Offices of Frank Rogoziensk Coronado, California Herbert J. Walberg Professor of Education University of Illinois Chicago, Ilinois Assistant Secretary for Educational Research and Improvement (Ex-Officio) U.S. Department of Education Washington, D.C Roy Truby Executive Director, NAGB Washington, D.C ive anc udent th h t conducte P guarantec appropriat d NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement in the VIRGIN ISLANDS The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement * U.S. Department of Education U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment’s individual State reports are available directly from the participating 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 Research and Improvement, by Educational Testing Service. Educational Testing Service is an equal opportunity/affirmative action employer. Educational Testing Service, ETS, and & are registered trademarks of Educational Testing Service. o Table of Contents EXECUTIVE SUMMARY ........... INTRODUCTION Overview of the 1990 Trial State Assessment ....... SESE EE Ln Guidelines for Analysis Ea ANA ALES A GEC MO AE TE POR ER ECT Profile of the Virgin Islands ............................ Eighth-Grade School and Student Characteristics . Schools and Students Assessed PART ONE How Proficient in Mathematics Are Eighth-Grade Students a a I sc sechssevssnsdnesncdvisannersssncnssnrdocpserscenadourbinieoutoons Chapter 1. Students’ Mathematics Performance Levels of Mathematics Proficiency Content Area Performance Chapter 2. Mathematics Performance by Subpopulations ...............0..........0..ccccccccccceseeeeeeesnseeeeeeneeeens .24 Race/Ethnicity Type of Community NS BALE ALA LAT TEC ITLL TARE AT PROMS TERT 2 Gender Content Area Performance ..... THE 1990 NAEP TRIAL STATE ASSESSMENT PART TWO Finding a Context for Understanding Students’ Mathematics Proficiency Chapter 3. What Are Students Taught in Mathematics? ....00.0000.000000000.0ccccceececeeeteeeees Curriculum Coverage Mathematics Homework Instructional Emphasis Summary Chapter 4. How Is Mathematics Instruction Delivered? Availability of Resources Patterns in Classroom Instruction ollaborating in Small Groups (sing Mathematical Objects Materials for Mathematics Instruction Summary Chapter 5. How Are Calculators Used? The Availability of Calculators The Use of Calculators When To Use a Calculator Summary Chapter 6. Who Is Teaching Eighth-Grade Mathematics? ...................0.0......... Educational Background Summary Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching ........7. Amount of Reading Materials in the Home . Hours of Television Watched per Day Student Absenteeism Students’ Perceptions of Mathematics Summary PROCEDURAL APPENDIX og BO Sg 2 i» SDR ee en Bes Saati nena : ~ + THE 1990 NAEP TRIAL STATE ASSESSMEN1 Virgin Islands THE NATION’S REPORT carp | 8 EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project’s history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Tnal State Assessment, eighth-grade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor’s staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands In the Virgin Islands, 6 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade studenits in this sample of schools were representative of 100 percent of the eighth-grade public-school students in the Virgin Islands. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 0 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 4 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 0 percent and 3 percent of the population, respectively. In total, 1,326 eighth-grade Virgin Islands public-school students were assessed. The weighted student participation rate was 93 percent. This means that the sample of students who took part in the assessment was representative of 93 percent of the eligible eighth-grade public-school student population in the Virgin Islands Students’ Mathematics Performance The average proficiency of eighth-grade public-school students from the Virgin Islands on the NAEP mathematics scale is 218. This proficiency is lower than that of students across the nation (261). The Virgin Islands participated in the 1990 Tnal State Assessment Program despite losing five weeks of school prior to the mathematics assessment as a result of Hurricane Hugo. Average proficiency on the NAEP scale provides a global view of eighth graders’ mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students’ proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. 9 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands In the Virgin Islands, 76 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 Virgin Islands (0 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in the Virgin Islands performed lower than students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Tnal State Assessment permits reporting on the performance of various subpopulations of the Virgin Islands eighth-grade student population defined by race/ethnicity, type of community, parents’ education level, and gender. in the Virgin Islands: Black students had higher average mathematics proficiency than did Hispanic students. Further, a greater percentage of Black students than Hispanic students attained level 300. The results by type of community indicate that the average mathematics performance of the Virgin Islands students attending schools in areas classified as “other” was higher than that of students attending schools in extreme rural areas. , In the Virgin Islands, the average mathematics proficiency of cizhth-grade public-school students having at least one parent who gaduated from college was approximately 11 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 Virgin Islands had a higher average mathematics proficiency than did eighth-grade females in the Virgin Islands. In addition, there was no difference between the percentages of males and females in the Virgin Islands who attained level 300. Compared to the national results, females in the Virgin Islands performed lower than females acsoss the country; males in the Virgin Islands performed lower than males across the country. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands F A Context for Understanding Students’ Mathematics Proficiency Information on students’ mathematics proficiency is valuable in and of itself, but it becomes more useful for iraproving instruction and setting policy when supplemented with contextual information about schools, teachers, and students lo gather such information, the students participating in the 1990 Tnal 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 descnbe 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 Virgin Islands are as follows: About half of the students in the Virgin Islands (52 percent) were in schools where mathematics was identified as a special priority. This is about the same percentage as that for the nation (63 percent). In the Virgin Islands, 85 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in the Virgin Islands were taking eighth-grade mathematics (88 percent) than were taking a course in pre-algebra or algebra (9 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 Virgin Islands spent 30 minutes doing mathematics homework each day; according to the students, most of them spent 15 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. 1] THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands ¢ In the Virgin Islands, 0 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 66 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 Virgin Islands, 21 percent of the students aever used a calculator to work problems in class, while 53 percent almost always did ¢ In the Virgin Islands, 37 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 half of the students (51 percent) had teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. ¢ S udents in the Virgin Islands who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of these materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. * Some of the eighth-grade public-school students in the Virgin Islands (18 percent) watched one hour or less of television each day; 27 percent watched six hours or more. Average mathematics proficiency was higher for students who spent four to five hours watching television than for students who watched television one hour or less each day. — raw) THE 1990 NAEP TRIAL STATE ASSESSMENT 5 Virgin Islands og HE NATION'S CARD |e INTRODUCTION As a sesult 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 lowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands i wD THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Virgin Islands This report describes the performance of the eighth-grade public-school students in the Virgin Islands 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 Virgin Islands. ¢ Part One describes the mathematics performance of the eighth-grade public-school students in the Virgin Islands and the nation. ¢ Part Two relates students’ mathematics performance to contextual information about the mathematics policies and instruction in schools in the Virgin Islands and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project’s history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survey instrument for the eighth grade and shall conduct a demonstration of the instrument in 1990 in States which wish to participate, with the purpose of determining whether such an assessment yields valid, reliable State representative data. (Section 406 (i)(2)(C)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i) (2) (C)(i))) As a result of the legislation, the 1990 NAEP program included a Tnal State Assessment Program in eighth-grade mathematics. National assessments jn mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions 8 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patterned after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National 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 program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-grade public-school students in the Virgin Islands and the naiion. Results also are provided for groups of students defined by shared characteristics -- race/ethnicity, type of community, parents’ education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for the Virgin Islands are based only on the students included in the Trial State Assessment Program. However, the results for the nation are based on the nationally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the national results from the 1990 national NAEP program was necessary because the voluntary nature of the Trial State Assessment Program did not guarantee representative national results, since not every state participated in the program. ' National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 9 Virgin Islands 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 Procedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for the Virgin Islands. TYPE OF COMMUNITY Results are provided for four mutually exclusive community types -- advantaged urban, disadvantaged urban, extreme rural, and other -- as defined below: Advantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students’ parents are in professional or managerial positions. Disadvantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students’ parents are on welfare or are not regularly employed. Extreme Rural: Students in this group live outside metropolitan statistical areas, live in areas with a population below 10,000, and attend schools where many of the students’ parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS’ EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting 16 10 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands GENDER Results are reported separately for males and females. REGION The United States nas been divided into four regions: Northeast, Southeast, Central, and West. States included in each region are shown in Figure 1. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURE | | Regions of the Country THE NATION'S REPORT CARD NORTHEAST SOUTHEAST CENTRAL Connecticut Delaware District of Columbia Maine Maryland Massachusetts New Hampshire New Jersey New York Pennsylvania Rhode Island Vermont Virginia Alabama Arkansas Florida Georgia Kentucky Louisiana Mississippi North Carolina South Carolina Tennessee Virginia West Virginia illinois Indiana lowa Kansas Michigan Minnesota Missouri Nebraska North Dakota Ohio South Dakota Wisconsin Alaska Arizona California Colorado Hawaii Idaho Montana Nevada New Mexico Oklahoma Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means Or proportions and the standard errors of those statistics lhe 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 1s strong (i.¢., the difference is statistically significant), the report descnbes 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 proporiions appear to be about the same or not. If the evidence is not sufficiently strong (1.e., the difference is not statistically significant), the means or proportions are described as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the apparent magnitude of the difference between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. When three or more groups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendix. 1§ THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a Statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.¢., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Profile of the Virgin Islands EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table | provides a profile of the demographic characteristics of the eighth-grade public-school students in the Virgin Islands and the nation. This profile is based on data collected from the students and schools participating in the Trial State Assessment. TABLE | Profile of Virgin Islands Eighth-Grade Public-School Students PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation DEMOGRAPHIC SUBGROUPS Race/Ethnicity White Black Hispanic Asian American Indian Type of Community Advantaged urban Disadvantaged urban Extreme rural Other Parents’ Education Did not finish high school Graduated high school Some education after high school Graduated college Gender Male Female The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages for Race/Ethnicity may not add to 100 percent because some students categorized themselves as “Other.” This may also be true of Parents’ Education, for which some students responded “I don’t know.”” Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Virgin Islands schools and students sampled for the 1990 Trial State Assessment. In the Virgin Islands, 6 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 Virgin Islands. TABLE 2 Profile of the Population Assessed in the Virgin Islands EIGHTH-GRADE PUBLIC SCHOOL EIGHTH-GRADE PUBLIC-SCHOOL STUDENT PARTICIPATION . PARTICIPATION Weighted student participation Weighted school participation 9 P p rate after make-ups rate before substitution Number of students selected to Weighted school participation participate in the assessment rate after substitution Number of students withdrawn Number of schools originally from the assessment sampled Percentage of students who were of Limited English Proficiency Number of schools not eligible Percentage of students excluded Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating schools In the Virgin Islands, the Trial State Assessment was based on all eligible schools schools. THE 1990 NAEP TRIAL STATE ASSESSMENT 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 Pian status Number of students to be assessed Number of students assessed 3% 1,427 1,326 There was no sampling of Virgin Islands In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 0 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 4 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 0 percent and 3 percent of the population, respectively. In total, 1,326 eighth-grade Virgin Islands public-school students were assessed. The weighted student participation rate was 93 percent. This means that the sample of students who took part in the assessment was representative of 93 percent of the eligible eighth-grade public-school student population in the Virgin Islands. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE NATION’S REPORT carp |@8P PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Virgin Islands Public Schools? Ihe 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 S00. This part of the report contains two chapters that describe the mathematics proficiency of eighth-grade public-school students in the Virgin Islands. Chapter 1 compares the overall mathematics performance of the students in the Virgin Islands to students in 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 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands CHAPTER | Students’ Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from the Virgin Islands on the NAEP mathematics scale is 218. This proficiency is lower than that of students across the nation (261). The Virgin Islands participated in the 1990 Trial State Assessment Program despite losing five weeks of school prior to the mathematics assessment as a result of Hurricane Hugo. FIGURE 2 Average Eighth-Grade Public-School Mathematics Proficiency ‘ Average NAEP Mathematics Scale saan CARD 225 250 275 300 500 Proficiency /\, \ee Virgin Islands 218 ( 0.5) Nation 261 ( 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within + 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations, ? Differences reported are statistically different at about the 9S percent certainty level. This means that with about 95 percent certainty there is a real difference in the a rage mathematics proficiency between the two populations of interest. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands 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 define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are given in Figure 3. It is important to note that the definitions of these levels are based solely 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 Virgin Islands, 76 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 Virgin Islands (0 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometnic properties, and simple algebraic manipulations (level 300). CONTENT AREA PERFORMANCE As previously indicated, the questions comprising the ‘nal State Assessment covered five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Figure 5 provides the Virgin Islands and national results for each content area. Students in the Virgin Islands performed lower than students in the nation in ali of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE 3 | Levels of Mathematics Proficiency z LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-step word problems and select the greatest four-digit number in a list. In measurement, 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 transiations of word problems to numerical sentences and extend simple pattern sequences LEVF?!. 250 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 and two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to other elementary two-step word problems. in these basic problem-solving Situations, they can identify missing or extraneous information and have some knowledge of when to use computational estimation, They have a rudimentary understanding of such concepts as whole number place value, “even,” “factor,” and “multiple.” In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and probability. In algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions ?6 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE NATION'S REPORT rege P ‘ : CARD FIGURE 3 Levels of Mathematics Proficiency “7 (continued) LEVEL 300 Reasoning and Problem Solving Involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations Students at this level are able to represent, interpret, and perform simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, and recognize the equivalence between common fractions and decimals, including pictorial representations They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expressions, including those with exponents and negative integers In measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open linear sentences and inequalities by substitution, and checking and graphing an interval representing a compound inequality when it is described in words. They can determine and apply a rule for simple functional relations and extend a numerical pattern. LEVEL 350 Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to include some properties of exponents. They can recognize scientific notation on a calculator and make the transition between scientific notation and decimal notation In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles to soive 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 solve problems, such as determining the slope of a line. In data analysis, these students can compute means from frequency tables and determine the probability of a simple event. in algebra, they can identify an equation describing a linear relation provided in a table and solve literal equations and a system of two linear equations. They are developing an understanding of linear functions and their graphs, as wel! as functional notation, including the composition of functions They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands REPT Pt FIGURE 4 Levels of Eighth-Grade Public-School — teins i Mathematics Proficiency Percentage LEVEL 350 Territory 0 ( 0.0) Nation 0( 0.2) LEVEL 309 Territory 0 ( 0.2) Nation = 12 ( 1.2) LEVE!. 250 Territory ee 11 ( 0.8) Nation —— 64 ( 1.6) LEVEL 200 Territory qunging 76 ( 1.5) Nation weal 97 ( 0.7) ) 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within + 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. @ wae) ad 22 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE 5 Territory Nation Territory Nation Territory Nation Territory Nation Territory Nation Eighth-Grade Public-School Mathematics Content Area Performance THE NATION'S [roma REPORT CARD lA { Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within + 2 errors of the estimated mean (95 percent confidence interval, denoted by 4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT standard 23 Average Proficiency NUMBERS AND OPERATIONS 4 227 ( 0.6) vy 266 ( 1.4) MEASUREMENT pare) 214 ( 1.3) —— 258 ( 1.7) GEOMETRY et 222 ( 0.8) —— 259 ( 1.4) DATA ANALYSIS, STATISTICS, AND PROBABILITY a] 196 ( 1.2) a" 262 ( 1.8) ALGEBRA AND FUNCTIONS he 218 ( 0.8) m4 260 ( 1.3) ay —— 0 200 225 250 275 300 500 Virgin Islands CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents’ education level, and gender. RACE/ETHNICITY The Trial State Assessment results can be compared according to the different racial/ethnic groups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for Black and Hispanic students from the Virgin Islands 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 a greater percentage of Black students than Hispanic students attained level 300. 30 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE 6 Average Eighth-Grade Public-School Mathematics Proficiency by Race/Ethnicity THE NATION'S NAEP Mathematics Scale — Average 225 250 Proficiency A Virgin Islands Black Hispanic Nation Black 238 { 2.8) Hispanic 243 ( 2.8) 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 R4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE 7 LEVEL 300 Territory Black Hispanic Nation Black Hispanic LEVEL 250 Territory Black Hispanic Nation Black Hispanic LEVEL 200 Territory Black Hispanic Nation Black Hispanic THE NATION'S REPORT [romp CARD Levels of Eighth-Grade Public-School a Mathematics Proficiency by Race/Ethnicity { 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within + 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations Proficiency level 350 1s not presented in this figure because so few students attained that level THE 1990 NAEP TRIAL STATE ASSESSMENT Percentage Virgin Islands TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in areas classified as “other” and extreme rural areas. (These are the “type of community” groups in the Virgin Islands with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Virgin Islands students attending schools in areas classified as “other” was higher than that of students attending schools in extreme rural areas. FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community | NAEP Mathematics Scale REPORT Average CARD 225 250 275 Proficiency Virgin Islands Extreme rural Other Nation Extreme rural Other The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within + 2 standard errors cf the estimated mean (95 percent confidence interval, denoted by 4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE 9 LEVEL 300 Territory Ext. rural Other Nation Ext. rural Other LEVEL 250 Territory Ext. rural Other Nation Ext. rural Other LEVEL 200 Territory Ext. rural Other Nation Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within + 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ' Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT Percentage Virgin Islands PARENTS’ EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In the Virgin Islands, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 11 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, a smaller percentage of students in the Virgin Islands (21 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 15 percent for the Virgin Islands and 10 percent for the nation. FIGURE 10 | Average Eighth-Grade Public-School Mathematics Proficiency by Parents’ Education NAEP Mathematics Scale pat Average CARO 225 250 Proficiency Virgin Islands HS non-graduate 208 .{ 2.5) HS graduate 220 { 1.4) Some college 227 { 2.6) College graduate 220 { 1.6) Nation HS non-graduate 243 { 2.0) HS graduate 254 { 1.5) Some college 286 { 1.7) College graduate 274 { 1.6) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within + 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 4). If the confidence intervals for the populations do not overlap, there is a Statistically significant difference between the populations. rHE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE 11 | Levels of Eighth-Grade Public-School Mathematics Proficiency by Parents’ Education LEVEL 300 Territory HS non-grad MS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 Territory HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 Territory HS non-grad HS graduate Some college College grad Nation HS non-grad HS graduate Some college College grad 20 40 60 80 Percentage at or Above Proficiency Levels I'he 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 4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 36 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands GENDER As shown in Figure 12, eighth-grade males in the Virgin Islands had a higher average mathematics proficiency than did eighth-grade females in the Virgin Islands. Compared to the national results, females in the Virgin Islands performed lower than females across the country; males in the Virgin Islands performed lower than males across the country. FIGURE 12 | Average Eighth-Grade Public-School Mathematics Proficiency by Gender NAEP Mathematics Scale rerum Average 250 rr Proficiency Virgin Islands Male 220 ( 0.9) Female 218 ( 1.0) Nation Male Female The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within + 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 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 Virgin Islands who attained level 200. The percentage of females in the Virgin Islands who attained level 200 was smaller than the percentage of females in the nation who attained level 200. Also, the percentage of males in the Virgin Islands who attained level 200 was smaller than the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE 13 LEVEL 300 Territory Male Female Male Female LEVEL 250 Territory Male Nation Female Male Female LEVEL 200 Territory Male Nation Female Male Female REP ONT Dot Levels of Eighth-Grade Public-School oom 4 Mathematics Proficiency by Gender pet 20 40 60 80 Percentage at or Above Proficiency Levels 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). Proficiency level 350 1s not presented in this figure because so few students attained that level 3§ THE 1990 NAEP TRIAL STATE ASSESSMENT Percentage Virgin Islands In addition, there was no difference between the percentages of males and females in the Virgin Islands who attained level 300. The percentage of females in the Virgin Islands 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 Virgin Islands 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 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 3 Eighth-Grade Public-School Mathematics Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS Data Analysis, 1900 NAEP TRIAL Numbers and Measurement Statistics, and Algebra and STATE ASSESSMENT Operations Probability Functions —EEEE TOTAL Territory Nation RACE/ETHNICITY Black Territory 2 216 ( 1.6) Nation 227 ( 3.6) Hispanic Territory 2) 208 ( 2.0) Nation 7) 238 ( 3.4) TYPE OF COMMUNITY Extreme rural Territory 1.3) 206 ( 3.3) 2.0) 179 ( 1.8) 205 ( 1.2) Nation 4.3)! 254 ( 4.2)! 45)! 257 ( 5.0)! 256 ( 4.8)! Other Territory 0.6) 216 ( 1.4) 0.8) 200 ( 1.4) 221 ( 0.9) Nation 2 1.9) 257 ( 2.4) 1.7) 261 ( 2.2) 261 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency 4() THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 3 Eighth-Grade Public-School Mathematics (continued) Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS Data Analysis Measurement Geometry Statistics, and Probability 1990 NAEP TRIAL Numbers and STATE ASSESSMENT Operations Algebra and Functions Proficiency Proficiency Proficiency Proficiency TOTAL Territory Y 0.6 1.3) 222 ( 0.8) 2) 218 ( 0.8) 196 ( 1. Nation i 1) 259 ( 1.4) 262 ( 1.8) 260 ( 1.3) PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation Coliege graduate Territory Nation GENDER Male Territory 22 220 | 225 ) 98 Nation 262 | ( 1.7) 262 | Female Territory : 209 ( 1.8) 2 0.8) 193 | Nation 253 ( 16 y 1.5) 261 | 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 rHE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE NATION'S REPORT [n= carp |SeeP PART TWO Finding a Context for Understanding Students’ Mathematics Proficiency Information on students’ mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students’ proficiency in the subject, and provide an educational context for understanding information on student achievement. It is important to note that the NAEP data cannot establish cause-and-effect links between various contextual factors and students’ mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers’ suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an enormous impact on future academic achievement. Yet, as shown in Chapters 3 and 7, large proportions of students report having spent much more time each day watching television than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students’ mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students’ home support for learning THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.’ This chapter focuses on curricular and instructional content issues in Virgin Islands public schools and their relationship to students’ proficiency. Table 4 provides a profile of the eighth-grade public schools’ policies and staffing. Some of the salient results are as follows: * About half of the eighth-grade students in the Virgin Islands (52 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. > Curtis McKnight, et al., The Underachieving Curriculum. Assessing U.S. School Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign, IL: Stipes Publishing Company, 1987). Lynn Steen, Ed. Everybody Counts. A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands In the Virgin Islands, 85 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Many of the students in the Virgin Islands (81 percent) were taught mathematics by teachers who teach only one subject. About half (45 percent) of the students in the Virgin Islands were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was more prevalent across the nation (63 percent). TABLE 4 Mathematics Policies and Practices in Virgin Islands Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Virgin Isiands Nation Percentage of eighth-grade students in public schools that identified mathematics as receiving special emphasis in school-wide goals and objectives, instruction, in-service training, etc. 52 ( 0.2) 63 ( 5.9) Percentage of eighth-grade public-school students who are offered a course in algebra for high school course placement or credit 85 ( 0.1) 78 ( 4.6) Percentage of eighth-grade students in public schools who are taught by teachers who teach only mathematics 81 ( 0.2) 91 ( 3.3) Percentage of eighth-grade students in public schools who are assigned to a mathematics class by their ability in mathematics 45 ( 0.6) 63 ( 4.0) Percentage of eighth-grade students in pubiic schools who receive four or more hours of mathematics instruction per week 25 ( 0.8) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample 45 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands 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 Virgin Islands are taking mathematics courses. Based on their responses, shown in Table 5: * A greater percentage of students in the Virgin Islands were taking eighth-grade mathematics (88 percent) than were taking a course in pre-algebra or algebra (9 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in the Virgin Islands who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 Students’ Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation Percentage What kind of mathematics class are you and taking this year? Proficiency Eighth-grade mathematics 4 62 ( 2.1) 251 ( 1.4) Pre-aligebra , 19 ( 1.9) 272 ( 2.4) Algebra ( 15 ( 1.2) 240 ( 4.3) 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Further, from Table A5 in the Data Appendix:* About the same percentage of females (8 percent) and males (9 percent) in the Virgin Islands were enrolled in pre-algebra or algebra courses. In the Virgin Islands, 9 percent of Black students and 5 percent of Hispanic students were enrolled in pre-algebra or algebra courses. Similarly, 8 percent of students attending schools in areas classified as “other” and 11 percent in schools in extreme rural areas were enrolled in pre-algebra or algebra courses. MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers’ and students’ responses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in the Virgin Islands spent 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent 15 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 (lable 6 and Table A6 in the Data Appendix): In the Virgin Islands, 3 percent of the students spent no time each day on mathematics homework, compared to | percent for the nation. Moreover, 10 percent of the students in the Virgin Islands and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. * For every table in the body of the report that iicludes 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 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands The results by race/ethnicity show that 10 percent of Black students and 13 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 3 percent of Black students and 4 percent of Hispanic students spent no time doing mathematics homework. In addition, 13 percent of students attending schools in areas classified as “other” and 2 percent in schools in extreme rural areas spent an hour or more on mathematics homework daily. In comparison, 2 percent of students attending schools in areas classified as “other” and 7 percent in schools in extreme rural areas spent no time doing mathematics homework. TABLE 6 Teachers’ Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation About how much time do students spend on mathematics homework each day? none 15 minutes 30 minutes 45 minutes An hour or more The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 7 Students’ Reports on the Amount of Time They Spent ca Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin isiands Nation About how much time do you usually Percentage spend each day on mathematics and homework? Proficiency None 9( 0.8) 251 ( 2.8) 15 minutes 30 minutes 45 minutes ‘ 1.9) An hour or more 0.9) 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 valuc for the entire population is within + 2 standard errors of the estimate for the sample And, according to the students (Table 7 and Table A7 in the Data Appendix): In the Virgin Islands, relatively few of the students (8 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 18 percent of the students in the Virgin Islands and 12 percent of students in the nation spent an hour or more each day on mathematics homework. The results by race/ethnicity show that 19 percent of Black students and 16 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 8 percent of Black students and 7 percent of Hispanic students spent no time doing mathematics homework. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands * In addition, 18 percent of students attending schools in areas classified as “other” and 16 percent in schools in extreme rural areas spent an hour or more on mathematics homework daily. In comparison, 7 percent of students attending schools in areas classified as “other” and 9 percent in schools in extreme rural areas spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement.’ Because the Trial State Assessment questions were designed to measure students’ knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students’ opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place “heavy,” “moderate,” or “little or no” emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: * Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. * Measurement. Teachers were asked about emphasis placed on one topic: measurement. * Geometry. Teachers were asked about emphasis placed on one topic: geometry. * Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. ¢ Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. * National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989) rHE 1990 NAEP TRIAL STATE ASSESSMENT 45 Virgin Islands 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 | to “little or no emphasis” responses. Each teacher’s responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- “heavy emphasis” and “little or no emphasis” -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 8 Teachers’ Reports on the Emphasis Given to Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin islands Nation Teacher “emphasis” categories by content areas Numbers and Operations Heavy emphasis ; 49 ( 3.8) 260 ( 1.8) Little or no emphasis i 15 ( 2.1) 287 ( 3.4) Measurement Heavy emphasis , 17 ( 3.0) 250 ( 5.6) Little or no emphasis } 33 ( 4.0) 272 ( 4.0) Geometry Heavy emphasis , 3.8) 3.2) Little or no emphasis d 3.3) 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 14 ( 2.2) 269 ( 4.3) Little or no emphasis J 53 ( 4.4) 261 ( 2.9) Algebra and Functions Heavy emphasis 47 ( 0. 46 ( 3.6) 227 ( 1: 275 ( 2.5) Little or no emphasis 19( 0. 20 ( 3.0) 209 ( 3. 243 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the “Moderate emphasis’’ category is not included. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: About half of the eighth-grade students in the Virgin Islands (52 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In the Virgin Islands, 85 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in the Virgin Islands were taking eighth-grade mathematics (88 percent) than were taking a course in pre-algebra or algebra (9 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 Virgin Islands spent 30 minutes doing mathematics homework each day; according to the students, most of them spent 15 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. In the Virgin Islands, relatively few of the students (8 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 18 percent of the students in the Virgin Islands and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands y2x* -22%-3 y Li Lili R CHAPTER 4 How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning 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 learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers’ use of resources is obviously constrained by the availability of those resources. Thus, the assessed students’ teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. ® National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991) & oJ > THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Virgin Islands From Table 9 and Table A9 in the Data Appendix: In the Virgin Islands, 0 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 66 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 Virgin Islands, 0 percent of students attending schools in areas classified as “other” and 0 percent in schools in extreme rural areas had mathematics teachers who got all the resources they needed. By comparison, in the Virgin Islands, 65 percent of students attending schools in areas classified as “other” and 69 percent in schools in extreme rural areas were in classrooms where only some or no resources were available. TABLE 9 Teachers’ Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation Which of the following statements is true to teach your Class? about how well supplied you are by your Percentage Percentage schoo! system with the instructional and and materials and other resources you need Proficiency Proficiency | get all the resources | need 0 ( 0.0) 13 ( 2.4) re ( ited | 265 | 4.2) | get most of the resources | need 34 ( 0.6) 56 ( 4.0) 223 ( 1.1) 265 ( 2.0) | get some or none of the resources | need 66 ( 0.6) 31 ( 4.2) 216 ( 0.8) 261 ( 2.9) The standard errors of the estimated statistics appear in parentheses. 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). 50 THE 1990 NAEP TRIAL STATE ASSESSMENT it can be said with about 95 percent Virgin Islands PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students’ mathematics learning. Increasing the use of “hands-on” examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.’ Students’ responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: About half of the students in the Virgin Islands (53 percent) worked mathematics problems in small groups at least once a week; some never worked mathematics problems in small groups (12 percent). The largest percentage of the students (65 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; some never used such objects (15 percent). In the Virgin Islands, 84 percent of the students were assigned problems from a mathematics textbook almost every day; 6 percent worked textbook problems about once a week or less. About half of the students (49 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (22 percent). ” Thomas Romberg, “A Common Curriculum for Mathematics,” /ndividual Differences and the Common Curriculum: Eighty-second Yearbook of the National Society for the Study of Education (Chicago, IL: University of Chicago Press, 1983) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 10 Instruction Teachers’ Reports on Patterns of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Isiands Nation About how often do students work and : are : problems in small groups? , Proficiency Proficiency At least once a week 53 ( 0.8) 50 ( 4.4) 211 ( 0.8) 260 ( 2.2) Less than once a week 36 ( 0.7) 43 ( 4.1) 233 ( 1.1) 264 ( 2.3) Never 12 ( 0.6) 8( 2.0) 215 ( 1.4) 277 ( 5.4)! About how often do students use objects Percentage Percentage like rulers, counting blocks, or geometric and and solids? Proficiency Proficiency At least once a week 20 ( 1.0) 22 ( 3.7) 214 ( 1.4) 254 ( 3.2) Less than once a week 65 ( 1.2) 69 ( 3.9) 220 ( 0.8) 263 ( 1.9) Never 15 ( 0.8) 9( 2.6) 222 ( 1.6) 282 ( 5.9)! of the estimate for the sample The standard errors of the estimated statistics appear in parentheses. certainty that, for each population of interest, the value for the entire population is within + 2 standard errors ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. It can be said with about 95 percent THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 11 Teachers’ Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAE? TRIAL STATE ASSESSMENT Virgin Isiands Nation About how often do students do problems from textbooks? Almost every day 84 ( 0.9) 221 ( 0.6) Several times a week 9 ( 0.8) 208 ( 1.3) About once a week or less 6 ( 0.2) 215 ( 3.7) About how often do students do problems Percentage on worksheets? and Proficiency At least several times a week 49 ( 0.7) 210 ( 0.9) About once a week 29 ( 0.6) 227 ( 1.0) Less than weekly 22 ( 0.6) 233 ( 1.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. The next section presents the students’ responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands COLLABORATING IN SMALL GROUPS In the Virgin Islands, 51 percent of the students reported never working mathematics problems in small groups (see Table 12); 34 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 Students’ Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation Percentage How often do you work in small groups and and in your mathematics Class? i Proficiency At least once a week . 28 ( 2.5) ’ 258 ( 2.7) Less than once a week , 28 ( 1.4) 267 ( 2.0) Never . 44 ( 2.9) 261 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percert certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. Examining the subpopulations (Table Al2 in the Data Appendix): In the Virgin Islands, 33 percent of students attending schools in areas classified as “other” and 34 percent in schools in extreme rural areas worked in small groups at least once a week. Further, 32 percent of Black students and 37 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 (30 percent and 37 percent, respectively). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands 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 A13 in the Data Appendix summarize these data: More than half of the students in the Virgin Islands (56 percent) never used mathematical objects; 25 percent used these objects at least once a week. Mathematical objects were used at least once a week by 28 percent of students attending schools in areas classified as “other” and 15 percent in schools in extreme rural areas. Males were more likely than females to use mathematical objects in their mathematics classes at least once a week (30 percent and 21 percent, respectively). In addition, 26 percent of Black students and 25 percent of Hispanic students used mathematical objects at least once a week. TABLE 13 Students’ Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation How often do you work with objects like Percentage Percentage rulers, counting blocks, or geometric and and solids in your mathematics Class? Proficiency Proficiency At least once a week 25 ( 0.9) 28 ( 1.8) 219 ( 1.4) 258 ( 2.6) Less than once a week 18 ( 1.0) art 42) 228 ( 1.3) 269 ( 1.5) Never 56 ( 1.1) 41 ( 2.2) 215 ( 0.8) 259 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in the Virgin Islands who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table A14 in the Data Appendix): About three-quarters of the students in the Virgin Islands (73 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 73 percent of students attending schools in areas classified as “other” and 70 percent in schools in extreme rural areas. TABLE 14 Students’ Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Isiands Nation How often do you do mathematics Percentage Percentage problems from textbooks in your and and mathematics Class? Proficiency Proficiency Almost every day 73 ( 1.4) 74 ( 1.9) 220 ( 0.7) 267 ( 1.2) Several times a week 17 ( 0.9) 14 ( 0.8) 216 ( 1.5) 252 ( 1.7) About once a week or less 10 ( 1.1) 12 ( 1.8) 207 ( 1.9) 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. 61 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands And, for the frequency of worksheet usage (Table 15 and Table A15 in the Data Appendix): ¢ Less than half of the students in the Virgin Islands (38 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 40 percent of students attending schools in areas classified as “other” and 34 percent in schools in extreme rural areas. TABLE 15 Students’ Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation How often do you do mathematics Percentage Percentage problems on worksheets in your and and mathematics class? Proficiency Proficiency At least several times a week 38 ( 1.5) 38 ( 2.4) 212 ( 1.0) 253 ( 2.2) About once a week 30 ( 1.5) 25 ( 1.2) 222 ( 1.1) 261 ( 1.4) Less than weekly 32 ( 1.3) 37 ( 2.5) 222 ( 1.1) 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. Table 16 compares students’ and teachers’ responses to questions about the patterns of classroom instruction and materials for mathematics instruction. THE 1990 NAEP TRIAL STATE ASSESSMENT 57 Virgin Islands TABLE 16 Comparison of Students’ and Teachers’ Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1980 NAEP TRIAL STATE ASSESSMENT Virgin isiands Nation jeasinsimesienone Patterns of classroom instruction Percentage of students who work mathematics probiems in small groups At least once a week d 53 ( 0.8) Less than once a week . 36 ( 0.7) Never A 12 ( 0.6) Percentage of students who use objects like rulers, counting blocks, or geometric solids At least once a vwweek Less than once a week Never Materials for mathematics instruction Percentage of students who use a mathematics textbook Aimost every day Several times a week About once a week or less Percentage of students who use a mathematics worksheet At least several times a week E 49 ( 0.7) , 34 ( 3.8) About once a week ' 29 ( 0.6) , 33 ( 3.4) Less than weekly ; 22 ( 0.6) . 32 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery practices and resources. It appears that mathematics textbooks and worksheets continue to play a major role in mathematics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students’ mathematics teachers: About half of the students in the Virgin Islands (53 percent) worked mathematics problems in small groups at least once a week; some never worked in small groups (12 percent). The largest percentage of the students (65 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and some never used such objects (15 percent). In the Virgin Islands, 84 percent of the students were assigned problems from a mathematics textbook almost every day; 6 percent worked textbook problems about once a week or less. About half of the students (49 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (22 percent). And, according to the students: In the Virgin Islands, 51 percent of the students never worked mathematics problems in small groups; 34 percent of the students worked mathematics problems in small groups at least once a week. More than half of the students in the Virgin Islands (56 percent) never used mathematical objects; 25 percent used these objects at least once a week. About three-quarters of the students in the Virgin Islands (73 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. Less than half of the students in the Virgin Islands (38 percent) used worksheets at least several times a week, compared to 38 percent in the nation. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Virgin Islands CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks." The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. * National Assessment of Educational Progress, Mathematics Objectives. 1990 Assessment (Princeton, NJ Educational Testing Service, 1988) National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 65 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Table 17 provides a profile of Virgin Islands eighth-grade public schools’ policies with regard to calculator use: * In comparison to 33 percent across the nation, 3 percent of the students in the Virgin Islands had teachers who allowed calculators to be used for tests. * A smaller percentage of students in the Virgin Islands than in the nation had teachers who permitted unrestricted use of calculators (1 percent and 18 percent, respectively). TABLE 17 Teachers’ Reports of Virgin Islands Policies on Calculator Use PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation Percentage Percentage Percentage of eighth-grade students in public schools whose teachers permit the unrestricted use of caiculators 41 ( 0.0) 18 ( 3.4) Percentage of eighth-grade students in public schools whose teachers permit the use of calculators for tests 3 ( 0.0) 33 ( 4.5) Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned by the school 25 ( 1.0) 56 ( 4.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample 66 THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Virgin Islands THE AVAILABILITY OF CALCULATORS In the Virgin Islands, most students or their families (92 percent) owned calculators (Table 18); however, fewer students (40 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In the Virgin Islands, 41 percent of Black students and 36 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 (38 percent and 42 percent, respectively). 18 Students’ Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin islands Nation Percentage Do you or your family own a calculator? and Proficiency 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( 3.8) Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes 40 ( 1.4) 217 ( 1.2) No 60 ({ 1.4) 219 ( 0.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample °—_— | THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE USE OF CALCULATORS As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment, students were asked how frequently (never, sometimes, almost always) they used calculators for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In the Virgin Islands, 21 percent of the students never used a calculator to work problems in class, while 53 percent almost always did. Some of the students (13 percent) never used a calculator to work problems at home, compared to 33 percent who almost always used one. About one-quarter of the students (27 percent) never used a calculator to take quizzes or tests, while 35 percent almost always did. TABLE 19 Students’ Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation How often do you use a calculator for the following tasks? Working problems in class Almost always 53 | 214 | Never 21 | 233 | Doing problems at home Almost always 33 | 1,3) 212 ( 1.8) Never 13 | 0.9) 227 | 1.8) Taking quizzes or tests Aimost always 35 ( 1.5) 27 ( 1.4) 212 ( 1.2) 253 ( 2.4) Never 27 ( 1.1) 30 ( 2.0) 232 ( 1.6) 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 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands 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 Tnal 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 categorized into two groups High -- students who used the calculator appropniately (i.c., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented Other -- students who did not use the calculator appropnately 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. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below ¢ A smaller percentage of students in the Virgin Islands 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, 34 percent of Black students and 30 percent of Hispanic students were in the High group. TABLE 20 | Students’ Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP T TATE ASSESSMENT Virgin Islands Nation y ‘ Percentage Percentage Calculator-use group and and Proficiency Proficiency High 33 ( 1.5) 42 ( 1.3) 223 ( 1.2) 272 ( 1.6) Uther 67 ( 1.5) 58 ( 1.3) 216 ( 1.0) 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 enure population is within of the estimate for the sample THE 1990 NAEP TRIAL STATE ASSESSMENT 2 standard errors Virgin Islands 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, 3 percent of the students in the Virgin Islands had teachers who allowed calculators to be used for tests. ¢ A smaller percentage of students in the Virgin Islands than in the nation had teachers who permitted unrestricted use of calculators (1 percent and 18 percent, respectively). ¢ In the Virgin Islands, most students or their families (92 percent) owned calculators; however, fewer students (40 percent) had teachers who explained the use of calculators to them. ¢ In the Virgin Islands, 21 percent of the students never used a calculator to work problems in class, while 53 percent almost always did. ¢ Some of the students (13 percent) never used a calculator to work problems at home, compared to 33 percent who almost always used one. ¢ About one-quarter of the students (27 percent) never used a calculator to take quizzes or tests, while 35 percent almost always did. a — 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has become an issue of increasing importance to federal, state, and local governments. As part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.” Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In the Virgin Islands, 37 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 half of the students (51 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. About half of the students (52 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate This compares to 84 percent for the nation. * National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 21 Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 1980 NAEP TRIAL STATE ASSESSMENT Virgin isiands Nation Percentage of students whose mathematics teachers reported having the following degrees Bachelor’s degree Master's or specialist's degree Doctorate or professional degree Percentage of students whose mathematics teachers have the following types of teaching certificates that are recognized by the Virgin Isiands No regular certification Regular certification but less than the highest available Highest certification available (permanent or long-term) Percentage of students whose mathematics teachers have the following types of teaching certificates that are recognized by the Virgin Isiands Mathematics (middie school or secondary) §2 ( 0.7) Education (elementary or middie school) 0.4) Other 0.7) 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 EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers’ educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Teachers’ responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: ¢ In the Virgin Islands, 56 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. ¢ Some of the eighth-grade public-school students in the Virgin Islands (19 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 Teachers’ Reports on Their Undergraduate and Graduate Fields of Study PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Virgin Isiands Nation What was your undergraduate major? Percentage Percentage Mathematics 56 ( 0.7) 43 ( 3.9) Education 15 ( 0.4) 35 ( 3.8) Other 30 ( 0.7) 22 ( 3.3) What was your graduate major? Percentage Percentage Mathematics 19 ( 0.3) 22 ( 3.4) Education 28 ( 0.7) 38 ( 3.5) Other or no graduate level study 54 ( 0.8) 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 ny 4 fs THE 1990 NAEP TRIAL STATE ASSESSMENT 69 Virgin Islands Teachers’ responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In the Virgin Islands, 26 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service cducation dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. About one-quarter of the students in the Virgin Islands (25 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. TABLE 23. | Teachers’ Reports on Their In-Service Training PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Virgin isiands Nation During the last year, how much time in education in mathematics or the teaching of mathematics? have you spent on in-service Percentage Percentage 25 ( 0.6) 11 ( 2.1) One to 15 hours 49 ( 0.9) 51 ( 4.1) 16 hours or more 26 ( 0.7) 39 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample my ae) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement.'° Further, results from NAEP assessments have indicated that students’ achievement in mathematics and science is much lower than educators and the public would like it to be.'’ In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher 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: ¢ Inthe Virgin Islands, 37 percent of the assessed students were being taught by mathematics teachers who reported having at least a master’s or education specialist's degree. This compares to 44 percent for students across the nation. ¢ About half of the students (51 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. ¢ In the Virgin Islands, 56 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major * Some of the eighth-grade public-school students in the Virgin Islands (19 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school '© Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Differences. An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress: Educational Testing Service, 1988) '! Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement’ NAEP's 1990 Assessment of the Nation and the Trial Assessment of the States (Princeton, NJ National Assessment of Educational Progress, Educational Testing Service, 1991) 76 THE 1990 NAEP TRIAL STATE ASSESSMENT 7) Virgin Islands In the Virgin Islands, 26 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. About one-quarter of the students in the Virgin Islands (25 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. THE 1990 NAEP TRIAL STATE ASSESSMEN Virgin Islands 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 lo examine the relationship between home environment and mathematics proficiency, students participating in the Tnal State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands 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. rABLE 24 Students’ Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Isiands Nation Does your family have, or receive on a regular basis, any of the following items Percentage more than 25 books, an encyclopedia, and newspapers, magazines? Proficiency Zero to two types 24( 1.4 21 ( 212 ( 1.3) 244 | Three types 36 ( 16 30 ( 216 ( 1.4 258 | Four types 40 ( 1.4 48 | 223 ( 1.2) 272 | 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 lhe data for the Virgin Islands reveal that: Students in the Virgin Islands who had all four of these types of materials in the home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types Py ( \ are, THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands About the same percentage of Hispanic students had all four types of these reading materials in their homes as did Black students. About the same percentage of students attending schools in areas classified as “other” as in extreme rural areas had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Tnal State Assessment were asked to report on the amount of television they watched each day (Table 25) TABLE 25 Students’ Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Isiands Nation Percentage Percentage and and How much television do you usually watch each day? Proficiency Proficiency One hour or less 18 | 12 ( 0.8) 214 ( 1.4) 269 ( 2.2) Two hours 15 ( 1.0 21 ( 0.9) 217 | ) 268 | Three hours 17( 13 22 | 220 ( 1.9 265 | Four to five hours 24 ( 1.5) 28 | 221 | 260 | Six hours or more 27( 1.0 16 ( 1.0) 217 | ) 245 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entre population is within + 2 standard errors of the estimate for the sample THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands From Table 25 and Table A25 in the Data Appendix: In the Virgin Islands, average mathematics proficiency was higher for students who spent four to five hours watching television than for students who watched television one hour or less each day. Some of the eighth-grade public-school students in the Virgin Islands (18 percent) watched one hour or less of television each day; 27 percent watched six hours of 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, 27 percent of Black students and 28 percent of Hispanic students watched six hours or more of television each day. In comparison, 17 percent of Black students and 17 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 Tnal 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 Virgin Islands, average mathematics proficiency was highest for students who did not miss any days of school and lowest for students who missed three or more days of school About half of the students in the Virgin Islands (50 percent) did not miss any school days in the month pnor to the assessment, while 22 percent missed three days or more In addition, 19 percent of Black students and 31 percent of Hispanic students missed three or more days of school S| THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands * Similarly, 20 percent of students attending schools in areas classified as “other” and 28 percent in schools in extreme rural areas missed three or more days of school. rABLE 26 Students’ Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin istands Nation Percentage Percentage How many days of schoo! did you miss and and last month? Proficiency Proficiency None 50 ( 1.5) 45 ( 1.1) 221 ( 0.9) 265 ( 1.8) One or two days 29 ( 1.2) 32 ( 0.9) 218 ( 1.2) 266 ( 1.5) Three days or more " 22 ( 1.2) 23 ( 1.1) | 212 ( 1.4) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample 9 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands STUDENTS’ PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not only to master essential skills and concepts but also to develop confidence in their mathematical abilities and to value mathematics as a discipline.’ ? Students were asked if they agreed or disagreed with five 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: / /ike mathematics; | am good in mathematics. Value of mathematics, including students’ perceptions of its present utility and its expected relevance to future work and life requirements: A/most 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 “perception index” was developed to examine students’ perceptions of and attitudes toward mathematics. For each of the five statements, students who responded “strongly agree” were given a value of | (indicating very positive attitudes about the subject), those who responded “agree” were given a value of 2, and those who responded “undecided,” “disagree,” or ‘strongly disagree” were given a value of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception index according to whether they tended to strongly agree with the statements (an index of 1), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statements (an index of 3) Table 27 provides the data for the students’ attitudes toward mathematics as defined by their perception index. The following results were observed for the Virgin Islands Average mathematics proficiency was highest for students who were in the “strongly agree’ category and lowest for students who were in (he “undecided, disagree, strongly disagree” category. Less than half of the students (37 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 Virgin Islands (16 percent), compared to 24 percent across the nation, were in the “undecided, disagree, or strongly disagree” category (perception index of 3) ‘2 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Restor . \ A Nationa! Council of T eache s of Mat rematics, 1989) § ) c y) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 27 | Students’ Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Nation « ” Percentage Student “perception index” groups and and Proficiency Proficiency Strongly agree 37 ( 1. 27 ( 1.3) (“perception index” of 1) 226 ( 1. 271 ( 1.9) Agree 47 ( 1. 49 ( 1.0) (“perception index” of 2) 215 { 1. 262 ( 1.7) Undecided, disagree, strongly disagree 16 ( 24 ( 1.2) (“perception index” of 3) 207 ( 1. 251 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, pzrents, 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 Virgin Islands who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Some of the eighth-grade public-school students in the Virgin Islands (18 percent) watched one hour or less of television each day; 27 percent watched six hours or more. Average mathematics proficiency was higher for students who spent four to five hours watching television than for students who watched television one hour or less each day. About half of the students in the Virgin Islands (50 percent) did not miss any school days in the month prior to the assessment, while 22 percent missed three days or more. Average mathematics proficiency was highest for students who did not miss any days of school and lowest for students who missed three or more days of school. Less than half of the students (37 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. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE NATION’S REPORT carp | S8eF PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon which the assessment was based, and the procedures used to analyze the results The objectives for the assessment were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Educational Testing Service. The development of the Tnal 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. THE 1990 NAEP TRIAL STATE ASSESSMENT - irgin Islands The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 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 booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as described in the introduction to this report.’ The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure Al). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for 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 common scale makes it possible to report on relationships between students’ characteristics (based on their responses to the background questions) and their overall performance in the assessment ' National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, NJ Educational Testing Service, 1988) ( — > 6 WW PrHE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE NATION'S REPORT [rege FIGURE Al | Content Areas Assessed CARD lA , Numbers and Operations This content area focuses on students’ understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-world situations, as well as computational and estimation situations Understanding numerical relationships as expressed in ratios, proportions, and percents is emphasized Students’ abilities in estimation, mental computation, use of calculators, generalization of numerical patterns, and verification of results are aiso inciuded 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 inciuded that require an ability to read instruments using metric, customary, or nonstandard units, with emphasis on precision and accuracy. Questions requiring estimation, measurements, and applications of measurements of length, time, money, temperature, mass/weight, area, volume, capacity, and angles are also included in this content area Geometry 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 al! levels of schooling as well as in practical applications. Students need to be able to model and visualize geometric figures in one, two, and three dimensions and to communicate geometric ideas. In addition, students should be able to use informal reasoning to establish geometric relationships Data Analysis, Statistics, and Probability This content area focuses on data representation and analysis across all disciplines and reflects the importance and prevalence of these activities in our society. Statistical knowledge and the ability to interpret data are necessary skills in the contemporary world Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysis 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 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE NATION'S REPORT CARD FIGURE A2 | Mathematical Abilities The following three categories of mathematical abilities are not to be construed as hierarchical. For example, problem solving involves interactions between conceptual knowledge and procedural skills, but what is considered complex probiem solving at one grade level may be considered conceptual understanding or procedural knowledge at another Conceptual Understanding Students demonstrate conceptual! understanding in mathematics when they 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 involving concepts in mathematical settings. Such understandings are essential to performing procedures in a meaningful way and applying them in problem-solving situations Procedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to select and apply appropriate procedures correctly, verify and justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors inherent Procedural knowledge inciudes the various numerical algorithms in mathematics that S the abilities problem settings have been created as tools to meet specific needs in an efficient manner. It also encompasse to read and produce graphs and tables, execute geometric constructions, and perform noncomputational skills such as rounding and ordering Problem Solving In problem solving, students are required to use their reasoning and analytic abilities when they encounter new situations. Problem solving includes the ability to recognize and formulate probiems: determine the sufficiency and consistency of data: use strategies, data, models, and relevant mathematics: generate extend, and modify procedures; use reasoning (i.e, spatial, inductive, deductive, statistical, and proportional): and judge the reasonableness and correctness of solutions THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands 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 of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics items from the 1990 assessment that discriminated well between adjacent levels. The criteria for selecting these ‘““benchrnark”’ items were as follows lo define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. lo 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 majonity (at least 50 percent) of the students performing at or near the next lower level The percentage of students at a level who answered the item correctly had to be at least 30 points higher than the percentage of students at the next lower level who answered it correctly THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands 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 | provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.* Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups MATHEMATICS TEACHER QUESTIONNAIRI 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 Tnal State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and the use of various instructional approaches. Because of the nature of the sampling for the Trial State Assessment, the responses to the mathematics teacher questionnaire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed * Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 1s from the twelfth-grade national assessment THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE A3 | Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 cone | Grade 4 saad V, Overall Percentage Correct: 73% Percentage Correct for Anchor Levels 200 230 200 350 o 65 91 100 —— Robt: Bais 7. Landa had three large boxes al) the same size and three different kinds of bells as shown above. Ii she (ills each box with the kind of balls shown which bos wil) have che fewest balls in 1! ® The box with the tennis balls ® The box with che gol/ balls ® The box with the rubber balls @® You can't call EXAMPLE 2 BOXES OF PRUIT PICKED AT FARAWAY FARMS Grade 4 Overall Percentage Correct: 80% Percentage Correct for Anchor Levels 200 250 200 350 75 91 100 —— Grade 8 Overall Percentage Correct: 89% Percentage Correct for Anchor Levels 200 250 300 350 76 87 96 100 se-eesebspess3ss *s 9. How many boxes of oranges were picked of Thursday! @ 45 I don't know THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE A3 | Example Items for Mathematics Proficiency Levels (continued) Level 250: Simple Multiplicative Reasoning and Two-Step Problem Solving EXAMPLE 1 7. What is the value of n + 5 when n = 3? Grade 8 Overall Percentage Correct: 76% Percentage Correct for Anchor Levels 200 250 200 350 28 69 95 o8 ARGC cen EXAMPLE 2 Grade 8 Beck Overall Percentage Correct; 73% Toul Percentage Correct for Anchor Levels 200 250 200 350 21 68 92 92 The table above shows une results of s survey of hal color. On ihe circle below, wake « curcle peph wo dbusware che devs in che todle Labei cach pan of tbe cucie gaph with the correct heir color \ ne Did you use the caleulasor on this quenion’ © Ve © Ne EXAMPLE 3 Kathicen is packing baseballs into boxes. Lach bo holds 4 baseballs She has 24 bells Which number sentence will help her tind out how many boxes she will need Grade 8 Overall Percentage Correct: 77% Percentage Correct for Anchor Levels eurests 200 250 300 = 350 ©u+6-T 37 71 95 100 @®u-6-[) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE A3 | Example Items for Mathematics Proficiency Levels (continued) Level 300: Reasoning and Problem Solving Involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE 1 Grade 8 Overall Percentage Correct: 60% . Percentage Correct for Anchor Levels 10. Which of the following shows the result of flapping the ebove tangle over 200 230 the line 2) 33 49 77 90 Grade 12 Overall Percentage Correct; 75% Percentage Correct for Anchor Levels 200 250 300 350 46 79 95 EXAMPLE 2 Ip the mode) town that « class is building « cay 15 beer hong @ represenied by s scale mode) 3 inches long. li the same scale u used, « house 35 fees Grade 8 bigh would be represemed by 6 scale mode! how many mches high! - Overall Percentage Correct: 59% @ } Percentage Correct for Anchor Levels 200 230 200 350 17 46 86 99 Dif you wae une caleulever on this question’ © Ve © No BEST COPY AVAILABLE THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE A3 | 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 B Questions 16 17 reier w the follow ing pation of dot figures Grade 8 Overall Percentage Correct: 34% : Late Si te e. Percentage Correct for Anchor Levels ' , 200 220 200 cS.) 13 19 53 88 16. it this patcern of dot figures is contiqued, how many dots will be int 1O0ch figure! Grade 12 Overall Percentage Correct: 49% © ior Percentage Correct for Anchor Levels — 200 220 200 350 » 100 22 48 9 > ivo ® 20) EXAMP & 2 Grade 8 Overall Percentage Correct: 15% Percentage Correct for Anchor Levels 200 20 200 390 1 4 28 74 Grade 12 Overall Percentage Correct: 27% Percentage Correct for Anchor Levels 200 250 3200 350 3 22 74 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Tnal 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 1s being reported. Having the student as the unit of analysis makes it possible to deseribe the instruction received by representative samples of eighth-grade students in public schools Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEP 's goal of providing information about the educational context and performance of students Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the rottormance of a carefully selected representative sample ot eighth-grade puble-schoo! students from the state or terntory lf a different representative sample of students were sclected and the assessment repeated it is likely that the estumates might vary somewhat, and both of these sample estimat 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 terntory were assessed. Virtualls all statistics that are based on samples (including those in NAF P) are subject to a certain degree of uncertainty. The uncertainty attnbutable to using samples of students 1s referred to as sampling error Like almost all cstumates based on assessment measures, NAEP ’s total group and ubgrouy proficiency estimates are subject to a second source of uncertainty, in addition to sampling error. As previously noted, each student who participated in the Inal State Assessment vas administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropnate, set of the assessment question or the entire set of questions -- somewhat different estimates of total group and subgrouy proficiency might have been obtained. Thus, a second source of uncertainty anses becau each student was administered a subset of the total pool of question Virgin Islands In addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a background question in a certain way or the proportion of students in certain racial/ethnic groups) reflect only sampling error. NAEP uses a methodology called the jackknife procedure to estimate these standard errors Drawing Inferences from the Results One of the goals of the Tnal State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inferences about the population The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population means and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency + 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within + 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state’s sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean + 2 standard errors = 256 + 2°(1.2) = 256 + 2.4 = 256 - 2.4 and 256 + 2.4 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4 Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than /0 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students’ responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defined 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 /5 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 gr> ip does have higher achievement than the group who reported spending 15 minutes or iess on homework. However, even though the means differ, there may be no real diffc: «nce in performance between the two groups in the population because of the uncertainty iated with the estimated average proficiency of the groups in the sample. Remember that the intent is to make a statement about the entire population, not about the particular sample that was assessed. The data from the sample are used to make inferences about the population as a whole As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a rea/ difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard error of the difference between the groups -- is obtained by taking the square of each group’s standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the manner in which the standard error for an individual group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups + 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between groups in the population. If the interval does not contain zero, the difference between groups is statistically significant (different) at the .05 level. THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands 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: Average Standard Proficiency Error Female 259 2.0 Group Male 255 2.1 The difference between the estimates of the of females and males is four points (259 - 255). The standard error of th Var? 2h = 25 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 = 4-58 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.¢., 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 descnbed 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 attnbute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a statistically significant difference in the population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. > The procedure described at ve (especially the estimation of the standard error of the difference) is, in a strict sense, only appropriate when the statistics being compared come from independent samples. For certain comparisons in the report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are ba ed 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 descnption of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol “!”. In such cases, the standard errors -- and any confidence intervals or significance tests involving these standard errors -- should be interpreted cautiously. Further details concerning procedures for identifying such standard errors are discussed in the Tnal State Assessment technical report Minimum Subgroup Sample Sizes Results for mathematics proficiency and background vanables were tabulated and reported for groups defined by race ethnicity and type of school community, as well as by gender and parents’ education level. NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian Pacific Islander, and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and or background vaniable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probability of .8 or greater THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or territory, divided by the standard deviation of the proficiency in the total population. If the true difference between subgroup and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical report. Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master’s degrees in mathematics might be described as “relatively few” or “almost all,” depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage Description of Text in Report None Relatively few Some About one-quarter Less than half About half More than half About three-quarters Many Almost ali All THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin islands THE NATION’S REPORT carp | SSP DATA APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains corresponding data for each level of the four reporting subpopulations -- race ethnicity, type of community, parents’ education level, and gender THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE AS Students’ Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pre-aigebra TOTAL Territory Nation RACE/ETHNICITY Black Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Extreme rural Territory 85 ( 1.5) 1.1) 204 { 1.1) since Nation 74 ( 4.5) 5.0) 249 ( 3.1)! ——s Other Territory 89 ( 0.8) 0.6) 5 | 218 ( 0.7) wee aig Nation 61 ( 2.2) : 2.1) 16 | 251 ( 2.0) 2.8) 294 | 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 1s 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 1s insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE AS | Students’ Reports on the Mathematics Class (continued) They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY STATE ASSESSMENT Mathematics Pre-aigebra Percentage and Proficiency TOTAL Territory 68 ( 0.7) 216 ( 0.6) Nation 62 ( 2.1) 251 ( 1.4) PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory *n = > = @ Nation 83 fn Some college Territory - * Nation 5 21 76 Lan) College graduate Territory Nation GENDER Maile Territory : 0.8) 4 ; tics Nation ; 1.8) 2.9) Female Territory E 0.5) i ite) Nation ; 2.3) 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. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A6 Teachers’ Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT 15 Minutes 30 Minutes 45 Minutes TOTAL Territory Nation RACE/ETHNICITY Black Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Extreme rural Territory 27 ( 0.7) 210 ( 2.1) 210 ( 2.9) 1.7) iad Nation 68 (14.9) 14 (10.9) 5.6) 7.3) 253 ( 5.4)! ee ( —. — Ts Other Territory 32 ( 0.9) 35 ({ 1.0) 0.6) 0.7) 212 ( 0.6) 228 ( 1.7) 1.6) 2.0) Nation 37 ( 4.3) 49 ( 5.1) 2.4) 1.1) 256 ( 3.1) 265 ( 2.5) 8.6)! 282 (11.6)! 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. ! 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 estumate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A6 Teachers’ Reports on the Amount of Time (continued) Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT 15 Minutes 30 Minutes 45 Minutes Percentage and Proficiency TOTAL Territory 31 ( 0.8) 212 ( 0.6) Nation 43 ( 4.2) 256 ( 2.3) PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some co'lege Terris ory Nation Coliege graduate Territory Nation GENDER Male Territory ; 6) 1.2) 2.5) Nation 4 j : 1.9) 7.3)! Female Territory ; 3) 21 ( 1.2) ; 218 ( 2.6) Nation 4 41 ( 4.4) : 11 ( 2.0) 255 ( 2.3) 272 ( 5.7)! 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 estumated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A7 Students’ Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT 15 Minutes 30 Minutes 45 Minutes and Proficiency TOTAL Territory ‘ : ; 18 {( 0.9) : 214 ( 1.9) Nation : 0) 5 : 12 ( 1.1) 258 ( 3.1) RACE/ETHNICITY Black Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Extreme rural Territory 5.1) 14 ( 2.0) 1 3.6) 2.6) { te ( sae) ~— Nation 7 4.6) , 18 ( 3.8) $7) 3.5)! : j ee ( _ —_— Other Territory , 4.5) ; 16 ( 1.2) 0.7) 1.5) ‘ 218 ( 2.0) 2.1) Nation j 1.8) ‘ 15 ( 1.1) a 1.1) 2.3) A 267 ( 2.1) 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. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A7_ | Students’ Reports on the Amount of Time They (continued) | Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT 15 Minutes 30 Minvies 45 Minutes Percentage and Proficiency TOTAL Territory ’ i : 1) 18 ( 0.9) : d 214 ( 1.9) Nation } : é A 12 ( 1.1) 19 258 ( 3.1) PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory : y 1.2) 2.9) Nation . , 1.4) ; : 4.1) Female Territory 18 ( 1.6) 1.5) ) 214 ( 2.4) 2.7) Nation 7 9) 2.0) : 17 ( 1.0) 1.3) 1.5) 267 ( 2.4) 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. *** Sample size 1s insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A8 Teachers’ Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Numbers and Operations Measurement Geometry 1980 NAEP TRIAL STATE ASSESSMENT Heavy Little or No Heavy Little or No Heavy Little or No Emphasis Emphasis Emphasis Emphasis Emphasis Emphasis Percentage Percentage Percentage Percentage Percentage Percentage and and and and and and Proficiency Proficiency Proficiency Proficiency Proficiency Proficiency TOTAL Territory 13 ( 0.5) 19( 0.8) 11( 02) 51( 1.0) 242 ( 2.5) 212( 25) 219( 1.6) 222( 1.3) Nation 15 ( 2.1) 33( 4.0) 28(38) 21( 3.3) ; 287 ( 3.4) 272( 4.0) 260( 3.2) 264( 5.4) RACE/ETHNICITY Black Territory r : 19 ( 0.9) 10 ( 0.5) 51 ( 1.3) j ‘ 4 217( 3.0) 221(29) 224( 1.2) Nation ; f r 23 ( 5.7) 33 ( 7.9) 24 ( 7.3) 238 ( 8.1)i| 242( 5.6)! 233 ( 4.7)! Hispanic Territory . 20 ( 2.1) 14 ( 1.8) 51 ( 3.8) , ee ( —) ee ( —s 212 ( 3.2) Nation . b 34 ( 5.8) 27 ( 6.8) 16 ( 5.5) 255 ( 4.4)! —s ee ( —s TYPE OF COMMUaiITY Extreme rural Territory 0.7) 1.1) 35 ( 1.2) 0.6) 77 ( 0.4) 218 ( 1.7) —s 3.6) 204 ( 3.9) we 216 ( 3.6) Nation 53 (12.4) 3.6) 4.9) 32 (11.7) 6.1) 16 ( 7.9) 257 ( 7.1 )! sales, aig 265 | 9.1)! —s rr ( —s Other Territory 3 0.5) 0.8) 16( 0.9) 0.2) 46( 1.2) 4 2.6) 1.5) 217( 3.1) 1.7) 224( 1.2) Nation 4 2.7) 3.9) 34( 5.3) 46) 24( 4.3) 3 286 ( 3.6) 253( 7.1)! 270( 4.6) 3.9) 265 ( 5.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because 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). 10° THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A8 Teachers’ Reports on the Emphasis Given to (continued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Numbers and Operations Measurement Geometry 1990 NAEP TRIAL STATE ASSESSMENT Heavy Little or No Heavy Little or No Heavy Little or No Emphasis Emphasis Emphasis Emphasis Emphasis Emphasis Percentage Percentage Percentage Percentage Percentage Percentage and and and and and and Proficiency Proficiency Proficiency Proficiency Proficiency Proficiency TOTAL Territory §3( 1. 13 ( 0.5) ; 19 ( 0.8) , 51 ( 1.0) 227 ( 1. 242 ( 2.5) ‘ 212 ( 2.5) ‘ 222 ( 1.3) Nation 49 ( 3. 15 ( 2.1) , 33 ( 4.0) . 21 ( 3.3) 260 ( 1. 287 ( 3.4) . 272 ({ 4.0) , 264 ( 5.4) PARENTS’ EDUCATION HS non-graduate Territory : : 21 ( 3.3) 11 ( 1.9) 53 ( 3.0) : ee ( wr ee ( sie 216 ( 3.7) Nation ‘ 7 : : 25 ( 5.3) 32 ( 6.3) 20 ( 6.7) ee ( “ra ree ( saat vee ( 7) HS graduate Territory i ; 18 ( 2.2) 14 ( 1.6) 48 ( 2.8) . : ete ( rd | eee ( ot 225 ( 1.6) Nation : : : 27 ( 5.0) 27 ( 4.5) 24 ( 5.1) 253 ( 4.7)! 255 4.2) 246 ( 4.8)! Some college Territory ? ; 20 ( 3.7) 9( 3.4) 50 ( 4.6) ee ( Ts wee ( wikes! = vee Nation P F : 39 ( 5.5) 27 ( 5.0) 23 ( 4.1) 279 ( 4.5) 262 ( 4.8)! 270( 4.7) College graduate Territory F ; 15 ( 2.6) 12 ( 1.3) 46 ( 3.5) d y +t? ( vary +t? ( ec) 224 ( 2.0) Nation ‘ 3) 3.8) 26 ( 3.4) 21 ( 2.9) 283 ( 3.8) 270 ( 3.8) 280 ( 6.4) GENDER Male Territory ‘ ( 1.2) 1.5) 1.5) 10 ( 0.9) 51 ( 1.3) : 4.2) 2.8) 4.3) ead Mise 226 ( 2.0) Nation ‘ 2.1) 3.3) 2 ( 3.9) 29 ( 4.1) 20 ( 3.3) 4.4) 6.7) 4.8) 263 ( 3.8) 266 ( 6.8) Female Territory : 1,9) 4.7) ( 18) 12 ( 0.9) 51 ( 1.6) 4,3) 2.9) 208 ( 3.8) 216 ( 3.4) 218 ( 1.8) i 08 Nation M 2.4) 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 3.3) 5.4) 268( 4.1) 256( 3.3) 263( 5.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is 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 naiure of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A8 | Teachers’ Reports on the Emphasis Given To (continued) | Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Data Analysis, Statistics, and Probability Algebra and Functions 1990 NAEP TRIAL STATE ASSESSMENT Little or No Emphasis Little or No Heavy Emphasis Emphasis Heavy Emphasis Percentage and and Proficiency Proficiency TOTAL Territory 11 ( 0.4) : ‘ 19 ( 0.7) 197 ( 2.8) ; : 209 ( 3.8) Nation 14 ( 2.2) . t 20 ( 3.0) 269 ( 4.3) A ; 243 ( 3.0} RACE/ETHNICITY Black Territory 11 ( 0.7) ‘ ‘ 19 ( 1.1) A 211 ( 4.9) Nation . s ‘ 27 ( 6.9) 225 ( 4.3) : 226 ( 2.2)! Hispanic Territory : 67 ( 3.3) 183 ( 4.6) Nation : 56 ( 6.3) 246 ( 4.4) TYPE OF COMMUNITY Extreme rural Territory 6( 0. 94 ( 0.2) wr ) 178 ( 2.5) Nation S( 65 (16.9) ere 254 ( 6.7)! Other Territory 42:( 6; 62 ( 1.2) 192 ( 2. 206 { 1.8) Nation 15 ( 2. 53 ( 5.2) 267 ( 4. 260 ( 3.4) . 245 ( 4.4)! The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages riay 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). 111 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A8 | Teachers’ Reports on the Emphasis Given To (continued) | Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Data Analysis, Statistics, and Probability Algebra and Functions 1980 NAEP TRIAL STATE ASSESSMENT Little or No Emphasis Little or No Heavy Emphasis Emphasis Heavy Emphasis Percentage Percentage Percentage and and and Proficiency Proficiency Proficiency TOTAL Territory 11 ( 0.4) J 47 ( 0.8) 197 ( 2.8) j 227 ( 1.0) Nation 14 ( 2.2) d 46 ( 3.6) 269 ( 4.3) , 275 ( 2.5) PARENTS’ EDUCATION HS non-graduate Territory ; 68 ( 2.9) 43 ( 3.2) 180 ( 4.3) Nation jf §3 ( 7.7) 240 ( 6.2) HS graduate Territory 11 ( 1.5) 68 ( 3.0) 49 ( 2.9) pate Figs 204 ( 3.4) 230 ( 3.3) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 261 ( 6.0)! 247 ( 2.9) 265 ( 3.5) Some college Territory J . 3.4) — Nation ; . 4.8) 3.0) College graduate Territory . 3) 4.2) 3.4) Nation , E 3.9) 3.0) GENDER Male Territory 1.3) 2.5) 4.1) 3.2) nd Nation Female Territory 1.6) 2.2) 3.6) 2.7) Nation SYeBZ BeBe 263 ( 4.4) nd 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). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A9 Teachers’ Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL | Get All the Resources | | Get Most of the | Get Some or None of STATE ASSESSMENT Need Resources | Need the Resources | Need and Proficiency TOTAL Territory 0 13 Nation 2. 265 $ RACE/ETHNICITY Black Territory 0 ( 0.0) re ( re Nation 15 ( 4.2) 241 ( 5.3)! Hispanic Territory 0( 0.0) re ( _—s Nation 7.6) 7.7)! TYPE OF COMMUNITY Extreme rural Territory 0.0) ited Nation 2.6) 54 (10.4) =" 260 ( 8.8)! 257 ( 5.0)! Other Territory 0.0) 35 ( 0.8) 65 ( 0.8) ninied 228 ( 1.2) 218 ( 1.0) Nation 2.9) 58 ( 5.4) 31 ( 5.6) 3.9)! 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A9 Teachers’ Reports on the Availability of (continued) Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL | Get All the Resources | 1 Get Most of the | Get Some or None of STATE ASSESSMENT Need Resources | Need the Resources | Need fs TOTAL Territory Nation SEs Sse PaO So-2 PARENTS’ EDUCATION HS non-graduate Territory = i en, | ~ — Ses BENY NAAN WAWN a Nation ao Se wooun EX 2S Uw) rh HS graduate Territory Nation Ba SREB Bee L Bows Some college Territory Ss as Nation College graduate Territory g Sy Nation S 8x ~) ns WwW wpa GENDER Male Territory 0.0) sina! Nation 2.6) 5.0)! Sets Fsse ora = ora ONee2 wO>> Female Territory 0.0) "2 Nation 2.4) 3.9) — Ld The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al0a| Teachers’ Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week | Less Than Once a Week Percentage Percentage and and Proficiency Proficiency TOTAL Territory 53 ( 0.8) ‘ 12 ( 0.6) 211 ( 0.8) : 215 ( 1.4) Nation 50 ( 4.4) . 8 ( 2.0) 260 ( 2.2) A 277 ( 5.4)! RACE/ETHNICITY Black Territory 12 ( 0.9) 217 ( 2.1) 9( 4.1) rer ( agit Nation --9o8 Hispanic Territory 4.7) sini 1.4) Stel ) Le) WR Le es) Nation ae eS wr @= TYPE OF COMMUNITY Extreme rural Territory 41 ( 1.1) 26 ( 0.8) 1.3) 203 ( 2.3) beta! tet 1.8) Nation 35 (14.6) 56 (17.1) 9.6) 255 ( 5.5)! 258 ( 5.9)! —_y Other Territory 55 ( 0.9) 38 ( 0.8) 0.7) 213 ( 0.8) 235 ( 1.2) 1.9) Nation 50 ( 4.4) 44 ( 4.5) 1.8) 260 ( 2.4) 264 ( 2.8) 8.3)! 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. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al0a| Teachers’ Reports on the Frequency of Small (continued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Percentage and anc Proficiency Proficiency TOTAL Territory 53 ( 0.8) , 12 ( 0.6) 211 ( 0.8) : 215 ( 1.4) Nation 50 ( 4.4) ‘ 8 ( 2.0) 260 ( 2.2) ; 277 ( 5.4)! PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory 1.0) baie 2.1) 5.3)! — 2828 Nation — Female Territory nn Le) 0.9) 2.4) 2.1) 6.6)! ge Nation w © 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 standar: errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al0b| Teachers’ Reports on the Use of Mathematical Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Once a Week | Less Than Once a Week Percentage Percentage and and Proficiency Proficiency TOTAL Territory 20 ( 1.0) A 15 ( 0.8) 214 ( 1.4) r 222 ( 1.6) Nation 22 { 3.7) ‘ 9( 2.6) 254 ( 3.2) : 262 ( 5.9)! RACE/ETHNICITY Black Territory 19 ( 1.0) 218 ( 1.7) Nation 22 ( 5.9) 233 ( 5.9)! Hispanic Territory 24 ( 2.8) re ( =, Nation 39 ( 7.5) 247 ( 3.8) TYPE OF COMMUNITY Extreme rural Territory 7 ( 0.2) tee ( tee Nation 27 (14.9) tre ( wi 1.1) 1.7) 3.9) aaa — Ld SRST pacts Le Sek=> Other Territory oF { 12) 214 ( 1.4) Nation 19 ( 4.3) 253 ( 3.9)! 0.9) 2.6) 3.3) 7.4)! Sv Bsses The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al0b| Teachers’ Reports on the Use of Mathematical (continued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Percentage Percentage and and Proficiency Proficiency TOTAL Territory 20 ( 1.0) } 15 ( 0.8) 214 ( 1.4) . 222 ( 1.6) Nation 22 ( 3.7) 1 9( 2.6) 254 ( 3.2) d 282 ( 5.9)! PARENTS’ EDUCATION HS non-graduate Territory tos 5328 Nation Ld HS graduate Territory Nation how Rove Some college Territory Nation bd 229 73 69 Ls College graduate Territory Nation GENDER Male Territory 19 ( 1.1) 1.2) 218 ( 2.2) ; 3.8) Nation 22 ( 4.1) : 2.0) 255 ( 4.1) ; 7.2)! Female Territory 20 ( 1.6) j 4.1) 210 \ 2.9) ; 3.5) Nation 21: 3.6) ‘ 3.3) 254 | 3.3) j 6.0)! 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). 118 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Alla| Teachers’ Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Less TOTAL Territory Nation RACE/ETHNICITY Black Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Extreme rural Territory Nation Other Territory Nation Percentage and Proficiency 84 ( 0.9) 221 ( 0.6) 62 ( 3.4) 267 ( 1.8) 85 ( 0.9) 224 ( 0.8) 56 ( 7.7) 244 ( 4.0) 84 ( 2.3) 210 ( 1.9) 61 ( 6.8) 251 ( 3.1) 74 ( 0.8) 206 ( 1.6) 50 (10.6) 268 ( 4.0)! 87 ( 1.0) 224 ( 0.7) 63 ( 3.9) 267 ( 2.3) 240 ( 4.3)! 3 ( 0.7) “er ( or 40 (10.0) 247 ( 7.6)! 11 ( 1.0) 208 ( 1.4) 31 ( 3.5) 255 ( 3.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population 1s within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Alla| Teachers’ Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY — 1990 NAEP TRIAL | About Once a Week or STATE ASSESSMENT Almost Every Day Several Times a Week Lees Percentage and Proficiency TOTAL Territory 84 ( 0.9) 221 ( 0.6 Nation 62 ( 3.4) 267 ( 1.8) PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory 3( 0.9) : 1,2) Nation 3.7) 2.1) Female Territory 1,3) 1.2) Nation 3.6) 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 standara errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Allb| Teachers’ Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Loss than Weeldy Percentage Percentage and and Proficiency Proficiency TOTAL Territory 49 ( 0.7) ! 22 ( 0.6) 210 ( 0.9) ‘ 233 ( 1.4) Nation 34 ( 3.8) ' 32 ( 3.6) 256 ( 2.3) ; 274 ( 2.7) RACE/ETHNICITY Black Territory Le) Nation Hispanic Territory rad bx} — > Nation Le) TYPE OF COMMUNITY Extreme rural Territory 43 ( 1.0) 48 ( 1.5) 205 ( 2.4) 211 ( 0.5) Nation 27 (14.3) 49 (12.7) 24 (10.1) ve ( ="s 258 ( 6.7)! “ve ( vers Other Territory 51 ( 0.8) 25 ( 0.7) 24 ( 0.8) 211 ( 1.1) 233 ( 1.2) 233 ( 1.3) Nation 30 ( 4.4) 35 ( 4.3) 36 ( 4.2) 256 ( 3.3) 259 ( 2.8) 272 ( 2.9) Ihe standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Allb| Teachers’ Reports on the Frequency of (continued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Less than Weekly Percentage and Proficiency TOTAL Territory . 22 ( 0.6) . d 233 ( 1.4) Nation . ’ 32 ( 3.6) 274 ( 2.7) PARENTS’ EDUCATION HS non-graduate Territory . Nation Lad HS graduate Territory S88e Seis Nation % Some college Territory Nation 29 35 78 Le) College graduate Territory Nation GENDER Male Territory 1.7) p 1.5) 1.2) ‘ 2.9) Nation 4.1) 3.5) 3.2) : 3.2) Female Territory 1.2) . 1.2) 1.5) 2.6) Nation 4.1) , 4.1) 2.1) ; 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al2 | Students’ Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Once a Week | Less Than Once a Week TOTAL Territory Nation RACE/ETHNICITY Black Territory Bane Nation ~) vray ses Hispanic Territory Ln) Nation Land hon o-o-— TYPE OF COMMUNITY Extreme rural Territory : 10 ( 1.8) ve ( sit Nation : 27 ( 3.8) 264 ( 3.5)! Bale Beds — o-W—-. — Hoh > Other Territory 17 ( 0.8) 225 ( 1.8) Nation ‘ 28 ( 1.7) 264 ( 2.1) — 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). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al2 | Students’ Reports on the Frequency of Small (continued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Once a Week | Less Than Once a Week TOTAL Territory Nation PARENTS’ EDUCATION HS non-gr aduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory 2.0) 1.7) Nation 2.9) : 41 ( 3.3) : 262 | Female Territory 2.1) : 52 ( 1.4) 5 216 ( Nation 2.4) ; 47 ( 2.8) 260 | The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al3 | Students’ Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Once a Week | Less Than Once a Week TOTAL Territory 25 ( 0.9) 219 ( 1.4) Nation 28 ( 1.8) 258 ( 2.6) — 62a8 2n0o2 aks: Ln] RACE/ETHNICITY Black Territory | NG Nation Land 6528 8S Hispanic Territory bend Nation Ld TYPE OF COMMUNITY Extreme rural Territory s 10 ( 75 ( 1.5) ae 207 ( 1.8) Nation 1) 37 ( 4. 43 ( 5.0) 262 | 251 ( 5.2)! Other Territory a 20 ( 1. 52 ( 1.3) ; 229 ( 1. 217 ( 0.9) Nation 2. ST ¢ WW 41 ( 2.4) 270 ( 1. 260 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al3 | Students’ Reports on the Use of Mathematics (continued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Once a Wee. | Less Than Once a Week Percentage and Proficiency | TOTAL Territory 25 ( 0.9) 219 ({ 1.4) Nation 28 ( 1.8) 258 ( 2.6) — 62a8 anos akes » PARENTS’ EDUCATION HS non-graduate Territory Bean SASeR Nation HS graduate Territory Ls) Nation ~ Some college Territory ~ Nation 50 24 35 63 NR College graduate Territory Nation GENDER Male Territory Nation Female Territory 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al4 | Students’ Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL About Once a Week or STATE ASSESSMENT Almost Every Day Several Times a Week Lees Percentage Percentage and and Proficiency Proficiency TOTAL Territory 73 ( 1.4) 17 ( 0.9) 220 ( 0.7) 216 ( 1.5) Nation 74 ( 1.9) 14 ( 0.8) 267 ( 1.2) 252 ( 1.7) RACE/ETHNICITY Black Territory 74 ( 1.3) 222 ( 0.8) Nation 71 ( 2.8) 240 ( 2.9) Hispanic Territory 69 ( 3.2) 210 ( 1.5) Nation 61 ( 3.7) 249 ( 2.3) TYPE OF COMMUNITY Extreme rural Territory 70 ( 4.0) ; 3.3) 207 ( 1.9) ( gi Nation 68 (11.3) t 8.2) 263 ( 4.2)! wad a Other Territory 7a ( 15) 0) 1.1) 223 ( 0.8) : 1.8) Nation 75 ( 2.2) t 1.9) 267 ( 1.6) i 4.3)! The standard errors of the estimated statistics appear in parentheses. It car be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al4 | Students’ Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY About Once a Week or Less 1990 NAEP TRIAL STATE ASSESSMENT Aimost Every Day Several Times a Week Percentage Percentage and Proficiency TOTAL Territory F 17 ( 0.9) 216 ( 1.5) Nation ‘ 14( 0.8) 252 ( 1.7) PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory ad Nation Some college Territory nd SS8a S253 Nation hm College graduate Territory NNN NN = Nation GENDER Male Territory 71 { 18 ( 1.3) aa7 i 4, 221 ( 2.6) Nation 7 £& 16 ( 1.2) 268 ( 1. 252 ( 2.5) Female Territory ee 16 ( 1.3) 218 ( 1. 211 ( 3.2) Nation 76 ( 1. 13 ( 1.0) 265 ( 1. 250 ( 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 size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A1S | Students’ Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEM,.7ICS PROFICIENCY 1980 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Less Than Weekly Percentage and Proficiency TOTAL Territory 38 ( 15) 212 ( 1.0) Nation 38 ( 2.4) 253 ( 2.2) RACE/ETHNICITY Black Territory Ls) Nation WROD Ws i] 2858 WAND Awa ARAP Sa Sw Sez Ls] & ADA Sek Hispanic Territory Nation ©-bO weae yo . %~ SESE © om &SES TYPE OF COMMUNITY Extreme rural Territory S8se Nation 249 ( 4.0)! — Other Territory 40 ( 1.6) 273 ( 4.9) Nation 36 ( 2.9) 252 ( 3.0) — Sans 88 — 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. 129 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE AlS | Students’ Reports on the Frequency of (continued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Less Than Weekly TOTAL Territory Nation PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory 2.0) . 1.7) 1.6) d 2.2) Nation 2.7) F 2.7) 2.7) : 2.4) Female Territory 2.1) m 1.8) 1.6) 7) 2.2) Nation 2.5) 5) 2.6) 2.1) 8) 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al8 | Students’ Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Own a Caiculator Teacher Explains Caiculator Use 1960 NAEP TRIAL STATE ASSESSMENT Yes No TOTAL Territory Nation RACE/ETHNICITY Black Territory Nation ~ %— S888 Hispanic Territory Nation 5888 TYPE OF COMMUNITY Extreme rural Territory @ © 2.1) aad 1.3) om Nation S res Other Territory 0.8) 1.7) 0.5) 5.4) ad Nation % BSSs 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). 13i THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al8 | Students’ Reports on Whether They Own a (continued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Own a Caiculator Teacher Explains Calculator Use 1980 NAEP TRIAL STATE ASSESSMENT Yes No Percentage and TOTAL Territory Nation PARENTS’ EDUCATION HS non-graduate Territory Ln Nation Rete 5858 HS graduate Territory i] UL) Nation wr a2 8 Ry Se Sfos Some college Territory ig Se8s 888s BS Nation College graduate Territory Land aa Sod Nation Le) nd GENDER Male Territory Nation Female Territory 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al9 | Students’ Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY eaten eae in | Doing Problems at Home | Taking Quizzes or Tests 1980 NAEP TRIAL STATE ASSESSMENT Almost Aimost Almost Always Always Always Percentage Percentage Percentage Percentage and and and and Proficiency Proficiency Proficiency Proficiency TOTAL Territory 1.1) 1.0 33 ( 1. 13 ( 1.0) 0.6) 3 a ) e 227 ( 2.9) Nation 1.5) 1.9 d 19 ( 0.9) 1.5) 1.4) d 263 ( 1.8) RACE/ETHNICITY Black Territory — Nation Hispanic Territory Lend Nation Sx8e Sets Land TYPE OF COMMUNITY Extreme rural Territory / 3.2) 15 ( : seer J er ( Nation j 6.5) . 23 ( 6.1)! 263 ( Other Territory i 1.0) d 13 ( ; ; 231 ( 3.4 N2iuon ; } , 18 ( 272 ( 1%) ; 263 ( The standard errors of the estimated statistics appear in parenthes*s. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the “Sometimes” category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A19 | Students’ Reports on the Use of a Calculator (continued) for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY eae jome in Doing Problems at Home | Taking Quizzes or Tests 1900 NAEP TRIAL STATE ASSESSMENT Almost Almost Almost Always Always Always Percentage Percentage Percentage Percentage Percentage and and and and and Proficiency Proficiency Proficiency Proficiency Proficiency TOTAL Territory 33 ( 1. 13 ( 1.0) d 27 212 ( 1. 227 ( 2.9) ; 232 30 ( 1. 19 ( 0.9) é 30 261 ( 1. 263 ( 1.8) ’ 274 La] Nation SS, YSa8 PARENTS’ EDUCATION HS non-graduate Territory 14 ( 2.5) 25 ( 3.2) ee ( ver) s ee ( —s 22 ( 2.6) . 24 ( 3.2) 244 ( 4.2) 251 ( 4.6) Nation Esse HS graduate Territory g Bese 15 ( 2.0) 29 ( 2.2) tee ( eee) 233 ( 2.4) 18 ( 1.5) 27 ( 2.2) 256 ( 2.4) 265 ( 2.0) Ld Ld Nation Fzse Some college Territory 14 ( 3.8) 32 ( 4.3) ee ( ini | re ( or) 20 ( 1.9) 2.5) 268 ( 3.2) 2.0) > Ld) Nation Qn 2*& N@ *% Lad nd College graduate Territory 12 ( 1.5) 2.0) ee ( —_y J 3.1) 16 ( 1.4) . 2.7) 278 ( 2.8) 2.0) — Nation Ral She02 ENo — Ses 28a8 GENDER Male Territory 14 ( 1.6) 1.8) 229 ( 4.1) 1.4) 19 ( 1.3) 1.5) 263 ( 2.5) 3.0) Land Nation — Female Territory 13 ( 1.2) 1.9) 226 ( 3.0) 2.0) 18 ( 1.2) 1.8) 263 ( 2.1) 2.4) Sese FBee a Nation — The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the “Sometimes” category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A20 | Students’ Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT High “Caiculator-Use" Group Other “Caiculator-Use” Group TOTAL Territory Nation RACE/ETHNICITY Black Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Extreme rural Territory 2.0) 1.6) Nation 5.6) 4.3)! Other Territory ; 1.8) 1.1) Nation F 1.4) 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) 135 42 V0 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A20 | Students’ Knowledge of Using Calculators (continued) PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT High “Caiculator-Use” Group Other “Caiculator-Use" Group aa TOTAL Territory Nation PARENTS' EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory 2.3) 71 | 2.4) 218 ( Nation 2.0) 61 ( 2.0) 255 ( Female Territory 1.8' 62 ( 4.7) 213 | Nation 1.8) 55 ( 1.7) 254 ( The standard errors of the estimated statistics appear in parentheses, It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A24 | Students’ Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Four Types TOTAL Territory asa Nation — N Ld RACE/ETHNICITY Black Territory Ld Ld Nation ind Hispanic Territory nm Rete Bess Nation Ess Bess ANNO Ws TYPE OF COMMUNITY Extreme rural Territory , 2.7) 3.9) t 2.2) Nation 4.9) F 5.1) sind : 5.6)! Other Territory 1.3) ; 1.6) 1.3) , 1.3) Nation 1.5) , 1.5) 2.6) , 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) 137 rHE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A24 | Students’ Reports on Types of Reading (continued) Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types TOTAL Territory Nation PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory Nation Female Territory Nation ‘ 1.4) 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A25 | Students’ Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL Four to Five STATE ASSESSMENT Two Hours | Three Hours Hours and Proficiency TOTAL Territory 18 ( 1.2) 214 ( 1.4) Nation RACE/ETHNICITY Black Territory ; d 25 ( 1.9) : : , R 224 ( 1.5) Nation d , A 32 ( 1.8) 239 ( 4.0) Hispanic Territory é ‘ 20 ( 2.9) re ( TT. Nation ’ 3 31 ( 3.1) 247 ( 3.5) TYPE OF COMMUNITY Extreme rural Territory 4.3) 16 ( 3. y 20 ( 2.1) _— ee ( re ( ee Nation 3.3) 19 ( 2. y 26 ( 2.7) tee) tee { 256 ( 3.6)! Other Territory 1.2) 14( 0. ' 25 ( 1.8) 1.7) 220 ( 2. , 223 ( 1.8) Nation 1.0) att Vs : art %2) 2.6) 269 ( 2. , 259 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) 139 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A25 | Students’ Reports on the Amount of Time Spent (continued) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Four to Five STATE ASSESSMENT Two Hours | Three Hours Hours and Proficiency TOTAL Territory 18 ( 1.2) j 17 ( 1.3) 214 ( 1.4) , 220 ( 1.9) Nation 12 ( 0.8) } 22 ( 0.8) 269 ( 2.2) , 265 ( 1.7) PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory 1.9) ; 20 ( 1.9) 1.5) 5 222 ( 2.7) Nation 0.9) d 22 ( 1.0) 3.3) ; 267 ( 2.2) Female Territory 1.3) : 15 ( 1.2) 2.7) ; 218 ( 2.7) Nation 1.1) ‘ 23 ( 1.4) 2.8) : 264 ( 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) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A26 | Students’ Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One or Two Days Three Days or More Percentage and Proficiency TOTAL Territory 22 ( 1.2) ’ 212 ( 1.4) Nation : aot 4.9) : 250 ( 1.9) RACE/ETHNICITY Black Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Extreme rural Territory 28 ( 3.4) 205 ({ 2.3) Nation ' 25 ( 3.9) ve ( oor) Other Territory . 20 ( 1.3) 1 214( 1.8) Nation : 32 | 23 ( 1.1) 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 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 es.imated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A26 | Students’ Reports on the Number of Days of (continued) | School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One or Two Days Three Days or More TOTAL Territory Nation PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Naby oo8s Nation — College graduate Territory Nation we a28S nm GENDER Male Territory 52 ( 223 | Nation 47 ( 266 | Female Territory 47 ( 220 ( Nation 43 ( 264 ( The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A27 | Students’ Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL Undecided, Disagree, STATE ASSESSMENT Strongly Agree Agree Strongly Disagree Proficiency TOTAL Territory ‘ ! 16 ( 0.9) * , 207 ( 1.9) Nation ‘ , 24 ( 1.2) ; ; 251 ( 1.8) RACE/ETHNICITY Black Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Extreme rural Territory ; P 3.0) 790) Nation ‘ : 1.4) wae) Other Territory 3 0.9) fH 1.6) Nation j : 1.4) 271 ( 2. j 1.9) The standard errors of the estimated statistics appear in parentheses, It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A27 | Students’ Perceptions of Mathematics (continued) PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Undecided, Disagree, STATE ASSESSMENT Strongly Agree Agree Strongly Disagree TOTAL Territory Nation PARENTS’ EDUCATION HS non-graduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory 1.7) 1.5) 1.8) 2.7) 1.2) 1.4) 2.0) 2.4) and Nation ws O2os Female Territory 1.9) 1.5) 1.2) 2( 2.5) 1.7) 1.9) 1.8) 1.9) Nation Bros Sane 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). 144 THE 1990 NAEP TRIAL STATE ASSESSMENT Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing Service (ETS), Westat, and National Computer Systems (NCS). The program benefitted from the contributions of hundreds of individuals at the state and local levels -- Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators -- who tirelessly provided their wisdom, experience, and hard work. Finally, and most importantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (CCSSO) for its considerable contributions to the program, especially its management of the National Assessment Planning Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In particular, we note the significant contributions of Ramsay Selden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff -- particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza -- worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people -- from school districts, colleges and universities, and State Education Agencies -- worked tirelessly to help ETS staff develop the assessment and a framework for interpreting the results. Under the NAEP contract to ETS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mazzeo, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffler, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zaback. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward 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 Koffler 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. 140 U.S. GOVERNMENT PRINTING OFFICE : 1991 O — 263-275 QL 3 (BK. 36)