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DOCUMENT RESUME ED 330 586 SE 052 096 TITLE The State of Mathematics Achievement in Virgin Islands: The Trial State Assessment lt Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-095. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Iv.thematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS National Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; Trtal State Assessment (NAEP); *Virgin Islands ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for che first ulme 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 desigaed 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 mat,' 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 Mathematics ..e e et in the VIRGIN ISLANDS The Trial State Assessment at Grade Eight 3EST COPY AVAILABLE U $ OEPANTMENT OF EDUCATION °eke ot Educational Roseate'', and lmproyemenl E CATIONAL RE SOURCES INFORMATION CENTER tERICI triia POCureeni has been feptoduced as received tiom the ovum ofganqation onating it Minor changes have been made to "gslOve reproduction QuIllity Points : yieyy Or opinions Stated ,n this clOcu mein! 00 not necessarily represent official OE Ri position or policy Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD, the National Assessment of Educational Progress (NAEP), is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1969, assessments have been conducted periodically in reading, mathematics, science, writing, history/geography, and other fields. By making objective information on student performance available to policymakers at the national. state, and local levels. NAEP is an integral part of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Edueation Statistics. the U.S. Department of Education. The Commissioner of Education Statistics is responsible. by law, for carrying out thc NAEP project t`Irougn competitive awards to qualified organizations. NAEP reports directly to the Commissioner, who is also responsible for providing continuing reviews, including validation studies and solicitation of public comment. on NAEP's conduct and usefulness. In 1988. Congress created the National Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The board is responsible for selecting the subject arras to be assessed, which may include adding to those specified by Congress: identifying appropriate achievement goals for each age and grade: developing assessment objectives: developing test specifications; designing the assessment methodology; developing guidelines and standards for data analysis and for reporting and disseminating results; developing standards and procedures for interstate, regional. and national compa.isons; improving the form and use of the National Assessment; and ensuring that all items selected for use in the National Assessment are free from racial, cultural, gender, or regional bias. The National Assessment Governing Board Richard A. Boyd. Chairman Executive Director Martha Holden Jennings Foundation Cleveland. Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.O.C.E.S. Saratoga Springs. New York Franck Alexander Associate Superintendent California Department of Education Sacramento, California David P. Battini High School History Teacher Ctiro-Durham High School Cairo. New York Parris C. Battle Teacher Horace Mann Eler.,eiliary Sehool Miami. Florida Mary R. Blanton Attorney Cromwell. Porter. Blanton & Blanton Salisbury. North Carolina Boyd W. Boehtic Attorney Gaass. Klyn. & Bvehlje Pella. Iowa Linda R. Bryant Teacher Greenway Middle School Teacher Center Pitts:Airgh. Pennsylvania 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. Professor of Education and Public Policy Vanderbilt University Washingt'ln, D.C. Michael S. Glode Wyoming State Board of Education Saratoga, Wyoming Christine Johnson Principal Abraham Lincoln High Schooi Denver. Colorado John Lindley Principal South Colby Elementary School Port Orchard. Washington Carl J. Maser Director of Schools The Lutheran Church Missouri Synod Idterninional Center St. Louis. Missouri Mark D. Musick President Southern Regional Education Board Atlanta. Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith, Arkansas Matthew W. Prophet, Jr, Superintendent Portland Oregon School District Portland. Oregon Honorable William T. Randall Commissioner of Education State Department of Education Denver. Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington, D.C. Honorable Richard W. Riley Attorney Nelson. Mullins, Riley and Scarborough Columbia, South Carolina Thomas Topuzes Attorney Law Offices of Frank Rogozienski Coronado. California Herbert J. Wa lberg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and I m p ro v e me n t (Ex-Officio) U.S. Department of Education Washington, D.C. Roy Truby Executive Director. NAGB Washington, D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathe ties Achievement in the VIRGIN ISLANDS The Trial State Assessment at Grade Right Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and improvement U.S. Department of Education 4 U.S. Department of Education Lamar Alexander Secetary Office of Educational Research and Improvement Bnmo V. Manna Acting Assistant Secsetary National Center fbr Education Statistics Emmen J. Elliott &dug Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP 'Trial State Assessment's individual State reports are available directly from the participating States. Far ordering informado a. please coat= the assessment division of your State Department of Education. For ordering Informstian on the composite report of results for the Nation and all State participants, or for single copies of the Executive Stmunary while supplies last, write: Educadon Infonnadon Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 2020$-5641 or call 1-800-424-1616 (in the Washingtoo, D.C. metropolitan area call 202-219-1651). Ubrary Carstass, Cataloi Caid Number: 91-61478 LON: 0411651444 The work upon which this publication is based was performed for the Natices1 Center for Education Statistics, Office of Educational Research and Improvement, by Educational Trains Service. Educaliceral Matins Service is an equal opponunity/afrumadve acdon employee Educatiowl Testing Strike, ETS, sod (-2f) are registered trademarks of Educational Tbsting Service. Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of the Virgin Islands 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Virgin Islands Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 Levels of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematks Performance by Subpopulaticas 24 Race/Ethnicity 24 Type of Community 27 Parents' Education Level 29 Gender 31 Content Area Performance 33 6 THE 2990 NAEP TRIAL STATE ASSESSMENT PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics? 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Ddivered? 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instniction 56 Summary 59 Chapter 5. How Are Calculators Used? 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics? 67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 iv THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the fust 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 naticiDai assessments that NAEP has conducted since its inception. As a result of the legislatiorl, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each 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 rercent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. Thc results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT 1 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 students in this sample of schools were representittive 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 seivices 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 Trial 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 2 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin !shads 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 problam solvkts 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 Trial 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 avm-age 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 eighth-grade public-school students having at least one parent who graduated from college was approximately 11 points higher than that of students whose parents did not gradulte from high school. The results by gendcr 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, female.; in the Virgin Islands performed lower than females across the country; maies in the Virgin Islands performed lower than males across the country. THE 1990 NAEP TRIAL STATE ASSESSMENT 3 Virgin Islands A Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information about student achievement. Some of the salient results for the public-school students in the 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 1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Wards 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 woe of the resources they ndeded. Across the nation, these figures were 13 percent and 31 percent, respectively. In the Virgin Islands, 21 percent of the students never wed 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 kast 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 figun for the nation, where 66 percent of students were taught by teachers who were ceitified at the highest level available in their states. Students in the Virgin Islands who had four types of reading materials (an encyclopedia, newspapers, magazines, and ny ve than 25 books) at home showed higher mathematics proficiency than did students with MD 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. 12 THE 1990 NAEP TRIAL STATE ASKSSMENT 5 INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhoda WOO Connecticut Minnesota Thais Delaware Montana Vblinia District of Columbia Nebraska Wed Virginia Florida New Hampshire Wisposia Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Wan& 13 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 kgislation for the National Assessment of Educational Progress (NAEP), which included for the first time in the project's hie iry -- a pnwision 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 instrwnent 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-I(i)(2)(C)(1))) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth gade 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 senions. 14 8 THE 1990 NAEP TRIAL. STATE ASSESSMENT Virgin Islands The Trial State Assessii-mt 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 :-ithorized 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 an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refmed by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial Statz 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 nation. 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). 15 THE 1990 NAEP T1UAL STATE ASSESSMENT 9 Virgin Islands RACE/ETHNICITY Results are presented for stmlents 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 w, rkers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. 6 10 THE 1990 NAEP TRIAL STATE ASSESSMENT Vbght Islands GENDER Results are reported separately for males and females. REGION The United States has been divided into four regions: Northeast, Southeast, Central, and West. States included in each region are shown in Figure 1. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURE 1 J Regions of the Country NORTHEAST , SOUTHEAST CENTRAL WESt _ Connecticut Alabama Minot. Alaska Delaware Arkansas Indiana Arizona District of Columbia Florida Iowa CsiKornis Maine Georgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Nampa** Mississippi Missouri Montana New Jersey North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexko Pennsylvania Tennessee Ohio Oklahoma Rhode Island South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming 1 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 11 Virgin Islands Guifielines for Analysis AlIPIIMMMIMM.PIP .01 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 -- ratherthan the entire population of eighth graders in publicschools 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. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistically significant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) -- regardless of whether the sample means or sample proportions appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the difference is not statistically significant), the means or proportions are described as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests rather than on the 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. I 12 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands It is also important to note that the confidence intesvals pictuncd 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 preficiencies 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 arc based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the grou p. 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). 1 fl THE 1990 NAEP TRIAL STATE ASSESSMENT 13 Virgin Islands Profile of the Virgin Islands EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERINICS Table 1 provides a profile of the demographic characteristia 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 1 I Profde of Viz& Islands Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS 1100 NW TRIAL STATE ASSESSMENT 11Inipkt Mande Nation DEMOGRAPHIC SUBGROUPS Race/Ethnicity White 2 0.2) 70 (01) Black 77 (1.1) 15 ( 0.3) Hispanic 20 1.0) 10 ( 04) Asian 0 02) 2 ( 0.5) American Indian 1 0.2) 2 ( 0.7) Type of Community Advantaged urban 0 ( 0.0) 10 ( 3.3) Disadvantaged urban 0 ( 0.0) 10 ( 21) Extreme rural 19 ( 02) 10 ( 3.0) Other 51 ( 0.2) 70 4.4) Parents' Education Did not finish high school 15 ( 1.0) 10 ( 0.3) Graduated high school 29 ( 11) 25 ( 12) Some education atter high school 10 ( OS) 17 ( 0.9) Graduated college 21 ( 1.4) 39 ( 1.3) Gender Male 49 ( 1.1) 51 ( 1.1) Female SI ( 1.1) 49 ( 1.1) AP. 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 03 percent are reported as 0 percent. 14 THE 3990 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 assesmient. The weiOted 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 eigith-grade public-school students in the Virgin Islands. TABLE 2 I Profile of the Population Assessed in the 1 Virgin Islands EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted School participation rate before substitution Weighted school participation rate after substitution Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating schools 100% 100% 8 EIGHTH-GRADE PUSUC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students selected to participate in the assessment Number of students withdrawn from the assessment Percentage of students who were of limited English Proficiency Percentage of students excluded from the assessment due to Limited English Proficiency Percentage of students who had art individualized Education Plan Percentage of students excluded from the assessment due to individualized Education Plan status Number of students to be assessed Number of students assessed 0% 4% 3% 1.42T i gas In the Virgin Islands, the Trial State Assessment was based on all eligible schools. There was no sampling of schools. 21 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Virgin Islands In each school, a random sample of students was selected to panicipate in the assessment. As estimated by the sample, 0 percent of the eighth-grade public-school population was classifted 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 aclivities 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 ane (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 digibk eighth-gyade public-school student population in the Virgin Islands. 22 16 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands ME NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Virgin Islands Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAEP mathematics scale, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficiency of eighth-grade public-school students in the 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. 23 THE 1990 NAM) TRIAL STATE ASSESSMENT 17 Virgin Islands CHAPTER 1 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).2 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 Hunicane Hugo. FIGURE 2 I Average Eighth-Grade Public-School Mathematics Proficiency NAEP Mathematics Scale 0 200 225 250 275 300 500 Average Prefflency Virgin islands ( 0.5) Nation *I ( 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 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations, 2 Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 24 18 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 incorrextly 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 meaningffil 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 perfotmance 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 acquited 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). CONTENT AREA PERFORMANCE As previously indicated, the questions comprising the Trial State Assessment covered five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Steistics, 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 all of these five content areas. 25 THE 1990 NAEP TRIAL STATE ASSESSMENT 19 Virgin Islands FIGURE 3 I Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a Calculator, they can extend these abilities to multiplication and division problems. These students can identity solutions to One-step word problems and Select the greatest four-digit number In a list. In measurement, these students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these students can recognize translations ot word problems to numerical sentences and extend simple pattern sequenceS. LEVEL 250 I Sim* 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 solations 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 prchlem. 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. 2. 6 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE 3 Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasonbg and Problem Solving involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simi* Mgebreic illasOpulations 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 deCimais on number Ilnett, 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 expressione, 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 simpfifying 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 figur^s 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 (-iambs, as welt as functional notation, including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. 27 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 FIGURE 4 I Levels of Eighth-Grade Public-School Mathematics Pmficiency LEVEL 350 Territory Nation LEVEL 300 Te rritory Nation LEVEL 250 Territory Nation LEVEL 200 Territory Nation 0 20 40 eta 80 100 Parcontago at or Allen Protitioncy Laval, The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within.ii 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-0-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 28 22 THE 1990 NAEP TRIAL STATE ASSESSMENT 0 ( 0.0) o ( 0.2) 0 ( 0.2) 12 ( 1.2) 11 ( 0.8) 64 ( 1.6) 76 ( 1.5) 97 ( 0.7) Virgin Islands FIGURE 5 I Eighth-Grade Public-School Mathematics i Content Area Performance Territory Nation Territory Nation Territory Nation Territory Nation Territory Nation . .. 0.. ' .... 3, , -';', . ., .... :5.--''''', . -,,, ,=., ''':' ,1".:,;...v",.. 1 24 ,,.,,.,,......: :ts?..,;'...,....."\:...,,'''::7:7=:;..- '''.',",..-7;-7,..;,:.:":.'..f...7, '.::Th \::,:2;\`.'":::: k kS,' ,',. s,1% '''Z'''' t ," ''.&\ " i'..'"''Hq.,C15.;'11,t ':, :_:.....- sl.-,;,e,-\.t-,.:..,,;:z' , !.,:::,,z,', -''''''.'';''' , ,....;:3' ."o' ';''.:;;'..,. ' ,:' '.'''';',t`,::61. '''''V.',..",;`. '''''!' '''' ;,,,ez.:k,'.., '-'31,-*,;f.',..r" "`"....;.5.; .". ''' '`. -, .4 '':''''',;''''s. ' Y.", ". ' ''' z '`'.''' . , .. :. ; " ". `.+. "' ,^Z.,. "i,: i; \ ?' : DATA ANALYSIst STAISTICII. AND PEWAINVIY . ; :;;;\. PINIONS ALOEDRA AND FUNCTI!"$ -. 0 200 225 250 275 300 Avenge Preach( Ay 227 ( 0.6) 266 ( 1.4) 214 ( 1.3) 25$ ( 1.7) 222 ( 0.8) 259 ( 1.4) 1N ( 1.2) 262 ( 1.8) 216 ( 0.8) 260 ( 1.3) 500 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 standard errors of the estimated mean (95 percent confidence interval, denoted by I-1-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 D THE 1990 NAEP TRIAL STATE ASSESSMENT CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall results, the 1990 Trial State Assessment included reporting on the paformance of various subgroups of the student population defined by racejethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY The Thal 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 ir 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. 3 0 24 THE 1990 NAEP TRIAL STATE ASSESSMENT FIGURE 6 I Average Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity Wein Islands Black Hispanic Nation Black Hispanic The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 31 THE 1990 NAEP TRIAL STATE ASSESSMENT 25 liE IIATIONT, RIPORT FIGURE 7 I Levels of Eighth-Grade Public-School CAM I Mathematics Proficiency by Race/Ethnicity LEVEL 300 Territory Black Hispanic Nation Block Hispanic LEVEL 250 Tanitory Black Hispanic Nation Black Hispanic LEVEL 200 Territory Black Hispanic Nation Black Hispanic '". . 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 100 32 26 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth.grade students attending public schools in areas damnified as "other" and extreme mral anesa (These art 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 klalhenuttles Seale 0 200 225 250 275 300 500 .0. 4 e, Average Prellelency 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 of the estimated mean (95 percent confidence interval, denoted by Ott). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 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 O ( 0.0) I ( 0.3) ( 2.3)! 12 ( 1.2) 20 40 80 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within + 2 standard errors of the ectimated percentage (95 percent confidence interval, denoted by 044). 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. 34 28 THE 1990 NAEP TRIAL STATE ASSESSMENT 11 ( 3.4) 79 ( 1.7) 97 ( 2.8)! 97 ( 1.0) 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 higi 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 colkge. In comparison, the percentage of students who reported that neitherpasent graduated from high school was 15 percent for the Virgin Islands and 10 percent for the nation. FIGURE 10 1 Average Eighth-Grade Public-School I Mathematics Proficiency by Parents' Education Virgin Wands HS non-graduate MS graduate Some college College graduate Nation HS non-graduate HS graduate Some college Collage graduate The standard errors are prevented 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 PH). 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 29 Virgin Islands THE 11. VAT FIGURE II I Levels of Eighth-Grade PulAic-School I Mathematics .Proficiency by Parents' Education LEVEL 300 Terribly MS non-grad. MS graduate Some college College grad. Nation MS non-grad. MS graduate Some college Ca 1090 Orad. LEVEL 250 Unitary MS non-grad. MS graduate Some college College grad. Nation MS non-grad. MS graduate Some college College grad. LEVEL 200 Unitary HS non-grad. MS graduate SOMe COM1945 College grad. Nation HS non-grad. mS graduate Some college College grad. 0 20 40 00 80 Permotaga at or Above Pronciancy Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 544). If the confidence intervals for the populations do not overlap, there is statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 100 36 30 THE 2990 NAEP TRIAL STATE ASSESSMENT o ( 0.0) o ( 0.4) 1 ( 0.8) 1 ( 0.6) ( 0.9) ( 1.5) 12 ( 1.4) 21(1.9) 7 ( 1.9) 12 ( 1.9) IS ( 3.7) 11 ( 2.4) 37 ( 4.8) ( 2.7) 71 ( 2.6) 79 ( 2.0) 63 ( 5.0) 77 ( 22) 57 ( 4.1) 70 ( 3.3) 1111 ( 1.9) 07 ( 0.8) ( 0.7) SO ( 0.7) Virgin Islands GENDER As shown in Figure 12, eighth-grade males in the Virgin Islands had a higher average mathematics pmficiency than did eighth-grade females in the Virgin hlands. Compared to the national results, females in the Virgin Islands performed lower than females across the country; males in the Virgin hlands performed lower than males across the country. FIGURE 12 I Average Eighth-Grade Public-School I Mathematics Proficiency by Gender The standard errors art presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not" overlap, there is a statistically significant 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. 3 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 31 Virgin Islands FIGURE 13 I Levels of Eighth-Grade Public-School I Mathematics Proficiency by Gender LEVEL 300 Territory Male Female Nation Male Female LEVEL 250 Territory Male Female Nation Male Female LEVEL 200 Tinitory Mate Female Nation Male Fernate 1 ( 0.4) 0 ( 0.2) 14 ( 1.7) 10 ( 1.3) 0 20 40 00 80 100 Porcentag. at or Moira Proticloncy Lewis 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 esumated mean (95 percent confidence interval). Proficiency level 350 is not presented in this figure because so few students attained that level. 38 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 70 ( 2.8) 73 ( 2.2) 97 ( 0.9) 97 ( 0.8) Virgin Islands In addition, these 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 at4ined 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. 39 THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Virgin Islands TABLE 3 f Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 11180 MEP TRIAL STATE ASSESSMENT - Numben and Owen; Mesemement Geometry _ Data Andyek, SIM**,a aml PretrabNy idgaara and Rinctions TOTAL Prelicianqr re: Proligiew t( tivilskiwg 21:I tt Territory Nation RACEJETHNICITY Sleek Territory 230 ( 03) 218 ( 1.8) 225 ( 0.9) Nation 244 ( 3.1) 227 ( 3.0) 234 ( 23) Hispanic Territory Nation 210 ( 243 ( 1.2) 2.7) 200 ( 23$ ( 2.0) 3.4) 213 ( 1. , 243 ( 3.4 TvPg OF COMMUNITY Extreme nral Territory 217 ( 1,3) 200 ( 33) 215 ( 2.0) Nation 258 ( 4.3)1 264 ( 4.2)1 253 ( 45)1 Wier Territory 229 ( 0.8) 218 ( 1.4) 224 ( 03) Nation 288 ( 1.9) 237 (24) 259 ( 1.7) Prallickasy ProlkaRION 1 1 Sol 1 1111 200 ( 1.8) 220 ( 0.9) 231 ( 33) 237 ( 2.7) 101 ( 2.7) 212 ( 2.0) 239 ( 3.4) 243 ( 3,1) 179( 13) 205 ( 1.2) 257 ( 5.0)1 258 ( 4.8)1 200 ( 14) 221 ( 0.9) 281 ( 2.2) 201 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for etch population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 4 0 34 THE 2990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 3 I Eighth-Grade Public-School Mathematics ("Intinued) i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1590 NAEP TRIAL STATE ASSESSMENT Numb___!_l_lind wilwarusin5 Measurement Geometry Data Analysis, ....,4 Stanitics. ,its Prided** - Ngebra and Functions _ TOM Madam Preildency PnVidenoy PraNINN$ PrelidetNY Territory 227' ( 0.6) 214 ( 1.3) 222 ( 0.$) 196( 1.2) 216 ( QS) Nation 206 ( 14) 2$4 ( 1.7) 259 ( 1.4) 262 ( 1.4I) 260 ( 13) FARINTImsagi NS non-graaate Territory 220 ( 3.3) 2(11( 3.4) 21$ t ISO ( 3.5) 207 ( 3.3) Nation 247 ( 2.4) 237 ( 3.8) 242 ( 2.2) 240 ( 3.1) 242 ( 3.0) NS graduate Territory 228 ( 1.6) 213 ( 3.0) 225 ( 1.2) 200 ( 2.0) 221 ( 2.0) Nation 259 ( 1.8) 248 ( 2.1) 252 ( 1.8) 253 ( 2.2) 253 ( 2.0) Sens wisp Territory 238 ( 2.3) 225 ( 2.6) 227 ( 2.8) 214 ( 4.3) 227 ( 3.3) NUM college graduate 270 ( 1.5) 264 ( 2.7) 262 ( 10) 269 ( 2.4) 263 ( 2.2) Territory 228 ( 2.3) 210 ( 2.2) 223 ( 1.9) 200 ( 3.1) 223 ( 2.0) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 270 ( 2.2) 273 ( 1.7) RENDER Nate Territory' 228 ( 1.0) 220 ( 1.9) 225 ( 1.2) 196 ( 1.9) 221 ( 1.3) Nation 208 ( 2.0) 262 ( 2.3) 200 ( 1.7) 262 ( 2.1) 200 ( 1.8) Female Territory 226 ( 1.2) 209 ( 1.8) 220 ( 0.8) 193 ( .6) 216 ( 1.3) Nation 208 ( 1.4) 253 ( 1.6) 258 ( 1.5) 261 ( 1.9) 200 ( 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. 41 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 ME NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students p., pating 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 eighthigade 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 Ectors and proficiency. The contextual idormation 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 4 2 37 Virgia Is loads 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 hie or educational researchers' suggestions about what strategies wort 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 workshc is. 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 teaming. 43 38 THE 1990 NAEP TRIAL STATE ASSESSMENT Virg* !skids 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 widesprexd reforms that ate 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 foeuses on cunicular 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. 3 Curtis McKnight, et al., The Underachieving Curriculum: Assessing U.S. School Mathematics item an International Perspective, A National Report on the Second International Mathematics Study (Champaign, IL: Stipes Publishing Cnr ?any, 1987). Lynn Steen, Ed. Everybody Counts. A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). 4 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Virgin Islands In the Vir?in Islands, 85 percent of the students could take an algebra course in eighth grade for high school come placement or cedit. 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 parent). TABLE 4 I Mathematics Policies and Practices in Virgin Islands Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1890 NAEP TRIAL. STATE ASSESSMENT Wain islamde Nation Pt centege of eighth-grade students in public sci ode that identified mathematics as receiving spacial amitosis in school-wide goats and objectives, instruction, In-service training, etc. Percentage of eighth-grade public-school students who are offered a cam In algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who Wadi only mathematics Percentage of eighth-grade students in public schools who are assigned to a mathematics class by their ability in mathematics Percentage of eighthgrade students in public schools who receive fair or more liars of mathematics instmetion per we* PerceMage Palate. 52 ( 0.2) 53 ( 5.9) 85 ( 0.1) 75 ( 4.8) 81 ( 0.2) 91 ( 3.3) 45 ( 0.8) ( 4.0) 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 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Ideas 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 Vir 'gin 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 percetn). 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 Vitsin Islands who were enrolled in pm-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eilAth-grade mathematics courses. This mutt 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 $ I Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY lab NAEP TRIAL STATI ASSESSMENT Virgin Islands Nation What kind of mathematics class are you taking this year? Pervaidage and Preideney Pateentage and Proildency Eighth-grade methane** SS ( 0.7) 62 ( 2.1) 216 ( 0.6) 251 ( 1,4) Pra-aigabra (( 03) .41 19 ( 272 ( 1.9) 2.4) Algebra ( 0.6) 15 ( 1.2) 240 ( 4,3) 290 ( 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). 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Virgin Islands Further, from Table AS in the Data Appendix:* About the same percentage of females (8 percent) and males (9 pacent) in the Virg,in Islands were enrolled in pie-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 gems courses. Similarly, 8 percent of students attending schools in areas classified as "other" and 11 percent in schools in extreme rural areas wem enrolled in pm-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 (Table 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 1 percent for the nation. Moreover, 10 t of the students in the Virgin Islands and 4 percent of the stu.. ts in the nation spent an hour or more on mathematics homework each day. For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations racejethnicity, type of community, parents' education level, and gender. 4 7 42 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 etch 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 azus spent an hour or more on mathematics homework daily. In commiwn, 2 percent of students attending schools in areas classified as "ot" 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 111110 MAEP TRIAL STATE ASSEASMENT Virgin Wanda Nation Percentage end Proficiency Percentage and Preadancy About how much time do students spend on mathematics homework each day? 3 ( 0.3) 1 ( 0.3) 16 minutes 31 ( 0.8) 43 ( 4.2) 212 ( 0.8) 258 ( 2.3) 30 minutes 34 ( 0.8) 43 ( 4.3) 225 ( 1.4) 208 ( 2.8) 45 minutes 23 ( 0.8) 10 ( 1.9) 220 ( 12) 272 ( 51)1 An hoe or more 10 ( 0.5) 4 ( 0.0) 221 ( 2.0) 278 ( 5.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. 1 Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ." Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 48 THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Virgin lskads TABLE 7 I Students' Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111S0 NAEP TRIAL STATE ASSESSMENT Virgin islands Nation About how much time do you usually spend each day on mathematics homework? Nom 15 minutes 30 minutes 46 minutes An hour or mon Pantentaso and Pralleismov ( 01) 21St 3.4) ( IA) 310 ( 1.4) 2( 1.1) 220 ( 1.1) 10 ( 1.1) 217 ( 1.0) 15 ( 0.9) 214 ( 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. 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. 49 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Ideas In addition, 18 percsent of students attending schools in areas classified as "other" and 16 percent in schools in extreme niral ems spent all hour or more on mathematics homework daily. In comparison, 7 percent of students attending schools in areas clauified as "other" and 9 percent in schools in extreme rural areaS spent no time doing mathematics homework. INSTRUCTIONAL EMPHASLS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should b: taught a broad range of mathematics topics, includingnumber concepts, computation, estimation, functions, algebra, statistics, probability, geometiy, and measurement.' Because the Trial State Assessment questions were designed tO MU= students' knowledge, skills, and understandings in these various content areas regardless cf the type of mathematics class in which they were enrolled thz, 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. 9 National Council of Teichers of Mathematics, Currkulum and &ablation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 50 THE 3990 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 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student pesformance 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. 51 46 THE 1990 NAEP TRIAL STATE ASSESSMENT *gin Islands TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11163 MAP TRIAL STATE ASSESSMENT Wein Wan s Nation Teacher "emphasis° categories by content areas Numbers and Operations Heavy emphasis Little Of no emphasis lausumment Heavy emphasis Little or no emphasis (Isometry Heavy emphasis Little or no emphasis Data Analysis, Statistics, and OrobabSity Heavy emphasis Little Of no emphasis Algebra and Functions Heavy emphasis Little Or no emphasis 113 ( 1.1) 221( 1.1) 13( 0.5) 242 ( 2.5) 35 ( 0.7) 216 ( 11) 19 ( 0.8) 212 ( 2.5) 11 ( 02! 219 ( 1.6) 51 ( 1.0) 222 ( 1.3) 40 SA) 260 IA) 15 ( 2.1) 267 ( 3.4) 17 3.0) 250 ( 5.6) 33 ( 4.0) 272 ( 4.0) 26 ( 3.8) 260 ( 3.2) 21 ( 3.3) 264 ( 54) 11 ( 0.4) 14 ( 2.2) 197 ( 2.8) 269 ( 4.3) 66 ( 1.0) 53 ( 4.4) 199 ( 11) 201 ( 2.9) 47 ( 0.8) 48 ( 3.6) 227 ( 1.0) 275 ( 2.5) 19 ( 0.7) 20 ( 3.0) 209 ( 3.8) 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 peroent because the "Moderate emphuis" category is not included. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 Virgin Islam& SUMMARY Although many types of mathematics laming 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 tauglit 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-wade 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, teac.hers 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. 53 48 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands CHAPTER 4 felts a4z-4 uuui 11111111111 all 11111111111111111111M 111M1111111811/ RIIIIII1111111111M11111 1`11I11111 ARO 111111111111111611111a11111 111111/1111111 III 111111111' 4171111111111111q11.11 lamina IlwaMIll ./1111111. Ir.111111 MIRE IMMIUR11 uauu 11111111118111 How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instnictional practices. Bemuse 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 obtim 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). THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Virgin Islands From Table 9 and Table A9 in the Data Appendix: NW' In the Virgin Islands, 0 parent 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 nose 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 mral 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 I Teachers' Reports OD the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Which of the following statements is true *bout how well supplied you ire by your Perostdege Pereentage school system with the Instructional end end materials and other resources you need to teach your class? Prellelency 0 ( 0.0) 441 Prelleiency 13 ( 2,4) 285 ( 4.2) get aN the moms I need, I get most of the resources I need 34 ( 0.8) 38 ( 4.0) 223 ( 1.1) 285 ( 2.0) I get some or none of the MOUrells i need. ee ( 011) 31 ( 42) 218 ( 0.8) 2431 ( 2.8) The standard errors of the estimated statistics appear In parentheses. It can be said with about 95 percent certainty that, k- 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). 55 so THE 1990 NABP TRIAL STATE ASSESSMENT 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 classrcom 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 /east 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." In(fividual Differences and the Common Currkulum: Eighty-second Yearbook of Me National Society for the Study of Education (Chicago, IL University of Chicago Press, 1983). 56 THE 1990 NAEP TRIAL STATE ASSESSMENT 51 TABLE 10 I Teachers' Reports on Patterns of Mathematics I Instniction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY VISO NAEP TRIM. STATE ASSESSMENT Virgin Wanda Madan About how often do sWdents work problems In small groupsn At least anon a weak Los Non anal a vim* Never About how often do students use objects like rulers, counting blocks, or geometric solids? At least =mask Lass than ant* a walla New Prellkioney 53 ( 0.8) 211 ( OA) 35 ( 0.7) 233 ( 1.1) 12 ( 0.5) 215 ( 1.4) amit 50 ( 4.4) 280 ( 2.2) 2143 ( 2.0) 277 ( 5.4)1 Pantentaga PoreiNtass and Proficiency Proiloleacy 20 ( 1.0) 22 ( 3.7) 214 ( 1.4) 254 ( 3.2) 65(12) ( 3.0) 220 ( 0.8) 283 ( 1.9) 15 ( 0.8) 9 ( 2.8) 222 ( 1.8) 282 ( 5.9)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 57 52 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE 11 I Teachers' Reports on Materials for I Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSINENT Vn Wands Madan About how oath do studonts do probfems from tutbooks? Nowt awry day deparal dam a week About OrICO a WO* Or 1411$ About how often do studimts do problems on worksheets? Al Nod moral dam a week Abss4 arm a weft Lass awn moldy 141:11 ( CUI) 31 ( 3.1) 205 ( 13) 254 ( 2.9) 0.2) 7 ( 1.5) 215 ( 3.7) 290 ( 5.1)4 POROOille Preasisnoy POODIONIO snit Palik4iNN 4111 ( 0.7) 34 ( 3.6) 210 ( 0.0) 258 ( 2.3) 20 ( 0.13) 33 ( 3.4) 227 ( 1.0) 200 ( 2.3) 22 ( 0.0) 32 ( 3.6) 233 ( 1.4) 274 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! 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. 58 THE 1990 NAEP TRIAL STATE ASSESSMENT 53 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 I Students' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY UM MEP TRIAL STATE ASSESSMENT Virgin Wanda Wien How often do you work in small groups I in your mathematics caws? At lust ant* a wsalt Loss than mut a week Mover Pinvetwit WW1 Prelkianav 84 ( 1A) 214 ( 1.0) 18 ( 0.7) 224 ( 1.5) Si ( 1.2) 214 ( 0.0) sPanItaleorimaimw 22 22.521 28720 21,40)) 44 ( 29) 281 ( 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. Examining II iubpopulations (Table Al2 in the Data Appendix): In the Virgin Islands, 33 percent of students attending schools in areas classified 33 "other" and 34 percent in schools in extreme =al areas worked in small groups at least once a u vek. Further, 32 percent of Black students and 37 percent of Hispanic students worked mathematics probltms 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). 59 54 THE 1990 NAEP TRIAL STATE ASSESSMENT *gin Ideals USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which tby used mathematical objects such as rulers, counting blocks, or geometric soli& Table 13 below and Table A 13 in the Data Appendix summarize these data: More than half of the students in the Vs* Islands (56 percent) never used mathematkal 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 =as. Males Were more Islay 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 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NW TRIAL STATE ASSESSMENT Virgin 41111011111POWNIMPII 01.1=11.0=1,1110.11111%. How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? losast atm a weak Lass Nun am* a oak Now Ponsidellw Pirvadage and one Prat:Wm Prelkakmer 212 ( 1.4) 25 ( 0.9) 2: i 1.11 is ( 1.0) 31 ( 12) 22$ ( 13) 205 ( 1.5) 215 ( 0.8) i 511( 1.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 ttandard errors of the estimate for the sample. Go THE 1990 NAEP TRIAL STATE ASSESSMENT 55 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 A 14 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 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATiCS PROFICIENCY 10110 NAEP TRIAL STATE ASSESSMENT Virell Wands Nation How often do you do mathematics problems from textbooks in your Partentaie Parlantalp mathematics class? and Praia/my Ind Prelkiency Almost every day 73 ( 1.4) 74 ( 1.0) 220 ( 0.7) 267 ( 12) Sawa times a weak 17 ( 0.0) 14 ( 04) 218 ( 1.5) 252 ( 1/) About once a week or loas 10 ( 1.1) 12 ( 1.5) 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. CI So :HE 1990 NAEP TRIAL STATE ASSESSMENT And, for the frequency of worksheet usage (Table 15 and Table A 15 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 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111110 NAEP TRIAL STATE ASSESSMENT Violin Wands NO' NOW How often do you do mathematics problems on worksheets in your Pannataga Pareentap mathematics class? and Pracianay old Prsgaisocy At but award times a weak 38 ( 1.5) 38 ( 24 ) 212 ( 1.0) 253 ( 2.2) About once a wait 30 ( 1.5) 25 ( 1.2) 222 ( 1.1) 2e1 ( 1.4) Lass Ow **My 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. 62 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 TABLE 16 Comparison of Students' and Teaches' Reports on Patterns of and Materials for Mathematics hmtruction PERCENTAGE OF STUDENTS IMO NAIR TRIAL !TATE 1111116111041311T Nation Patterns of classroom instruction Pententage el students yam wet inithsmatics problems ks MOgrafi At least once a week Less then once a week Never Percentage Of Mudents see use elliects NM Men, counting er gemustric saNds At least once a week Less than once a week Never Materials for mathematics instnichon Percentage of students 4ho use a mathematics textbook Almost every day Several times a week About once a week or less Percentage ef Mudente nem use a mathematics wen:sheet At least several times a week About once a week Less than weekly 34 ( 14) 53 0.6) 121116 111 11( 0.1) 30 0.21 54 I 441 51 ( 13) 12 0A 44 0.0 25 ( 0.2) 1.0) 20 ( 111( 1.0) 85 1.2) 31 ( SO ( 1.1) 15 03) 41 ( 1.2 2.2 22 3. Oa UP a 24 Perosniose Percentage Students ileachers alsolonls Taufters 73 ( 1A) 84 ( 02) 74 ( 14) 02 ( 3.4) 17 ( 0.9) 9 ( 0.3) 14 ( 0.8) 31 ( 3.1) W ( 1.1) 5 ( 0.2) 12 ( 1.8) 7 ( 1.11) 38 ( 1.5) 49 ( 0.7) 38 ( 2.4) 34 ( 34) 30 ( 14) 29 ( 0.8) 25 ( 1-2) 33 ( 3.4) 32 ( 1.3) 22 ( 0.8) 37 ( 25) 32 ( 30) 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. 63 58 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 Lad practices are emerging, they are not yet commonplace. According to the students' matbesnatks 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 assigged 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 itudents 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 pmblems from textbooks almost every day, composed 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. 6 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 , Virgin !shwa 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. Teachars were asked to report the extent to which they encouraged or permitted calculator use for various activitk.s. 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 Evahiation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 65 60 THE 3990 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 I Teachers' Reports of Virgin Islands Policies on l Calculator Use PERCENTAGE OF STUDENTS 1NO MEP TRIAL. *TATE ASSESSMENT Virgin Wands Nation Percentege of eighth-grade students in public schools whose teachers permit the unrestricted use at calculators Percentage of eighth-grade students In public schools whose teachers permit the use of calculators for tests Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators mod by the school Peressitege Percentage ( 0.0) 16 ( 3.4) 3 ( 0.0) 33 ( 4.5) 25 ( 1.0) Se ( 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 '7D Pitt la Islands THE AVAILABILFTY OF CALCULATORS In the Virgin Islands, most students or their families (92 percent) owned calculators (Tabk 18); however, fewer students (40 percent) had teachers who explained the use of oticulators to them. From Table A 18 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 thm use of calculators explained to them (38 percent and 42 percent, respectivaly). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NMP TRIAL STATE ASSESSMENT Virllin Wands Nation Do you or your fomily own a calculator? Yes Priadency 319 ( OS) Perollass9 mid iPreidanav 97 ( 0.4) 283 ( 1.3) No 204 Percontigo and Prollkdonoy ( 0.8) ( 1.7) 3 ( 0.4) 234 ( 3.8) Personae. and Proficiency Does your mathematics teacher explain Row to use a calculator for mathematics problems? Yes 40 ( 1.4) 49 ( 2.3) ' 217 ( 1.2) 258 ( 1.7) No 00 ( 1A) 51 ( 2.3) 219 ( 0.9) 200 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certaimy that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 6 7 62 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands ME 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, s, .Amts were asked how frequently (never, sometimes, almost always) they used cam 4ors for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In the V Islands, 21 percent of the students never used a calculator to work pro . in class, while 53 percent almost always did. Some of the students (13 percent) never used a calculator to work problems ai home, compared to 33 percent who almost always used one. About one-quarter of the students (27 . t) never used a calculator to take quizzes or tests, while 35 percent II ost always did. TABLE 19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY INO NAEP TRIAL STATE ASSESSMENT Virgin Wanda Nation How often do you use a calculator for the following tasks? Percentage and Prosaism Pffentlip and PraNcianay Working problems in class Almost always 53 ( 1,1) 411 ( 1,5) 214 ( 0.5) 254 ( 1.5) Never 21 ( 1.0) 23 ( 1.9) 233 ( 4.7) 272 ( 1.4) Doing problem at home Almost always 33 ( 1.2) ( 1.3) 212 ( 1.4) ( 1.8) Never 13 ( 1.0) 19 ( 0.9) 227 ( 2.9) 263 ( 1.8) Taking quizzes or tests Almost always 35 ( 14) 27 ( 1.4) 212 ( 1,2) 253 ( 2A) 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. s THE 1990 NAEP TRIAL STATE ASSESSMENT 63 Virgin Islands WHEN TO USE A CALCULATOR Part of the Trial State Assessnunt WAS designed to investigate whether students know when the use of a calculator is helpful and when it is not. Them 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 eAlculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology Used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the cale; Tator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 69 64 THE 1990 NAEP TRIAL STATE ASSESSMENT 7,- :1-.7,7-'7 Virgin Islands The data presented in Table 20 and Table A20 in the Data Appendixare 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 maks 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 ao I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT "Calculator-use group Peraningo and mvd Prolleima Prflidency 33 ( 1.5) 42 ( 1.3) 223 ( 1.2) 272 ( 1.6) 67(1.5) 58 ( 1.3) 218 ( 1.0) 25$ ( 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 mterest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 Virgin Islands SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instructkmal 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, compaled 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. 71 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin blends 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. 9 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 67 Pipes Islands TABLE 21 I Profde of Eighth-Grade Public-School I Mathematics Teachers PERCENTAGE OF STUDENTS MO NW TRIAL STATE ASSESSMENT -me Wein Mande Nation IMP Percentage of students *hoes mathematics teachers reported having the tollowing degrees Bachelor's degree Master's Or specialist's degree Doctorate or professional degree Percentage et students when mathematics teachers have the Mask* toes et teaching certificates Nut an recognized by the Vligki islands No regular certification Regular certification but less than the highest available Highest certification available (permanent or tong-term) Percentage of students agues mathemetice teachers have the blowing types of teaching certificates that are recognized by the WO kande Mathematics (middle school or secondary) Education (elementary or mleAlle school) Other 170 IF0 42 ( 41 SO ( 2 ( 1.4 52 23 29 1.0) 0.8) 29 0.7) 0.7) ( 0.4) 12 ( 0.7) 4 ( 12 4.3 2.2) 24) 14) 11. The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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 arca. Accoidingly, the Trial State Assessment gathertd details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. 73 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 teachess who had a graduate major in mathematics. Amass the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports On Their Undergraduate and Graduate Fields of Study PERCENTAGE OF STUDENTS 11100 NAER TRIM. STATE ASSESSMENT Virgin islands Nation What was your undergraduate major? Mathematics Education Other What was your graduate major? Mathematics Education Other or no graduate level study liermegage 56 ( 0.7) 15 ( 0.4) 30 ( 03) Percentage 43 ( 3.9) 35 ( 3.8) 22 ( 3.3) Percentage 19 ( 0.3) 22 ( 3.4) 26 ( 0.7) 36 ( 35) 54 ( 0.6) 40 ( 3.4) 11 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT 69 Might Islay& 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 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 similu types of in-service training. About one-quartex of the students in the Virgin Islands (25 percent) had mathemalics teachers who spent no time on in-service ethicai, devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students bad mathematics teachers who spent no time on similar in-service training. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS MO SAP TIUAL STATE ASSESSMENT Wgin Mina During the last year, how much time in total have you spent on In-service education in mathematics or the teaching of mathematics? Now Ono to i5 hours 18 hours or more Poundage 25 ( 0.6) Peramtase 45 ( 0.2) 51 ( 4.1) 28 ( 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. 75 70 THE 1990 NAEP TRIAL STATE ASSESSMENT Vireo Islamic 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, resuhs 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 tenitories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In the 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 !iffiest 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 mathematici. 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. ACToss the ration, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. 1° Archie E. Lapointe, Nancy A. Mead, and Gar y W. Phillips, A World of Differences. An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Asseimnent of Educational Progress, Educational Testing Service, 1(188). " Ina VS. Mullis, John A. Doisey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement NAEP's 1990 Assessment of the Nation and the Thal Assessment of the States (Princeton, NJ: National Assessment of Educational Progiiiis, Educational Testing Service, 1991). 76 THE 1990 NAEP TRIAL STATE ASVSSMENT 71 *gin 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 mathesnatics 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 Vir*in Islands (25 percent) had mathematics teachers who spent no time on m-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachess who spent no time on similar in-service training. 77 72 THE 1990 NAEP TRIAL STATE ASSESSMEN' ;:" Virgin blends 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, teach= and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment and mathematics proficiency, students participating in the Trial State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education. 73 THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Virgin Islands AMOUNT OF READING MATERIALS IN ME HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by paresis on learning yid schooling. Students participating in the Trial State Msessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports On Types of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AvERAGE MATHEMATICS PROFICIENCY NAEP TRIAL STATE ASSESSMENT Islands Nation Does your family have, or receive on a regular basis, any of the following items: more than 25 books, an encyclopedia, newspapers, magazines? Zoro to Iwo typos Tiros typos For typos Porooniago and Poelloianoy Parosata. and Pralkdonay 24 ( 1.1) 21 ( 1.0) 212 ( 1.3) 244 ( 2,0) 38 ( 1.8) 30 ( 1.0) 218 ( 1.4) 25$ ( 12) 40 ( 1.4) 41 ( 1.3) 223 ( 1.2) 272 ( 1.5) The standard errors of the estimated statistics appear in parentheses. ft can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. The 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. 71) 74 THE 1990 NAEP TRIAL STATE ASSESSMENT -. Vkgin 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 Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11190 NAEP TRIAL STATE ASSESSMENT Virgki Wands Nam How much television do you usually watch each day? One how or less Two hours Three hours Four to eve haws lax hours w more panindaaa and Prolicienoy 15 ( 12) 214 ( 1.4) 15 ( 1.0) 217 ( 2.1) 17 Paraentage and PraNdancy 12 ( 0.8) 200 ( 2.2) 21 ( 0.9) 25S ( 1.8) 22 0.8) ( 1.3) no t 1.8) 24 ( 1.$) 221 ( 1.7) 27 ( 1.0) 217 ( 1.0) ( 26$ ( 1.7) 2$ ( 1.1) 210 ( 1.7) 10 ( 1.0) 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 interests the value for the entire population is within ± 2 standard errors of the esthnate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT s 75 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 t) watched one hour or less of television each day; 27 percent watched six hours or more. A smaller percentage of males than females tended to watch six or more hours of television daily. However, about the same percentage of males and females watched one hour or less per day. In addition, 27 percent of Black students and 28 percent of Hispanic students watched six hours or more of tekvision 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' MVOs in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix; In the 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 prior 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. 81 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Island's Similarbr, 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. TABLE 26 I Students' Reports on the Number of Days of School Mined PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRU ;7*ATE ASSESSMENT Virgin Viands How many days of school did you miss last month? Ono or two dari Throw days or mon Pamentaie Ponord1110 Pnickmay Proioisney 25021 I 1.5)) 2:55 29 ( 12) 32 ( 0.9) 219 ( 1.2) 2911 ( 1.5) 22 ( 12) 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 Mterest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 82 THE 1990 NAEP TRIAL, STATE ASSESSMENT 77 Virgin Islands STUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics. Laming 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: I like mathematics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people ase 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 usefid 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 I (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "indecided," "disagree," or "strongly disagree" were given a value of 3. Each student's :esponses were avenged 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 the "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). la National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 83 78 THE 1990 NAEP TRIAL S '41 'a ASSESSMENT TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 RAW TRIAL !TATE ASSESSEENT Virgin bland' Nation Student "perception Index" groups Strongly wee ("perception Index" of 1) Aim ("perception index" of 2) Undeddod, disagree, strongly disagree ("perception index" of 3) Ilaroodage finedlacr $7 ( 1.4) 920 ( 1.1) 47 ( 1.2) Illemistap foralii9F9 2r1 11.11] 49 ( 1.0) 215 ( 1.0) 292 ( 1 .7) teal 24 ( 1.2) 20 251 ( 14) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. The data related to out-of-school factors show that: Students in 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. 84 THE 1990 NAEP TRIAL STATE ASSESSMENT 79 -- . Virgin Naas 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 (SO percent) did not miss any school days in the month prior to the assessment, while 22 missed three days or more. Average mathematics proficiency VMS for students who did not miss any days of school and lowest for students who missul 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. A mathematics proficiency was highest for students who were in the "stro agree" category and lowest for students who wer: in the disagree, strongly disagree" eategotY. I El 85 80 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appeadix 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 assessmrzt were developed through a consensus process managed by the Council of Chief Stat.; School Officers, and the items were developed through a similar process managed by Educational Testing Setvice. The development of the Trial State Assessment Program benefitted from the involvement of hundreds of representatives from State Education Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the program. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The first step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT 81 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 appeased 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 Thal State Assestment Program were developed using a broad-based consensus process, as described in the introduction to this repo& The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measumnent; Geometry; Data Analysis, Statistics, and Piobability; and Mgebra 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' charactetistics (based on their responses to the background questions) and their ovetall performance in the assessment. National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). 82 87 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands FIGURE Al I Content Areas Assessed INumbers 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 end estimation situations. Understanding numerical relationships as expressed in ratios, proportions, and perCents Is emphasized. Students' abilities in estimation, mental computation, use of Calculators, Generalization of numerical patterns, and verification of results are also Included. IMeasurement This content area focuses on students' ability to describe real-world objects using numbers. Students are asked to identify attributes, select appropriate units, apply measurement concepts, and communicate measurement-related ideas to others. Questions are included that require im ability to read Instruments using metric, customary, or nonstandard units, with emphasis on precision and accurocy. Questions requiring estimation, measurements, and applicattonS of measurements Of length, time, money, temperature, masstwelght, 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 ai all levels of schooling as well as in practical applications. Students need to be able to model and visualize geometric figures in one, two, and three dimensions and to communicate geometric ideas. In addition, students should be able to use informal reasoning to establish geometric relationships, IData Analysis, Statistics, and Probabilfty 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. 88 THE 1990 NAEP TRIAL STATE ASSESSMENT 83 Virgin Islands FIGURE A2 I Mathematical Abilities The following throe categories of mathematical abilitieS are not to be mnstrued ALS hierarchicai. For example, problem solving involves interactions between conceptual knc;. ....So and procedural skills, but what is considered complex problem solving at one grade level rifay be considered conceptual understanding or procedural knowledge It another. IConceptual Understanding Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts: can use and Interrelate models, diagrams, ond varied representations of concepts: can Identify and apply principles: know and can apply facts and definitions: can compare, contrast, and integrate related concepts end principles: can recognize, interpret, end 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. IProcedural 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 ta.tors inherent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have beein creioted as tools to meet specific needs in an efficient manner. it also encompasses the abilities to read JIM produce graphs and tables, execute geometric constructions, and perform noncompvtational skills such as rounding and ordering. 1 Problem Solving In problem solving, students are required to use their reasoning and analytic thilities when they encounter new situations. Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, data, mociels, 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 Ideas 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 assesaed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scal,e 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 arca 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 04o-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 mathematic., 'tents from the 1990 assessment that discriminated well between adjacent levels. The eliteria for selecting these "benchmark" items were as follows: To define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To define performance at each of the higher levels on the scale, items were chosen that were: a) answered correctly by at least 65 percent of students whose proficiency was at or near that level; and b) answered incorrectly by a majority (at least 50 percent) of the students performing at or near the next lower level. The percentage of students at a level who answered the item correctly had to be at least 30 points higher than the percentage of students at the next lower level who answered it correctly. 90 THE 1990 NAEP TRIAL STATE ASSESSMENT 85 Virgin !skalds 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 understandinp of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a surmnary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.2 Questionnaires for Teachers and Schools As part of the Trial S'Attc Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each patticipating 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 teaches and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and refonm, schcol 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 advisoty groups. MAMEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topic and the use of various instnictional approaches. Because of the nature of the sampling for the Trial State Assessment, the responses to the mathematics teacher quest'onnaire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 91 86 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Maas FIGURE A3 I Example Items for Mathematics Proficiency Levels 2O Sbnp AWN* Ressoning and Probkin SoMng th Whole Numbers A EXAMPLE 41 .e1=7 (41teir Vti 0 lario Gaff h e T. Linke boll dal imp Iwo a de am dm AM difteme WI of bib as am oboTA Alos fib sea bee wil lie DM al 1102 skews. yolisli Ma will kw dile tom bob OS 0 The boa will is sorb Di 0 TM bon rub obs ND Mb 0 The bow vie 'be abbot 111116 Dm solL EXAMPLE 2 z N WON Olt MDT PICEID AT IMIATfAT MOD No DNA TANI Ike Dap Mille UNA Dreg tors CANA** 11111 O. lbw Amy Dim of omen way sichml as TheerA04 CD to op ro * 10 0 AD O 1 Asset know. Grad. 4 Ontall Pwcantaoa cam* 7311. Pwcantago Cam* far Mahar Lovely ER MI ER Ea 55 91 100 Grade 4 00n5 Perosatapi 80% Perowlage Carnet far at Lively ME Me MO MI 75 91 100 Grade S Oarall Percentage Cornet 14% Poramtage Owed for Anchor Lewis: 222 220 TS ST 96 100 9 2 Virgin Wan_ noun A3 Example Items for Mathematics Proficiency Izvels (continued) EXAMPLE 7. Wine is die value of n + whoa is 3 1 Mons: EXAMPLE 2 Tbe obis skis lbws dos mods al s may al bob ads. Oa dis sad* bilowt sake s Ottigsab &MKdos dats fro dos able. LAW stab lan st she axis wide de mama bat mks. VIII vowvos the coicalsoat wassolsat Witt ON. EXAMPLE 3 4. was,* M pocking bombaiii Imo boom. tak Um holds b baobab. Sbo bas 24 kr& Volidt maim mamamill back OW find 00 WW1 WWI boom sW oma CD U .0 0 24 + 0244.4- 0 24 0. a 0 00 I don't know, sa Gods enroll Pereontgle Com* le% Perosnisas Corse for Anchor um* Oa 2E2 2E2 222 28 a) 96 96 Grads 6 Oman POKOMOD41 Correct 7316 Pomo. Comet for And*, Wats: 222 2112 Zi2 21 05 92 92 Grids 8 Ovine Porconis90 CAMet 77% Comet for Anchor Urnels: 292 222 ZS 222 37 71 95 100 9 3 Tlitt 1990 NAEP TRIALsr= Antiguan Wain Islaads FIGURE A3 1 Example Items for Mathematics Proficiency Levels (continued) It WM* dd. ham* alow. *awe of ago% cgs skpa sow* we *I* it EXAMPLE 2 4 b soda owe 1g, s dos is WAAL s gat 0 km loureseaca by rah mold intim M. It the mat info leat taw A* web toe oviettivald s *We mobt bar way *ha bight 0 g 0 g 0 7 Dit yea be do Wads* shit gum*? to 0 No BEST COPY AVAILABLE ME 1990 NAEW TRL4L STATE ASSESSMENT 94 Grads 0aors2 Poroontogo Comm 00% roroontage corm( for Mchor Envois: 222 Ma IN Mt 33 49 7? 90 Grads 12 pare Poroontleo Coma 75% Parcentree Cornet tot Moho. Lows: 242 312 4. 79 06 &ono 3 Pmenta3 conirct 50% roroontogo Correa for Annhor Lowy 222 2212 322 MO 17 48 80 90 39 Virgin Islands FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Laval 350: floasonkig and Problam Solving Involving Geometric Ralationahlps, Algabrala Equations, and lagInnbig StatlatIca and Probability EXAMPLE 11/661561s IS- Maim *the kilos** ihoswa al dat-fisulaa * a a a I 2 5 4 1. 121 dad el det-figare la eastioNst bow way am 10 be Is lee CP 100 lot 0 169 0 200 41)=1 EXAMPLE 2 11. Whin bow pee lausil row au mu quescia. 16. Arwa4r Grade Owe Paroontage Come 34% Pordentiga Owed far Imhof Laois: 1211 MO Age AM 13 19 53 SI Grade 12 Onnil Perventags Carract 49% Peva*** Coma for Mahar !AWL fA2 21111 22 48 90 Grad* 8 Omall Parcentage Corm*: 15% Parentage Carnal for Moho' Weft AM AM MO 1 4 2. 74 Grade 12 0400111 Pere1111001 *ant 27% Peraaatap Came tat Mahal Woks: 21:2 212 MI 3 22 74 95 90 ME 1990 NAV TRIAL STATE ASSISSMENT ' Virgin Naas SCHOOL CHARACTERIS11CS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was fmmpleted by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there wen questions about school policies, course offerings, and special priority WM, among other topics. It is important to note that in this report, as in all NAEP repons, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student Ls the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEFs 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 Audents 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 peiformance of a carefully selected, representative sampk of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAEP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as santpling error. Like almost all estimates based on assessment measures, NAETs total group and subgroup proficiency estimates are subject to a second source of uncertainty, in addition to sampling error. As previously noted, each student who participated in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropriate, set of the assessment questions or the entire set of questions -- somewhat different estimates of total group and subgroup proficiency might have been obtained. Thus, a second source of uncertainty arises because each student was administered a subset of the total pool of questions. 96 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 Virgin Islands In addition to xrporting 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 Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population mew .s and proportions in a manner that reflects the unmrtainty 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 follow,: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. 7 92 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 warted spending 45 minutes or more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is higher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in performance between the two grewps in the population because of the uncertainty associated with the estimated zwerage proficiency of the groups in the sample. Remember that thc 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 popelttion had been assessed, rather than a sample of students, or if the assessment had been n peated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the 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 statiAtically significant (different) at the .05 level. THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Virgin Islands As an exampk, suppose that one were interested in determining whether the average mathematics proficiency of eighth-grade females is highes than that of eighth-grade males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard esrors for females and males were as follows: Group Average Proficiency Standard Error Female 259 2.0 Male , , 255 2.1 The difference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is Ni 2.02 + 2.12 = 2.9 Thus, ar: ,Ipproxirnate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this rerfnt, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 pzeent confidence interval for the difference beim= groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attiibute 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 sliglit 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. 3 The procedure described above (especially the estimation of the standard error of the difference) is, in a strict sense, only appropriate when the statistics being compared corny 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. 9 94 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 confidmrce interval or test of statistical significance is being performed. However, in each chapter of this report, many different groups sue 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 Bonferrord method was used in the analyses described in this report to form confidence intervals for the differearces between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni promdure 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 Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for grnups 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 variable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probability of .8 or greater. 0 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 Virgin Islands The effect size of .2 pertains to the The difference between the average proficiency of the subgroup in question and the average proficiency for the total eignh-grade public-school population in tlw state or territory, divided by the standanl deviation of the proficiency in the total population. If the tne difference between subgroup and total group mean is .2 total-group standard deviation units, then a sample size of at kiut 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 niagnitude 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 Dual Ption of Text In Report ... p = 0 None J < p 5 10 Relatively few 10 < p .5 20 Some 20 < p 5 30 About one-quarter 30 < p 5 44 Less than half 44 < p 5 55 About half 55 < p 5 69 More than half 89 < p S. 79 About three-quarters 79 < p 5 89 Many 89 < p < 100 Almost aq p = 100 AO , 101 96 THE 1990 NAEP TRIAL STATE ASSESSMENT THE NATION'S REPORT CARO DATA APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains corresponding data for each level of the four reporting subpopulations -- race/ethnicity, type of community, parents' education level, and gender. r t /02 THE 1990 NAEP TRIAL STATE ASSESSMENT 97 Virgin Maids TABLE AS I Students' Reports On the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Bei Swath, Mathematics Pro-algebra Algebra . - _ TOTAL Peroentese and Pradmienes $9 0.7) 218 0.8) 62 2.1) 251 1.4) 87 ( 0.9) 218 ( 0.7) 72 ( 4.7) 232 ( 3.4) 93 ( 1;7) 209 ( 1.3) 75 ( 4.4) 240 ( 2.4) 85 ( 1.5) 204 ( 1.1) 74 ( 4.5) 249 ( 3.1)1 89 ( 0.8) 218 ( 0.7) 2.2) 251 ( 2.0) Pommies, Prellekeley 3 ( 0.5) 0.9 19 ( 1.9) 272 ( 2.4) 3 0.0) *44 GM) 10 ( 3.0) 241$ 8.4) 2 ( 06) 73 ;.) *4* ( $114) 3 ( 1.1) 14 ( 5.0) - -*) 114* 20 ( 2.1) 272 ( 2.8) Pon:~ and Prolieloncs 8 ( 0.6) 24°15 1 2 4121 296 ( 2.4) O ( 0.6) 245 ( 4.7) 9 } 2.2) .4* Pthl 4 ( 12) iblve ( ( 1.5) 4,8,* ..**) 9 ( 1.6) ( e") 7 ( 2.2) *** ( "*) 5 ( 0.6) 41,4* F1111 16 ( 1.4) 294 ( 2.7) Territory Nation RACE/ETHNICITY Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Extreme nral Territory Nation Other 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. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. 1 Interpret with caution - the nature of the sample does not allow accurate determination of the variability of' this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 98 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE AS I Students' Reports on the Mathematics Clam (c4312tinued) They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL /Ugh Ih-grade STATE ASSESSMENT Mathematics Pro-algebra Algebra .---...- MA Territory Nation magrinasem HS nen-graduate ilaramass le 0.1) 2115 MS) e2 2.1) 251 (1.4) Territory 88 ( 2.0) 209 2.3) Nation TT 3.7) 241 2.1) NS graduate Territory 91 ( 1.5) 217 ( 1A) Nation 70 ( 2.8) 249 ( 1.9) Sone coStop Territory 85 ( 3.5) 225 ( 2.3) Nation 80 ( 3.1) 257 ( 2.1) 0**gs graduate Territory 85 ( 2.0) 218 ( 1.6) Nation 53 ( 2.7) 259 ( 1.5) GENDER M. Territory 86 ( 1.2) 219 ( 1.1) Nation 83 ( 2.1) 252 ( 1.6) Portal* Territory 90 ( 1.1) 214 ( 0.9) Nation 61 ( 2.6) 251 ( 1.5) .1104 is( is) 272 ( 2 (( 43 I** In 2 0.4) 0.11) 18 ( 2.4) 286(3.5) 5 (1.9) 04* yfr.) 21 2.9) 276 ( 2.8) 4 ( 1.7) 21 ( 2.3) 278 ( 2.8) 1511 240 1.2 ,2,A) 24) 2911 1.1) 7 3.4) 3 3 ( 0.8) .4* ( 18 ( 1.8) 275 ( 2.9) 2 ( 0.5) 20 ( 2.3) 2641( 3.0) II, 4 (12) ifra* «In ( 1.1) 277 ( 5.2) 7 2.7) 44) 15 (1.9) 295 ( 32) 8 ( 1.0) 24 1.7)) 303 ( 2.3) ( 1.0) fr- ( Mr* ) 15 ( 1.2) 299 ( 2.5) ( 0.7) 15 ( 1.7) 293 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 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. "" Sampk size is insufficient to permit a reliable estimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ,SSESSMENT 99 Virgin Islands TABLE Ab Teachers' Reports on tie Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF 3TUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO MEP TINAL STATE ASSESSMENT None 18 Minas. 30 Minutes 48 Mintage An Hour or Mars ix& Territory Nation MardaliMa Made Territory Porcsatise mot *Widow 3 OS) 1 ( 00 ( 0.6) iran Nation 1 ( 0.7) ( eel Hispanic Territory 4 ( 1.3) Nation 1 ( 04) vim) TYPE OF COMMUNITY &Immo rural Temtory 7 ( 1.0) HI* ( Nation 0 ( 0.0) Other Territory 2 ( 0.3) Nation 1 ( 0.4) Ilavutimo ilsoventeso ilwasotags and sod wed Preficioncy Prldidany Prilideow *Wicklow 31 0.11) 10 212 0.0) 2E5 141 2138 I 11:29 221 2.0 43 4.2) 4 0.0 258 2.3) 268 272 Li 278 Li 30 ( 1.1) 35 ( 0.9) 22 ( 10 ( 01) 215 ( 1.1) 227 ( 14) 224 ( 1.4 223 2.2) 55 ( 7.8) 40 ( 6.7) 3 [ 1.2 2 0.8) 232 ( 3.1) 248 ( 5.3) direet .4*) 34 ( 2.4) t5 1 i.01 I4 f ,e1 13 2.5) 202 ( 2.2) 081 40 ( 74) 34 ( OA) 13 i 2.9) 7 2.4) 245 ( 3.0)1 251 ( 4.2)1 *** ( ***) "" 26 ( 0.9) 210 ( 2.1) 08 (141) 253 ( 5.4)1 32 ( 09) 212 ( 0.0) 37 ( 4.3) 256 ( 3.1) 27 ( 0.7) 210 ( 21) 14 (10.9) I44.) 35 ( 1.0) 228 ( 1.7) 40 ( 5.1) 265 ( 2.5) 38 ( 1,4) 207 ( 1.7) ( 5.6) 19 ( 0.6) 227 ( 1.0) 10 ( 2.4) 276 ( 8.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 105 100 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Naas TABLE A6 Teachers' Reports on the Amount of Time (cmitinued) Studenb Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAV TRIAL STATE ASSESSMENT Now 15 Minubs 30 Alkagas 46 Mims An Hour or Mai TOTAL Territory Nation PARENTS EDUCATION HS non-graduato Territory Nation HS graduate Territory Nation Som college Territory Nation College graduate Territory Nation DPW Male Territory Nation Female Territory Nation Poway. 04111/10490 sot sod PesOsisasv PrOkkom 3 01 1 0.3) 4141, 5 ( 1.5) 1 (0.8) 2 ( 0.1) .41 ( 0.5) .1. 3 ( 1.5) ( 0.9) ( 4.1 2 ( 0.5) ( ( 0.3) ( **) 3 ( 0.6) 44. ( ( 0.3) *41 3 ( 0.5) 1 ( 0.4) ( "41 $1 OA) 212 04) 43 42) 265 23) 34 ( 4.1) 4.41 49 ( 63) 240 ( 23) 29 ( 2.8) 21E ( 2.7) 43 ( 5.2) 249 ( 3.1) 32 ( 2.3) ( 44 ( 5.4) 265 ( 2.6) 31 ( 33) 212 ( 2.5) 40 ( 4.7) 265 ( 2.5) 30 ( 1.0) 215 ( 1.6) 44 ( 4.4) 257 ( 2.9) 31 ( 1.7) 209 ( 1.8) 41 ( 4.4) 255 ( 2.3) Parceltals siwi Prolisliony 34 ( GA 225 14 43 431 206 2.4 31 2.7) *so .4.) 40 ( 8.1) 24i; 3.7) 36 ( 2.3) 229 ( 2.8) 44 ( $3) 259 ( 2.7) 28 ( 3.6) Vine ( 43 ( 5.8) 270 ( 3.0) 36 ( 3.2) 228 ( 24) 44 ( 4.1) 277 ( 3.0) 33 ( 1.6) 327 ( 1.7) 43 ( 4.3) 268 ( 2.9) 34 ( 1.3) 223 ( 1.9) 43 ( 4.7) 284 ( 2.8) reiramitsie sof Preldeney 23 ( 220 (1.2 10 (1.9 272 5.7)1 18 ( to) IMO 1.7) from ete) 23 ( 13) 222 ( 2.6) 9 ( 3.1) 23 ( 4.1) vim ( ( 2.1) oto, ( 24 ( 2.4) ..**) 11 ( 2.3) 287 ( 6.1)1 24 ( 1.2) 222 ( 23) 9 ( 1.9) 273 ( 7.3)1 21 ( 1.2) 218 ( 2.8) 11 ( 2.0) 272 ( 5.7)1 tiontoidels sad PROOkolgt 10 221 ( 21) 4 ( OA 271 ( 5.1 12 2.3) 4 ( 1.3) ft e 11 (1.8) .41 3 ( 1.0) ( 13 ( 34) I** ( 4111 4 ( 1.0) ( 24) *Al 5 ( 13) 10( 1.1)) 5 ( 13) 279 ( 7.7)1 11 ( 1.1) 219 ( 3.5) 4 ( 0.9) 44* ( 441 The standard errors of tne estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the val,.4 for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with canon - 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 301 Virgin Munk TABLE A7 I Students' Reports on the Amotmt of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAP TRIAL STATE AESSMENT SS Nona 15 Minu Ms 30 Minutes 45 Minu Ms An Hour or Mans TOTAL Territory Nation laatinglea Mack Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Eidrenie neat Territory Nation Other Territory Nation and and PfacirliN Proadony Proacksay Prellakmay Prelokinov .2194 9 0.5) 251 ( 2.11) 8 ( 222 ( 14 ( ipoi ( 1.6) 12 ( 11) air* ( 414t/ 9 1.8) 2.3) foe *4..) 7 01) 221 ( 3.9) 9 1.0) 250 3.8) SS 219 1.4 31 2.0 2.4 1 A 32 ( 221 1.4 26 25 241 3.8 34 ( 3.6) 209 ( 3.1) 27 ( 3.0) 246 ( 3.8) 36 ( 5.1) 206 ( 2.6) 38 ( 4.6) 290 ( 3,5), 32 ( 1.5) 222 ( 1.5) 30 ( 11) 23( 2.3) 26 ( $2 203 26 ( 223 ( 33 ( 237 ( 28 ( 210 ( 30 ( 24$ ( ( 31 ( 255 ( 27 ( 222 ( 32 ( 264 ( 1.1 1.2 1.9) 1.0) 1.1 3.5 2.4 2.8 2.6 3.4) 441 2.9) 5.1)1 1.3) 1.2) 1.3) 2.3) 217 16 266( 15 ( 220 ( 1$ ( 240 ( 17 ( 241 ( 14 ( .44 ( 18 ( 16 ( 218 ( 15( 267 ( 1.1 1.91 1.0 11 12) 2.5) 2.3) 3.6) 2.1) 4.3) 2.0) .41 3.8)o 1.2) 2.0) 1.1) 2.1) 214 12 258 ( 19 ( 216 ( 161 14 ( "1" ( 16 ( ( *NI ( 18 ( 217 ( 13 ( 256 ( 0.9) 1.9) 1.1) 3.1) 0.9 2.2 1.111 1.7) ***) 3.6) 11,111 0.7) 2.1) 1.1) 39) The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the /.stimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 107 102 THE 1990 NAEP TRIAL STATE ASSESSMENT Vbigin IsIgurds TABLE A7 I Students' Reports on the Amount of Time They (continued) i Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1160 NAEP TRIAL STATE ASSESSMENT Nona 15 Mimeos -. 30 Minato* 43 MInunts - . An Nur or Mara TOTAL Perandage and Prodicianoy Pamela"' Paraentaga and and RIVINININy Prellaknay Paraentago and PraNalanoy Parana. and Praticioncy Territory 6 ( 0.7) 33( 1.5) 24 15 ( 1.1) 15 ( 0.9) 219 ( $.4) 21$ ( 14 220 1.1 217 ( 214 1.9) Natcon 9 ( 0.8) 31 ( 2.0 32 t 1.2 16 ( 1.0 12 1.1) 251 ( 2.8) 264(1.9) 263 ( 1.9) 206 ( 1.9 258 3.1) PARENTS' EDUCATION NS non-graduato Territory 8 ( 1-7) .044, 94 ( 4.2) 213 ( 3.6) 25 ( 3.8) 4- ..**) 10 ( 2.2) ( INP1 Nation 17 ( 3.0) .44 ( .) 26 ( 3.3) 248 ( 4.0) 34 ( 44) 248 ( 2.6) 12 2.5) 4.1m. 10 ( 2.2) 41* ( It) HS graduat. Territory 1 ( 1.0) 32 ( 3.1) 27 ( 2.8) 17 ( 2.5) 8 ( 2.4) MI* 218 ( 2.8) 225 ( 22) 219 ( 3.9) v.* yin Nation 10 ( 1.7) 33 ( 2.2 31 ( 1.9) 18 ( 14) 11 ( 1.5) 246 ( 4.2) 259 ( 3.2 254 ( 2.4) 258 ( 2.8) 244 ( 34) Some contge Territory 5 ( 1.6) * welt) 31 ( 5.5 ( «iv 20 ( 2.6) 414* ***) 20 ( 3.9) .- ( *el 23 ( 3.5) 4*4(4*$ Nation 9 ( 1.2) 30 ( 2.7 2e6 ( 3.0) 96 ( 2.1) 266 ( 2.8) 14 ( 1.8) 274 ( 3,5) 11 ( 1.5) .41 Collage gradual* Territory 9 ( 1.9) 30 ( 2.3) 26 ( 2.9) 11, 11411^ 223 ( 2.7) 220 ( 2.9) *** ( Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Mal* Territory 11 ( 1.1) 34 ( 2.1) 28 ( 1.7) 13 ( 1.2) 16 ( 1.2) 222 ( 3.7) 223 ( 1.5) 214. ; 1.8) 222 ( 2.4) 217 ( 2.9) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 268 ( 2.4) 265 ( 3.0) 258 ( 4.1) Female Territory 4 ( 0.9) 31 ( 1.9) 27 ( 1.4) 18 ( 1.6) 20 ( 1.5) *** ( **) 215 ( 1.8) 221 ( 1.9) 214 ( 2,4) 212 ( 2.7) Nation 7 I 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 248 ( 4.1) 263 ( 1.5) 260 ( 2.0) 287 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It ca.n be said with about 95 percent certainty that, for etch population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insult-mit. to permit a reliable estimate (fewer than 62 students). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT 103 Virgin Islas& TABLE AS I Teachers' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAP TRIAL STATE ASSESSMENT Numbers and Operation Oeenwery Heavy I , Emphasis Little Of No Emphasis Heavy Emphasis I Littl or No Emphasis Heavy Emphasis I Utile or No EmPhasis , L2T112 Territory Nation Matan_NEM Mack Territory Nation Illspank Territory Nation TYPE OF commuting Extreme nral Territory Nation Other Territory Nation lkweeraimpi Paysatios Paroatope Parsotspo Payola. Parandapi and and and awl end sod Pre Manna Pride Was Pre Odom Pesikketv Madam INIMMINN/ 53 1.1 13 0.5 25 0.7 19 OA 11 0.2 51 i 927 1.1 242 2.5 215 1. 212 LS 210 1 222 1 49 3.0 15 2.1 17 3.0 33 4.0 a 3.8 21 280 LS 4017 ( 3.4 250 5.0) 272 4.0 Me 3.2 204 $2 ( 1.5) 13 ( 38 ( 1.1) 19 ( 10 0.5 51 1.3 229 ( 1.5) 244 ( 2.3 218 ( 2.4) 217 ( 3.0 221 2.9 224 1.2 54 ( 7.9) 11 ( 3.3 25 ( 7.4) 22 ( 8.7 23 7.9 24 7.3 243 ( 4.3) *** ( -1 228 1 2.2)1 2$1 ( sAy 242 5.11 233 4.7 57 ( 3.4) 12 ( 2.6) 33 ( 20 1 2.1) 14 ( 11 2t 3s..:1 218 ( 2.4) *** ( "*) 210 ( 4.7 *el 47 ( ill) 8 ( 2.2) 23 ( 4.1 34 ( 54) 27 1 5.2) 15 LS; 248 ( 4.6) *** t .") ... ( ***) 255 ( 4.4p *4* ( ) ...) 1 79 ( 1.0) 2 ( 0.7) 49 ( 1.1) 35 ( 1.2 10 ( 0.6) 77 0.4 218 ( 1.?) "" ( ***) 201 ( 3.6) 204 ( 31 ( ") 216 3.6 53 (12.4) 8 ( 3.8) 6 ( 4.9) 32 (11.7 9 ( 8.1) 16 7.9 257 ( 7.1); ". ( "") *** ( eel 255 ( 9.1 1 ... ( ...) "" ( ***) 47 ( 1.3) 15 ( 0.5) 33 ( 0.3) 18 ( 01) 11 ( 48 ( 12) 230 ( 1.4) 244 ( 2.8) 221 ( 1.5) 217 ( 3.1) 221 ( 1.7 224 ( 12) 52 ( 4.1) 18 ( 2.7) 1$ ( 3.9) 34 ( 5.3) 28 ( 4.8 24 ( 4.3) MO ( 2.3) 238 ( 3.8) 253 ( 7.1)4 270 ( 4.6) 200 ( 31) 285 ( 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 estrmate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A8 I Teachers' Reports on the Emphasis Given to (continued) I Specific Mathemafics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111/80 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Msuursml Geometry Heav71 Little Or No Emphasis Emphasis Heavy Emphasis Little Or No Emphasis Heavy Emphasis Little Or No Emphasis . TOTAL Territory Nation 21161111312MINE KS non.graduate Territory Nation FIS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Mal* Territory Nation Female Territory Nation Peramese Panunive Panwlege PeouNtie IFerowlitw Porosnlase 41110 Pralidencg Pralicissay Pranciamy lonvickmiky Preficiency Prat:bail/ SS 1.1 13 0.5 35 0.7 19 01) 11 0.2 51 ( 1.0) 227 1.1 242 2.5 215 1.5 212 2.5) 219 1 222 49 SA 15 2.1 17 S. SS 4.0) 2$ 3.11 21 250( 14 217 3.4 250 51 272 4.0) WO 3.2 254 5.4 55( 2.9) 14 ( 1.3) 37 ( 2.9) 21 ( 3.3) 11 ( 1.9) 53 ( 3.0) 219 ( 4.0) * ( ) ( ***) 44," t ...il *4,.. .41 tie ( 3.7) so 1 8.9) 7 ( 2.3) 22 ( 5.31 25 ( 5.3) 32 0.3I 20 ( 6.7) 251 3.4) ... ( .4) ... ( ... ... ( N) ... ( 4.) 50( '4 ( 1.5) 39 ( 16 22) 14 ( 1.5) 45 ( 2.8) 229 ( 2.7 ( ***) 213 ( la "4' ***) *" ( ) 225 55 ( 4.10 11 ( 2.8) 17 ( 3.9 27 5.0) 27 ( 4.8) 24 5.1 250 ( 2.9) *** ( ") 251 ( 15.1), 253 ( 4.7$ 255 ( 4.2) 246 4.8 40 ( 4.7) 18 ( 4.6) 30 1 3.8) 20 ( 3.7) 9 ( 3.4) 50 ( 4.8) i.e. I mil ..* ( ..41.) .44 *en so. ( «4) ( **di) ***.( *Il) 47 ( 4.4) 17 ( 3.3) 12 ( 2.7) 39 ( 54) 27 ( 5.0) 23 ( 4.1) 265( 2.6) 2$4 ( 4.1); *" ( "1 279 ( 44) 262 ( 4.1s 270 ( 4.7) 55 ( 3.4) 11 ( 2.0) 35 ( 4.1) 15 ( 2.8) 12 ( 1.3) 48 ( 3.5) 229 ( 3.5) "" ( "*) 217 ( 3.5) .... ( ..ii.) 4~ ( "1 224 ( 2.0) 44 ( 4.1) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 269 ( 2.8) 296 ( 3.41 284 ( 7.2y 283 ( 3.8) 270 ( 3.8) 280 ( 6.4) 55 ( 1.8) 12 ( 1.2) 33 ( 1.5) 19 ( 1.5) 10 ( 0.9) 51 ( 1.3) 228 ( 1.9) 248 ( 42) 225 ( 2.5) 218 ( 4.3) ( ***) 22e ( 2.0) 43 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 261 ( 2.5) 267 ( 4.4) 255 ( 6.7) 275 ( 4.5) 263 ( 3.8) 266 ( 84) 51 ( 2.0) 14 ( 1.1) 38 ( 1.7) 20 1.5) 12 ( OA) 51 ( 1.8) 225 ( 1.5) 23(I ( 4.3) 200 ( 2.9) 206 3.6) 215 ( 3.4) 216 ( 1.6) 54 ( 36) 15 ( 2.4) 17 ( 3.2) 35 4.3) 27 ( 3.9) 23 ( 3.5) 260 ( 2.0) 256 ( 3.3) 241 ( 5.4) 250 4.1) 258 ( 3.3) 263 ( 5.0) The Standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certiinty that, for each population of interest, the value for the entire population is within ± 2 standahi errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAB? TRIAL STATE ASSESSMENT 105 Virgin Islands TABLE ASI Teachers' Reports on the Emphasis Given To (cmtinued)I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111116 NAEP TRIAL STATE ASSESSMENT _ Da Its MINI* Statistics, and Probability . Ngsbra and Roctione - Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or NO Emphasis :tom Poraudasa and firdialonai Parma. Iftlakaky Territory 11( 04) 60( 197( 196 1 Nation 14( 2.2) 1.3 44{ 2tC,f 4.3) 291 IS RACEIETHNICITY Slack Territory 11( 0.7) 08( 1.3 200( 3.1) 203( Nation 14 3.4) .44) 53 225( 8.2( 4.3 Hispanic Territory 12( ,0. 1.8) ..**) 67 183( 3.3)( 4.6) Nation 15( 4.1) 50( 8.3) 246( 4.4) TYPE Of COMMIINITY Baron rural Territory ( 0.2) 94 0.2) 440( 444) 178( 2.5) Nation ( 5.4) ***) 05 254 (18.9) 8.7)1 Other Territory 12( 05) 02 1 .2) 192( 2.9) 206 12) ill at on 15( 22) 53 5.2) 287( 4.7) 260( 3.4) Parmatair and Pratialanay PersokIP Orellidealg 147I 02:851 191 0.1 227 12 209 IS 48 SS 20 3,0 275 24$ 3.0/ 4( 11 2281 1.3 39 7.1 253 8.3 43( 3.0) 224( 3.6) 48( 5.9) 257( 4.op 6 33 4 50 227 47 276 19( 1.1j 211( 4.9 27f 229( 2.2)1 19( 22 imht,( IN1 181 42 40. 44) ( 02)( eel 46 204 ( 8.1)( 4.4) 42 241( ( 1.0) 13 ( 1.0) 212 ( 4.3) 17 ( 2.8) 245 2.1 18.0 52)1 02) 8.1) 3.3) 4,4)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within *2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphuis" 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 permita reliable estimate (fewer than 62 students). 111 106 THE 1990 NAM) TRIAL STATE ASSESSMENT .':!12! Vimix IshurdsIMs11=.1.11111 TABLE AS I Teachers' Reports on the Emphasis Given To (cmitinued) I Specific Mathematics Cogent Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 18IM NAEP TRIAL STATE ASSESSMENT Data &ways* $4aUttk id Probability Algebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis , Little or No Emphasis MI& Territory Nation unimjpiriArm NS non-gratbsate Territory Nation NS graduate Territory Nation Sense college Territory Nation Collage graduate Territory Nation GENDER Mal* Territory Nation Female Territory Nation and forsidancY (9481118/30.8 Illanonses and Pralkinny Peromiese and Prallaisasy 11 0.4) 1.0) 111/ 21 199 1.0) 21171 1.11 3.9 14 2.21 53 4.4) 46 20 3.0 299 43 251 2.0) 275 2.5) 243 ( 2.0) 14 1.8) 9 s ( .44 11 ( 1.5) *OR 441 17 3.7) 261 ( 6.0)1 10 ( 2A) ( 13 ( 2.5) lips ( *4,1 12 ( 1.5) ***) 15 ( 2.4) 282 ( 4.5) 9 ( p.7) +.4.) 13 ( 2.2) 275 ( 5.8) 13 ( 1.0) 191 ( 2.4) 16 ( 2.4) 263 ( 4.4) 68 ( 180 4.3 53 7.7 240 r...2) 68 ( 3.0) 204 ( 3.4) 54 ( 5.4) 247 ( 2.9) 66(4.3) 221 ( 5.8) 57 ( 5.8) 270 ( 3.7) 62 ( 3.3) 200 ( 4.8) 53 ( 4.4) 275 ( 3.8) es ( 1.2) 203 ( 2.7) 54 ( 4.7) 280( 3.5) 68 ( 2.0) 195 ( 2.3) 53 ( 4.5) 202 ( 2.8) 43 ( 3.2 219 ( 5.11 .2 2$ 51 49 ( 2.9) 230 ( 3.3) 44 ( 4.8) 265 ( 3.5) 47 ( 3,4) 49 4.0) 278 ( 3.0) 49 ( 4.2) 229 ( 3.4) 80 ( 3.9) 26 ( 3.0) 45 ( 1.3) 231 ( 2.5) 44 ( 4.1) 276 ( 3.2) 48 ( 1.8) 224 ( 22) 48 ( 3.6) 274 ( 2.7) la ... 19 ( 2.7) 29 39} oht * 18 ( 2.4) 23 ( 3.9) 239 ( SA) 19 ( 4.6) ( «pe) 17 ( 3.1) ( ***) 16 ( 2.1) 18 ( 2.4) 249 ( 4.0) 20 ( 1.0) 216 ( 34) 22 ( 3.8) 243 ( 3.0) 16 ( 1.1) 201 ( 5.5) 18 ( 2.9) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT 107 Virgin Islands TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL I Oot AM the Resources I 1 I OM Meet et the 1 Oet Seats or Nene et STATE ASSESSMENT Need Itemources I Need Ito Rseetives I Need , , 1,21.6k Territory Nation Begranffign Mak Territory Nation Illspenk Territory Nation TYPE OF COMMUNITY EXtralle nral Territory Nation Other Territory Nation terter41111* sad 0.0) 044. *en Persemings Prallisiencv $4 223 13 ( 2.4) 56 4.0 205 ( 4.2) 263 ( 2A 0 ( 0.0) mil 34 ( 220 ( 1.5 15 { 4.2) 52 ( 8.6 241 5.sp 242 2.4 a 4 am ... ( ...) 23 ( 7.8) 248 ( 7.7)1 0 ( 0.0) 2 ( 2.8) 0 0.0) ,24. 4.4m) 11 ( 2.9) 285 ( 3.9)1 31 2.5) 213 1.7) 44 4.0) 250 2.0) 31 ( 0.1) 205 ( 2.4) 54 (104) 200 ( 8.8)1 33 ( 0.4) 228 ( 1.2) 58 ( 5.4) 264 ( 2.1) gni Praidasel SS WWI 01 $1 4.2 261 ( 2.9 OS ( 219 ( 1.1 $3 ( 7.2 238 ( 4.9 89 ( 208 34 ( 7.7 244 ( 3.0 06 0.9) 205 1.0) 43 10.3) 251 5.0)1 85 ( 01) 218 ( 1.0) 31 ( 5.8) 283 ( 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 intemt, 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). 113 108 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A9 f Teachers' Reports on the Availability of (continued) Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAP TRIAL I Oat All Ow Smarm 1 I Oat Most of Ste 1 Oil Sain se None of STATE ASSESSIMEST Mod Mown= I Hood Ss Itesources I Wad TOTA1_ Prallaknow o ft* ( ( 2.4 205 ( 4.2 0 ( 0.0) eel $ ( 2.6) 11.841 ( 0.0) ( *in 10 2.5) 253 ( 4.8)1 old tralialissv 2231 tj 0$ 4.0 205 23 ( 2.1) ***) $4 1 53) 244 2.7) 37 ( 2.7) 22$54 422 256( 1.9i Territory Nation ENIER:Mireeliffi Ill non-graclude Territory Nation NS graduate Territory Nation Same college Territory 0 ( 0.0) ( 32 ( 3.7) «NI Nation 43 3.3) 62 4.3) Me It*/ 209 (2.5) College gradual. Territory 0 ( 0.0) 3$ ( 2.1) 227 ( 3.1) Nation 15 ( 2.9) 50 ( 4.9) 276 ( 54)1 276 ( 2.2) OMER M. Territory 0 ( 0.0) 34 1.4) 226 ( 2.0) Nation 13 ( 2.8) 57 ( 4.0) 284 ( 5.0)1 285 ( 2.0) Folisolo Territory 0 ( 0.0) 34 ( 1.6) 221 ( 2.3) Nation 13 ( 24) 55 ( 44) 268 ( 311) 264 ( 2.0) Si 42 201 2.0 216 oni 32 s.j 2 011 7t 2.1 243 ( 3.5)1 $ ( .8 ( 21 1 35 258 2h 40 ( SS) 22$ ( 2.4) 2$ ( 4.1) 287 ( 34) 62 ( 2.7) 217 ( 1.9) 30 f 5.1) 27S ( 3.7) lOt 1.4) 218 ( 1.1) 30 ( 4.0) 264 ( 3.3) 68 ( 1.6) 213 ( 1.4) 32 ( 4.7) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of imerest, the value for the entire population is within ± 2 standard errors of the estiMate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 Virgin Islands TABLE AlOa I Teachers' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11180 NAP TRIAL STATE ASSESSIMENT Ai Lust Once a Wa* Lass Than Once a Week tiavor - TOTAL Pertentape mid Pralklaacy 0.8) 211 0.$ 50441 280 2.2 51 ( 1.3) 215 ( 1.0) 47 ( 9.1) 240 ( 3.4) 52 ( 3.1) 202 ( 12) 194 ( 7 2) 248 ( 2.5) 41 ( 1.1) 203 ( 2.3) 35 (14.3) 255 ( 5.5)1 55 ( 0.9) 213 ( 0.5) 50 ( 4.4) 280 ( 2.4) Posaradapi aid firallaisecar 38 ( 0.7) 233 ( 43 ( 4.1 204 ( 2.3 3$ ( 0.9) 234 ( 12) 45 ( 7.0) 238 ( 4.0) 29 ( 2.8) 224 ( 2.1) 32 ( 8.9) 247 ( 8.3)1 28 ( 0.8) *4.1 58 07.1) 258 ( 5.9)1 38 ( 235 ( 1.2) 44 ( 4.5) 264 ( 2.8) Pariardsop and *Midway 12 ( ) 215 4111 277 ( 5.4 12 ( 0.9) 217 ( 2.1) 9 ( 4.1) ay. ) 12 ( 1.7) 4 ( 1.4)) 93 ( 1.3) 209 ( 1.8) 9 ( 4,64 441 ( 0.7) 221 ( 12) ( 1.3) 277 ( 8.3)1 Territory fNation BactilDIEM Mach Territory Nation lUspanic Territory Nation TYPE OF 0,40AUNITY Barone rural Territory Nation Other Territory Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certamty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *0* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 110 1 5 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE AlOa I Teaches' Reports on the Frequency of Small (continued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAV TRIAL STATE mussuen. AI West Once a Week Lan Mien Owe a Week Mover NIA Territory Nation EMINIEMSATEN RS nonireclueft Territory Nation NS gradual. Territory liaresalsos aml Pniliciony 53( 0.1) 2t1 0.8) 50( 4.4) 250 ( 2.2) 59 ( 3.1) 205 ( 2.6 ) 24460 I 3.261 47 ( 2.7) 212 ( 2.6) Nation 49 ( 4.1) 252 ( 2A) Some college Territory 47 ( 4.5) I *el Nation 51 52) 296 ( 3.1) College graduate Territory 59 ( 3.3) 213 ( 2.1) Nation 48 ( 5.2) 271 ( 2.8) OENDER Male Territory 53 ( 1.5) 214 ( 1.3) Nation 50 ( 4.5) 281 ( 3.0) F11Sei Territory 52 ( 1.1) 209 ( 1.8) Nation 50 ( 4.7) 250 ( 2.2) fliferia. PreeliaN0, 21`3 1 1:711 43 ( 41) 29 ( 2.0) 11/41,11 59(6.5 ) 244 ( 3.2), 42 ( 2.3) 233 ( 1.6 45 ( 5.1 257 ( 2.7) 42 ( 4.1) *di 42 ( 5.1) 2.3 ( 3.2) 33 ( 3.4) 233 ( 3.1) 43 ( 4.4) 276 ( 3.0) 38 ( 1.2) 235 ( 1.5) 42 ( 4.0) 285 ( 3.1) 38 ( 1.2) 231 ( 2.1) 43 ( 4.7) 283 ( 2.1) ,IParalobse lad Prillishmay 12 2151 (41 2.0 277 SA 11 ( 1.0) 111Hr ( 41 ( 2.1) 278 ( 5.3)1 12 ( 0.9) 208 ( 2.4) 7 ( 2.1) 275 ( 0.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT 111 Virgin Islands TABLE AlOb I Teachers' Reports on the Use of Mathematical I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1190 NAEP TRIAL STATE ASSEMENT At Lust Onco a Week Less Then Onu a Week New Praielanoy 20( 1.0) 214 ( 14) 22 81) 254 ( 82) and ;7) PriiidIMWM 65 i 1.2 220 ( 05 119 ( 9.9 201 ( 1.91 aid 15 ( 0.8 9 2.6 222 1511 262 5.9 Territory Nation fienginfieaa Mm* Territory 96 15) 18( 1.2) 21: 31 222 0.9) 226 ( 2.9) Nation 22 5.9) 23$ ras I 70 133) 241 2.9) 8 ( 3.81 ./.44 141apanic Territory 24 ( 2.8) 83 ( 3.0) 213 ( 15 14 ( 2.0) «we Nation SS ( 73 7 ( 2.8) 245 ( 3.811 TYPE OF COMMUNITY Wrens rural Territory 7 ( 0.2) 441 54 ( 1.1) 209 ( 2.2) 38 ( 1.1) 207 ( 1.7) Nation 27 (14.9) 95 (14.8) 3.9) 282 ( 2.8)1 IMO *MI) Other Territory 22 ( 1.2) 88 ( 1.4) 10 ( 0.9) 214 ( 1.4) 222 ( 0.9) 235 ( 2.8) Nation 19 ( 4.3) 72 ( 5.0) 9 ( 33) 253 ( 3.9)1 283 ( 22) 281 ( 7.1)1 Imlimum The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 1 7 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE AM I Teachers' Reports on the Use of Mathematical (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11110 NAEP TRIAL STATE ASSESSMENT At Least Once a Weak Less Than Once a Week Never 70141- Territory Nation pARMLLEGAM MS non-gradoato Territory Nation HS radiate Territory Nation Some college Territory Nation College graduate Territory Nation OENDER forossaage and Proficiency 20 ( 214 1.4 22 3.7 254 3.2 24 2.71 111Mk 21 ( 2.3) 218 ( 3.0) 23 ( 4.8) 248 ( 4.os 19 ( 3.4) 4,&*) 18 ( 4.0) 281 ( 4.4)1 19 ( 3.1) 20 ( 3,9) 205 ( 3.5)1 19 ( 1.1) 218 ( 2.2) 22 ( 4.1) 255 ( 4.1) 20 ( 1.8) 210 ( 2.9) 21 ( 3.8) 254 ( 3.3) Porcentege and Prodoiency 85 ( 1.2 220 0.41 id 3.91 263 1.9 62 ( 23) 214 ( 2.5) 66 ( 7.2) 243 ( 2.2) 64 ( 3.1) 222 ( 1.8) 70 ( 5.3) 255 ( 2.2) 64 ( 4.4) 229 ( 24) 73 ( 4.3) 289 ( 2.3) 89 ( 31) 220 ( 2.0) 80 ( 3.7) 274 ( 2.2) 65(1.1) 223 ( 1.1) 89 ( 4.1) 255 ( 2.1) 85 ( 1.9) 218 ( 1.1) ( 4.2) 202 ( 1.9) perowne8.8 and Priaciency 222 14 9 2.8 282 ( SA 15 ( 2.0) 9 84) ( MN) 15 ( 2.0) *in ( 2.8) .44 ( 17 ( 3.1) ( 9 ( 2.4) ( *A* ) 12 ( 2.2) 4+1 11 ( 2.5) 297 ( 4.2)1 15 ( 1.2) 227 ( 3.8) ( 2.0) 287 ( 7.2)1 15 ( 1.1) 219 ( 3.5) 10 ( 3.3) 278 ( 8.0)1 Male Territory Nation Ronal. Territory Nation The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the 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). I I 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Virgin Islands TABLE Al la I Teachers' Reports on the Frequency of Mathemalics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1963 NAEP TIDAL STATE ASSESSMENT Minos* Every Dsty Several Una a Week About Coos a Weak or Loos TOTAL Pronelhomy S4 ( DS) 221 ( 00) 02 ( 3.4) 207 1.1) PINNINMOMil XS(13 31 2.1 254 2,3 Territory Nation WVETNNIITY Mack Territory 15 ( OA 9 ( DA) 224 ( DS 210 ( OA) Nation 50 ( 7.7 41 ( 7.9) 244 ( 4.0I 233 ( 3.9)1 Hispanic Territory 54 ( 2.3) 1.9) 210 ( 11) Nation 61 ( OA) 32 53) 251 ( 3.1) 240 ( 4.3)I TYPE 9F COMMUNITY Extrom rwaI Territory 74 ( 0.6) 3 ( 0.7) 20i ( 1.0) Nation 50 (10.15) 40 (10.0) 200 ( 4.0)1 247 ( 74)1 Other Territory 67 ( 1.0) 11 ( tO) 224 ( 0.7) 206 ( 1A) Nation 03 ( 3.9) 31 ( 3.5) 267 ( 2.3) 255 ( 3.1) Ilannalana ant 24 I $4131 7 1.4 23 OA) IN* 10 73) oft, +el 3 ( 0.1) ( 1.9) 257 ( 5.15)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 Ow entire population is within ± 2 standard errors of the estimate for the sample. 1. Interpret with clution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 2990 NABP TRIAL STATE ASSESSMENT Virgin Islards TABLE Al la I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1980 NAEP TRIAL Times About Once a Week or STATE ASSESSMENT Aknost Every Day Several a Week Lees , - , TOTAL Parolada. tad Proficiency 84 221 02 3.4 207 ( 19) 82 ( 2.7) 211 ( 2.7) 87 ( 5.5) 245 ( 3.2) 88 ( 2.0) 224 ( 1.7) 01 ( 4.4) 257 ( 2.5) 88 ( 3.1 231 ( 22) 88 ( 42) 272 ( 2.7) 88 ( 2.1) 223 ( 1.8) 81 ( 4.0) 281 ( 2.2) 83 ( 0.9) 224 ( 12) 80 ( 3.7) 289 ( 2.1) 85 ( 1.3) 218 ( 1.2) 85 ( 3.8) 288 ( 1.8) Peroaatega ihirosniage and Maoism Mildew 9 ( 0.8 8 47.2) 2011 ( 1.3) ( 31) 31 ( 11.1) ( 1E) 234 ( 2.9) 200 ( 5.1)1 10 ( 2.6) 9 ( 1.0) Re* ( 27 ( 5.2) 8 ( 2.1) ire* ( wan IMP ( 7 ( 1.8) 7 ( 1.1) .44 .0.11 ~1, ( 34 3.1 ) 293 ( 2.9)`-\ ( 9 ( 22) 3 ( 12) «4 ( ( eon 28 ( 3.7) 258 ( 5.2) 8 ( 1.9) ( 1.2) ***) ( 31 ( 3.9) 8 ( 3.1) tree ( ***) 285 ( 3.1) 10 ( 0.8) 7 ( 0.4) NMI ( 4 «41 33 ( 3.4) 7 ( 1.9) 258 ( 3.8) 281 ( 8.7)1 9 ( 1 .1 ) ( 0.4) *V* ( *HP ) ( 28 ( 3.3) ( 2.2) 253 ( 2.5) «.h.) Territory Nation NS nunireduate Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Male Territory Nation Female Territory Nation "ftl=11111=, The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 115 Virgin Islands TABLE Al lb I Teachers' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1180 NAEP TRIAL STATE ASSESSMENT Al Least Several Times a Week Mold *we a Week Len Son Wee* TOTAL Poonstogo and Potoolup and Prollology llovooloyo Patiology Territory 49 ( 0.1 22 (al) 2t0 ( 2r7 2$3 Nation 34 ( 3.8 33 3.4) 32 ( 3,8) 258 ( 23 280 ( 2.3) 274 ( 2.7) gtainiNf_CITY Slack Territory 45 ( 1.1) 29 ( 0.9) 28 ( 0.0) 212 ( 12) 229 ( 1.4) 235 ( 1.5) Nation 45 ( 7.5) 31 ( 7.8) 23 ( 8.3) 232 ( 3.1)1 243 ( 2.3p 248 ( 7.0)1 Hispanic Territory 55 ( 3.1) 203 ( 1,5) 28 (2.4) .64. imp) 17 ( 2.8) Nation 41 ( 7.7) 211( 5.3) 33 ( 7.5) 242 ( 3.2)1 244 ( 5.1p 257 ( 2.3)1 TYPE OF COMMUNITY Extreme rural Territory 43 ( 1.0) 48 ( 1.5) 9 ( 08) 205 ( 2.4) 211 ( 0.5) Nation 27 (14.3) 411 ( *41 49 (12.7) 258 ( 8.7)1 24 (10.1) Other Territory 51 ( 03) 25 1 0.7) 24 ( 0.8) 211 ( 1,1) 233 ( 1.2) 233 ( 1.3) Nation 30 ( 4.4) 35 ( 4.3) 30 ( 42) 258 ( 3.3) 250 ( 23) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the valu: for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 student4. 121 116 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al lb I Teachers' Reports on the Frequency of (colAinucd) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAIEP TRIAL STATE ASSESSMENT AI Least Several Times a Ws* About Once a Week Lass than Weekly MI6 Territory Nation maimajormsei 1411 nanireduste Territory Nation NS graduate Territory Nation Semi aiMItge Territory Nation Coley graduate Territory Nation GENKR Male Territory Nation Female Territory Nation and Pra Wow 03) 210 54 SA 266 ( 23 55 ( 3.0) 203 ( 23) 35 ( 23a ( 3.5) 46 ( 2.3) 211 ( 2.4) 35 ( 5.3) 250 ( 3.8) 42 ( 4.5) 4, 33 ( 4.7) ( 2.8) 58 ( 43) 212 ( 2.3) 35 ( 3.8) 254 ( 2.8) 52 ( 1.7) 214 ( 1.2) 35 ( 4.1) 257 ( 3.2) 47 ( 1.2) 206( 1.5) 34 ( 4.1) 254 ( 2.1) and Itrallaisney 29 ae 2271.01 S3 3.4 200 ( 27 } 2.7) ommi 29 ( 6.3) 29 ( 2.5) 231 ( 2.8) 35 ( 4.5) 250( 2.7) 29 ( 4.2) .441 22 ( 4.0) 205 ( 4.2) 25 ( 2.9) ( 441 32 ( 3.4) 271 ( 2.4) 28 ( 1.4) 230 ( 1.7) 35 ( 3.8) 281 ( 2.8) 30 ( 1.3) 224 ( 1.7) 32 ( 3.7) 258 ( 2.3) and Pnalidanay 22 ( 223 ( 1.1 32 ( 274 ( 2. 36 ( 6.9) 250 ( 4.5)4 25 ( 2.0) 233 ( 3.0) 30 ( 4.5) 263 ( 3.4) 29 ( 4.2) 11111, 35 ( 4.1) 278 ( 2.6) le ( 3.2) *44. ( ( 3.5) 299 ( 2.51) 21 ( 1.5) 218 ( 2.9) 31 ( 3.5) 275 ( 3,2) 23 ( 1-2) 230 ( 2.8) 34 ( 4.1) 273 ( 2.8) The standard errors of the estimated statistics appear in parenthens. 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. se* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT 117 Virgin Islands TABLE Al2 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IOW NAV TRIAL STATE ASSESSMENT At Least Once a Week Lau Than Once a Week New Peron lap and Pries/Wm Panetta. Prolideogy Territory 24 ( 1.4) 18 ( 0.7) 214 ( 1.0) 224 Nation 28 ( 24) 22 (144 258 ( 2.7) 287 ( 2.0 Maanp Mad( Territory 32 ( 13) 17 ( 0.$) 218 ( 1.1) 228 ( 1.8) Nation 2$ ( 3.0) 24 ( 3.8) 234 ( 3.0) 245 ( 4.11) Hispanic Territory 37 ( 207 ( 2.6) 2.4) 12 «pa ( 1.4) ( 001 Nation 37 ( 5.2) 22 ( 3.8) 242 ( 3.2) 250 ( 3.4) TYPE OF COMMUIOTY Extreme nrai Territory 34 ( 203 ( 1.4) 2.6) 10 ( 1.5)1 Nation 34 (10.8) 27 ( 3.6) 242 ( 5.2)1 264 ( 3.5)1 Other Territory 33 ( 1.8) 17 ( 01) 215 ( 1.0) 225 ( 1.8) Nation 27 ( 2.6) 28 ( 1.7) 260 ( 3.3) 254 ( 2.1) Parceellep *sideway 51 1.2) 218 0.8) 44 2.9) 281 14) 51 ( 1.3) 222 ( 4$ ( 4.7) 234 ( 3.1) 51 2.6) 210 1.7) 41 5.0) 240 ( 24) 56 ( 1.4) 206 ( 1.4) 38 (11B) 256 ( 6.2)1 50 1.4) 223 0.7) 45 3.3) 282 ( 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). 118 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE Al2 I Students' Reports On the Frequency of &nail (ccatinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT At Least Once a Week Lem Than Once a Weak Never , . TOTAL aid 34 ( 214 ( 1.0 26 ( 251 ( 30(3.6 ) 207 ( $.9) 29( 4.5) 242 ( 3.4) 27 ( 2.2) 214 ( 2.7) 28 ( 3.0) 251 ( 3.7) and Praiiiimay 0.7) 224 20 1.4 267 2.0 11 44. 4.4 29 ( 3.0 244 ( 3.0 lit 2.0) ne 3.4) 20 1 A) 261(24 ) Territory Nation hintamareass MS non-graduate Territory Nation 10 graduate Territory Nation Some college Territory *et ( 20 ( 32) .41 Nation 27 ( 34) 27 ( 2.4) 265 ( 3.6) 268 ( 3.3) College graduat Territory 41 ( 3.3) 15( 1.9) 210 ( 2.4) ( 1141 Nation 20 ( 3.0) 28 ( 1.9) 270 ( 2.7) 278 ( 2.8) GENDER Territory 37 ( 2.0) 13 ( 1.3) 210 ( 1.7) 220 ( 2.4) Nation 31 ( 24) 26( 1.1) 250 ( 3.3) 208 ( 2.8) Fiats* Territory 30 ( 2.1) 18 ( 1.2) 212 ( 1.4) 222 ( 2.2) Nation 2e ( 2.4) 27 ( 1.8) 257 ( 24) 200 ( 1.7) mid Prialcitraw 21%1 Itt 44 2.9) 261 IA) 50 ( 3.4) 210 ( 34) 24242 "2.7i 56 ( 24 ) 221 ( 1.5) 43 ( 3.4) 252 ( 1.7) 50 ( 4.11) 231 ( SA) 46 ( 34) 2116 ( 44 ( 3.2, 223 ( 2.6) 44 ( 3.0) 275 ( 2.2) 49 ( 1.7) 223 ( 1.4) 41 ( 24) 262 ( 1.11) 52 ( 1.8) 218( 1.2) 47 ( 3.2) 200 ( 1.8) The standard errors of the estimated statistics appear M parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 24 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Virgin Islands TABLE A13 I Students' Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1200 NW TRIAL STATE ASSESSMENT At Least Once a Weak Lass Than Once a Week NOW , - TOTAL and fisadasey 212591 .9 01.41 28 f 1.14 258 ( 2.6) 28 ( 1.0) 221 ( 1.3) 2? ( 3.3) 234 ( 3.?) 25 ( 2.8) 209 ( 2.9) 38 ( 4.2) 241 ( 4.0) 15 ( 1.1) 21 ( 3.1) **a ( 28 ( 1.1) 221 ( 1.4) 27 ( 2.0) 256 ( 2.9) and rad Prelkeancv Ilralklasay 1$ ( 55 22$ ( 1.3 215 0.4 $1 ( 1.2 41 2.2 209 ( 1.5) 250 ( 1.0) 19 ( 1.2 55 ( 1.3) 231 ( 217 0.9) 27 ( 3.2 48 ( 4.5) 248 ( 4.5 232 ( 2.13) 15 ( 1.9) 80 ( 3.1 *4* ( 04111) 20? ( 1.9 23 ( 2.0) 40 ( 4.0) 253 ( 4.3) 240 ( 1.9) 10 ( 1.2) 75 ( 1.5) .14. ( 207 ( 1.3) 37 ( 4.7) 43 ( 5.0) 282 ( 4.7)1 251 ( 5.2)1 20 ( 1.2) 52 ( 1.3) 229 ( 1.4) 217 ( 0.9) 31 ( 1.4) 41 ( 2.4) 270 ( 1.8) 200 ( 2.2) Territory Nation ISMEMAM Mack Territory Nation Hispanic Territory Nation TYPE OF COMMUNITY Wron nral Territory Nation Other Territory Nation IMh. The standard errors of the estimated statistics appear in parentheses. It can be said with &bow 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample docs not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 125 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A13 1 Students' Reports on the Use of Mathematics (cmtinued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1660 NAEP TRIAL STATE ASSESSMENT , At Least Once a Week Less ran Owe Week Never TOTAL Pereotelie Proficiency Pirmulage mad Prellaimy fluniodoge sad Polkkaag Territory 26 VI tO) 56 1.1 219 1A 226 1.3) 215 041 Nation 28 1.8 31 t2) 41 L2I menniarimia 25$ ( 200 ( 15) 259 1.6 Hs nen-graduate Territory 22 ( *00 25) 13 ( 3.2) es. ( 66 ( 206 ( 3.5) 3.2) Nation 27 ( 4.2) 26 ( 2.7) 4? ( 5.0) 237 ( 3.0) 253 ( 34) 240 ( 2.3) HS graduate Territory 27 ( 2.7) 18 ( 22) 55 ( 222 ( 32) 233 ( 24) 215 ( 1.9 Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3 250 ( 2.4) 25e 2.7) 253 ( 2.1 Some college Territory 29 ( 3.0) 24 3.2) 50 ( 3.0) 1111M 1110 224 ( 3.3) Nation 29 ( 2.6) 36 ( 2.3) SS ( 26) 261 (3.5) 274 ( 22) 283 ( 2.1) College graduate Territory 28 220 ( 2.3) ( 2.6) 19 ( 2.3) din 53 ( 217 ( 2.7) 2.6) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.6) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER M. Territory 30 ( 1.7) 17 ( 1.5) 52 ( 15) 220 ( 2.0) 231 ( 2.6) 217 ( 12) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 258 ( 22) 271 ( 2.1) 280 ( 1.8) Female Territory 21 ( 1.1) 19 ( 1.0) 80 ( 1.5) 217 ( 2.7) 225 ( 1.7) 212 ( 1.1) Nation 25 ( 2.0) 31(1.9) 44 ( 2.5) 257 ( 3.0) 26$ ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 126 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Virgin Islands TABLE A14 1 Students' Reports OR the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11180 MAD TRIAL STATE ASSESSIIENT 4knost Evary Day Mating Times a Wask About Once a Week ar UNIS TOTAL Territory Nation BillgantaM Seek Territory Nation Hispanic Territory Nation MUESSIMAILLY Extreme rural TarfitOry Nation Other Territory Nation 220 D 74 1 217 1.2 74 ( 222 ( 0.6 71 ( 2.6 240 ( 2A 00 ( 3.2) 210 ( 15) 61 ( 3.7) 249 ( 2.3) 70 ( 4.0) 207 ( 1.9) 6$ (113) 263 ( 4.2)1 13 ( 1.5) 223 ( 0.11) 75 ( 2.2) 267 ( 1.8) BIS prookair 17 218 I 41/ 14 1 OA 2$2 17 ( 1.0) 219 ( 15 ( 1.7 232 ( 3.1 19 ( 2.5) 21 ( 2.9) 242 ( 5.1) 16 2.6) 40, 414r.) . 15 35) 17 ( 1.0) 219 ( 1.3) 14 ( 1.0) 252 ( 2.6) Parciiiap and Praikiam 10 1.1) 207 144 12 1.1) 242 4.5) 10 ( 0.9) 209 14 3.2 223 6.1 11 ( 2.9) ..... i on 17 i 2.7) 224 ( 3.4) 12 ( 3.3) ( 17 1.2) Ite4t fel 10 ( 1.1) 206 ( 1.4) 10 ( 1.9) 239 ( 4.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample site is insufficient to permit a reliable estimate (fewer than 62 students). 127 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Isknds TABLE A14 I Students' Reports on the Frequency of (continued) i Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Almost Even, Day Several Times a Week Mad Once a Week or Lass TOTAL. Parosahapo and Prallohnoy POINN101. and Proilakmay Parasidaga and Prolickney Territory 73 ( 1.4 17 0A 10 1.1) 220 ( 0.7 2161 14) 20? 1.9) Nation 74 ( 1.01 14 0.8) 12 1.8) fammumage W ( 1.2 252 ( 1.7) 242 ( 44) NS non-graduate Territory 87 ( 4.3) 21 ( 3A) 11 ( 2.2) 211 ( 2.6) ( *ft ( 441 Nation graduate 64 ( 245 ( 3.4) 2.3) 18 ( 2.0) so* 44.1 le ( 3.1) *Mb ft *el Territory 73 ( 2.2) 17 ( le 1.3) 221 ( 14 222 ( 3.3) 04. On Nation 71 ( 3.8 16 ( 4.8) 13 2.8) ftme college 258 1 1.8) 249 ( 3.2) 299 ( 3.4); Teirritory 76 ( ( 3.5) 2.8) 19 ( 3.9) .06.1 5 2.0) 44. .14.) Nation 80 ( 270 ( 2.0) 1.9) 11 ( 12) 044, #.4) 9 ( 1.7) Callow gradusta Territory ( 4.1) 20 ( 2.0) 9 ( 2.9) 222 ( 1.7) Nation 77 ( 2.7) 13 ( 09) 10 ( 2.3) 279 ( 1.8) 290 ( 24) 257 ( 8.4)1 GENDER M. Territory 71 ( 1.7) 18 ( 1.3) 10( 1.2) 222 ( 1.2) 221 ( 2.8) 209 ( 29) Nation 72 ( 2.4) 18 ( 1.2) 12 ( 2.1) 288 ( 14) 252 ( 2.5) 242 ( 8.1) Female Territory 74 ( 1.7) 16 ( 1.3) 10 ( 1.4) 21$ ( 1.0) 211 ( 3.2) 205 ( 2.1) Nation 78 ( 1.8) 13 ( 1.0) 11 ( 1.8) 26$ ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of 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). 128 THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Virgin Islands TABLE A IS I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAE1P TRIAL At Lust Several Thou STATE AUESIMEMT a Weak About Onat, a Ws* Las Thmt *sole ..- Territory Nation ISTIMMX Black Territory Nation Hispanic Territory Nation TY11 9F COMMUNITY Eskimo mai Territory Nation Other Territory Nation 214 IA) 2;12 4.3) 41 22) 37 1.11) 30 ( 1.5) 224 ( 241 ( 32 ( 2.7 225 14 20 3.1 241 4A 206 ( 2.3) 231 ( 34) 44 ( 4.1) 26 3.4) 32 4.3 30 3.1) 213 2.4) 0$ 2 2.41 44 ( 2A) 247 32) 24$ 3.3 34 ( 4.2) 205 ( 2.9) 42 (10.1) 249 ( 4.0)4 40 ( 1.6) 213 ( 1.1) 36 ( 24) 252 3.0) 33 ( 2.6 256 3.4)1 30 4.4 29 ( 1.5) 225 ( 1.0) 28 ( 12) 281 ( 2.1) 33 ( 22220 7211 267 7.3)1 225 ( 1.2 32 ( 36 ( 2.9 `272 ( 14) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 12 ;) 124 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A 15 I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRAIL STATE ASSESSMENT At Least Several Times a Week Aboid Once a Week Ins Than Weekly 1 Mr& Territory Nation feigamizsams nortiradust disresteass and Prallediesy 33 ( 1.5) 212 ( 1.0) 38 ( 2A) 253( 2.2) Patamlap sod Pnamisetcv 222 1.1 25 12 tA Territory 30 201 (35) (3.5) ave.t Nation 41 4.5) 30 ( 2.7) 235 ( 3.1) 243( 2.7) NS gradiat. Territory 32 ( 3.0) 31 ( 210 ( 2.2) 222 ( 2.2 Nation 40 ( 32) 29 ( 22 247 ( 2.7) 256 ( 25) Some coNege Territory 31 ( 4.3) 32 ( 3.2) 1144t 411 ( Nation 34 3A) 28 ( 2.2) 259 ( 2.3) 289 ( 2.8) C.olloge graduate Territory 42 ( 3.0) 27 ( 2.8) 212 ( 1.8) 222 ( 25) Nation 38 ( 2.8) 22 ( 284 ( 2.8) 273 ( 2.5) GENDEil M. Terntory 40 ( 2.0) 30 ( 22) 215 ( 1.8) 225 ( 1.8) Nation 39 ( 2.7) 25 ( 1.8) 253 ( 2.7) 283 ( 2.3) Female Territory 37 ( 2.1) 29 ( 12) 209 ( 1.8) 218 ( 1.7) Nation 37 ( 2.5) 25 ( 1.5) 253 ( 2.1) 259 ( 18) Paramdaps sad .Prolloisacy 22 22 1.1 37 2.5 272 1.0) 31 ( 3.4) .443 29 ( 4.0) 253 ( 2.8) 32 ( 2.7) 223 ( ZS) 32 ( SS) 262 ( 22) 37 ( 3.7) 40 3.6) 271 ( 2.6) 32 ( 2.3) 229 ( 3.7) 41 ( 2.6) 285 ( 2.3) 30 ( 1.7) 224 ( 2.2) 35 ( 2.7) 274 ( 2.4) S4 ( 1.9) 220 ( 2.2) 35 ( 25) 209 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. s" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 TABLE Al8 Rills Islands Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1. MO NAP 1441AL STATE ASISESSMEXT Om a Ca WNW Teacher Oohing CakeilMor Use Yes No Yes No TOTAL 1111a tivilakmay 02 ( OA) 218 ( 97 ( 044 283 ( 11 Territory Nation RegignIM Mack Territory 93 ( 0.8 222 ( 0.8 Nation 93 ( 1.51 237 ( 2.8) HIspank Territory 90 ( 1.8) 209 ( Nation 92 ( 12 245 ( 2.1 TYPE OF COMMUNITY Extreme rural Territory 89 ( 2.1) 208 ( OA) Nation 98 ( 1.3) 257 ( 3.9)1 Other Territory 93 ( 0.8) 222 ( 0.6) Nation 97 ( 0.5) 263 ( 1.7) and and Prolidimay Pridelaw "Woozy 40 1.4 217 1.2 14 ce 234210 I 1311 48 2.$1 2151 2.3 288 1 258 1.7) 7 0.5) 207 22) 7 1.51 10 ( 1.1) 8 ( 1.2) 11 (( 4 ( 1.3) 44,* op.) ( 0.8) 208 ( 1.7) 3 0.5) 233 54) 41 1.5 210 1.2 $3 491 235 3.6 38 ( 206 ( 1.1 63 ( 4.3 243 ( 3.4) 36 ( 3.0) 207 ( 1.5) 42 ( 07) 251 ( 4.sy 41 ( 1.6) 219 ( 1.3) 50 ( 2.7) 258 ( 2.1) SO ( 1.5) 222 47 4.0 238 2.7 84 ( 3.0) 210 ( 1.8) 37 ( 4.3) 245 ( 2.9) 64 34 2001.11 58 ( 8.7) 261 ( 4.4)1 549 ( 1.6) 222 ( 1.0) 50 ( 2.7) 266 ( 2.0) The standard errors or the animated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 131 126 THE IWO NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A18 ..Q.frill ents' Reports on Whether They Own a (cmtinued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAN num. STATE AM/4MM Own a Canister Teadier bp labs Cacti law Use . Yes I No Yes - 1 , No . TOTAL, Territory Nation 149 naairaduata Territory Nation 118 graduate Territory Nation Some coNego Territory Nation Colkep graduate Territory Nation GENDER llains01111 Pasioniage and lyndaisney PrOokincy OA 6 219 0A 111 0.41 31 263 ( 1.3 234 89 ( 11 ( 210 2.6 92 1.6 8 ( 243 2.0) ( 93 ( 1.2 ( 221 ( 1.4 6. 97 ( 0.6) 3 i 255 ( 1.5) ( 99 ( 0.8) 1 ( 228 ( 2.7) .0* 1 90 ( 0.9) 4 ( 268 ( 1.8) eee ( 98 ( 1.3) 4 ( 221 ( 1.6) ( 99 ( 0.2) I ( 275 ( 1.6) ee ( 93 ( 1.1) 7 ( 212 ( 04) eee ( 97 ( 0.5) 3 ( 264 ( 1.7) 32 ( 0.9) ( 217 ( 1.0) 97 ( 0.5) 262 ( 1.3) 04 ) ( 8.41) 2.3) **di) 1.6) *el 12) 0.6) 0.8) «HI 0.9) eee) 1.3) fin 0.2) eee) 1.1) eee) 09) *eel OA) ***) Male Territory Nation Female Territory Nation krandaip faroaidade and and Preickway Oralkiancy 40 ( 1.2 49 2.3 266 1.7 2g2 I 2.61 4 53 49) 242 2.9) 41 ( 2.5) 219 ( 2.1) 54 ( 3.0) 252 ( 1.9) 39 ( 4.1) 43 ( 3.2) 2S5 ( 2.4) 40 ( 29) 219 ( 2.3) 48 ( 2.6) 268 ( 21) 42 ( 2.1) 218 ( 1.9) 51 ( 2.6) 258 ( 2.1) 38 ( 2.0) 215 ( 2.0) 47 ( 2$) 258 ( 1.7) 00 ( 219 ( 0.9 51 ( 2.3 266 ( 66 ( 3.2) 212 ( 2.41) 47 ( 4.41) 243 ( LS) 59 ( 2$) 221 ( 1.6) 46 ( 3.0) 258 ( 2.0) ( 4.1) 232 ( 291 52 ( 32) 268 ( 2.2), 2.6) 222 ( 2.1) 54 ( 2.6) 280 ( 1.9) Se ( 2.1) 223 ( 1.1) 49 ( 2.6) 209 ( 2.1) 2.0) 216 ( 1.1) 53 ( 2$) 263 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 3 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 Virgin Islands TABLE A19 I Students' Reports on the Use of a Calculator 1 for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111110 NAEP TRIAL STATE ASSESSMENT Working Problems in Class Doing Problems at Name Taidng Quizzes or Teats Almost Always Never I Almost Always NOM I Almost I Always Never Territory Nation MainEttery Mode Territory Nation Hispanic Territory Nation TYPE Of COMMUNITY Extreme rural Territory Nation Mar Territory Nation I111 Pacandasa Paraodaea Pareaday Parandoes Perandass Perandaga and and god and and and PnilleisnoV Pradiaintay Prallolanay PrailakM01, 11411.01mY PrelidowlY 21: 18.1) 2:13(1..1) 219,!..1 2; I LI 211( ;1) 48 1.51 231 1.11 30 13 19 MS 2? 1.4 30 2.0 232 1.15 2? 254 ( 1.5 272 1.4 261 1.1 283 1.0 253 24 274 ( 1.3 2 234 ( 1.9) 214 52 ( 22 ( 1.1) $4 218 ( 0 ( 3.2 20 ( 3.9) 31 232 ( 2.4) 249 ( 40) 233 ( 203 ( 1.8) *** ***) 206 00 ( 1.9) 17 1.8) 51 ( 2.9) 18 3.5) 20 230 ( 2.8) 252 ( 3.3)1 238 ( 58 ( 12) 208 ( 1.0) 48 ( 7.4) 248 ( 4.3)1 53 ( 1.3) 216 ( 0.8) 48 ( 1.9) 254 ( 2.1) 18 ( 3.2) ( .41 29 ( 6.5) 285 OAP 22 ( 1.0) 236 ( 1.8) 22 ( 2.0) 272 ( 1.8) 38 ( 201 ( 20 ( 32 ( 215 ( 32 ( 263 ( 1.7 2.9 3.3) 2.8) 2.4) 3.2) 4.8) 1.7) 1.9) 2.5) ea.) 1.4) 1.7) 1.7) 2.3) 14 ( 1.1) 229 ( 3.3) 16 ( 1.9) 248 ( 5.5) 14 ( 1.9) *** ( "") 21 ( 2.1) 244 ( 3.1) 1$ ( 2.5) 6. «pli) 23 ( 3.9) 263 ( 4.4)4 13 ( 1.1) 231 ( 3.4) 18 ( 1.1) 263 ( 2.8) 30.8 214 38 230 ( 31 ( 203 ( 28 ( 237 ( 32 ( 206 ( 24 ( 35 ( 213 ( 27 ( 253 ( 1 1.2 3.3 3.6 2.7) 2.5) 2.7) 3.2) 2.7) 1.5) 8.8) 1.7) 1.4) 1.8) 2.7) 29( 413) 2 33 ( 1.8) 24 ( 3.1) 251 ( 4.1) 19 ( 2.0) *" ( ***) 22 ( &I) 258 ( 42) 20 ( 3.3) .Hr *NI 37 ( 8.3) 270 ( 4.0)t 29 ( 12) 234 ( 1.7) 29 ( 2.1) 275 ( 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. The percentages may not total 100 percent because the "Sometimes" category is not included. 1 Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 133 128 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A19 I Students' Reports on the Use of a Calculator (mitinued) i for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT , Welting Problems in at Nome ease Problem Tang Qu luds or Toes kis . Almost Always I Almost 1 NOM Always NOM Almost &rays I Never Ism Territory Nation Eaagnu Esans2 NS nen-graduate Territory Nation NS graduate Territory Nation Some college Territory Nation College graduate Territory Nation 2fim mate Territory Nation Female Territory Nation Pannatage Paraidep Parepoisie knot Opp Posentais owl oil apt awl soi Prildwri Piddentv Pralleisnoy WaIuu P41319)214, I A 233 1.7 212 1A 227 212 ( 11 232 , 21 ( 35 ( 1.5) 21 1.1 214 O 44 1.5 23 11 30 1.3 19 01 ) 2?(1430 254 1.5 272 14 291 11 263 ( 1.111) 233 ( 2,44 274 1 49 2.2) 18 2.4) 34 ( $A) 14 ( 2.5) 2726 ti 2 el 208 2.2) "ft "1 202 ( 3.0 54 3.3) 19 3.111) 26 ( 3.1 22 ( 24 14 3.2) 240 2.3) ***) 244 ( 311 244 ( 4.2) 237 23 251 4.0) 55 ( 2.1) 23 33 ( 2.2 15 ( 2.0) 35 ( 3.2) 29 2.2 215 ( 1.4) 234 3.0 210 ( 2.7 ( ***) 214 ( 233 24 52 ( 21) 20 24 29 ( 1.9 11 ( 1.5) 24 ( 11 21 3.2 249 ( 1.4) 265 ( 23) 230 ( 24 256 ( 2.4) 248 ( 24 216 2.0 51 ( 54) 22 ( 33) 32 5.3) 14 ( 3,8) 41 4.2) 32 ( 4.3) 219 ( 2.9) *** ( ***) 0.1 elks ( *es) *** ,D.H1 $44.) 4$ ( 2.8) 26 ( 21) 26 2.0) 20 ( 11) 26 2.4) 35 ( 2.5) 238 ( 2.1) 272 ( 2.5) 267 3.0) 206 ( 32) 255 ( 3.5) 275 ( 2.0) 57 ( 1.8) 21 ( 24) 33 ( 2.4) 12 ( 1.5) 36 ( 2.4) 211 ( 2.0) 216 ( 1.6) '1" ( "1 215 ( 24) ( ') 214 ( 1.8) 237 ( 3.1) 45 ( 1.9) 25 ( 2.4) 33 ( 2.0) 16 ( 1.4) 26 ( 11) 33 ( 23) 265 ( 1.7) 2$4 ( 1.8) 274 ( 2.2) 278 ( 2.8) 268 ( 21) 285 ( 2.0) 57 ( 1.7) 16 ( 1.3) 33 ( 1.8) 14 ( 1.8) 34 ( 1.8) 23 ( 1.4) 217 ( 1.0) 240 ( 2.3) 216 ( 229 ( 4.1) 215 ( 1.4) 238 ( 2.3) 50 ( 1.7) 20 ( 2.0) 29 ( 1.8 19 ( 1.3) 27 ( 1.5) 23 ( 2.1) 255 ( 1.9) 275 ( 2.2) 204 ( 21 263 ( 2.5) 256 ( 3.0) 271 ( 1.9) 50 ( 1.3) 26 ( 11) 34 ( 2.1) 13 ( 1.2) 35 ( 11) 32 ( 11) 211 ( 1.4) 229 ( 2.1) 200 ( 2.4) 226 ( 3.0) 210 ( 2.0) 229 ( 1.9) 46 ( 2.0) 26 ( 2.1) 32 ( 1.6) 18 ( 1.2) 27 ( 1.8) 33 ( 2.1) 252 ( 1.7) 289 ( 1.8) 254 ( 1.7) 263 ( 2.1) 251 ( 2.4) 271 ( 13) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for th: entire population is within * 2 standard errors of the estimate for the sample. The permntages may not total 100 percent because the *Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 Virgin Islands TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1140 NAEP TRIAL NCalcutator-Uaa" "Cakatater-Use" STATE ASSESSMENT 10911 Grow 13th1 r Orem _ TOTAL Peramtalp and Poidididdif 223 1.2 42 13 272 1.8 Iftromds. and Pratiektaqi e7 ( 218( 1.0 58 ( 1.3 255( 1 Territory Nation SACEIETHNICITY Meek Territory 34 ( 16) 226 ( 1.4) 21$ 1.2 Nation 37 ( 3.4) 83 3.4 246 ( 3.0) 231 SA Hispanic Territory 30 ( 3.1) .44.) 70 3.1) 207 1.8) Nation 36( 4.2) 64 4.2) 254 ( 4.6) ( 3.0) TYPE OF COMMUNITY Extrema rural Territory 30 ( 2.0) 54 ( 2.0) 213 ( 2.3) 204( 1.5) Nation 39 ( 5.0) 61 ( 5.0) 280 ( 4.4)1 248 ( 4.3)1 Other Territory 33 ( 16) 87 ( 1.8) 225 ( 1.5) 218 ( 1.1) Nation 42 ( 1.4) 5$ ( 1A) 271 ( 1.9) 255 ( 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 rehable estimate (fewer than 62 students). 1 3 5 130 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgil: Is lamis TABLE A20 1 Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1SW NAEP TRIAL STATE ASSESSMENT NO "Calm later-thsew Orate Other "Calotdater.Ove" Orate yam Territory Nation Emir japsaro and PreitiNNY 1.5) 223 1.2) 42 1.3) 272 14) NS non-graduate Territory 29 ( 4.4) ***) Nation 34 ( 3.3) 241 ( 4.4) NI graduate Territory 341 ( 2.8) 223 ( 2.2) Nation 40 ( 22) 283 ( 2.0) Sante WSW Territory 33 ( 5.1) ..44) Nation 48 ( 22) 277 ( 2.8) College graduate Territory 32 ( 4.3) 228 ( 3.7) Nation 48 ( 2.0) 282 ( 2.1) GENDER, M. Territory 29 ( 2.3) 22$ ( 2.4) Nation 39 ( 2.0) 274 ( 2.0) Female Territory 38 ( 1.8) 219 ( 1.7) Nation 45 ( 1.8) 269 ( 1.7) 672111 I III 59 1.3 256 1.5) 71 ( 4.4) 2025 9 ( 242 ( 2.4 84 ( 22) 217 ( 2.1) 80 ( 2.2) 249 ( 1.8) 87 ( 5.1) *Ira ( NIP) 52 ( 22) 258 ( 2.5) 88 ( 4.3) 218 ( 1.8) $4 ( 2.0) 268(12) 71 ( 2.3) 218 ( 1,4) ( 2.0) 255 ( 2.3) 02 ( 1.8) 213 ( 1.4) 55 ( 1.8) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 Virgin Islands TABLE A24 I Students' Reports on Tnt. Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 MEP TRIAL STATE AMISIIIEST Zero to Two nine Was Typos Four 'NM , 12.TiSk Territory Nati On BiedgangiEn Moak Territory Nation Ripe* Territory Nation TYPE of cespiumw Extrooto mai Territory Nation attar Territory Nation Paramesp PM Maw 24 1.1 212 131 21 1.0 244 2.0 23 ( 1.5) 215 ( 31 ( 1 232 ( 22 27 ( 2.8) 204 ( 23) 44 ( 3.0) 237 ( 3.4) 26 1.15) 204 3.9) 17 4.9) «ND) 22 ( 1.3) 215 ( 1.3) 22 ( 15) 244 ( 2.6) Poremialle am1 Prifielsocat and .Pfelkitmcg ie i ale 223 1.2 30 1 45 13 258 ( 1.7) 272 1.5 37 ( 12) 40 ( 1.6) 219 ( 1.8) 225 ( 1.4) 38 ( 22) 33 ( 2.4) 233 ( 3.9) 245 ( 33) 38 ( 3.6) 33) 208 ( 2.1) 214 23) 30 ( 2.4) 20 2.3) 244 ( 4.3) 253 ( 2.4) 38 ( 4.0) 98 ( 2.7) 204 ( 33) 212 ( 2.2) 33 ( 92) 50 ( 5.1) 253 ( 4.3)I 263 ( 5.8)! 30 ( 1.7) 41 ( 1.6) 215 ( 1.5) 225 ( 1.3) 30 ( 1.3) 40 ( 1.5) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. s" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 137 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Virzi* Islamic TABLE A24 I Students' Repoits on Types of Reading ("Mtintled) I Materials in the Home PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . 11100 RAO TRIAL STATE ASSEITUNT bye to Two Ton Three TM* For TWIN _ liefeenhtle ant PrenehNIcy Rereenis. and Pneeleari Territory 24 ( 1.1) 30 ( 1.0) 212 ( 1.3) 910 ( 1.4) Nation 21 ( 1.0) $O ( 1.0) 244 ( 2.0) 258 ( 1.7) MBLECULDIEME 1411 eon-graduate Territory 30 ( ( 3$) 041 36 ( 207 ( 3.3) 3.8) Nation 47 ( 4.0) 28 ( 3.0) la gratitude 240 ( 3.4) 243 ( 3.3) Territory 20 ( 2.3) 40 ( 2A) 210 ( 2.9) 220 ( 2.7) Nation 26 ( 2.2) 33 ( 1.9) 2413 ( 2.2) 253 ( 2.7) Some college Territory 19 ( 4144 32) 34 ( 44* ( 3.8) *41 Nation 17 ( 1.5) 32 ( 1.7) 251 ( 4.0) 282 ( 2.6) College graduate Territory 31 ( 2.9) 214 ( 2.8) Nation 10 ( 0.8) 28 ( 1.8) 254 ( 2.8) 209 ( 2.5) GENDER Mate Territory 24 ( 1.4) 37 ( 2.3) 215 ( 1.9) 219 ( 2.2) Nation 21 ( 1.5) 31 ( 1.5) 244 ( 2.3) 259 ( 2.1) Female Territory 23 ( 1.7) 35 ( 1.7) 209 ( 1.7) 213 ( 1.7) Nation 22 ( 1.2) 29 ( 1.4) 244 ( 2.2) 258 ( 1.9) theinerdsge and 40 223 1.2 4$ 1.3 272 1.5 30 ( 2A) .41 25 2.8) 248 ( 3.3) 40 ( 2.5) 222 ( 2.3) 40 ( 1.7) 280 ( 2.1 47 ( 3.9) 233 ( 3.1) 51 ( 2.0) 274 ( 1.9) $5 ( 3.1) 226 ( 22) 82(2.0) 280 ( 1.8) 38 ( 2.0) 225 ( 1.7) 48 ( 1.4) 273 ( 2.0) 42 ( 1.8) 221 ( 1.5) 49 ( 1.9) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate ,,fewer than 62 students). 138 THE 1990 NAEP TRIAL STATE ASSESSMENT 133 Virgin Islands TABLE A25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1160 NAEP TRIAL STATE ASSESSMENT CO* Hour or Lau Two Hours Throe Routs Par to Five Nowa , Ilbt Hours or Moro Mak Territory Nation &CR ETHNICITY Perasniage me 11( 1.2 1.41 12 01 MR 2.2) 17 ( 1.2) 215 ( 1.7) 0.6) OM NI/ 17 ( 2,9) 14 ( 2.4) SOO ( grin 19 ( 4.3) 444 ( .41 14 ( 33) go. ( Mack Territory Nation Hispanic Territory Nation int-e-WANNITY Wren's mat Territory Nation Other Territory 17 ( 1.2) 218 ( 1.7) Nation 12 ( 1.0) ( 2.8) "II "Tr. 111. "Tr" Prolloiway Prelkikom Poitikoir iøuIuNsV 211/ 1111 211111 111 2111 ( 11 245 ( 21 ( 0.9 22 ( OA) 14 1.1 218 2.3) 13 1.7 239 ( 11.0 17 ( 2.7) 0,41 edp 20 ( 2.51 245 ( 3.2 18 ( 3.3) 19 2.8) ihe* ( «iv) 14 ( 0.9) 220 ( 2.3) 21 ( 1.0) 289 ( 2.3) 2? 1 221" { 21? 1 21 1.1 1.0 260 ( 4.7 245 1. 17 ( 1.4) 223 ( 2.2) 17 ( 2.1) 2394 5.0) 11( 3.1) .**1 10 ( 2.11 242 ( 5,8) 20 ( 23 17 ( 223 ( 23 ( 285 ( 25 13) 224 t5) 32 1.8) 23. 4.0) 20 2.9) se..) 31 3.1) 24? 3.5) 34) 2.01 44.e) 1.4) 2.3) 1.2) 2.1) 20 ( 258 25 ( 223 ( 27 ( 252 ( 27 13) 221 14) 32 2.2) 23$ 4 25) 25(2.0) 203 17 1. 2M 31 27 ( 1.1) 219 ( 1.3) 17 ( 1.4) 248 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 3 ;) 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A25 I Students' Reports 011 the Amount of Time Spent (continued) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TAAL STATE ASSESSMENT One NOUr or WI Two Noun 1 Throe NOVI Far to FM NOWS Six Rows or U(3111 Pavalogo ant Prillohmay 16 12) 214 14 ) 12 0.8) 209 2.2) Territory Nation Eamminsamit 14$ toon.grodualo Territory 15 ( 2.3) Nation 12 ( 22) HS graduate Territcfy 20 ( 2,4) 215 ( 2.3) Nation IS ( 1.0) 249 ( 4.7) Some cologe Territory 18 ( 3.4) ft** 444) Nation coley gradual. 10 (. 1.4) Territory 18 ( 1.7) ( Nation 17 ( 1.3) 282 ( 2.8) GENDER M. Territory 20 ( 1.9) 218( 15) Nation 11 ( 0.9) 209 ( 3.3) Famaio Territory 10 ( 1.3) 211 ( 2.7) Nation 14 ( 1.1) 29 ( 2.8) Poroonloila ant PuIiIp 15 ( 1.0) 217 ( 2.1) 2(021 I "14 111( 3.1) of* 20 ( 3.1) IN* ( *411 13 ( 1.7) oeir 17 ( 1.4) 257 ( 2.8) 15 ( 2.8) ( 441 2$ ( 2.4) 275 ( 2.7) 14( 1.7) n ( 1.6) 260 ( 2.5) 15 ( 1.5) 222 ( 2.8) 22 ( 1.2) 287 ( 21) 14 ( 1.2) 212 ( 3.7) 20 ( 1.3) 209 ( 2.2) PoroW00119 *ad rsSiiket Ponamkol, sad Pralisimay V 24 1.5) 220 1.9 221 1.7) 22 0.6 20 '1.1) 205 ( 1.7 200 1.7) 17 ( 2.9) ( 4.1) .441 21 2.6) ..) 20 ( 244 ( 2.9) 3.2) 17 2.2) 20 ( 2.6) 220 3.3) 220 ( 21) 23 2.0) 32 ( 2.3) 259 ( 3.2) 253 ( 2.5) 20 ( 3.3) .44) 27 ( 3.4) 23 ( 21) 26 ( 2.2) 269 ( 3.5) 207 ( 2.5) 17 ( 22) wee) 27 ( 222 ( 3.0) 2.7) 23 ( 1.1) 25 ( 1.5) 277 ( 2.2) 270 ( 2.4) 20 ( 1.9) 22 ( 1.0) 222 ( 2.7) 224 ( 2.1) 22 ( 1.0) 28 ( 1.3) 2437 ( 2.2) 282 ( 2.1) 15 ( 1.2) 26 ( 2.0) 218 ( 2.7) 218 ( 2.0) 23 ( t.4) 28 ( 11) 284 ( 1.8) 25$ ( 1.9) awl PrOlialam 27 1.0) 211 SS5 ( 43 30 ( 3.1) 20 2.41 25 220 2.6 19 1 240 3.0 23 ( 4.4) 011* ( 041 44 ( 1.5) 242 ( 3.4) 26 ( 3.0) 215 ( 3.1) 12 ( 1.1) 256 ( 3.2) 23 ( 11) 220 ( 2.1) 17 ( 1.5) 248 ( 2.5) 291 1.4) 215 ( 1.7) 15 ( 1.2) 241 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 140 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Virgin Islands TABLE A26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MCI MEP TRIAL TAT SE ASSEISMENT , Nano Ono or too Days 4 Tam Days sr More _ 191Als Territory Nation Preldsfacir 50( 15) 221 40) 46 ( 1.1) 285 ( 1.8) BielatONSin Territory 53 ( 1.5) 223 ( 1.0) Nation 58 ( 3.1) 240 ( 3.2) Hispanic Territory 37 ( 211 ( 2,4 Nation 41 ( 3.3 245 ( 4,8) TYPE OF COMMUNITY Mune mill Territory 45 ( 3,3) 206 ( 2.0) Nation 43 ( 4,4) 257 ( 4.1)I Other Territory 51 ( 1.6) 224 ( 1.1) Nation 45 ( 1.3) 285 ( 2.2) 26 ( 1.2) 19 ( 1.2) 220 ( 1.8) 215 ( 21 ( 1.8) 23 ( 2 240 ( 4,1) 224 ( 92 ( 2.6) 31 ( 2.8) 210 ( 3.2) 207 $2 ( 2.2) 27 2.8 250 ( 3.3) 235 3.1 27 ( 2.8) 26 ( 3.4) 200 ( 1.7) 205 ( 2.3) $2 264 ( 4.2) ( 5.8)1 25 (39) 44* In 20 ( 1.3) 20 ( 1.3) 210 ( 1.4) 214 ( 1.6) 32 ( 1.1) 23( 1.1) 286 ( 1.0) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 141 THE 1990 NAEP TRIAL STATE ASSESSMENT Virgin Islands TABLE A26 I Students' Reports on the Number of Days of (continued) I school missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 'IMO NAEP TRIAL STATE ASSESSMENT None Ono or Two Days _ Throe Days or Mors 191K Territory Nation feaunionsam NS non-gradusas Territory Nation NS Territory Nation Sew collage Territory Nation College graduate Territory Nation 2ftegg male Territory Nation Female Territory Nation 221 45 255 0.9 1.1 1.$ 3.4 211 3.01 38 3.2 245 ( 3.0) 47 ( 3.1) 224 ( 2.1) 43 ( 2.1) 256 ( 2.0) 67 ( 4.1) 233 ( 3.0) 40 ( 1.8) 270 ( 3.0) 50 ( 3.4) 222 ( 2.1) 51 ( 1.6) 275 ( 2.1) 52 ( 1.9) 223 ( 1.4) 47 ( 1.0) 206 ( 2.0) 47 ( 1.0) 220 ( 1.3) 43 ( 1.4) 204 ( 2.3) 21: ;11 32 0.9 1.9 30 2.11) iose 28 3.1) 249 3.3) 2$ ( 2.0 220 2.4 31 1.01 257 2.6) 90 ( 3.5) 37 ( 1.6) 271 ( 2.5) 31 ( 3.1) 222 ( 3.1) 33 ( 12) 277 ( 1.7) 27 ( 2.2) 221 ( 1.9) 31 ( 1,4) 207 ( 2.1) 31 ( 1.3) 215 ( 2.3) 32 ( 1.1) 205 ( 1.7) and M ( 1.2 212 1A 23 1.1 250 1A1 31 3.1) 3$ 3.51 237 ( Al) 25 213 2.7 27 1.9 249 ( 2.4) 14 ( 12) .144, 23t 1.8) 253 ( 3.1) 19 ( 3.0) ( 1.3) 2e5 (3.1) 21 ( 217 ( 2.1) 22 ( 1.4) 250 ( 2.6) 22 ( 1.5) 208 ( 1.0) 25 ( 1.3) 250 ( 1.0) The standard errors of the estiniated 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 reliabte estimate (fewer than 62 students). 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 FIrgls Islands TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11M0 NAM TRIAL Sifonilb Alm AMP* - Uadaelded, Skagree, STATE ASSESSMENT Strongly Mumps Porasaba. aaa 220 1.1 27 13 271 ( 11) Territory Nation wag Territory 37 ( 11) ta ( 1.2) Nation 32 ( 2.5) 247 ( 4.1) Hispanic Territory 3111 ( 21) 219 ( to) Nation 24 ( 2.5) 257 ( 51) IlEUESSIELVILU Exams@ rural Territory 34 ( 3.0) 213 ( 1.6) Nation 34 ( 21) 270 ( 34)1 Other Territory 37 ( 1.6) 229 ( 1.3) Nation 27 ( 1.4) 271 ( 2.4) Pensanfiella lad 47 ( 1.2) 314 1.11 2(12 1.7) 46 14) 217 1.3) 52 23) 2$3 ( 3.3) 201 / "24 46 ( 2.6) 244 ( 2.2) 49 ( 2.4) 205 ( 2.6) 49 ( 22) 252 ( 4.1)1 47 ( 1.3) 217 ( 1.0) 46 ( 12) 283 ( 22) 04naadaga aid Pralk4amay 18 114 24 1.2) 251 1.8) 13 ( 211 ( 31 18 ( 11 227 ( 42 1$ 21) in 20 2.1) 230 ( 31) 17 ( 3.0) *in 17 ( 1.4) NO, ( 16 ( 0,9) 200 ( 1.6) 25 ( 14) 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. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 138 143 THE 1990 NAEP TRIAL STATE ASSESSMENT ` MO Islands TABLE A27 I Students/ Perceptions of Mathematics (continued) 1 PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1180 NAEP TRIAL STATE AUEUMENT Won* *Om NA* I Undecided. Disagree, Sim* Disagree Mehe Territory Nation naniraduste Territory Nation HS graduate Territory Nation Some college Territory Nation College graduate Territory Nation GENDER Mtge Territory Nation Female Territory Nation and Pre 11,00a5v 33 ( 3.7 217 ( 3.4 20 ( 2.81 *** ( 33 ( 2.4) 22$ ( 2.3) 27 ( 2.1) 282 ( 2.7) 43 ( 3.5) 14) 28 ( 2.5) 274 ( 3.1) 42 ( 3.4) 228 ( 2.8) 30 ( 2.3) 200 ( 2.4) 30 ( 2.0) 229 ( 1.7) 28 ( 1.5) 273 ( 2.3) 38 1.7) 225 1.5) 28 1.7) 289 ( 2.1) 2175 1 ttii 40 1.0) 282 ( 1.1) 47 32) 207 3.2 50 331 243 22 51 ( 2 217 ( 47 ( 2.3 255 ( 2.3) 41 ( 4.1) 47 2.4) 287 ( Ca) 48 ( 3.4) 217 ( 3.3) $1 ( 1.45) 274 ( 2.2) 48 ( 1.7) 217 ( 1.8) 44 ( 1.2) 283 ( 2.0) 47 ( 1.9) 213 ( 1.2) 50 ( 1.7) 282 ( 14) 18 ( 207 ( 24 ( 1.2 251 ( 10 ( 3.8) 4100 ( 4101 231 4311 15 ( 1.4) on* 28 245 2.4 18 ( 2.8) 25 238 ( 3.2) 12 ( 1.5) .44) 19 ( 12) 288 ( 2.5) 17 ( 1.5) 213 ( 2.7) 24 ( 1.4) 251 ( 2.4) 1$ ( 1.5) 202 ( 2.5) 25 ( 1.9) 2$2 ( 12) 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 139 Acknowledgments The design, developsnent, analysis, and reporting of the first Trial State Assessment was truly a collaborative Mut among staff from State Education Agencies, the National Center far Education Statistics (N(S), Educational Testing Service (ETS), Westat, sad National Computer Systems (NCS). The program benefitted from the contributions of Ituadreds of individuals at the state and local levels Governors, Chief State School Officers, State and District Test Directocs, State Coordinators, and &strict administrators who tirelessly provided their wisdom, experience, and hard work. Really, and most impoetantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Counal 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 (rammed and objectives for the assessment and recommendations shod reporting the results of the program. In particular, we note the sigaificant contribution of Ramsay Se Idea, Director of the State Education Assessment Center for the CUSO and the members of the Steering, Mathematics Objectives, and Analysis sod Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded thro* NCES, in the Office of Educational Research and Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, peovided consistent suppoct and gaidance. The staff particularly Gary Phillips, Eugene Own, Stephen Gorman, Maureen Treacy, and Raul Gana worked closely and collegially with ETS, %stet, 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 &arias, colleges and universities, and State Education Agencies worked tirelessly to help ETS staff develop the assessment and a framework for interpredng the results. Under the NAEP contract to ETS, Archie Lapointe saved as the project director and ba Mullis as the deputy director. Statistical and psychometric activities were led by John Mimeo, 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 actMties 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 &action 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 dea 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 Soaker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Korner wrote the text for the report. Kent Ashworth was responsible for coordinating the cover desigp 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. 145 00VERNIU4T MINTING OFFICIR : 1101 0 - 2N475 QL.3 OIL SO NM- - 146