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DOCUMENT RESUME ED 330 573 SE 052 083 TITLE The State of Mathematics Achievement in North Carolina: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively: see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EARS PRICE MF01/PC06 Plus Postage. JESCRIPTORS Academic Achievement; Calcula,-.ors; *Educational Assessmert; Family Environment; *Grade 8; Homework; Junior Hi,jh Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS National Assessment of Educational Progress; *North Carolina; *Numeracy; State Mathematics Assessments; Tri.al State Assessment (NAEP) ABSMACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In North Carolina, 2,843 students in 106 public schools were assessed. This report describes the mathematics proficiency of North Carolina eighth-graders, compares their overall performance to students in the Southeast region of the United States and the nation (using data from the NAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, parents' educational level, and gender). To provide a context for the assessment data, participating students, their mathematics teachers, and principals completed questionnaires which focused on: instructional content (curriculum coverage, amount of homework); delivery of math instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, North Carolina students had an average proficiency of 250 compared to 261 nationwide. Many fewer students (North Carolina-7%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS 1111111P The SUM If M .11 *evement in NORTH CAROLINA The Trial State Assessment at Grade Eight THE NATION'S REPORT CARO Pvvr'PB''' t U S DEPARTMENT Of EDUCATION of E duca#Kmat Resnar( n and [mptnvement FOX IONAL RFSOuRCES tNFORMATION CE NT E R tERIC document ha, Dee^ tetploduced as ,etehvert1 ChM, the E.a7t#S00 0# 0:0401,tat,0rt oripnatMij r Molot changes, hawe Ewen made t0 Imptmat reptoductn)n g,tatI'rt Pomts ,on* 0. opmtong stted,n thSdOeu tnpnt do not necesSnly reptesent ott,c4I OE RI 005.1#0not Pokcs 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 19'69. 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 progres.s of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics. the U.S. Department of Education. The Commissioner of Education Statistics is responsible, by law. for carrying out the NAEP project through competitive awards to qualified organizations. NAEP reports directly to the Commissionei. 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 wlecting the subject areas to he assessed, which may include adding to those specified by Congress; identifying appropriate achievement goals for each age and grade: developing assessment -thjectives; developing test specifications; designing the assessment methodology; developing guidelines and standards for data analysis and for reporting and disseminating o.sults; developing standards and procedures for interstate. regional, and national comparisons: improving the form and use of the National Assessment; and ensuring that all items selected for use in thc 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 Fronde Alexander Associate Superintendent California Department of Education Sacramento, California David P. Batini High School History Teacher Cairo-Durham High School Cairo, New York Parris C. Battle Teaeher Horace Mann Elementary School Miami. Florida Mary R. Blanton Attorney Cromwell. Porter. Blanton & Blanton Salisbury, North Carolina Boyd W. Boehlje Attorney Gams. Klyn, & Bochlje Pella. Iowa Linda IL Bryant Teacher Greenway Middle School Teacher Center Pittsburgh. 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 Pol cy Vanderbilt University Washington. D.C. Michael S. Glode Wyoming State Board of Education Saratoga. Wyoming Christine John.son Principal Abraham Lincoln High School Denver. Colorado John Lindley Principal South Colby Ele'nentary School Port Orchard. Washington Carl J. Moser Director of Schools The Lutheran Church International Center St. Louis. Missouri Missouri Synod Mark D. Musick President SoutIrm 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 Honorabk 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. Honorabk Richard W. Riley Attorney Nelson. Mullins. Riley and Searbormgh Columbia. South Carolina Thomas Topuzes Attorney Law Offices of Frank Rogozienski Coronado, California Wrbert Walberg Professor of Education University of Illinois Chkago. Illinois Assistant Secretary tor Niucational Research and Improvement (Ex-Officio) l!.S. Department of Education Washington. D,C. Roy Truby Executive Director, NAGS Washington. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The HIM of Mathematics Achievement in NORTH CAROLINA The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education 4 U.S. Department of FAlucation Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Munk) Acting Assistant Secretary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessme.nt's individual State reports are available directly from the participating States. For adering information, please contact the assessment division of your State Department of Education. For or*ring information on the composite report of results for the Nation and all Stateparticipants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). 1.1braty of Congreu, Catalog Card Number: 91-61478 ISSN: 0-110685-14-9 The woo: upon which this publication is based was perfonned for the National Center for Education Statistics, Office of Educational Research and Improvement, by Educational Mating Service. Educatiectal Mating Sesvice is an equal opponunityfafftmlative action employer. £4ssca2ion4 Testig Service, ETS, and O. are mgistered trademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of North Carolina 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in North Carolina Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 Levels of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race/Ethnicity 24 Type of Community 27 Parent& Education Level 29 Gender 31 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics' 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Delivered? 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used? 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics? .67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyorid School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 7 iv THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina NE NATION'S REPORT CARD EXECUTIVE SUMMARY in 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history a piovision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessmaits that NAEP has conducted since its inception. As a result of the legislation, the 1990 NAEP progam 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 As-...tssrnent, 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 carefiilly designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT 1 North Carolina In North Carolina, 106 public schools participated in the assessment. Theweighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in North Carolina. 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 9 percent had an Individualized Education Plan (IEP). All IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who wese 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, 2,843 eighth-grade North Carolina public-school students were assessed. The weighted student participation rate was 95 percent. This means that the sample of students who took part in the assessment was representative of 95 percent of the eligible eighth-grade pubric-school student population in Noith Carolina. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from North Carolina on the NAEP mathematics scale is 250. This proficiency is lower than that of students across the nation (261). Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to defme the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT In North Carolina, 94 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in North Carolina (7 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 North Carolina 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 North Carolina eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In North Carolina: White students had higher average mathematics proficiency than did Black, Hispanic, or American Indian students. Further, a greater percentage of White students than Black, Hispanic, or American Indian students attained level 300. The results by type of community indicate that the average mathematics performance of the North Carolina students attending schools in advantaged urban areas was about the same as that of students attending schools in disadvantaged urban arms and higher than that of students attending schools in extreme rural areas or areas classified as "other". In North Carolina, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 31 points higher than that of students whose parents did not graduate from biEh school. The results by gender show thRt there appears to be no difference in the average mathematics proficiency of eighth-gxade males and females attending public schools in North Carolina. In addition, there was no difference between the percentages of males and females in North Carolina who attained level 300. Compared to the national results, females in North Carolina performed lower than females across the country; males in North Carolina performed lower than males across the country. I 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 3 North Carolina 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 North Carolina are as follows: About three-quarters of the students in North Carolina (71 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 North Carolina, 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 ill North Carolina were taking eighth-grade mathematics (58 percent) than were taking a course in pre-algebra or algebra (39 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 North Carolina spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 1 1 4 THE 1990 NAEP TRIAL STATE ASSESSMEW North Carolina In North Carolina, 19 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 36 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In North Carolina, 26 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. In North Carolina, 35 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 (50 percent) had teachers who had the highest level of teaching certification available. This is different from the figure for the nation, wliere 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in North Carolina who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of these materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. Relatively few of the eighth-grade public-school students in North Carolina (10 percent) watched one hour or less of television each day; 21 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. THE 1990 NAEP TRIAL STATE ASSESSMENT ME NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assesament 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 Oitgon California Maryland Pennsylvania Colorado Mgan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois Noith Carolina Guam Indiana North Dakota Virgin Islands THE 1990 NAEP TRIAL STATE ASSESSMENT 7 North Carolina This report describes the performance of the eighth-grade public-school students in North Carolina 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 North Carolina. Part One describes the mathematics performance of the eighth-grade public-school students in North Carolina, the Southeast region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in North Carolina, the Southeast region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing itb primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survey instrument for the eighth grade and shall conduct a demonstration of the instrument in 1990 in States which wish to participate, with the purpose of determining whether such an assessment yields valid, reliable State representative data. (Section 406 ( 1)( 2 )(C)(1) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1 (i)(2)(C)(i))) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality ass-ranee program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 1 4 8 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patterned after the consensus process described in Public Law 98-511, Section 405 (E), which a lhorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council of Chief State School Officers in mid-1987 to develop the objectives. The development process included carefill attention to the standards developed by the National Council of Teachers of Mathematics,' the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEFs Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-get.erated report that describes the performance of eighth-grade public-school students in North Carolina, in the Southeast region, and for 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 su, populations referred to in this report are presented below. The results for North Carolina are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nationally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAEP program was necessary because the voluntary nature of the Trial State Assessment Program did aot guarantee representative national or r;gional results, since not every state participated in the progam. I National Council of Teachers of Mathematics, Curriculum and Evaluation Standard; for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 9 North Carolina RACE/ETHNICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Procedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for North Carolina. 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 att. ld schools where many of the students' parents are farmers or fatm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. 6 )0 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina 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 I Regions of the Country NORTHEAST SOUTHEAST CENTRAL WEST _ Connecgcut Alabama Illinois Alaska Delaware Arkansas Arizona District of Columbia Florida Iowa California Maine Gaorgia Kansas Colorado Maryland Kentucky Michigan Hawsii Massachusetts Louisiana Minnesota Idaho New Hampshirs Mississippi Missouri Montana New Jersey North Carolina Nebraska Nevada Now York South Carolina North Dakota Now Mexico Pennsylvania Tennessee Ohio Oklahoma Rhode isismd Vnia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT 11 North Carolina Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As Atch, 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 describe! the group means or proportions as being different (e.g., one group peiformed 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 Or aOme attribute was about the same for two goups, the confidence interval included zero, and thus no difference could be assumed between the group.- 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. 8 12 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not ovalap, it is true that there is a statistically significant differeme between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the perceritage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables arc rowtded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). 1 9 THE 1990 NAEP TRIAL STATE ASSESSMENT 13 North Carolina Profile of North Carolina EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in North Carolina, the Southeast region, and the nation. This pmfi1.4 is based on data collected from the students and schools participating in the Trial State Assessment. TABLE I I Profile of North Carolina Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS MO NAEP TRIAL STATE ASSESSMENT North Carviina Southeast Nation .. DEMOGRAPHIC SUBGROUPS Percentag Porcontage Percentage Race/Ethnicity White 62 ( 1.7) 83 ( 3.0) 70 ( 0.5) Black 30 ( 1.3) 32 ( 3.0) 16 ( 0.3) Hispanic 6 ( 0.5) 3 ( 0.8) 10 ( 0.4) Asian 1 ( 0.2) 1 ( 0.4) 2 ( 0.5) American Indian 3 ( 0.9) 0 ( 0.1) 2 ( 0.7) Type of community Advantaged urban 4 ( 2.2) o ( 0.0) 10 ( 3.3) Disadvantaged urban 4 ( 1.8) 2 ( 2.3) 10 ( 2.8) Extreme rural 17 ( 3.3) 9 ( 5.3) 10 ( 3.0) Other 7$ ( 4.3) 89 ( 5.8) 70 ( 4.4) Parents' Education Did not finish high school 11 ( 0.7) 14 ( 2.1) 10 ( 0.8) Graduated high school 32 ( 1.0) 27 ( 1.8) 25 ( 1.2) Some education after high school 17 ( 0.8) 16 ( 11) 17 ( 0.9) Graduated college 33 ( 1.3) 32 ( 3.3) 39 ( 1.9) Gender Male 51 ( 1.0) 49( 2.8) 51 ( 1.1) Female 49 ( 1.0) 51 ( 2.8) 49 ( The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages for Race, Ethnicity may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know," Throughout this report. percentages less than 0.5 percent are reported as 0 percent. 14 2 0 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for North Carolina schools and students sampled for the 1990 Trial State Assessment. In North Carolina, 106 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in North Carolina. TABLE 2 I Profile of the Population Assessed in I North Carolina 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% 111 5 106 106 THE 1990 NAEP TRIAL STATE ASSESSMENT EIGHTH-GRADE PUBL/C-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 an Individualized Education Plan Percentage of students excluded from the assessment due to individualized Education Plan status Number of students to be assessed Number of students assessed 3,257 142 0% 9% 3% 3,005 2,643 15 North Canalina 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 9 percent had an Individualized Education Plan (IEP). An IEP is a plan, mitten for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 0 percent and 3 percent of the population, respectively. In total, 2,843 eighth-grade North Carolina public-school students were assessed. The weighted student participation rate was 95 percent. This means that the sample of students who took part in the assessment was representative of 95 percent of the eligible eighth-grade public-school student population in North Carolina. 2 2 16 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in North Carolina Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geomeuy; 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 North Carolina. Chapter 1 comparvs the overall mathematics performance of the students in North Carolina to students in the Southeast region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 summarizes the students' overall mathematics performance for subpopulations defined by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. 4. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 17 No-11: Carolina CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from North Carolina on the NAEP mathematics scale is 250. This proficiency is lower than that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency NAEP Mathematics Scale 200 225 250 275 300 500 Average Proficiency I-101 North Carolina Southeast Nation 250 25$ 261 ( ( ( 1.0) 2.1) 1.4) 41111111111111111 41111111ININNI~INO, The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 3 Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 2 4 18 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina 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 greatei detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are Oven in Figure 3. It is important to note that the definitions of these levels are based solely on student performance on the 1990 mathematics assessment. The levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In North Carolina, 94 percent of the eighth graders, compared to 97 percent in the nation* appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in North Carolina (7 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). CONTENT AREA PERFORMANCE As previously indicated, the questions comprising the Trial State Assessment covered five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Figure 5 provides the North Carolina, Southeast region, and national results for each content area. Students in North Carolina performed lower than students in the nation in all of these five content areas. t) THE 1990 NAEP TRIAL STATE ASSESSMENT 19 North Carolina FIGURE 3 I Levels of Mathematics Proficiency I LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers .1111111 Students at this level have some degree of understanding of simple quantitative relationships Involving Whole numbers. They can solve simple as;dition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-step word problems and select the greatest four-digit number in a list. In measurement, these students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students con recognize simple figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numerical sentences and extend simple pattern $ squences. ,..! LEVEL 250 r;imple Multiplicative Reasoning and Two-Step Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-step addition and subtraction problems involving money. Using a calculator, they can Identify solutions to other elementary two-step word problems. In these basic problem-solving situations, they can Identify missing or extraneous Information and have some knowledge of when to use computatonal estimation. They have a rudimentary understanding of such concepts as whole number place value, "even," "factor," and "multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. in geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and probability. In algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions. 0 C! 20 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina FIGURE 3 I Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasoning and Problem Solving Involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simpie Algebraic Manipulations Students at this level are able to represent, interpret, and perform simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, and recognize the equivalence between common frictions and decimals, including pictorial representations. They can interpret the meaning of percents less than and greater than 100 end apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expreeSiOns, 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, pictOgrenhs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open linear sentences and inequalities by subStitution, and checking and graphing an interval representing a compound inequality when it is described in words. They can determine and apply a rule for simple functional relations and extend a numerical pattern. LEVEL 350 Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to include soma 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 Irk. solve problems. They can find the circumferences of circles and the surface areas of solid figures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirect surement. These students also can apply their knowledge of the properties of geometric figures to sok problems, such as determining the slope of a line. In data analysis, these students can compute meanS from frequency tables and determine the probability of a simple event. In algebra, they can identify an equation describing a linear relation provided In a table and solve literal equations and a system of two linear equations. They are developing an understanding of linear functions and their graphs, as well as functional notation, including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. THE 1990 NAEP TRIAL STATE ASSESSMENT 21 North Carolina FIGURE 4 LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation I Levels of Eighth-Grade Public-School I Mathematics Proficiency 0 20 40 so 110 o ( 0.0) ( 0.0) 0 ( 0.2) 7 ( 0.7) 8 ( 1.8) 12 ( 49 ( 1.4) 52 ( 3.2) 64 ( 1.6) 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percert confidence biterval, denoted by I-04). 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 94 ( 0.6) 94 ( 2.2) 97 ( 0.7) North Carolina FIGURE 5 I Eighth-Grade Public-School Mathematics I Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation AND OPERATIONS TRY DATA ANALYSIS, STATISTICS, AND PROSAIIILITy pei ALGEBRA AND FUNCTIONS 0 200 225 250 275 300 Average Proficiency 255 ( 1.0) 259 ( 2.9) 266 ( 1.4) 241 ( 1.1) 248 ( 3.8) 258 ( 1.7) 249 ( 1.0) 249 ( 2.6) 259 ( 1.4) 247 ( 1.3) 250 ( 3.3) 262 ( 1.8) 251 ( 1.0) 254 ( 2.7) 260 ( 1.3) 500 Mathematics Subscals 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+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difTereme between the populations. t2 THE 1990 NAEP TRIAL STATE ASSESSMENT 23 North Carolina CH APTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the .1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents' education level, and gender. RACE/ETKNICITY The Trial State Assessment results can be compared according to the different racial/ethnic groups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Black, Hispanic, and American Indian students from North Carolina are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black, Hispanic, or American Indian students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Black, Hispanic, or American Indian students attained level 300. 30 24 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina FIGURE 6 I Average Eighth-Grade Public-School Mathematics Proficiency by Race/Ethnicity North Carolina Mite Rack Hispanic American Indian Southeast White Black Hispanic American Indian Nation White flack Hispanic American Indian 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 t-0-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 11" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 31 THE 1990 NAEP TRIAL STATE ASSESSMENT 25 North Carolina THE NATION'S REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARO 1 Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White 3leck Hispanic Amer. Indian Region White Black Hispanic Amer. Indian Nation White Black Hispanic Amer. Indian LEVEL 250 State White Black Hispanic Amer. Indian Region White Black Hispanic Amer. Indian Nation White Black Hispanic Amer. Indian LEVEL 200 State White Black Hispanic Amer. Indian Region White Black Hispanic Amer. Indian Nation White Black Hispanic Amer. Indian 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 04-4). If the confidence intervals for 'the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). Perciatage 100 32 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 10 ( 1.0) 1 ( 0.5) 1 ( 1.1) 1 ( 1.6)1 11 ( 2.7) 2 ( 1.6) tbdt *** ) 15 ( 1.5) 2 ( 1.3) 3 ( 1.1) 1 ( 2.3)1 64 ( 1.9) 24 ( 1.8) 12 ( 3.6) 32 ( 5.8)1 06 ( 3.6) 27 ( 5.1) mix *..) mu, ..) 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) 45 (16.0)1 ( 0.4) $ e ( 1.3) 76 ( 4.3) ( 5.4)1 ( 1.3) ( 5.3) pijk *** ** ) ( 0.4) 06 ( 3.1) 93 ( 1.6) 97 ( 6.7)1 North Carolina TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, &advantaged urban areas, =tram rural areas, and areas classified as "other". (These are the "type of community" groups in North Carolina with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the North Carolina students attending schools in advantaged urban areas was about the same as that of students attending schools in disadvantaged urban areas and higAer than that of students attending schools in extreme rural areas or areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community NAEP Ualheetwilcs Scala 0 200 225 250 275 300 500 Average Pevacianey North Cirolina Advantaged urban IAA NS$ 1 Disadvantaged urban 40 pins ." Extreme rural , e43 2.3) ite Other Peg Southeast Advantaged urban Disadvantaged urban Extreme rural Other Nation Advantaged urban 111 Disadvantaged urban 111 Extreme rural 211 Other INN 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 (9-5 percent confidence interval, denoted by 0.1-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 33 THE 1993 NAEP TRIAL STATE ASSESSMENT North Carolina FIGURE 9 LEVEL 300 State Adv. urban Disadv. urban Ext. rural Other Reckon Adv. urban DIsadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other LEVEL 250 State Adv. urban DIsadv. urban Ext. rural Other Region Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other LEVEL 200 Stat. Adv. urban Disadv. urban Ext. rural Other Raglon Adv. urban Ditadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community THE MOWS IEPORT CARD l111 20 40 60 50 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). toNI11.01 .1 I I I 22 ( 4.5)f 7 ( 4.0)1 3 ( 1.4) 7 ( 0.8) RSA *** mol 4 4 ( 4.2)1 9 ;, 1.9) 26 ( 4.8)1 7 ( 2.1)1 ( 2.3)1 12 ( 1.2) 70 ( 9.4)1 40 (14.8)1 ( 3.7) 60 ( 1.6) mut *-) 41 (17.4)1 53 ( 3.9) $3 ( 4.6)1 49 ( 5.0)1 511 ( 6.2)1 95 ( 2.4)1 Oa ( 8.3)1 02 ( 1.2) 96 ( 0.6) wen ) mix ) 90 (13.5)1 94 ( 2.2) 100 ( 0.0) 95 ( 1.5)1 97 ( 2.8)1 0+4 97 ( 1.0) 100 34 28 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina 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 I I). In North Carolina, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 31 points higher than that of students who reported that neither patent graduated from high school. As shown in Table 1 in the Introduction, a smaller percentage of students in North Carolina (33 percent) than in the nation (39 percent) had at least one parent who graduated from college. In comparison, the pescentage of students who reported that neither parent graduated from high school was I I percent for North Carolina and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School I Mathematics Proficiency by Parents' Education NAEP Mathematics Scale 200 225 250 275 300 500 Memo Proficiency HI N4 144 144 North Carolina HS non-graduate HS graduate Some college College graduate Southaast HS non-graduate P-40-04 HS graduate Some college College graduate Nation HS non-graduate tea HS graduate 1.4 Some C011ege t44 College graduate The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1.44). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 3 Ij THE 1990 NAEP TRIAL STATE ASSESSMENT 29 North Carolina 11E NATION'S REPORT rimy FIGURE 1 1 I Levels of Eighth-Grade Public-School CARO I Mathematics Proficiency by Parents' Education LEVEL 300 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. Raglan HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 Stat HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. O ( 0.6) 3 ( 0.7) ( 1.1) 15 ( 1.8) 1 ( 0.0) 3 ( 1.7) ( 2.3) 19 ( 3.8) ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.9) 25 ( 2.8) ( 2.0) 42 ( 2.9) OS ( 2.3) 29 ( 6.9) 45 ( 5.4) 01 ( 6.3) 72 ( 3.5) 37 ( 4.8) NI ( 2.7) 71 ( 2.6) 79 ( 2.0) 00 ( 1.9) 92 ( 1,4) ( 0.8) ( 0.6) 93 ( 3.5) h.--fol"of 03 ( 2.4) 97 ( 2,5) 97 ( 2.8) 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estirnatid percentage (95 percent confidence interval, denoted by H-I). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 30 THE 1990 NAEP TRIAL STATE ASSESSMENT ( 1.9) 97 ( 0.8) SO ( 0.7) 99 ( 0.7) North Carolina GENDER As shown in Fig= 12, there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in North Carolina. Compared to the national results, females in North Carolina performed lower than females across the country; males in North Carolina performed lower than males across the country. FIGURE 12 I Average Eighth-Grade Public-School 1 Mathematics Proficiency by Gender MEP Mathematics sere 200 225 250 275 300 500 Average 141 North Carolina Male ("*.44) Female Southeast Male Female *a 24) thitieff Mate 1.11) Female .13) 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 I4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in North Carolina who attained level 200. The percentage of females in North Carolina who attained level 200 was smaller than the percentage of females in the nation who attained level 200. Also, the percentage of males in North Carolina who attained level 200 was smaller than the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASS2SSMENT 31 North Carolina FIGURE 13 I Levels of Eighth-Grade Public-School Mathematics Proficiency by Gender LEVEL 300 State Male Female Region Male Female Nation Male Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female 0 7 ( 0.8) 7 ( 0.9) 10 ( 1.9) ( 2.0) 14 ( 1.7) 10 ( 1.3) 45 ( 1.7) 50 ( 1.7) 50 ( 3.6) 54 ( 3.8) 54 ( 2.0) 94 ( 1.8) 1-404 94 ( 0.9) ( 0.6) 93 ( 3.0) F-4.4 99 ( 1.9) 97 ( 0.9) 01.4 97 ( 0.8) 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-4-1). If the confidence intervals for the populations do not overlap, there is a statistically significant diffnenoe between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 3S 32 THE 1990 NAEF TRIAL STATE ASSESSMENT North Carolina In addition, there was no difference between the percentages of males and females in North Carolina who attained level 300. The percentage of females in North Carolina who attained level 300 was smalles than the percentage of females in the nation who attained level 300. Also, the percentage of males in North Carolina who attained level 300 was smaller than the pescentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a slimmary of content area performance by race/ethnicity, type of community, parents' education level, and gender. 3 THE 1990 NAEP TRIAL STATE ASSESSMENT 33 North Carolina TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT Numbers ind Operations Geometry Data Analysis' $ tatistics, and il Probabity Algebra and ilmetIons TOTAL Proackno Mildewy Proficiency Pfvficiency Praidency State 255 ( 14) 241 ( 1.1) 249 ( 1.0) 247 ( 1.3) 251 ( 1.0) Region Nation 259 ( 268 ( 2.9) 1.4) 246 ( 258 ( 3.8) 12) 249 259 ( 2.6) ( 1.4) 250 262 ( 3.3) ( 1.8) 254 260(1.3) ( 2.7) RACE/ETHNICITY State 264 ( 1.4) 255 ( 1.6) 259 ( 1.2) 262 ( 1.6) 262 ( 1.3) Region 258 ( 3.0) 258 ( 42) 259 ( 3.5) 263 ( 3.4) 264 ( 3.4) Nation 273 ( 1.6) 267 ( 2.0) 267 ( 1.5) 272 ( 1.5) 268 ( 1.4) Slack State 240 ( 12) 219 ( 1.4) 233 ( 1.4) 2 ( 1.9) 233 ( 1.2) Region 242 ( 5.1) 222 ( 5.8) 225 ( 42) 227 ( 0.5) 235 ( 4.5) Nation 244 ( 3,1) 227 ( 3.6) 234 ( 25) 231 ( 3.8) 237 ( 2.7) Hispanic State 225 ( 2.7) 210 ( 3.6) 222 ( 3.0) 210 ( 42) 222 ( 3.4) Region ( ( ( Nation 248 ( 2.7) 238 ( 3.4) 243 ( 32) 23S ( 3.4) 243 ( 3.1) American Indian State 242 ( 4.0)1 225 ( 8.2)1 236 ( 4.4)1 226 ( 5.4)1 237 ( 4.4)1 Region ( Sr/ ( ( ( Nation 249 ( 7.8)1 247 ( 8.6)! 248 ( 8.8), 242 ( 5.2)1 242 ( 4.9)1 TYPE Of COMMUNITY Advantaged urban State Region 276 ( ( 6.5)1 260 ( ( 7.3)1 265 ( 8.6)1 ( *..) 267 ( 6.9)1 ( 271 ( 7.1)1 ( Nation 283 ( 3.2)1 281 ( 32)1 277 ( 5.2)1 285 ( 4,191 277 ( 4.8)1 Disadvantaged urban State 250 ( 03)1 233 (10.8)1 242 (11.7)1 233 (13.5)1 242 (12.0)1 Region ( qv') ( ( ( Nation 255 ( 3.1)1 242 ( 4.9)1 248 ( 3.7)1 247 ( 4.6)1 247 ( 3.2)1 Extrema rural State 250 ( 2.2) 234 ( 2.8) 241 ( 2.7) 241 ( 3.0) 245 ( 2.4) Region 254 ( 9.8)1 241 (47.1)1 244 (18.4)1 245 (13.7)1 251 (14.7)1 Nation 258 ( 4.3)1 254 ( 4.2)1 253 ( 4$)1 257 ( 5.0)1 256 ( 4.8)1 Other State 255 ( 1.2) 243 ( 1.3) 251 ( 1.3) 249 ( 1.5) 252 ( 1.0) Region 259 ( 3.3) 246 ( 4.0) 249 ( 2.7) 251 ( 3.8) 25$ ( 3.0) Nation 266 ( 1.9) 257 ( 2,4) 259 ( 1.7) 261 ( 2.2) 261 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determmation of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 34 THE 1990 NAM' TRIAL STATE ASSESSMENT 4' Carolina TABLE 3 I Eighth-Grade Public-School Mathematics (wntinued) Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Numbers and Operations esonletrY Data Analysis, Statistics, end Probabilit, Ali*" arid Functions TOTAL Proficiency Proliciency Proficiency Proficiency Proficioncy State 255 ( 1.0) 241 ( 1.1) 249 ( 1.0 247 ( 1.3) 251 ( 1.0) Region 250 ( 2.9) 248 ( 3.8) 249 ( 2.6) 250 ( 3.3) 254 ( 2.7) Nation 208 ( 1.4) 258 ( 12) 250 ( 1.4) 262 ( 14) 280 ( 1.3) PARENTS EDUCATION NS non-graduate State 240 ( 1A) 221 ( 2.3) 234 ( 2.2) 225 ( 2.6) 233 ( 1.4) Region 243 ( 4.5) 227 ( 6.1) 237 ( 4.1) 234 ( 4.7) 240 ( 3.5) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) 240 ( 3.1) 242 ( 3.0) HS trading. State 247 ( 1.3) 233 ( 1.7) 241 ( 1.4) 236 ( 1.7) 243 ( 1.4 Region 252 ( 4.7) 235 ( 5.3) 242 ( 3.3) 242 ( 5.4) 247 ( 4.5) Nation 259 ( 1.8) 248 ( 2.1) 252 ( 1.8) 253 ( 21) 253 ( 2.4) Sarno collaga State 262 ( 1.4) 250 ( 1.7) 256 ( 1.9) 261 ( 1.9) 259 ( 1.7 Region 265 ( 3.5) 257 ( 8.3) 253 ( 41) 240 ( 3.9) 240 ( 5.7 Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 263 ( 2.2) Colley* graduals State 268 ( 1.7) 256 ( 2.0) 262 ( 1.5) 293 ( 2.1) 245 ( 14) Region 27$ ( 3.9) 264 ( 44) 263 ( 3.6) 267 ( 4.6) 270 ( 4.1) Nation 278 ( 1.8) 272 ( 24) 270 ( 1.6) 276 ( 21) 273 ( 1.7) GENDER Ma State 254 ( 1.3) 244 ( 1.4) 250 ( 1.2) 247 ( 1.6) 248 ( 1.3) Region 257 ( 3.6) 249 ( 4.4) 249 ( 3.2) 244 ( 3.9) 253 ( 3.2) Nation 266 ( 2.0) 242 ( 2.3) 260 ( 1.7) 262 ( 2.1) 200 ( 1.6) Femal State 256 ( 1.1) 239 ( 1.3) 248 ( 1.2) 247 ( 1.5) 254 t 1.2) Region 261 ( 2.9) 243 ( 4.0) 244 ( 2.4) 251 ( 3.7) 255 2.6) Nation 208 ( 1.4) 253 ( 1.8) 258 ( 1.5) 201 ( 1.9) 280 ( 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 35 North Carolina 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 ats. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information on student achievement. It is important to note that the NAEP data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qttalifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. 4 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 37 North Carolina Through the questionnaires administered to students, teachers, and piincipals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning,. incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an ...:)rmous impact on future academic achievement. Yet. as shown in Chapters 3 and 7, Tge proportions of students report having spent much more time each day watching television than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 4 3 38 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.' This chapter focuses on curricular and instructional content issues in North Carolina public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: About three-quarters of the eighth-grade students in North Carolina (71 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curtis McKnight, et al., The Underachieving Curriculum: Assessing U.S. School Mathematics from an International Perspective, A National P port on the Second International Mathematics Study (Champaign, Stipes Publishing Company, 1987), Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). 4 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 North Carolina In North Carolina, 85 percent of the students could take an algebra course in eighth grade for high school course placement or credit. About three-quarters of the students in North Carolina (71 percent) were taught mathematics by teachers who teach only one subject. . Many (80 percent) of the students in North Carolina were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was less prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in 1 North Carolina Eighth-Grade Public Schools PERCENTAGE OF STUDENTS _ 11160 NAEP TRIAL STATE ASSESSMENT North Carolksa Southeast Nation , . Percentage of eighth-grade students in public schools that identified mathematics as receiving special emphasis in school-wide goals and objectives, instruction, 1n-service training, etc. Percentage of eighth-grade public-school students who are Owed a coarse in algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who teach only mathematics Percentage of eighth-grade students in public schools who are assigned to a elathaMatiCS class by their ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics instruction per week Percentage Pareentar Percentage 71 ( 4.6) 70 (10.8) 83 ( 5.2) 8$ ( 3.5) 60 (10.8) 78 ( 4.6) 71 3.7) 77 (10.6) 01 ( 3.3) ( 3.0) 58 ( 8.0) 83 ( 4.0) 47 ( 4.0) 51 (11.1) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 45 40 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in North Carolina are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in North Carolina were taking eighth-grade mathematics (58 percent) than were taking a course in pre-algebra or algebra (39 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in North Carolina who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency I What kind of mathematics class are you taking this year? Eighth-grade mathematics 58( 1.8) 64 ( 3.7) 62 ( 2.1) 234 ( 1.1) 241 ( 3.4) ( 1.4) Pre-algebra 22 ( 1.4) 23 ( 4.4) 19 ( 1.9) 262 ( 1.4) 289 ( 4.6)1 272 ( 2.4) Algebra 17 ( 1.3) 11 ( 2.2) 15 ( 12) 290 ( 1.3) 296 1 4611 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 4 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 41 North Carolina Further, from Table A5 in the Data Appendie A greater percentage of females (44 percent) than males (34 percent) in North Carolina were enrolled in pre-algebra or algebra courses. In North Carolina, 46 percent of White students, 28 percent of Black students, 15 percent of Hispanic students, and 37 percent of American Indian students were entolled in pre-aIgebra or algebra courses. Similarly, 71 percent of students attending schools in advantaged urban areas, 34 percent in schools in disadvantaged urban areas, 31 percent in schools in extreme rural areas, and 39 percent in schools in areas classified as "other" were enrolled in pre-algebra or algebra courses. MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in North Carolina spent either 15 or 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes daily. Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix): In North Carolina, 3 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 3 percent of the students in North Carolina and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations -- race ethnicity, type of community. Parente edt:cation level, and gender. 4 7 42 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina Thc results by race/ethnicity show that 3 percent of White students, 2 percent of Black students, 3 percent of Hispanic students, and 1 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 3 percent of White students, 4 percent of Black students, 6 percent of Hispanic students, and 5 percent of American Indian students spent no time doing mathematics homework. In addition, 5 percent of students attending schools in tdvantaged urban areas, 12 percent in schools in disadvantaged urban areas, 3 percent in schools in extreme rural arras, and 2 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 2 percent of students attending schools in advantaged urban areas, 0 percent in schools in disadvantaged urban areas, 2 percent in schools in extreme rural areas, and 4 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1S69 NAEP TRIAL. STATE ASSESSMENT North Carolina Southeast Nation ] Percentage and Proficiency Pimentos* and Proficiency Percentage and Proficiency About how much time do students spend on mathematics homework each day? 3 ( 0.9) 1 ( 1.0) 1 ( 0.3) 218 ( 2.8)i 15 minutes 40 ( 2.8) 44 ( 7.5) 43 ( 4.2) 242 ( 1.7) 248 ( 5.1)1 256 ( 2.3) X minutes 46 ( 2.5) 44 ( 7.6) 43 ( 4.3) 254 ( 2.1) 280 ( 5.4)1 266 ( 2.6) 45 minutes 8 ( 1.5) 8 ( 2.7) 10 ( 1.9) 271 ( 5.4) fr ( 61 272 ( 5.7)1 An hour or more 3 ( 0.7) 3 ( 1.3) 4 ( 0.9) 284 ( 6.0)I 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 z 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 43 North Carolina TABLE 7 I Students' Reports on the Amount of Time They i Spent on Mathematics Homework Each Day PERCENTAGE CP STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . , 1900 NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation About how much time do you usually Percentage iswwee-nisge Percentage spend each day on mathematics and and and homework? Prot Idency Madam Pro &fancy 15 minutes 30 minutes 45 minutes An hour or mon 9 ( 0.7) 11 ( 1.9) 9 ( 0.8) 239 ( 2.4) 237 ( 5.4) 2.51 ( 2.8) 29 ( 1.1) 25 ( 1.6) 31 ( 2.0) 250 ( 1.4) 253 ( 3.3) 264 ( 1.9) 33 ( 0.9) 33 ( 2.5) 32 ( 12) 254 ; 1.4) 258 ( 3.0) 283 ( 1.9) 17 ( 0.8) 17 ( 2.2) 10 ( 1.0) 250 ( 2.1) 281 ( 2.5) 298 ( 1.9) 13 ( 0.8) 14 ( 1.4) 12 ( 1.1) 249 ( 2.1) 247 ( 4.6) 258 ( 3.1) The standard errors of the estimated statistics appear in parenthesin. 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 North Carolina, relatively few of the students (9 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 13 percent of the students in North Carolina 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 12 percent of White students, 14 percent of Black students, 15 percent of Hispanic students, and 18 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 9 percent of White students, 9 percent of Black students, 10 percent of Hispanic students, and 12 percent of American Indian students spent no time doing mathematics homework. 44 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina In addition, 9 percent of students attending schools in advantaged urban areas, 22 percent in schools in disadvantaged urban areas, 13 percent in schools in extreme nual areas, and 12 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 4 percent of students attending schools in advantaged urban areas, 7 percent in schools in disadvantaged urban areas, 6 parent in schools in extreme rural areas, and 10 percent in schools in areas classified as "other" spent no tune doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement.5 Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they wcre enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one tt,1;c: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. National Council of Teachers of Mathematics, Curriculum and Evaluation Standard.s for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 5o THE 1990 NAEP TRIAL STATE ASSESSMENT 4$ IVorth Carolina The responses of the assessd 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 pf 3 waS given tc, "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 euiphasis" -- and the Average stLient proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student peifonnance in the Numbers and Operations ccntent area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose toachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than stud _nts whose teachers placed little or no emphasis on the same areas. 4 6 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE 8 I Teachers' Reports on the Emphasis Given to Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation Percentage and Proficiency Percentage and Plifidency Penmen. end Prollicioncy Teacher "emphasis" categories by content areas Ntanbers mid Operations Heavy emphasis 10) ( 2.7) ( 7.3) 49 ( 3.8) 246 ( 1.4) 256 ( 3.1)4 200 ( 1.8) Little or no emphasis 14 ( 1.7) 15 ( 4.8) 15 ( 2.1) 287 ( 2.9) 282 1 7.7)I 287 ( 3.4) Ateasurement Heavy emphasis 17 ( 2.3) 13 ( 6.8) 17 ( 3.0) 228 ( 3.2) 242 ( 7.6)4 250 ( 5.6) Little or no emphasis 31 ( 2.7) 22 ( 6.1) 33 ( 4.0) 255 ( 3.0) 259 (10.7)1 272 ( 4.0) Geometry Heavy emphasis 17 ( 2.4) 22 ( 7.3) 28 ( 3.8) 254 ( 2.5) 253 ( 7.6)1 280 ( 32) Little or no emphasis 29 ( 2.7) 22 ( 8.8) 21 ( 3.3) 253 ( 2.8) 253 ( 151)1 264 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 13 ( 22) 19 ( 5.9) 14 ( 2.2) 251 ( 4.0) 274 ( 5.8)1 269 ( 4,3) Little or no emphasis 60 ( 3.0) 54 (10.4) 53 ( 4,4) 247 ( 1.9) 246 ( 5.4)1 261 ( 2.9) Algebra and Functions Heavy emphasis 44 ( 2.6) 42 ( 6.0) 46 ( 3.6) 273 ( 1.8) 277 ( 5.6) 275 ( 2$) Little or no emphasis 28 ( 2.3) 21 ( 8.1) 20 ( 3.0) 227 ( 1.7) 238 ( 6.7)1 243 ( 3.0) The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. T-*t) THE 1990 NAEP TRIAL STATE ASSESSMENT 47 North Carolina SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on cuniculum coverage, mathematics homework, and instructional emphasis has revealed the following: About three-quarters of the eighth-grade students in North Carolina ('71 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In North Carolina, 85 percent of the students could take an algebra course in 60th grade for high-school course placement or credit. A greater percentage of students in North Carolina were taking eighth-grade mathematics (58 percent) than were taking a course in pre-algebra or algebra (39 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 North Carolina spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. In North Carolina, relatively few of the students (9 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 13 percent of the students in North Carolina 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 and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 45 THE 1990 NAEP TRIAL STATE ASSFSSMENT North Carolina CHAPTER 4 yaxs-taz...9 mrssIsse as MIR& MO le1111-11-111-11 OON 11111111111111/ MO 81111111111111-11111-1114-4111111 1115111111111111111 MOW 111 11 111111111 N111.1111111 iUiRii ISMmai.. OM IIIERN MIMS Anne. 21111111111 How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning or for those who come from different cultural backgrounds is an important aspect of teaching.° An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. ° National Council of Teachers of Mathematics. Professional Standards for the Teachin,g of Mathematics (Reston. VA: National Council of Teachers of Mathematics, 1991). t THE 1990 NAEP TRIAL STATE ASSESSMENT 49 North Carolina From Table 9 and Table A9 in the Data Appendix: In North Carolina, 19 percent of the eighth-grade students had mathematics teachers who morted getting all of the resources they needed, while 36 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In North Carolina, 22 percent of students Mending schools in advantaged urban areas, 36 percent in schools in disadvantaged urban areas, 13 percent in schools in extreme rural areas, and 19 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in North Carolina, 32 percent of students attending schools in advantaged urban areas, 43 percent in schools in disadvantaged urban areas, 51 percent in schools in extreme rural areas, and 33 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had higher mathematics achievement levels than those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of 1 Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - . 19a0 NAEP TRIAL. STATE ASSESSMENT North Carolina Southeast Nation _ Which of the following statements is true about how well supplied you ere by your school system with the instructional materials and other resources you need to teach your class? L_ I get an the resources I med. I get most of the resources I neihd. I get some or none of the resources I need. 4rwroNis Parcentage and Proficiency Pettentage Parcentage and and ProRdency Proficiency 19 ( 2.8) ( 4.0) 13 ( 2.4) 259 ( 2.2) 258 (12.2)1 2155 ( 4.2) 45 ( 3.0) 71 ( 9.5) 56 ( 4.0) 252 ( 1.5) 255 ( 3.3)1 265( 2.0) 36 ( 3.3) 21 ( 9.7) 31 ( 4.2) 243 ( 2.0) 257 ( 8.0)1 201 ( 2.9) 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. rti 50 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina 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.7 Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on matenals used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: About half of the students in North Carolina (45 percent) worked mathematics problems in small groups at least once a week; some never worked mathematics problems in small groups (11 percent). The largest percentage of the students (63 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (9 percent). In North Carolina, 70 percent of the students were assigned problems from a mathematics textbook almost every day; 4 percent worked textbook problems about once a week or less. 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 (21 percent). 7 Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Curriculum: Eighty-second Yearbook of the National Society for the Study of Education (Chicago. IL: University of Chicago Press, 1983). THE 1990 NAEP TRIAL STATE ASSESSMENT 51 North Carolina TABLV 10 I Teachers' Reports on Patterns of Mathematics 1 Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL. STATE ASSESSMENT North Carolina So Wisest Nation Perceriage and Perceithape and Pen:enter! and About how often do students work problews in small groups? Prendincy Pendency krulldency At least once a week 45 ( 3.6) 44 ( 6.2) 50 ( 4.4) 247 ( 1.9) 25$ ( 4.7)1 200 ( 2.2) Less than once a week 44 ( 3.4) 48 ( 8.3) 43 ( 4.1) 255 ( 1.9) 258 ( 3.9)1 204 ( 2.3) NOW 11 ( 1.8) 247 ( 3.4) ( 4.1) ( 0,1 ( 2.0) 277 ( 5.4)1 About how often do students use objects Percentage Percentage Percentage him rulers, counting blocks, or geometric and and and solids? Pronclency Proaciemy Profit:lona At least once a week 29 ( 3.2) 19 ( 8.2) 22 ( 3.7) 245 ( 2.3) 243 ( 4.3)1 254 ( 3.2) Less than once a week 63 ( 3.5) 65 (10.3) 69 ( 3.9) 250 ( 1.5) 257 ( 3.8)1 263 ( 1.0) Never 0( 1.8) 16 ( 8.1) 0 ( 2.6) 267 ( 5.4)1 ( ***) 282 ( 5.9p 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 a 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). 57 52 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE ii Teachers' Reports on Materials for i Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT North Caroline Southeast Nation Percentage Percentage Percentage About how often do students do problems and and and from textbooks? Proficiency Pretkiency Proficiency Almost every day 70 ( 3.2) TS ( 7.8) 62 ( 3.4) 2S4 ( 1.3) 259 ( 3.1) 267 ( 1.8) Several tknes a week 26 ( 3.1) 22 ( TA) 31 ( 3.1) 244 ( 2.4) 248 ( 5.2)1 254 ( 2.9) About once a week or kiss 4 ( 0.9) 229 ( 5.8)1 3 ( 2.8) VP* (41 7 ( 1.8) 200 ( 5.1)1 About how often do et.:.-:crnts do problems Percentage Percentage Percentage on worksheets? and and and Proficiency Proficiency Proficiency Al least several times a week 49 ( 3.3) 30 ( BA) 34 ( 3.8) 246 ( 1.9) 251 ( 3.4)1 256 ( 2.3) About once a week 30 ( 2$) 44 ( 9.1) 33 ( 3.4) 254 ( 2.6) 256 ( 3.7)1 280 ( 2.3) Less than weekly 21 ( 2.8) 27 ( $.6) 32 ( 3.6) 257 ( 3.1) 263 ( 8.0)1 274 ( 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). The next section presents the students' responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT 53 North Carolina COLLABORATING LS SMALL GROUPS In North Carolina, 49 percent of the students reported never working mathematics problems in small groups (see Table 12); 23 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 I Students' Reports on the Frequency of Small 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11MO NAER TRIAL STATE ASSESSMENT North Carolina Southeast Nation Percentage and Prondency Percentage and Pro& Macy Percentage and Proficiency How often do you work in small groups in your mathematics class? At least one* a week 23 ( 1.4) 25 ( 3.9) 26 ( 2.5) 245 ( 1.9) 251 ( 4.6) 258 ( 2.7) Lass than once a week 28 ( 1.3) 26 ( 2.2) 26 ( 1.4) 257 ( 1.8) 259 ( 3.9) 287 ( 2.0) Never 49 ( 2.1) 49 ( 4.8) 44 ( 2.9) 249 ( 1.3) 252 ( 2.4) 281 ( 1.8) 111a. The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. Examining the subpopulations (Table A 12 in the Data Appendix): In North Carolina, 13 percent of students attending schools in advantaged urban areas, 37 percent in schools in disadvantaged urban areas, 20 percent in schools in extreme rural areas, and 23 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 20 percent of White students, 26 percent of Black students, 27 percent of Hispanic students, and 25 percent of American Indian students worked mathematics problems in small gxoups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (21 percent and 24 percent, respectively). 59 54 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina USING MATHEMATICAL OBJECTS Students were asked to rtport on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: Less than half of the students in North Carolina (43 percent) never used mathematical objects; 26 percent used these objects at least once a week. Mathematical objects were used at least once a week by 10 percent of students attending schools in advantaged urban areas, 35 percent in schools in disadvantaged urban areas, 30 percent in schools in extreme rural areas, and 26 percent in schools in areas classified as "other". Males were more likely than females to use mathematical objects in their mathematics classes at least once a week (29 percent and 23 percent, respectively). In addition, 22 percent of White students, 33 percent of Black students, 32 percent of Hispanic students, and 30 percent of American Indian 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 11100 NAEP TRIAL STATE ASSESSMENT North Carolina St 4theast Nation , How often do you work with objects hke rulers, counting blocks, or geometric solids in your mathematics class? Percentage and Prolidency Paceritaile and PnIfkislicy Percentage and Proficiency Al least once a walk 26 ( 1.7) 23 ( 3.4) 23 ( 1.8) 241 ( 1.5) 242 ( 3.6) 258 ( 2.6) LOSS than moo a week 31 ( 1.3) 29 ( 2.5) 31 ( 1.2) 256 ( 1.6) 261 ( 15) 269 ( 1.5) New 43 ( 2.1) 48 ( 4-5) 41 ( 22) 251 ( 1.4) 254 ( 3.0) 259 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -I-, 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT GO 55 North Carolina MATERIALS FOR MATHEMATICS INSTRUCTION The permnages of eighth-grade public-school students in North Carolina 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 North Carolina (77 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of the students in the nation. Textbooks were used almost every day by 74 percent of students attending schools in advantaged urban areas, 63 percent in schools in disadvantaged urban areas, 83 percent in schools in extreme rural areas, and 77 percent in schools in areas classified as "other". TABLE 14 Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation How often do you do mathematics problems from textbooks in your mathematics class? Porcentage and Pronciency Percentage and Proficiency Percentage and Proficiency Almost every day 77 ( 1.4) 78 ( 2.4) 74 ( 1.9) 254 ( 1.1) 257 ( 2.8) 287 ( 1.2) Several dines a week 15 ( 1,0) 14 ( 1.9) 14 ( 0.8) 238 ( 1.8) 248 ( 4.4) 252 ( 1.7) About once a week or less 8 ( 0.7) 8 ( 2.7) 12 ( 1.8) 230 ( 10) 222 ( 5.3)! 242 ( 4,5) The standard errors or 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. C I 56 TH E 1 no NAEP STATE ASSESSMENT North Carolina And, for the frequency of worksheet usage (Table 15 and Table A 15 in the Data Appendix): About half of the students in North Carolina (45 percent) used worksheets at least several times a week, compartd to 38 percent in the nation. Worksheets were used at least several times a week by 37 percent of students attending schools in advantaged urban areas, 56 percent in schools in disadvantaged urban areas, 44 percent in schools in extreme rural areas, and 44 percent in schools in areas classified as "other". TABLE 15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1999 NAEP TRIAL STATE ASSESSMENT North Carolina - Southust _ Nation i 111, 1111.111011.101 How often do you do mathematics pmblems on worksheets In your mathematics class? Percentage and Proficiency Recent.. and Proficiency Percentage Ind Proficiency At least towel times a week 45 ( 2.1) 38 ( 4.3) 36 ( 2.4) 244 ( 1.7) 245 ( 4.3) 253 ( 2.2) About once a week 29 ( 1.3) 32 ( 1.5) 25 ( 12) 252 ( 1.5) 254 ( 2.6) 261 ( 1.4) Leer than muddy 27 ( 1.8) 29 ( 3.9) 37 ( 2.5) 258 ( 1.8) 263 ( 3.3) 272 ( 1.9) The standard errors of the estimated statistic :. appear in paren:heses. It can be said with about 95 percent certainty that, for each copulation of interest, tilt 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. 6 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 North Carolina TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1890 NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation Patterns of classroom Instruction Percentage Manes traduce Perceatege Sul feats Teachers lissom gaga *Weft Teachers Percentage of students who woe* mathematics problems In smell groups At least once a week 23 ( 1.4) 43 ( 3.8) 26 ( 3.9) 44 ( 8.2) 26 ( 2.5) 50 ( 4.4) Less than once a week 25 ( 1.3) 44 ( 3.4) 28 ( 2.2) 41 ( 8.3) 28 ( 1.4) 43 4.1) NO VW 49 ( 2.1) 11 ( 1.8) 49 ( 4.8) 7 ( 4.1) 44 ( 2.9) $ ( 2.0) Percentage of students *to use obtects Nke Mem, camein9 blocks, or geometric sande At least once a week 28 ( 1.7) 29 ( 3.2) 23 ( 3.4) 19 ( 82) 28 ( 1.8) 22 ( 3.7) Less than once a week 31 ( 1.3) 83 ( 3.5) 29 ( 2.5) 85 (10.3) 31 ( 1.2) 59 ( 3.9) Never 43 ( 2.1) 9 ( 1.8) 4$ ( 4.5) 18 ( 8.1) 41 2.2) 9 ( 2.8) Materials for mathematics instruction Percentage Students Teachers Percentage Students Teachers Percentage Students Teachers Percentage of students %law use a mathematics twdbook Almost every day 77 ( 1.4) 70 ( 3.2) 78 ( 2.4) 751 7.8) 74 ( 1.9) 62 ( 3.4) Several times a week 15 ( 1.0) 28 ( 3.1) 14 ( 1.9) 22 ( 74) 14 ( 0.8) 31 ( 3.1) About once a week Of less 8 ( 0.7) 4 ( 0.9) 8 ( 2.7) 3 ( 2.8) 12 ( 1.8) 7 ( 1.8) Percentage of students who use a mathematics worksheet At least several times a week ( 2.1) 49 ( 33) 38 ( 4.3) 30 ( 8.8) 38 ( 2.4) 34 ( 3.8) About once a week 29 ( 1.3) 30 ( 2.5) 32 ( 1.5) 44 ( 9.1) 25 ( 11) 33 ( 3 4) Less than weekly 27 ( 1.8) 21 ( 2.8) 29 ( 3.9) 27 ( 8.8) 37 ( 2.5) 32 (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 vidue for the entire population is within ± 2 standard errors of the estimate for the sample. 63 58 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what IS Icnown about effective instructional delivesy practices and resources. It appears that mathematics textbooks and worksheets continue to play a major role in mathematics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachers: About half of the students in North Carolina (45 percent) worked mathematics problems in small groups at least once a week; some never worked in small groups (11 percent). The largest percentage of the students (63 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (9 percent). In North Carolina, 70 percent of the students were assigned problems from a mathematics textbook almost every day; 4 percent worked textbook problems about once a week or less. Alwmit 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 (21 percent). And, according to the students; In North Carolina, 49 percent of the students never worked mathematics problems in small groups; 23 percent of the students worked mathematics problems in small groups at least once a week. Less than half of the students in North Carolina (43 percent) never used mathematical objects; 26 percent used these objects at least once a week. About three-quarters of the students in North Carolina (77 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. About half of the students in North Carolina (45 percent) used worksheets at least several times a week, compared to 38 percent in the nation. c 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 North Carolina CHAPTER 5 ,MIMIMPIM 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 fiDIX1 time-con.suming computations and to permit them to focus on more challenging tasks.' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. National Assessment of Educational Progress, Mathematics 00jectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Nortie Carolina Table 17 provides a profile of North Carolina eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 18 percent of the students in North Carolina had tmchers who allowed calculators to be used for tests. A smaller percentage of students in North Carolina than in the nation had teachers who permitted unrestricted use of calculators (10 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of North Carolina Policies on Calculator Use PERCENTAGE OF STUDENTS MISO NAEP TRIAL STATE ASSESSMENT tior1h Carolina Southeast Nation gl=111mmeolimminmalI111MICIIMIIMInmiamENTIpipppmftwomppomml.M1=111m0=11, Percentage of eighth-grade students in public schoOIS whose teachers permit the ',restricted use or calculators Percentage of eighth-grade students in public schools whose teachers permtt the use of calculators tor tests Percentage of eighth-grade students in public Schools whose teachers report that students have access to calculators armed by the school Percentage PerfaN10111 Percentage 10 ( 1.8) ( 11) 14 ( 3.4) 18 ( 2.3) 15 ( 8.1) 33 ( 4.8) Si ( 3.2) 56 (11.8) 66 ( 4.6) The standard errors of the estinrted 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, 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 61 North Carolina THE AVAILABILTTY OF CALCULATORS In North Carolina, most students or their families (96 percent) owned calculators (Table 18); however, fewer students (53 percent) had teachers who explained the use of calculators to them. From Table A 18 in the Data Appendix: In North Carolina, 50 percent of White students, 55 percent of Black students, 70 percent of Hispanic students, and 63 percent of American Indian students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (52 percent and 53 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation IDo you or your family own a calculator? volt No Does your mathematics teacher explain how to use a calculator for mathematics 1 problems? Yes No Percentage and Pro Seism Percentage Percentage and and Proficiency Proficiency 96 ( 0.3) 96 ( 1.2) 97 ( 0.4) 251 ( 1.0) 254 ( 2.4) 263 ( 1.3) 4 ( 0.3) 4 ( 1.2) 3 ( 0.4) 224 ( 2.9) 234 ( 3.8) Percentage Percentage Percentage and and and Proficiency Proficiency Proficiency 53 ( 2.4) 46 ( 5.9) 49 ( 2.3) 245 ( 1.2) 250 ( 3.9) 258 ( 1.7) 47 ( 2.4) 54 ( 5.9) 51 ( 2.3) 255 ( 1.4) 256 ( 2.5) 266 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina THE USE OF CALCULATORS As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As pan of the Trial State Assessment, studants t--re asked how frequently (never, sometimes, almost always) they used calculatoA.. : working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In North Carolina, 26 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. Some of the students (18 percent) never used a calculator to work problems at home, compared to 29 percent who almost always used one. Less than half of the students (38 percent) never used a calculator to take quizzes or tests, while 24 percent almost always did. TABLE 19 Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation _ Parcentige and Proficiency Percentage and ProNciency Percentage. and Proaciency How often do you use a calculator for the following tasks? Woddng problems in Wass Almost always 45 ( 1.2) 48 ( 3.0) 48 ( 1.5) 238 ( 1.0) 243 ( 2.8) 254 ( 1.5) Never 28 ( 1.3) 261 4.0) 23 ( 1.9) 283 ( 1.5) 296 ( 3.1) 272 ( 1.4) Doing problems at home Almost always 29 ( 1.2) 29 (3.1) 30 ( 1.3) 245 ( 1.3) 252 ( 3.8) 261 , 1.8) Never 18 ( 0.9) 18 ( 1.8) 19 ( 0.9) 280 ( 1.9) 258 ( 4.4) 283 ( 1.8) Taking quizzes or tests Almost always 24 ( 1.0) 31 ( 2.1) 27 ( 1.4) 238 ( 1.4) 240 ( 3.8) 253 ( 2.4) Never 38 ( 1.4) 35 ( 3.1) 30 ( 2.0) 264 ( 1.4) 270 ( 3.1) 274 ( 1.3) . The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. Cs THE 1990 NAEP TRIAL STATE ASSESSMENT 63 North Carolina WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathmnatics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were cateorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they hoc"; used the calculator for less than half of the calculator-active items they were presented. Cs() 64 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina The data ...resented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in North Carolina were in the High group than were in the Other group. A smaller percentage of males than females were in the High group. In addition, 48 percent of White students, 37 percent of Black students, 27 t of Hispanic students, and 45 percent of American Indian st .44 were in the High group. TABLE 20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation Peroontage xid Proficiency °Calculator-use" group Nigh 44 ( 0.9) 42 ( 2.4) 42 ( 1.3) 200 ( t4) 264 ( 2.9) 272 ( 1.6) Other 56 ( 0.9) 56 ( 24) 56 ( 1.3) 243 ( 1.2) 247 ( 2.6) 265 ( 14) 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. 7o THE 1990 NAEP TRIAL STATE ASSESSMENT 65 North Carolina SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instructional time to teaching students how to perform routine calculations by hand. Using calculators to replace this time-consuming process would create more instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 18 percent of the students in North Carolina had teachers who allowed calculators to be used for tests. A smalles percentage of students in North Carolina than in the nation had teachers who permitted unrestricted use of calculators (10 percent and 18 percent, respectively). In North Carolina, most students or their families (96 percent) owned calculators; however, fewer students (53 percent) had teachers who explained the use of calculators to them. In North Carolina, 26 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. Some of the students (18 percent) never used a calculator to work problems at home, compared to 29 percent who almost always used one. Less than half of the students (38 percent) never used a calculator to take quizzes or tests, while 24 percent almost always did, 71 66 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina 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 pait 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 North Carolina, 35 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 (50 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. Many of the students (89 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). 72 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 North Carolina TABLE 21 I Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS L NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation Percentage of students voles* mathematics teachers reported having the fallowing degrees Bachelors degree 85 ( 2.9) 68 ( 82) 58 ( 4.2) Master's or specialist's degree 35 ( 2A) 39 ( $.4) 42 ( 4.2) Doctorate or professional degree 0 ( 0.0) 5 ( 5.1) 2 ( 1.4) Percentage et students 'Mese mathematics teachers have the teeming types et teaching certificates that are recognized by North Carolina No regular certification 5 ( 1.5) S ( 2.3) 4 ( 1.2) Regular certification but less than the highest available 45 ( 3.3) 53 (104) 2$ ( 4.$) Highest certification available (permanent or long-term) 50 ( 3.3) 42 (10I) 06 ( 4.3) Percentage of students Wiese mathematics teachers have the Mowing types of teaching certificates that are recognized by North Carolina Mathematics (middle school or secondary) 89 ( 1.1) 84 ( 5.1) 64 ( 22) Education (elementary or middle school) Other ( 3 ( 1.1) 0.8) 14 2 ( 4.6) ( Is) 12 ( 4 ( 2.6) 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standee, errors of the estimate for the sample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Thal State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. 3 68 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina Teachers' responses to questions concerning their undergraduate and gaduate fields of study (Table 22) show that: In North Carolina, 34 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 North Carolina (14 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and I Graduate Fields of Study PERCENTAGE OF STUDENTS 111110 !MEP TRIAL. STATE ASSESSMENT North Carolina Southeast Nation _ What was your undergraduate major? Percentage Percentage Percentage Mathematics 34 ( 32) 44 ( 9.0) 43 ( 3.9) Edtacadon BO ( 3.5) 43 ( 9.0) ( 3.8) Other 7 ( 1.6) 14 ( 8.5) 22 ( 3.3) What was your graduate major? Percentage Percentage Mathematics 14 ( 2.1) 15 ( 5.4) 22 ( 3.4) Education 36 ( 3.6) 43 ( OA) 38 ( 3.5) Other or no graduate level study 51 ( 3.6) 41 ( 81) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent oertainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 69 North Carolina Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In North CarolinE., 51 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 teachexs who spent at least that much time on similar types of in-sexvice training. Relatively few of the students in North Carolina (10 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on raimilar in-service training. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS 1NO NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? None One to 15 hours 15 hours or more Percentage Partestaws Peraiwitip 10 ( 2.3) 11 ( ILO) 11 ( 2.1) 39 ( 3.6) 4$ (12.0) 51 ( 4.1) 51 ( 3.5) 43 (10.1) 39 ( 3.5) 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. 75 70 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement." Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In North Carolina, 35 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 (50 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In North Carolina, 34 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 North Carolina (14 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. 10 Archie E. Lapointe, Nancy A. Mead. and Gary W. Phillips, A World of Differences: An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). " Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement NAErs 1990 Assessment of the Nation and the Thal Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). 7 6 THE 199 0 NAEP TRIAL STATE ASSESSMENT 71 North Carolina In North Carolina, 51 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. Aaross the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Relatively few of the students in North Carolina (10 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. 7 7 72 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina CHAPTER 7 The Condition Beyond School that Facilitate Mathematics Learning and Teaching Because students spend much more time out of school each day than they do in school, it is reasonable to expect that out-of-school factors greatly influence students' attitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, encouragement, and participation in student learning experiences are powerful influences. Together, teachers and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment.and mathematics proficiency, students participating in the Trial State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education. 7S THE 1990 NAEP TRIAL STATE ASSESSMENT 73 North Carolina AMOUNT OF READING MATERIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students participating in the Trial State Assessment were asked about the availability of newspapers, =twines, 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 1990 NAEP TRIAL STATE ASSESSMENT Margit Carolina Southeast Nation Does your family have, or receive on a regular basis, any of the following items: more than 25 books, an encyclopedia, newspapers, magazines? Zero to two types Three types Four types ,MIaw Percentage and Prolidency Percentage and Proficiency Percentage and Prolkdency 22 ( 0.8) 26 ( 2.3) 21 ( 1.0) 234 ( 1.3) 235 ( 3.4) 244 ( 2.0) 32 ( 0.0) 29 ( 2.4) 30 ( 1.0) 245 ( 1.2) 248 ( 4.4) 258 ( 1.7) 46 ( 1.1) 40 ( 2.7) 48 ( 1.3) 261 ( 1.4) 266 ( 2.8) 272 ( 1.5) The standard errors of the eitimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The data for North Carolina reveal that: Students in North Carolina 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. 7 $) 74 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina A smaller percentage of Black, Hispanic, and American Indian students had all four types of these reading materials in their homes than did White students. About the same percentage of students attending schools in advantaged urban areas as in disadvantaged urban areas, extreme rural areas, and areas classified as "other" had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen so detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10)0 NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation How much television do you usually watch each day? Ono hour or less Two hours Three hours Four to five hours Six hours or more Percentage Percentage and and Pleilciency Proficiency 10 ( 0.6) 259 ( 3.1) 18 ( 0.7) 258 ( 1,6) 12 ( 1.3) 262 ( 62) ( 2.1) 258 ( 4.2) Percentage and Preiciency 12 ( 200 ( 2.2) 21 ( 0.9) 266 ( 1.8) 20 ( 0.6) 256 ( 1.5) 32 ( 1.0) 24$ ( 1.3) 21 ( 1.0) 235 ( 1.6) 22 ( 1.9) 258 ( 3.3) 2$ ( 19) 251 ( 3.0) 1$ ( 1.4) 230 ( 2.8) 22 ( 0.6) 295 ( 1.7) 26 ( 1.1) 200 ( 1.7) 10 ( 1.0) 245 ( 1.1) The standard errors of the estimated statistics appear in parentheces. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. S THE 1990 NAEP TRIAL STATE ASSESSMENT 75 North Carolina From Table 25 and Table A25 in the Data Appendix: In North Carolina, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Relatively few of the eighth-grade public-school students in North Carolina (10 percent) watched one hour or less of television each day; 21 percent watched six hours or more. About the same percentage of males and females tended to watch six or more hours of television daily. Similarly, about the same parentage of males and females watched one hour or less per day. In addition, 14 percent of White students, 32 percent of Black students, 32 percent of Hispanic students, and 28 percent of American Indian students watched six hours or more of television each day. In comparison, 12 percent of White students, 6 percent of Black students, 8 percent of Hispanic students, and 10 percent of American Indian students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix: In North Carolina, average mathematics proficiency was lowest for students who missed three or more days of school. Ixss than half of the students in North Carolina (42 percent) did not miss any school days in the month prior to the assessment, while 25 percent missed three days or more. In addition, 27 percent of White students, 23 percent of Black students, 30 percent of Hispanic students, and 24 percent of American Indian students missed three or more days of school. 81 76 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina Similarly, 29 percent of students attending schools in advantaged urban areas, 29 percent in schools in disadvantaged urban areas, 27 percent in schools in extreme rural areas, and 24 percent in schools in areas classified as "other" missed three or more days of school. TABLE 26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STMF f!"*OISIAENT North Carolina Southeast Nation Percentage end Pro 'deny Percentage and Proficiency Percoltads Proficiency How many days of school did you miss last month? None 42 ( 1.1) 46( 1.8) 45 ( 1.1) 252 ( 1.4) 253 ( 3.4) 285 ( 1.8) One or two days 32 ( 0.9) 32 ( 1.7) 92 ( 0.9) 254 ( 1.1) 260 ( 2.8) 268 ( 1.5) Three days or more 25 ( 0.8) 22 ( 1.5) 23( 1.1) 242 ( 1.4) 242 ( 3.7) 250 ( 1.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest. the value for the entire population is within ± 2 standard errors of the estimate for the sample. 82 THE 1990 NABP TRIAL STATE ASSESSMENT 77 North Carolina STUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not only to master essential skills and concepts but also to develop confidence in their mathematici 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 use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for soMng everyday problems. A student "perception index" was developed to examine students' perceptions of and altitudes toward mathematics. For each of the five statements, students who responded "strongly agree" were given a value of 1 (indicating very positive attitudes about the subject\ those who responded "agree" were given a value of 2, wid those who responded mdecided," "disagree," or "strongly disagree" were given a value of 3. Each student's responses were averaged over the five statements. Th..! 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 ihe statements (an index of 2), or :ended to be undecided, to iisagree, 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 North Carolina: Average mathematics proficiency was highest for students who were in the "strongiy agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. Less than half c: the students (32 percent) were in the "strongly agree" category (perception index of 1). This compaies to 27 percent across the nation. Some of the students in North Carolina (20 perceat), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). 12 National Council of Teachers of Mathematica, Currkulurn and (Reston, VA: National Council of Teachers of M. matics, 1 tion Standards for School Mathematics 78 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MO NAEP TRIAL STATE ASSESSMENT North Carolina Southeast Nation - Student "perception index" groups Poroenteae wtd Proficiency Percentage and Proficiency Percentage and Prenciancy Strongly agre 32 ( 1.0) 30 ( 2.7) 27 ( 1.3) ("perception indee of 1) 256 ( 1.3) 265 ( 3.7) 271 ( 1.9) Area 48 ( 1.0) 45 ( 2.4) 49 ( 1.0) ("perception index" of 2) 250 ( 1.3) 251 ( 3.4) 262 ( 1.7) Undecided, disagree, strongly disagree 20 ( 0.9) 25 ( 3.0) 24 ( 1.2) ("perception index" of 3) 241 ( 1.4) 244 ( 2.7) 251 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. .1 he data related to out-of-school factors show that: Students in North Carolina 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 2.ero to two types. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 79 North Carolina Relatively few of the eighth-grade public-school students in North Carolina (10 percent) watched one hour or less of television each day; 21 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Less than half of the students in North Carolina (42 percent) did not miss any school days in the month prior to the assessment, while 25 percent missed three days or more. Average mathematics proficiency was lowest for students who missed thin or more days of school. Less than half of the students (32 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics pmficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. 80 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon which the assessment was bascxl, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State ri..1,0o1 Officers, and the items were developed through a similar process managed by Educational Testing Service. The development of the Trial State Assessment Program benefitted from the involvement of hundreds of representatives from State Education Agencies who attended numerouq 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 fast step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. 66 THE 1990 NAEP TRIAL STATE ASSESSMENT 51 North Carolina 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 wetv 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 B13 design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets were spiraled or interleaved in a systematic sequence so that each booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as descdbed in the introduction to this report.' The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (sec Figure Al). The three mathematical ability arras 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 ha I 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 subpopuf itions, even when all students do not answer the same set of questions. This common scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Pnnceton, NI: Educational Testing Service, 1988). 7 82 THE 1990 NAEP TRAM. STATE ASSESSMENT North Carolina FIGURE AI I Content Areas Assessed Numbers and Operations This content area tocuses on students' understanding of numbers (whole numbers, fractions, decimals, Integers) and their application to real-world situations, as well as computational and estimation situations. Understanding numerical relationships as expressed in ratios, proportions, and percents Is emphasized. Students' aPintles In estimation, mental computation, use of calculators, generalization of numerical patterns, and verification of results are also included. [Measurement This content area focuses on students' ability to describe real-world objects using numbers. Students are asked to identify attributes, select appropriate units, apply measurement concepts, and communicate measurement-related ideas to others. Questions are included that require an ability to read instruments using metric, customary, or nonstandard units, with emphasis on precision and accuracy, QuestlOns requiring estimation, Meleurements, and applications of measurements of length, time, money, temperature, mass/weight, area, volume, capacity, and angles are also included in this content area. Geometry This content area focuses on students' knowledge of geometric figures and relationships and on their skills in working with this knowledge. These skills are important at 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 lc etas. In addition, students should be able to use informal reasoning to establish geometrir, relationships. IData Analysis, Statistics, and Probability This content area focuses on data repreSentation and analysis across all disciplines and reflects the importance and prevalence of these activities in our society. Statistical knowledge and the ability to interpret data are necessary skills in the contemporary world. Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysis. Algebra and Functions This content area is broad in scope, covering algebraic and functional concepts in more informal, exploratory ways for the eighth-grade Trial State Assessment. Proficiency in this concept area requires both mantpulettve 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 ot algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. 68 THE 1990 NAEP TRIAL STATE ASSESSMENT 83 North Carolina FIGURE A2 f Mathematical Abilities Tne following three categories of mathematical abilities are not to be construe(' hierarchical. For example, problem Solving involves interactions between conceptual knowledge and procedural skills, but What is considered complex problem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. Conc.ptual Wing Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts; can use and Interrelate models, diagrams, and varied repreSentations of concepts; can identify and apply principles; know and can apply facts and definitions; can compare, contrast. and integrate related concepts and principles; can recognize, interpret, and apply the signs, symbols, and tafrhs 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 factors inherent In problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have been Created as tools to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncompulational skills such as rounding and ordering. Problem Solving In problem solving, students are required to use their reasoning and analytic abilities when they encounter new situations. Problem solving includes the ability to recognize and forr Jtata problems: determine the Sufficiency and consistency of data: use strategies, data, models, and relevant mathematics: generate. extend, and modify procedures: use reasoning (I.e., spatial, inductive, deductive, statistical, and proportional): and judge the reasonableness and correctness of solutions. 84 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina A scale ranging from 0 to 500 was crated to report performance for each content area. Each content-area scale was based on the distribution of student performance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created RS an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In contrast, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. My attempts to define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics items ft m the.1990 assessment that discriminated well between adjacent levels. The criteria Er selecting these "benchmark" items were as follows: To de ine 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 North Carolina Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the Imowledge, skills, and understandings of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their charactesistic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.' Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-pade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and fln use of various instructional approaches. Because of the nature of the sampling for ..he Trial State Assessment, the responses to the mathematics teacher questionnair 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 North Carolina FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Simple Addftive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 LETI DA Towel Was Cot Rib 0 T. Ueda hal awes twos sexes i1 the woe sin dad three Aib lame loads of hells es shows sham II she NU each her wich luad al balls aspra. *kWh Mu wsll Wm the Wows Ws le Se fTs The lee well the tsessie balk CD The bee the loll balls ce mlbee *Oa the rubber las Yar can NIL EXAMPLE 2 SOUS l V1T PIC= AT FARAWAY FARMS Chow Lawn Chapstwit .1,7916. R. Haw Laity boxes of octavo wen picked as Tliundayt CD 45 4) 60 CD TO CID 10 CD 90 CD 1 doit's know. Grade 4 Overall Percentage Correct 73% Percentage Correct for Anchor Levels: Z50 12Q 111/ es 91 100 92 Grade 4 Overall Percentage Percentage Correct 20 rig 75 91 Grad. 8 Overall Percentage Percentage Correct 254 76 87 Correct: for Anchor Levels: QQ 222 100 Correct: 89% for Anchor Levels: 22Q 2§Q 96 100 [ Level 250: Simple Multiplicative Reasoning and Two-Step Problem Solving I North Camlina FIGURE M I Example Items for Mathematics Proficiency Levels (continued) EXAMPLE 1 IP. What is the value oi n + 3 when a 3 r Answer EXAMPLE 2 MAX MILON NOW WW1 r--"Pwtrnm CON Knit Swan Took al 21 193 Tbe talk Ask Owl ihe tanks Si I imsny ol Iten color. On ibt ends kbw, mat tuck graph to Awns sib dab io Laki ebb pin al die aide staph imb et mesa ban Woe. Dad you nit Ow Wallow so Ai* questioot 0 Yes 0 No EXAMPLE 3 6. Kalb= u winos bkebsilt Leto boxes. &eh box bolds 6 Nubia' She hot 24 b.1k. Much ousabst imams will kip fiet nod out how sway bou4cwtfla.sd (20 24 6 flo 24 + 6 24 + 6 tio 24 6 CD I don't bow. Grade 8 Overall Percentage Percentage Correct 222 2:11 28 80 Grade 8 Overall Percentage Percentage Correct Nig IN 21 88 Correct 78% for Mohor Levels: 242 asz 05 98 Correct 73% for Anchor Levels: agg 92 02 Grade 8 Overall Percentage Percentage Correct Z24 222 37 71 P3 Correct 77% for Anchor Levels: a22 05 100 'MB 1990 NAM' TRIAL STAIE ASSESSMENT FIGURE A3 (continued) Love 300: EXAMPLE .1 North Carolina Example Items for Mathematics Proficiency Levels Reasoning and Problem Solving involving Fractions, Mimi*, Pfrefits, EI*Mentiry GOCinerie Propettint and Simple Algebraic Manlpulations 16. itto folhowtos Awes die emit at Moos di. awe atingle ova ths 4 EXAMPLE 2 io wall Iwothat dam it Imagist s cat 15 ka lor a mammal In auk asolle) Wis. 11 lb* ow asks load. ions IS ha MO wawa bit tspnwasid by orAlr ,-r4414 bowsaw/ *au bight to II I ap DO you ow she esksilsose ow ibis issatiost 0 WO 0 No THEi990 NAEP TRIAL srAm Assessmem Grade 8 Overall Pircantliga Correct 60% Piwcwitaga Wired for Mchor Levels: 2t22 22S1 242 MA 33 49 77 90 Gracia 12 Overs11 Pencintip Correct 75% Peroenteae Correct for Anchor Levels: al UR IN 46 79 95 Grade 8 ("wall Peroentar$ Nrcentspe correct al IN 17 46 94 Correct 59% for anclior Laves: 222 2§2 se 99 BEST COPY AVAILABLY 89 North Carolina FIGURE A3 j Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving involving Geometric ttelau^nehips, Algebraic Equation, and Beginning Statistic* and Probability EXAMPLE 1 Outs Imo WO mkt tasks tellowtag pasts= v4 4014 MAW.* IP in a * 0 * I a I i 1 A 16. It this yottona of dot-hquees is mutual& how "any dots will be ot tke 100tk hoots/ 100 @ 101 41:1199 ID 200 41) 20 ; EXAMPLE 2 1?, tsploan hew you found yaw answer to question 16. Grade 3 OveraN Percentage Correct 34% Percentage Conoct for Anchor Levels: Mil Mil 222 2112 13 19 53 se Grads 12 Overall Percentage Correct 49% Percentage Correct for Anchor Levels: 2§Q 271 214 22 48 90 Grade 8 Overall Percentage Correct 15% Percentage Correct for Anchor Levels: Mil Oil 242 122 1 4 28 74 Grade 12 Overall Percentage Correct: 27% Percentage Correct for Anchor Levels: M2 2E2 Sit 212 3 22 74 f THE 1990 NAEP TRIAL SIAM ASSE&MENT ' North Carolina SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priotity areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to descaibe 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 NAErs goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are basedon the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or tenitory were assessed. Virtually all statistics that are based on samples (including those in NAEP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like almost all estimates based on assessment measures, NAEP's total group and subgroup proficiency estimates are subject to a second source of uncvstainty, in addition to sampling error. As previously noted, each student who participated ;n the Trial State Assessment was administered a subset of questions from the total set cf questions. If each student had been administered a different, but equally appmpriate, set of the assessment questions -- or the entire set of questions somewhat clifferer.± 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 91 North Carolina In addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard effors 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 tenitory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population means and proportions in a manner that reflects the uncertainty associated with the sampl estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above matmer may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. 92 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina 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 haw much time do you usual& spend each day on mathematics homework? Still other subgroups are defined by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As an example, one might be interested in answering the question: Do students who reported spending 45 minutes or more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is higher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in performance between the two groups in the population because of the uncertainty associated with the estimated average proficitncy of the groups in the sample. Remember that the intent is to make a statement about the entire population, not about the particular sample that was assessed. The &la from the sample are used to make inferences about the population as a whole. As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances ofvarious 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 dyference can be used te help determine whether differences between groups in the population are real. The difference betweeo 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 colitain zero, the difference between groups is statistically significant (different) at the .05 level. THE 1990 NAEP TRIAL STATE ASSESSMENT 93 North Carolina As an example, suppose that one were interested in determining whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard errors for females and males were as follows: Group Average Proficiency Standard Error , Female 259 2.0 Male I 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 si 2.02 + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference 4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., =To is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. Whr., a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a stacistically significant difference in thc population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. The procedure described above (especially the estimation of the standard error of the difference) is. in a stnct sense, only appropriate when the statistics being compared come from independent samples. For certain comparisons in the report. the groups were not inlependent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMEN1 North Carolina The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significance is being performed. However, in each chapter of this report, many diffennt groups are being compared (i.e., multiple sets of confidence intervals are being analyzed). When one considers sets of confidence intervals, statistical theory indicates that the certainty associec-4 with the entire set of intervals is less than that attributable to each individual comparison from the set. Ifone wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain dew::: 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 procedms for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defined by race/ethnicity and type of school community, as well as by gender and parents' education level. NAFP collects data for five racial/ethnic sulwoups (White, Black, Hispanic, ksian/Pacific Islander, and American Indian/Alaskan Native) and foil; types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Conununities). 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 tu 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 reater. 100 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 North Carolina The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-gade public-school population in the state or territory, divided by the standard deviation of the proficiency in the total population. If the true diffesence between subgroup and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to dent 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 depees 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 magnkude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage Description at Text In Report , p = 0 None 0 < p 5 10 Relatively few 10 < p 5 20 Some 20 < p 5 30 About one-quarter 30 < p 5 44 Less than half 44 < p 5 55 About half 55 < p 5 69 More than half 69 < p 5. 79 About three-quarters 79 < p 5 89 Many 89 < p < 100 Almost all p = 100 All 101 96 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina NE NATION'S REPORT CARD DATA APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains corresponding data for each level of the four reporting subpopulations -- race/ethnicity, type of community, parents' education level, and gender. 102 THE I 990 NAEP TRIAL STATE ASSESSMENT 97 North Carolina TABLE A5 I Students' Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT , Eighth-grade Mathematics Pre-algebra Aigebra TOTAL ind Prodekney Paraantage and Prandency Percantege and Prallaioncy State 58 ( 1.8) 22 ( 1.4) 17 ( 1,3) 234 ( 1.1) 202 ( 1.4) 290 ( 1.3) Nation 62 ( 2.1) 19 ( 14) 15 ( 12) 251 ( 1.4) 272 ( 2.4) 200 ( 24) RACE/ETHNICITY Mite State 52 ( 2.4) 24 ( 1.8) 22 ( 1.9) 244 ( 1.4) 269 ( 1.6) 225 ( 1.3) Nation 59 ( 2.5) 21 ( 2.4) 17 ( 1.5) 259 ( 1.6) 277 ( 2.2) 300 ( 2.3) Slack State 69 ( 2.0) 18 ( 1.7) 10 ( 1.1) 223 ( 1.1) 244 ( 2.4) 271 ( 2.8) Nation 72 ( 4.7) 19 ( 3.0) 9 ( 2.2) 232 ( 3.4) 246 ( 6.4) VOID Hispanic State 78 ( 4.3) 11 ( 3.0) 4 ( 2.0) 214 ( 2.4) "44 ( Nation 75 ( 24.0 ( 4.4) 2.4) 13 ( ". 3.9) .+1 ( 1,5) .41 Amoican Indian State 83 ( 44) .1140 Nation 84 ( ** ( 5.7) 8 ( *** 7.2) ***) 5 ( 44* ( 2.7) 90,) TYPE OF COMMUNITY Advantaged urban State 28 ( 8.2) Nation 55 ( 9.4) 21 ( 4.4) 289 ( 2.5)1 **4 ( 44 Diudvantaged urban State 20 ( 2.9) ( *el Nation 85 ( 6.0) 14 ( 3.3) 240 ( 4.0)1 287 ( 4.2)1 Extreme rural State 88 ( 4.9) 15 ( 3.8) 17 ( 2.1) 232 ( 2.6) 256 ( 4.2)1 277 ( 4.3)1 Nation 74 ( 4,5) 14 ( 5.0) 249 ( 3.1)1 e" ( eeei Other State 58 ( 1.9) 23 ( 1.6) 16 ( 1.5) 236 ( 1.3) 263 ( 1,7) 292 ( 1.6) Nation 61 ( 2.2) 20 ( 2.1) 16 ( 1.4) 251 ( 2.0) 272 ( 2,8) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size i: insufficient to permit a rehable estimate (fewer than 62 students). 1 C 3 98 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE AS I Students' Reports on the Mathematics Clan (continued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY LS 1 SO NAEP TRIAL TATE ASSESSMENT _ WM-grade Malhetnatlos Pre-algebra TOTAL. Perm lage and Pro& Ism 55 ( 1.8) 234 ( 1.1) 62 ( 2.1) 251 ( 1.4) Peroantage mtd Prolkling n 14) 262 ( 1A) 19 ( 1.9)- 272 ( 2.4) Peromeage mid Profcleagy 17 ( 1.3) 290 ( 1.3) 15 ( 1.2) 290 ( 2.4) State Nation PARENTS EDUCAM NS non-graduate State 72 ( 225 ( 2.7) 1.6) 17 ( 2.5) ( 1.3) 041 Nation 77 ( 3.7) 13 ( 3.4) 3 ( 1.1) 241 ( 2.1) NS graduate State 68 ( 2.1) 20 ( 1.7) 10 ( 1.3) 231 ( 1.3) 25$ ( 2.2) 280 ( 2.9) Nation 70 ( 2.6) 18 ( 2.4) ( 1.1) 24.9 ( 1.9) 266 ( 3.5) 277 ( 5.2) Some college State 54 ( 2.7) 25 ( 2.5) 19 ( 2.1) 245 ( 2.1) 264 ( 2.3) 286 ( 2.4) Nation 60 ( 3.1) 21 ( 2,9) 15 ( 1.9) 257 ( 2.1) 2/6 ( 2,8) 295 ( 3.2) College graduate State 43 ( 2$) 26 ( 2.1) 29 ( 2.5) 241 ( 1.7) 267 ( 1.7) 296 ( 1.5) Nation 53 ( 2.7) 21 ( 2.3) 24 ( 1.7) 159 ( 1.5) 278 ( 2.8) 303 ( 2.3) GENDER Mate State 63 ( 1.9) 19 ( 1.7) 15 ( 1.4) 236 ( 14) 264 ( 2.1) 291 ( 2.0) Nation 63 ( 2.1) 18 ( 1.t) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 2.5) Female State 54 ( 2.2) 25 ( 1.7) 19 ( 14) 232 ( 1.1) 200 ( 1.4) 290 ( 1.5) Nation 61 ( 2.6) 20 ( 2,3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 24) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). o 4 THE 1990 NAEP TRIAL. STATE ASSESSMENT 99 North Carolina TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1$00 NAEP TRIAL STATE ASSESSMENT None 16 Minutes 30 Minutes 46 Minutes An Nour or More TOTAL and Prolidancy 3 ( 0.9) 218 ( 26p ( 0.3) *4.1 3 ( 1.2) ( .11 ( 0.3) ( ***) 4 ( 1.0) *44(44*) 1 ( 0.7) ( m) 6 ( 1.9) *** ( ***) 1 ( 0.8) ( "*) 0 ( 0.0) ( ***) 2 ( 2.7) ( 0.9) ( 0 ( 0.0) *44(444) 0 ( 0.0) *** ( ***) 2 ( 1.2) ( 0 ( 0.0) ( 4") 4 ( 1.2) 210 ( 2.9)1 ( e") and Proildanay 40 ( 2.3) 242 ( 1.7) 43 ( 4.2) 250 ( 2.3) 39 ( 2.9) 253 ( 1.9) 39 ( 4.5) 206 ( 2.2) 42 ( 3.7) 225 ( 1.8) 55 ( 7.8) 232 ( 3.1) 46 ( 7.8) 245 ( 3.0)1 34 (18.8) 74 (31.9) ( "") 29 (11.1) *44 ( elP4 81 (11.3) 273 ( 3.1)1 32 (17.7) 4** ( 41 (12.6) 236 ( 2.1)1 32 ( 7.9) 236 ( 5.0)1 68 (14.9) 253 ( 5.4)1 44 ( 3.1) 243 ( 1.8) 37 ( 4.3) 256 ( 3.1) and Proficiency 46 ( 2.5) 254 ( 2.1) 43 ( 4.3) 2138 ( 2.8) 48 ( 2.7) 265 ( 2.3) 45 ( 5.1) 270 ( 2.7) 44 ( 3.4) 236 ( 2.3) 40 ( 6.7) 248 ( 5.3) 47 ( 5.6) 34 ( 6.8) 251 ( 4.2)1 53 (19.2) *4* ( 4.4 22 (28.2) 444 ( 4+4) 50 (17.4) 32 ( 11.6) .14.) 42 (15.4) *44(4*4) 38 ( 9.4) 253 ( 9.0)1 55 ( 8.4) 245 ( 3.5)1 14 (10.9) *b. ( 43 ( 2.7) 258 ( 2.5) 49 ( 5.1) 265 ( 2.5) and Proficiency 8 ( 1.5) 271 ( 5.4) 10 ( 1.9) 272 ( 5.7)1 9 ( 1.8) 2111 ( 5.0)1 11 ( 2.4) 277 ( 7.8)1 8 ( 1.8) 246 ( 7.0)1 3 ( 1.2) *** 441 2 ( 1.4) 13 ( 2.9) ( 4.3) 0114 4** ) 0 ( 0.0) 11-114 ( 13 ( 5.7) 5 ( 3.4) 14 ( 8.8) *44(44.) 12 ( 5.9) *** ( 8 ( 2.8) 8 ( 5.6) ( *In 8 ( 1.9) 273 ( 8.8)1 10 ( 2.4) 278 ( 8.6)1 and Prolidancy 3 ( 02) 284 ( 8.0)1 4 ( 0.0) 278 ( 5.1)1 3 ( 0.9) IV* ( 4 ( 0.9) 279 ( 5.8)1 2 0.9) 04, *an 2 ( 0.8) ( 3 ( 1.1) ( 2.1) **** ( 1 ( 1.3) .**) 4 ( 4.8) 5 ( 5.8) 0 ( 0.0) *44(44* 12 ( 9.3) 10 ( 8.2) ( 3 ( 1.7) IN** ( **IV ) 1 0 ( 7.3) 441 2 ( 0.7) 4,4 ( 14.) 4 ( 1.1) 282 (11.8)1 State Nation RACEIETHNICITY WM, State Nation Black State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Advantaged trban State Nation Oisadvcntagod urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the 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 North Carolina TABLE A6 (continued) Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO SUP TRIAL STATE ASSESSMENT None 15 Mit nutes 30 Allnues 45 Mi nutes An Hour or Mare TOTAL Percentage and Proldency Percentage and Proldency Percentage and PreNaleacy Percentage and Prat/dem Percentage and Proadoncy State 3 ( 0.9) 40 ( 2.8) 48 ( 2.5) 8 ( 1.5) 3 ( 0.7) 218 ( 2.8)/ 242 ( 1.7) 254 ( 2.1) 271 ( 5.4) 264 ( 0.0)1 Nation 1 ( 0.3) ye. r 44-41 43 ( 256 ( 42) 2.3) 43 ( 266 ( 4.3) 2.6) 10 ( 1.9) 272 ( 5.7)1 4 ( 276 ( 0.9) 5.131 PARENTS' EDUCATION HS non-graduate State 6 ( 2.6) 43 ( 42) 44 ( 4.3) 8 ( 1.7) ( 0.6) RI* ( MIR) 228 ( 1.8) 236 ( 2.6) r Nation ( 0.8) 49 ( 8.3) 40 ( 8.1) 6 ( 1.7) 4 ( 1.3) 240 ( 2.8) 248 ( 31) *** ( ".) HS graduate State ( 1.3) r4+1 4$ ( 238 ( 3.6) 1.9) 43 ( 244 ( 3.3) 2.3) 6 ( 1.8) r ( 0.4) Nation ( OS) 43 ( 249 ( 5.2) 3.1) 44 ( 258 ( 5.8) 2.7) 9 ( 3.1) 01.4 3 ( .44 r 1.0) Some college State ( 0.7) 37 ( 3.1) 48 ( 3.0) ( 251 ( 2.6) 260 ( 2.4) "*. ( Nation I ( 0.9) ( **) 44 ( 285 ( 5.4) 2.6) V 43 ( 270 ( 5.8) 3.6) 7 ( 2.1) 4 ( *v. 1.0) College graduate State 2 ( 0-5) 34 ( 2.7) 48 ( 2.8) 11 ( 1.7) ( 253 ( 2.9) 269 ( 2.8) 279 ( 5.9) ) Nation 0 ( 0.3) 40 ( 4.7) 44 ( 4.1) 11 ( 2.3) ( 265 ( 2.5) 277 ( 3.0) 287 ( 6.1)1 ( GENDER Male State 3 ( 0.9) *gm. 43 ( 244 ( 3.0) 2.2) 45 ( 253 ( 2.9) 2.4) 7 ( 1.5) 271 ( 5.7)1 2 ( 0.4) Nation 1 ( 0.3) 44 ( 4.4) 43 ( 4.3) 9 ( 1.9) 5 ( 1.3) 257 ( 2.9) 268 ( 2.9) 273 ( 7.3)1 279 7.7)1 SIMI* State 3 ( 1.1) *** ( ) 37 ( 240 ( 3.0) 1.8) 46 ( 254 ( 2.7) 2.2) 9 ( 1.8) 271 ( 6.3)1 4 ( 1.0) Nation 41 ( 4.4) 43 ( 4.7) 11 ( 2.0) 4 ( 0.9) 255 ( 2.3) 264 ( 2.8) 272 ( 5.7)1 ( ".1 sa The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value 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 (2 students). tOG THE 1990 NAEP TRIAL STATE ASSESSMENT 101 North Carolina TABLE A7 I Students' Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1690 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes An Hour or More TOTAL Percentage and Pre Salem Pettentage and prosakety Percentage and prockinvi Percentage and prahdency Percentage and Pradoiena State 9 ( 0.7) 29( 1.1) 33 ( 0.9) 17 ( 02) 13 ( 02) 239 ( 2.4) 250 ( 14) 254 ( 1,4) 250 ( 2.1) 249 ( 2.1) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 12) 18 ( 1.0) 12 ( 1.1) 251 ( 2.8) 284 ( 1.9) 263 ( 1.9) 268 ( 1.9) 258 ( 3.1) RACVETHNICITY White State 9 ( 1.0) 30 ( 12) 34 ( 1.1) 10( 1.1) 12 ( 0.9) 249 ( 2.5) 250 ( 1.9) 268 ( 1.13) 264 ( 2.7) 262 ( 2.5) Nation 10 ( 1.0) S3 ( 2.4) 32 ( 1.3) 15 ( 0.9) 11 ( 1.3) 259 ( SA) 2TO ( 12) 270 ( 2.1) 277 ( 2.2) 263 ( 3.3) Iliadc State 9 ( 0.9) 26 ( 1.8) 34 ( 15) 17 ( 1.4) 14 ( 1.5) 222 ( 4.3) 232 ( 2.0) 235 ( 1.7) 232 ( 3.3) 231 ( 2.7) Nation 7 ( .4.00 ( 1.5) *41 26 ( 241 ( 2.5) 3.8) 33 ( 237 ( 2.7) 3.5) 18 ( 240 ( 2.3) 3.6) 16 ( 232 ( 1.9) 3.7) Hispanic State 10 ( ( 3.0) 0+1 24 ( 4.7) 27 ( *0* 4.1) 24 ( 4.4) 15 ( 3.7) Nation 12 ( 1.4) ***) 27 ( 246 ( 3.0) 3.6) 30 ( 248 ( 2.6) 3.4) 17 ( 241 ( 2.1) 4.3) 14 ( 1.7) American Indian State 12 ( 52 ) 26 ( 9.7) 24 ( 5.6) 1$ ( 4.7) 04* ( 4+1 *00(0*4) ( Nation 13 ( 5.3) «br.) 30 (10.0) 0*0(04*) 27 ( 04 ( 6.7) 24 (14.2) 00* ( eirt 6 ( 6.4) ( al TYPE OF COMMUNITY Ao`vantaged urban State 4 ( 0.9) 31 ( 4.6) 36 ( 2.5) 9 ( 2.6) Nation ( 2.5) 41 (12.5) 31 ( 6.6) 12 ( 3.3) 7 ( 3,4) 27$ ( 3.0); 280 ( 4.6)1 Disadvantaged State 7 ( 3.0) *v.) 31 ( 25) 23 ( 1.1) 4.4) 22 ( ( 7.7) Nation 12 ( ***. 3.7) 24 ( 253 ( 3.3) 4.9)1 31 ( 247 ( 3.0) 4.7)1 20 ( 250 ( 1-9) 4.8)i 14 ( 2.2) ***) Extreme rural State 6 ( 0.9) 26 ( 2.4) 36 ( 22) 19( 2.1) 13 ( 2.2) 245 ( 3.3)1 247 ( 2.6)1 240 ( 6.0)! 240 ( 4.0)1 Nation 8 ( 2.3) 38 ( 4.6) 31 ( 2.9) 18 ( 3.8) ( 2.7) 260 ( 3.5)! 255 ( 5.1)1 Other State 10 ( 1.0) 28 ( 1.4) 33 ( 1.0) 16 ( 0.9) 42 ( 0.8) 242 ( 2.7) 250 ( 1.7) 255 ( 1.6) 251 ( 2.6) 251 ( 2.3) Nation 9 ( 1.0) 30 ( 1.8) 32 ( 1.3) 15 ( 1.1) 13 ( 1.1) 250 ( 3.8) 283 ( 2.3) 264 ( 2.3) 267 ( 2.1) 258 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within i 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). 1C7 102 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A7 Students' Reports on the Amount of Time They (continued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes An Hour or Mora TOTAL Percentage and Praliciam Percentage and Preedincy Percentage and Prolidam Peroentage and Pronclancy Partentage and Prondency State 9 ( 0.7) 29 ( 1.1) 33 ( 0.9) 17 ( 0.8) 13 ( 0.6) 239 ( 2.4) 250 ( 1A) 254 ( 1.4) 250 ( 2.1) 249 ( 2.1) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 18 ( 1.0) 12 ( 1.1) 251 ( 2.8) 264 ( 1.9) 263 ( 1.9) 266 ( 1.9) 254 ( 3.1) PARENTS EDUCATION NS non-graduats State 15 ( 2.1) 29 230 ( 2.1) ( 3.1) 33 ( 234 ( 2.4) 2.4) 15 ( 2.0) 8 ( 1.3) «al Nation 17 ( 3.0) **or voip) 26 246 ( 3.3) ( 4.0) 34 ( 246 ( 4.4) 2.6) 12 ( 4 ( 2.5) 0.1 10 ( *** ( 2.2) HS graduate State 9 ( 1.1) 31 ( 1.5) 32 ( 1.3) 18 ( 1.1) 1 1 ( 1.2) 239 ( 3.9) 24$ ( 1.8) 243 ( 2.2) 239 ( 3.1) 241 ( 3.5) Nation 10 ( 1.7) 33 ( 2.2) 31 ( 1.9) 10 ( 1.4) 11 ( 1.5) 248 ( 4.2) 259 ( 3.2) 254 ( 2.4) 256 ( 2.8) 244 ( 3.4) Some cogege State 9 ( 1.4) 27 ( 2.1) 35 ( 2.5) 16 ( 1.6) 14 ( 1.7 258 ( 2.6) 262 ( 2.2) 258 ( 3.5) 259 ( 4.3 Nation 9 ( 1.2) 30 ( 2.7) 36 ( 2.1) 14 ( 1.8) 11 ( 1.5 444 414-1 288 ( 3.0) 268 ( 2.6) 274 ( 3.5) 41 *** Collage graduate State $ ( 0.8) 26 ( 1.6) 35 ( 1.7) 13 ( 1.4) 15 1.6 *41 282 ( 2.1) 269 ( 2.5) 265 ( 3.1) 261 ( 3.5) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 26$ ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.3) GENDER Mal* State 11 ( 0.9) 31 ( 1.6) 32 ( 1.3) 16 ( 1.0) 11 ( 1.0) 242 ( 3.0) 251 ( 1.7) 254 ( 1.9) 250 ( 2.6) 245 ( 3.1) 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) 285 ( 3.0) 258 ( 4.1) Female State 6 ( 0.8) 27 ( 1.3) 35 ( 1.5) 18 ( 1.3) 14 ( 1.1) 234 ( 2.7) 24.8 ( 2.0) 254 ( 1.6) 251 ( 2.6) 253 ( 2.4) Nation 7 ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 246 ( 4.1) 263 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 S THE 1990 NAEP TRIAL STATE ASSESSMENT 103 North Carolina TABLE AS I Teachers' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT Numbers and Operations M.a.irsms Oarameby Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy EmphasJ Little or No Emphasis- TOT1L Peeventage and Praacioncy Percentage and Madam State 49 ( 2.7) 14 ( 1.7) 2443 ( 1.4) 287 ( 2.9) Nation 49 ( 3.8) 15 ( 2.1) 280 ( 1.8) 287 ( 3.4) RACE/ETNNICITY *tilt State 44 ( 3.2) 18 ( 2.3) 255 ( 1.7) 292 ( 2.7) Nation 4$ ( 3.7) 16 ( 2.4) 287 ( 2.2) 289 ( 3.5) Black Stat.s 56 ( 3.1) 9 ( 1.8) 234 ( 2.0) 207 ( 4.6)1 Nation 54 t 7,9) 11 ( 3.3) 243 ( 4.3) *** ( "") Hispanic State 61 ( 8.3) 7 ( 2.3) 221 ( 4.0) ( *") Nation 47 ( 8.7) 8 ( 2.2) 248 ( 44.8) ( "") American Indian State 75 (10.8) 0 ( 0.0) *I* ( *IN ) VI* ( Nation 84 (18.5) 441 6 ( 6.9) TYPE OF COMMUNITY Advantaged urban State 42 ( 9.6) 40 ( 8.1) Mir ( 1111P1 ( Off ) NatiOn 28 (13.0) 04. ***) 16 ( 4.2) voro) Dludvantaged urban State 54 (19.2) .44 ( 16 ( 4** 7.3) Nation 48 (12.1) 9 ( 4.0) 255 ( 6.3)1 *" ( "11) Extreme rural State 57 ( 8.9) 6 ( 2.3) 246 ( 3.2)1 ( "") Nation 53 (12.4) 6 ( 3.6) 257 ( 7.1)1 41Nri Other State 47 ( 3.1) 15 ( 2,2) 246 ( 1.7) 285 ( 3.2) Nation 52 ( 4.1) 16 ( 2.7) 280 ( 2.3) 266 ( 3.6) Percentage Pemataga Pareantafe Ponantap and and and and Pro kidney Pro edam, Pneacaancy Poidiciancy 1 17 2.3) 31 ( 2.7 17 29 ( 228 32) 255 ( 3.0 254 2.5 253 ( 2.6 17 3.0) 3$ ( 4.0 2$ 3.$ 21 ( 3.3 250 ( 5.6) 272 ( 4.0 200 3.2) 264 ( 5.4) 13 ( 2.6) 34 ( 3.3) 18 ( 2.8 ) 30 ( 3.2) 245 ( 3.0) 285 ( 3.4) 283 ( 2.7 ) 282 ( 34) 14 ( 3.4) 36 ( 4,7) 27 ( 44 ) 22 ( 34) 259 ( top 277 ( 4.3) 265 ( 3.3) 273 ( 5.8) 24 ( 3.2) 27 ( 3.0) 16 ( 2.8) 29 ( 34) 212 ( 3.5) 231 ( 3.7) 239 ( 2.9) 236 ( 2.9) 25 ( 7.4) 23 ( 5.7) 33 ( 7.9) 24 ( 7.3) 228 ( 2.8)1 238 ( 8.1)1 242 ( 5.8y 233 ( 4.7$ 24 ( 4.3) 23 ( 5.1) 13 ( 3.9) 24 ( 4.3) ( "") "fli 14. ( ( 23 ( 4.1) 34 ( 5.8) 27 ( 6.8) 16 ( 5.5) *** ( ***) 255 ( 4.4)I ( '") *4" ( `") 17 ( 6.9) 13 ( 7.2) 13 ( 8.2) 18 (11.3) **a ( 444.) **49,) 44. ( *4) 7 ( 8.7) 13 (155) 18 (19.7) 8 (10.4) 4,44,) ( *in 8 ( 5.2) 38 (12.5) 14 (15.3) 27 (11.4) *** 114.11) 4N4 4.1 Ire* ( ***) (11M1 9 ( 7.0) 40 ( 8.5) 36 ( 9.4) 13 ( 3.2) ( awe) 287 ( 4.9)1 ***) 36 (20.4) 37 (17.0) 23 (12.9) 18 (12.4) 44* ( Mira (On *Olt (Hit) IIP4N 39 (10.3) 21 ( 6.5) 33 (11.8) 18 ( 7.8) 238 ( 8.4)1 ( 4+1 248 ( 8.2)1 "4' ( *I") 34 ( 7.4) 13 ( 5.4) 19 ( 4.9) 13 ( 4.1) 226 ( 4.1)1 ** ( ***) 251 ( 5.8)1 251 ( asp 6 ( 4.9) 32 (11.7) 9 ( 6.1) 16 ( 7.9) Olt* 285 ( 0.9 11%04. 12 ( 2.3) 34 ( 3.4) 47 ( 2.9) 34 ( 3.3) 234 ( 3.8)1 253 ( 3.1) 253 ( 2.7) 252 ( 3.0) 18 ( 3.9) 34 ( 5.3) 28 ( 4.8) 24 ( 4.3) 253 ( 7.1$ 270 ( 4.8) 260 ( 3.9) 205 ( 5.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. 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). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A8 I Teachers' Reports on the Emphasis Given to (continued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 /MEP TRIAL STATE ASSESSMENT Numbers and Operations Heavy Empb. sis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Empbasis TOTAL Percentage end Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proliciency Percentage and Proliciancy State 49 ( 2.7) 14 ( 1.7) 17 ( 2.3) 31 ( 2.1) 17 ( 2.4) 29 ( 2.7) 246 ( 1.4) 287 ( 2.9) 228 ( 3.2) 255 ( 3.0) 254 ( 25) 253 ( 2.8) Nation 49 ( 3.0) 15 ( 2.1) 47 ( 3.0) 33 ( 4.0) 28 ( 3.8) 21 ( 3.3) 280 ( 1.8) 287 ( 3.4) 250 ( 5.6) 272 ( 4.0) 280 ( 3.2) 264 ( 5.4) PARENTS EDUCATION HS non-graduate State ( 238 ( 4.7) 25) 44. ( 17 ( Itiff 2.8) 29 ( 229 ( 4.0) 3.9) 19 ( 3.0) ***) 27 ( 232 ( 3.9) 3.7) Nation graduato 80 ( 251 ( 6.9) 3.4) ( 2.3) 22 ( 5.3) 25 ( 5.3) ***) 32 ( 6.3) 20 ( se. ( 6.7) .41 State 54 ( 3.4) 8 ( 1.6) 19 ( 2.9) 27 ( 3.1) 17 ( 2.8) 27 ( 3.0) 241 ( 1.8) 271 ( 4.4)1 221 ( 4.7) 240 ( 3.4) 247 ( 2.8) 240 ( 2.8) Nation 55 ( 259 ( 4.8) 2.9) 11 ( 04 2.8) **4) 17 ( 251 ( 3.9) 6.1)1 27 ( 253 ( 5.0) 4.7)1 27 ( 2SS ( 4.5) 4.2) 24 ( 24$ ( 5.1) 4.8)1 Some collage State 48 ( 3.5) 18 ( 2.3) 16( 3,1) 33 ( 3.5) 19 ( 3.5) 27 ( 3.4) 256 ( 2.8) 282 ( 4.2) 243 ( 3.5) 259 ( 3.9) 259 ( 4.7) 2eo ( 4.2) Nation 47 ( 4.4) 17 ( 3.3) 39 ( 5.5) 27 ( 5.0) 23 ( 4.1) 265 ( 2.6) 284 ( 4.1)1 279 ( 4.5) 282 ( 4.8)I 270 ( 4.7) Collage graduate State 40 ( 3.1) 23 ( 3.2) 15 ( 2.3) 35 ( 3.7) 17 ( 2.8) 31 ( 3.8) 253 ( 2.3) 296 ( 3.0) 235 ( 4.5) 274 ( 3.7) 262 ( 3.1) 271 ( 3.8) Nation 44 ( 4.1) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 289 ( 2.8) 296 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 8,4) GENDER Mak) State 52 ( 2.8) 12 ( 1,5) 16 ( 22) 30 ( 2.8) 16 ( 2.7) 29 ( 3.0) 246 ( 1.8) 284 ( 3$) 231 ( 3.8) 25$ ( 3.3) 257 ( 2.9) 251 ( 3.1) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 281 ( 2.5) 287 ( 4.4) 258 ( 6.7) 275 ( 4.8) 263 ( 3.8) 2ee ( 8.8) Female State 46 ( 3.0) 16 ( 2.1) 18 ( 2.7) 32 ( 3.0) 19 ( 2$) 29 ( 2.7) 246 ( 1.7) 28$ ( 3.4) 226 ( 3.7) 254 ( 3.4) 251 ( 2.9) 255 ( 3.3) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 35) 260 ( 2.0) 288 ( 3.3) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 263 ( 5.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent bevause the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 105 North Carolina TABLE A8 I Teachers' Reports on the Emphasis Given To (mntinued) I Specific Mathematics Content Areas PERCF 1TAGE OF STUDENTS AND AVERAGt. MATHEMATICS PROFICIENCY 10110 NAEP TRIAL STATE ASSESSMENT Data AiWysis, Statistics, and ProbabilitY Algebra and Functions Little or No Heavy Emphasis Little or No Emphasis TOTAL Percentage and Proficiency 13 ( 2.2) 251 ( 4,0) 14 ( 2.2) 2d9 ( 4.3) 12 ( 2.3) 270 ( 4.0) 14 ( 2.4) 276 ( 4.1) 18 ( 3.0) 227 ( 3.8) 14 ( 3.4) 10 ( 3.5) 15 ( 4.1) 13 ( 6.5) 44r* ( *41 15 (12.4) 1 1 ( 6.6) 44/4 2 ( 2.3) 19 ( 9.4) 0-0, 20 ( 5.4) 244 ( 9.3)1 5 ( 5.4) 4,4. 12 ( 2.5) 253 ( 4.3)1 15 ( 2.9) 287 ( 4.7) Percentage and Preliciency 00 ( 3.0) 247 ( 1.9) 53 ( 4.4) 261 ( 2.9) 84 ( 3,5) 261 ( 2.4) 53 ( 5.0) 271 ( 3.1) 53 ( 3.4) 222 ( 2.0) 53 ( 82) 225 ( 4.3) 00 ( 4.9) 206 ( 5.8) 58 ( 8.3) 246 ( 4.4) $2 (29.i) ( ***) 47 ( 8.2) 44- ( *44 ) 65 (19.4) 284 ( 7.4)1 55 (11.9) 34 (11.4) 238 ( 8.2)1 54 ( 7.0) 240 ( 43)1 65 (16.9) 254 ( 6.7)1 63 ( 3.6) 24$ ( 2.3) 53 ( 5.2) 260 ( 3.4) Percentage and Proficiency 44 273 46 275 49 281 48 261 35 253 39 253 28 4ti( 257 *** 16 70 288 41 296 33 53 254 45 259 42 275 47 276 2.6) 1.8) ( 3.6) ( 2.5) ( 3.2) ( 1.7) ( 4.2) ( 3.0) ( 3.0) ( 2.6) ( 7.1) ( 6.3) ( 5.4) 5.9) ( 4.0)1 (21.5) ( ( 8-5) ( 7.8)1 ( 8.9) ( 7.9)1 (12.7) (11.8) ( 8.3)1 ( 8.0) ( 4.2)1 «4.) ( 2.8) ( 2.1) ( 4.3) ( 2.8) Percentage and Proficiency 26 ( 23) 227 ( 1,7) 20 ( 3.0) 243 ( 3.0) 25 ( 2.7) 237 ( 22) 18 ( 2.6) 251 ( 3.3) 32 ( 2.6) 215 ( 2.1) 27 ( 0.9) 226 ( 22)1 43 ( 8.2) ( 18 ( 4.2) 444, 441 *** 67 (51.6) .4.4) 18 ( 5.3) ( 4-641 37 (24.2) *** *4 27 ( 5.3) 223 ( 4.1)1 42 (18.0) 241 ( 5.9)1 29 ( 2.8) 228 ( 1.9) 17 ( 3.3) 245 4.4)1 State Nation RACEiETHNICITY Mgt. State Nation Wadi State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *4" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 1 1, 10 6 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A8 I Teachers' Reports on the Emphasis Given To (continued) Specific Mathematics Content Areas PERCV4TAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 ?MEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability -. Algebra and Functions Heavy Emphasis Little or No Emphasis Em Heavy phasis _ Little or No Emphasis TOTAL Pereentega and Pro& lancy Percentage and Proadancy Percentage and Proito lona Percentage and Volk:Nona State 13 ( 2.2) 00 ( 3.0) 44 ( 2.8) 28 ( 2.3) 251 ( 4.0) 247 ( 1.9) 273 ( 1.3) 227 ( 1.7) Nation 14 ( 2.2) 53 ( 4A) 48 ( 20 ( 3.0) 209 ( 4.3) 201 ( 2.9) 275 2.5) 243 ( 3.0) PARENTS' EDUCATION HS non-graduata State 14 ( 3.1) 62 ( 4.1) 34 ( 4.4) 34 ( 4.4) *44 ( *01 223 ( 3.0) 250 ( 4.1) 218 ( 3.6) Nation ( 3.0) 53 ( 240 ( 7.7) 6.2) 2$ ( .44 5.2)) 29 ( 1111* 6.9) ItS vacbtata State 13 ( 2.4) 60 ( 2.8) 35 ( 2.9) 34 ( 3.0) 239 ( 6.3) 235 ( 2.2) 263 ( 2.3) 227 ( 2.5) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 261 ( 6.0)1 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Solna collage State 17 ( 3.3) 57 ( 4.2) 51 ( 3.8) 22 ( 2.8) 261 ( 5.7) 261 ( 2.9) 273 ( 2.5) 218 ( 4.0) Nation 13 ( 2$) 57 ( Si) 48 ( 4.8) 17 ( 3.1) 270 ( 3.7) 278 ( 3.0) *Maw graduat State 13 ( 2.5) 59 ( 3.6) 57 ( 2.6) 19 ( 1.9) 262 ( 4.8) 266 ( 3.1) 284 ( 2.0) 232 ( 2.6) Nation 15 ( 2.4) 53 ( 4.4) SO ( 3.9) 18 ( 2.4) 262 ( 4.5) 275 ( 3.6) 288 ( 3.0) 249 ( 4.0) GENDER Male State 12 ( 2.3) 62 ( 3.1) 40 ( 2.9) 30 ( 2.6) 251 ( 4.9) 247 ( 2.3) 271 ( 2.3) 226 ( 1.9) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.6) 275 ( 5.8) 200 ( 3.5) 278 ( 3.2) 243 ( 3.0) Female State 15 ( 2.4) 58 ( 32) 4$ ( 2.9) 25 ( 2.4) 251 ( 4.6) 247 ( 2.2) 274 ( 2.1) 229 ( 2.5) Nation 16 ( 2,4) 53 ( 4.5) 46 ( 3.6) 18 ( 2.9) 283 ( 4.4) 262 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution - the nature ot 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 North Carotin': TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 11103 NAEP TRIAL 1 Clet All the Resources 1 1 001 Most o1 the 1 Gel Some or None of STATE ASSESSMENT Need Resources 1 Need the Resources 1 Need TOTAL Pesventage and Proficiency Percentage and Proficiency Percentage arid Pronciency State 19 ( 2.8) 45 ( 3.6) 38 ( 3.3) 259 ( 2.2) 252 ( 1.5) 243 ( 2.0) Nation 13 ( 2.4) 56 ( 4.0) 31 ( 4.2) 285 ( 4.2) 285 ( 2.0) 261 ( 2.9) RACE/ETHNICITY White State 22 ( 3.5) ( 4.0) 29( 3.5) 288 ( 2.3) 261 ( 1.7) 258 ( 2.2) Nation 11 ( 2.5) ( 4.6) 30 ( 4.6) eladc 275 ( 3.5)1 270 ( 2.3) 267 ( 3.3) State 14 ( 2.2) 37 ( 4.0) 50 ( 4.1) 238 ( 2.9) 233 ( 1.8) 229 ( 1.8) Nation 15 ( 4.2) 52 ( 8.8) 33 ( 7.2) 241 ( 5.3)1 242 ( 2.4) 236 ( 4.9) Hispanic State 45 ( 6.0) Mr* ( *41 Nation 23 ( 7.6) 44 ( 4.9) 34 ( 7.7) 246 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 American Indian State 10 ( 8.2) 83 (18.1) 27 (12.9) V** Rie Nation /NM ( 72 (28.8) **a ( its ) 22 (20.7) TYPE Of COMMUNITY Advantaged urban State 22 (24.9) 48 (15.4) 32 (11.4) 44 ( *41 Nation 38 ( 9.2) 272 ( 8.5)1 59 ( 8.9) 286 ( 1.3)1 3 ( 3.1) **el Disadvantaged urban State 36 (20A) 21 ( 8.0) 43 (27.9) 11.1111 1,141 IP** ( Nation 10 ( 8.8) G.* 40 (13.1) 251 ( 5.4)I 50 (14.5) 253 ( 53)1 Extreme rural State 13 ( 4.6) 36 ( 9.3) 51 (10.0) 256 ( 9.3)1 250 ( 4.3)1 236 ( 2.1)1 Nation 2 ( 2.6) ...) 54 (10.4) 260 ( 8.3)1 43 (10.3) 257 ( 5.0)1 Other State 19 ( 3.3) 48 ( 4.1) 33 ( 3.8) 257 ( 19) 252 ( 1.6) 247 ( 2.4) Nation 11 ( 2.9) $8 ( 5.4) 31 ( 5.8) 265 ( 3.9)1 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 108 1 t) THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A9 I Teachers' Reports on the Availability of (continued) I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL 1 Gat AM the Resources 1 1 Gat Most of !ha I Oat Soma or Nona of STATE ASSESSMENT hood Resources I Need ths Resources I hood TOTAL Parominga md Praddency 19 ( 2.8) 258 ( 2.2) 13 ( 2.4) 285 ( 4.2) Perandage Percentage and and Pralkianqf Pralialencat 45 ( 2.8) $e ( 3.3) 252 ( 1.5) 243 ( 2.0) 58 ( 4.0) 31 ( 4.2) 2es ( 2.0) 281 ( 2.9) State Nation PARENTS EDUCATION NS non-graduate State 21 ( 3.9) 41 ( 4.7 39 ( 4.2) 238 ( 3.5) 233 ( 2.7) 229 ( 2.4) Nation ( dolt ( 2.8) 54 ( 244 ( 5.7) 2.7) 38 ( 243 ( 8.3) 35)1 1113 graduate State 20 ( 3.0) 43 ( 3.9) 38 ( 3.4) 250 ( 3.0) 243 ( 1.8) 230 ( 2.4) Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.9) 253 ( 4.6)1 250 ( 1.9) 258 ( 21) Soma collov State 18 ( 32) 48 ( 4.4) 36 ( 4.1) 270 ( 2.6) 258 ( 2.4) 253 ( 2.4) Nation 13 ( 3.3) van 82 ( 289 ( 4.3) 2.5) 25 ( 267 ( 4.1) 3.8) Cattalo graduate State 19 ( 3.2) 48 ( 4,2) 33 ( 3.9) 274 ( 3.3) 286 ( 2.1) 255 ( 3.0) Nation 15 ( 2.9) 50 ( 4.9) 30 ( 5.1) 276 ( 5.4)1 276 ( 2.2) 273 ( 3.7) GENDER State 19 ( 2.6) 44 ( 3.6) 37 ( 3.4) 257 ( 2.3) 253 ( 1.9) 243 ( 2.1) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4.0) 264 ( 5.0)1 265 ( 2.0) 264 ( 3.3) Female State 10 ( 2.9) 48 ( 3.0) 35 ( 3.5) 282 ( 2.6) 251 ( 1,0) 243 ( 2.3) Nation 13 ( 2.4) 55 ( 4,4) 32 ( 4.7) 260 ( 3.9) 284 ( 2.0) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the 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 ntimate (fewer than 62 students). 1 1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 North Carolina TABLE Al Oa I Teachers' Reports on the Frequency of Small 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 !MEP TRIAL. STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never - TOTAL Percentage and Proficiency 45 ( 3.6) 247 ( 1.9) 50 ( 4.4) 280 ( 2.2) 41 ( 4.0) 2eo ( 2.1) 49 ( 4.6) 265 ( 2.7) 52 ( 4.3) 229 ( 1.8) 47 ( 8.1) 240 ( 3.4) 52 ( 5.7) 220 ( 4.3) 64 ( 72) 246 ( 2.5) 64 (15.4) 14 (243) *v. ( 34 (11,6) 39 (22.9) IN* ( 71 (14.4) 244 (10.0)1 70(11.7) 248 ( 4.8)1 53 ( 8.8) 23$ ( 3.7)1 35 (14.6) 255 ( 5.5)1 42 ( 4.0) 249 ( 2.3) 50 ( 4.4) 280 ( 2.4) Percentage and Proficiency 44 ( 3.4) 255 ( 1.9) 43 ( 4.1) 244 ( 2.3) 48 ( 3.8) 264 ( 22) 43 ( 4$) 271 ( 22) 39 ( 3.9) 235 ( 2.1) 45 ( 7.0) 238 ( 4,0) 37 ( 8.2) 32 ( 8.9) 247 ( 8.3)1 25 (12.9) MO* ( 011 80 (27.2) .44 ..**) 58 (12.9) ( *44) 41 (17.9) 273 ( 8.0)1 29 (14.4) 21 ( 9.0) 249 ( 8.7)1 34 ( 8.0) 253 ( 54)1 58 (17.1) 258 ( 5.9)! 47 ( 3.8) 254 ( 22) 44 ( 4.5) 264 ( 2.8) Percentage and Proficiency 11 ( 1.8) 247 ( 3.4) 8 ( 2.0) 277 ( 5.4)1 11 ( 2.1) 256 ( 3.7) 8 ( 2.3) 285 ( 4.9)1 9 ( 1.9) 230 ( 4.3) 9 ( 4.1) ** f" 12 ( 3.1) ( 041 4 ( 1.4) ( *el 12 ( 5.9) 4,-** ( *IN% 9 ( 7,5) 444 ( 1) 20 (12.2) ( *1,1 I** MI* ) 9 ( 8.5) 13 ( 4.2) HI* 4.0 9 ( 9.6) .11 11 ( 2.4) 244 ( 4.5)1 ( 1.8) 277 ( 8.3)1 State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Advantaged 'titan State Nation Disadvantaged urban State Nation Wren,. rivet State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *1* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I 5 110 THE 1990 NAEP TRIAI TATE ASSESSMENT North Carolina TABLE A 10a I Teachers' Reports on the Frequency of Small (continued) i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ...1.11M11=141 1.110 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a week Never TOTAL Preiciancy Pen:MOP and Residency Penssidalle eiW Preldency State 511.9i 44 ( 3.4) 11 ( 1.8) 24745 255 ( 1.9) 247 ( 3A) Nation 50 ( 44) 43 ( 4.1) 8 ( 2.0) 280 ( 2.2) 204 ( 2.3) 277 ( 5.4)1 PARENTS EDUCATION NS non-graduate State 49 ( 5.3) 30 ( 4.9) 12 ( 2.6) 230 ( 2.9) 235 ( 2.6) Nation 00 ( 244 ( 8.4) 3.2) 39 ( 244 ( 8.5) 3.2)1 ( 1.4) .441 HS graduate State 44 ( 4.1) 45 ( 4.1) 11 ( 2.0) 239 ( 4.0) Nation 49 ( 4.6) 45 ( 5.1) 8 ( 2.5) Vi Sem college State 48 ( 42) 44 ( 4.4) .4.e) Nation 51 ( 5.2) 42 ( 5.1) 7 ( 2.3) College graduate State 44 ( 4.0) 48 ( 3.4) 10 ( 2.0) 281 ( 2.6) 269 ( 2.9) 258 ( 4.9) Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 278 ( 3.0) 215 ( 4.9)1 GENDER Mats State 45 ( 3.7) 44 ( 3.6) 11 ( 1.8) 247 ( 2.3) 253 ( 2.3) 24$ ( 3.7) Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 265 ( 3.1) 278 ( 5.3)1 Forma* State 45 ( 3.9) 44 ( 3.6) 10 ( 2.0) 248 ( 2.1) 258 ( 2.1) 246 ( 3.8) Nation 50 ( 47) 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT 111 North Carolina TABLE AlOb I Teachers' Reports on the Use of Mathematical Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Loss Than Once a Week hover TOTAL Percentage and Prelateacy 29 ( 32) 245 ( 22) 22 ( 3.1) 254 ( 3.2) 26 ( 3.6) 257 ( 2.4) 17 ( 4.0) 261 ( 3.8)1 34 ( 16) 230 ( 2.7) 22 ( 5.9) 233 ( sinf 34 ( 6.6) *41 39 ( 7.5) 247 ( 3.8) 29 (12.9) ***) 78 (34.6) Mr* ( 1111 15 ( 5.1) 23 (14.4) gm/ 98 (15.6) 39 (11.4) 247 ( 7.5)1 25 ( 7.9) 241 ( 2,5)1 27 (14.9) **,.) 29 ( 3.6) 248 ( 2.9) 19 ( 4.3) 253 ( 3.9)1 Peraintaga end Prelkdaney $3 ( 3.5) 250 ( 15) Oa ( 3.9) 263 ( 1.9) 65 ( 3.9) ( 2.0) 72 ( 42) 260 ( 2.1) 58 ( 3.9) 231 (. 1.3) 70 ( 8.3) 241 ( 2.9) 60 ( 7.0) 221 ( 2.8) 55 ( 7.3) 24$ ( 3.8)! 62 (16.R) ( 4440 ) 22 (34.6) .44) 84 ( 5.6) 278 ( 5.6)1 63 (11.5) 278 ( 5,6)1 84 (15.6) 11414t 59 (12.1) 253 ( 7.0)1 87 ( 8,3) 244 ( 2.4)1 65 (14.6) 262 ( 2.8)1 ( 3.7) 250 ( 1.7) 72 ( 5.0) 263 ( 22) Percentage and Prcectency 9 ( 1i) 267 ( 5.4)1 9 ( 2.6) 282 ( 5.91! 9 ( 2.0) 280 ( 6,7)1 10 ( 2.7) 288 ( 8.2)1 8 ( 2.3) 243 ( 6.2)1 ( 3.9) *a* ( «el ( 2.5) 7 ( 2.6) ( ( 0.0) ( 0.7) 15 ( 9.3) *on 0 ( 0.0) ( 444) 7 ( 3.7) ( *41 8 ( 3.9) 10 ( 2.3) 270 ( 6.1)1 9 ( 3.3) 281 ( 7.1)1 State Nation RACE/ETHNICITY Wt. State Nation Sladc State Nation Hispanic State Notion American Wien State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extrema rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! 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 North Carolina TABLE AlOb Teachers' Reparts on the Use of Mathematical (continued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency Perventage and Profidency Percentage and Proficiency State 29 ( 3.2) 83 ( 33) ( 1.8) 245 ( 2.3) 250 ( 1.5) 267 ( 5.4)1 Nation 22 ( 3.7) 09 ( 3.9) 9 ( 2.6) 254 ( 3.2) 263 ( 1.9) 282 ( &S)! PARENTS' EDUCATION NS non-graduate State 28 ( 4.4) 65 ( 4.8) 7 ( 2.1) 230 ( 3.0) 233 ( 1.9) Nation 25 ( ( 5.6; *01 66 ( 7.2) 243 ( 2.2) 9 ( 4.** 6.5) NS graduate State 30 ( 3.8) 62 ( 4.1) 6 ( 2.0) 237 ( 2.9) 242 ( 1.6) 252 ( 5.8)1 Nation 23 ( 4.8) 70 ( 53) 7 ( 2.6) 246 ( 4.0)1 255 ( 2.2) *44 ( .41 Som callow State 28 ( 3,5) 63 ( 4.0) 10 2.4) 256 ( 2.9) 257 ( 2.2) Nation 18 ( 4.0) 73 ( 4.3) 9 ( 2.4) 261 ( 4.4)! 269 ( 2.3) ) College graduate State 29 ( 3-5) 61 ( 3.9) 10 ( 2.2) 256 ( 3.0) 265 ( 2.3) 286 ( 5.3)t Nation 20 ( 3.9) 69 ( 3.7) 11 ( 2.5) 286 ( 3.5)i 274 ( 2.2) 297 ( 4.2)i ()ENDER Male State 28 ( 3.3) 84 ( 3.7) 8 ( 1.9) 244 ( 2.6) 250 ( 1 3) 264 ( 6.0)' Nation 22 ( 4.1) 60(4.1) 8 ( 2.0) 255 ( 4.1) 265 ( 2.1) 287 ( 7.2)/ Female State 30 ( 3.3) 61 ( 3.5) 9 ( 1.9) 248 ( 2.7) 250 ( 1.8) 270 ( 5.5)1 Nation 21 ( 3.6) 69 ( 4.2) 10 ( 3.3) 254 ( 3.3) 262 ( 1.9) 278 ( 8.0)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 sundard 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. E** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 113 North Carolina TABLE Alla I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Weak About Once a Week or Lass TOTAL Pocondage and Pro Ilidency 70 ( 32) 254 ( 1.3) ( 3.4) 287 ( 1.6) 72 ( 3.8) 265 ( 111) 64 ( 3.7) 272 ( 1.9) 87 ( 4.0) 234 ( 1.8) $O ( 7.7) 244 ( 4.0) 89 ( 5.8) 224 ( 3.8) 81 ( 8.8) 251 ( 3,1) 70 (11.8) 15 (25.9) IHN1 76 (10.8) 277 ( 7.9)1 $3 (15.9) 283 ( 7.3)1 82 ( 4.3) ( 4.) 66 (40.7) 252 ( 4.7)1 78 ( 8.8) 248 ( 10)1 50 (10.6) 268 ( 4.0)1 70 ( 3.9) 264 ( 1.8) 83 ( 3.9) 267 ( 2.3) Pireentage Parandmis and linadency Preftionw 28 ( 3.1) 4 ( 0.6) 244 ( 2A 229 ( 5.8)1 31 ( 3.1 7 ( 1.8) 234 ( 2A) 280 ( 5.1)1 25 ( 3.4) 3 ( 1.1) 256 ( 2.8) "48 2".3)) 25 ( 32) 264 ( 3.4) 20 5.4)1 29 ( 34) 4 ( 1.0) 229 ( 2.4) «. 41 ( 7.9) 2 ( 1.4) it* 4101r1 233 ( 32)1 27 ( 5.1) 4 ( 2.1) ( *01 ( 441 32 ( 5.3) 240 ( 4.3)1 ( 19 ( 8.8) 5 ( 42) 4,1 tel 83 (28.3) 2 ( 3.0) ( *el ( 14 ( 5.7) 10 ( 7.1) *41 *v.) 23 ( 5.2) 14 (14.6) *0* .41 38 ( 4.3) 0 ( 0.0) 31 (11.1) 4 ( 2.2) 243 ( 8.0)1 19 ( 6.3) 5 ( 2.8) 239 ( 6.7)1 40 (10.0) 247 ( 7.6)1 *** ( 27 ( 3.7) 3 ( 0.9) 247 ( 2.7) *et, 31 ( 3.5) 6 ( 1.9) 255 ( 3.1) 257 ( 5.8)1 State Nation NACE/EDINWY White State Nation Black State Nation Hispanic State Nation American ktdian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation EXtreirl rural State Nation Other Stab° Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 A 7 114 THE 1990 NAV 'MAL STATE ASSESSMENT Nrnh Carolina TABLE Alla Teachers' Reports on the Frequency of (oantinued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL STATE ASSESSMENT "Unmet Every Day Several Thews a Week About Once a Week or Less =1 TOTAL Parcentage and PrefloienCy Percenaige and Preadult:1f Perventage mid Prat:lacy State 70 ( 3.2) 26 ( 3.1) 4 ( 0.91 254 ( 1.3) 244 ( 2.4) 229 ( 5.6e Nation 02 ( 3.4) 31 ( 3.1) 7 ( 1.6) 267 ( 1.6) 254 ( 2.9) 260 ( 5.1)1 PARENTS EDUCATION KS non-graduate Stata 67 ( 3.9) 27 ( 3.8) 6 ( 2.3) 234 ( 1.9) 230 ( 3.8) ( Nation 87 ( 245 ( 5.5) 3.2) 27 ( ( 52) *MI) 6 (( 2.1) .41 NS graduate State 70 ( 244 ( 3.4) 1.7) 28 ( 238 ( 3.4) 2.4) 4 ( ( 1.1) 041 Nation 81 ( 4.4) 34 ( 3.7) 8 ( 1.5) 257 ( 2.5) 250 ( 2.9) Some college State 71 ( 4.3) 27 ( 4.1) 2 ( 0.8) 280 ( 1.9) 254 ( 3.1) N-Aion 88 ( 272 ( 4.2) 2.7) 26 ( 25$ ( 3.7) 5.2) 6 (( 1.9) .41 College graduate State 73 ( 3.7) 24 ( 3.7) 3 ( 1.0) 269 ( 1.9) 254 ( 3.9) ( Natioii 61 ( 4.0) 31 ( 3.9) 8 ( 3.1) 281 ( 22) 265 ( 3.1) ( .") ()ENDER Male State 68 ( 3.3) 28 ( 3.2) 4 ( 1.1) 254 ( 1.5) 243 ( 2.8) Nation 80 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2.1) 258 ( 3.6) 261 ( 3.7)1 Female State 73 ( 3.4) 24 ( 3.2) 3 ( 0.9) 254 ( 1.5) 245 ( 2.9) ( `") Nation 85 ( 3.8) 28 ( 3.3) 7 ( 2.2) 286 ( 1.8) 253 ( 2.5) *4* ( "41 The standard errors of the estimced 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). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT 115 North Carolina TABLE Al lb Teachers' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Least Several Tknes STATE ASSESSMENT a Week About Once a Week Leu than Weekly , . TOTAL PereMdige aid Preaciency Pereentage and Prellelency Pereentege and Prellictency State 49 ( 3.3) 30 ( 24) 21 ( 2.8) 245 ( 1.9) 234 ( 2.6) 257 ( 3.1) Nation 34 ( 10) 33 ( 3A) 32 ( 3.8) 250 ( 2.3) 260 ( 2.3) 274 ( 2.7) RACEMilNICITY White State 45 ( 3.8) 30 ( 2.7) 25 ( 3.5) 258 ( 2.3) 284 ( 2.8) 285 ( 2.9) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 284 ( 2.7) 264 ( 2.7) 270 ( 2.9) Black State 55 ( 4.3) 2$ ( 3.8) 17 ( 3.0) 2213 ( 2.0) 23$ ( 2.2) 238 ( 5.8) Nation 45 ( 7.5) 31 ( 7.8) 23 ( 8.3) 232 ( 3.1)1 243 ( 2.3)1 248 ( 7.011 Hispanic State 51 ( 6.3) 217 ; 3.9) 34 ( 8.8) vo.) 15 ( 3.4) «61 Nation 41 ( 7.7) 28 ( 5.3) 33 ( 7.5) 242 ( 3.2)1 244 ( 5.1)1 257 ( 2.3)1 American Indian State 87 (14.9) ,.**) 23 (12.0) ( ) 10 ( 4.9) Nation 10 (18.6) ( *44 ) 76 (36.2) «J.) 13 (18.5) TYPE OF COMMUNITY Advantaged urban State 27 (10.8) 1-fr MIR ) 34 (12.4) * *It ( 39 (16.4) *4.1 Nation 59 (13.9) 20 ( 6.0) 21 ( 8.2) 273 ( 3.4)i Disadvantaged urban State 88 (19.9) 236 (16.1)1 *44) 21 (19.6) Nation SO (13.9) 22 (11.2) 28 (10.7) 237 ( 2.4)1 258 ( 8.3)1 263 ( 4.1)1 Extreme rural State 51 (10.0) 33 ( 8.8) 16 ( 8.4) 243 ( 3.3)1 237 ( 42)1 280 ( 3.8)1 Nation 27 (14.3) 49 (12.7) 258 ( 8.7)1 24 (10.1) *4. Other State 49 ( 3.5) 29 ( 2.8) 22 ( 3.2) 247 ( 2.2) 257 ( 2.6) 254 ( 3.6) Nation ( 4.4) 35 ( 4.3) 36 ( 4.2) 256 ( 3.3) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. certainty that, for each population of interest, the value for the entire p of the estimate for the sample. ! Interpret with caution the nature determination of the variability of this estimated mean proficiency. ** reliable estimate (fewer than 62 students). )16 t can be said with about 95 percent t n is within ± 2 standard errors Ce sample does not allow accurate Sam e size is insufficient to permit a .1. 2 1 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE Al lb I Teachers' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Weak About Mee a Week Liss than Weeidy TOTAL and Iftwecioncv Peraentage and Pm/Money Pannintaga and Pala:Amoy State 49 ( 31) 30 ( 2.5) 21 21) 245 ( 1.9) 254 ( 23) 257 3,1) Nation 4 ( 3.8) 33 ( 3A) 32 3.8) 256 ( 2.3) 2eo ( 2.3) 274 2.7) EbRENTS' EDWATION non-graduat State 52 ( 5.3) 230 ( 2.8) 28 ( 3,1) 235 ( 2.9) ( eel Nation 35 ( 6.0) 239 ( 3.5) 29 ( 6.3) gin 3B ( 6.9) 250 ( 4.5)1 NS graduate State 52 ( 31 28 ( 3.0) 20 ( 3.0) 237 ( 2.01 245 ( 2/) 249 ( 3.0) Nation 35 ( 5.3 36 ( 4.5) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 263 ( 3.4) Some cotlege State 43 ( 4.0) 37 ( 3.7) 21 ( 32) 257 ( 2.2) 259 ( 3.0) 258 ( 3.4) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 266 ( 4.2) 278 ( 2.6) College graduate State 46 ( 3.4) 30 ( 2.8) 24 ( 3.1) 258 ( 2.7) 269 ( 3.7) 271 ( 3.9) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 21) 271 ( 2.4) 289 ( 2.9) °ENDER, Male State 50 ( 3.4) 29 ( 2.7) 21 ( 2.8) 243 ( 2.1) 255 ( 2.8) 258 ( .3.2) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3a) 261 ( 2.45) 275 ( 3.2) Female State 47 ( 3.4) 31 ( 2.6) 22 ( 3.0) 247 ( 22) 254 ( 2.9) 256 ( 3.4) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT 117 North Carolina TABLE Al2 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1 ME 990 P TRIAL STATE ASSESSMENT At Least Once a Week Les,: Than Once a Week Never TOTAL Percentage and Preadency Percentage and Prodictency Percentap ana Preadency State 23 ( 14) 2$ ( 1.3) 49 ( 2.1) 245 ( 1.9) 267 ( 1.6) 249 ( 1.3) Nation 2$ ( 2.5) 2$ ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 261 ( 1.6) RACE1ETIINICITY Whitt State 20( 14) 29 ( 1.6) 50 ( 2.6) 258 ( 2.3) 267 ( 1.7) 259 ( 1.7) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 268 ( 3.1) 272 ( 1.9) 270 ( 1.7) Black State 26 ( 1.6) 20 ( 1.8) 48 ( 2.4) 227 ( 2.0) 240 ( 2.2) 230 ( 1.5) Nation 28 ( 3.0) 24 ( 3.6) 45 ( 4.7) 234 ( 3.0) 245 ( 4.6) 234 ( 3.1) Hispanic State 27 ( 3A) 30 ( 4.5) 44 ( 4.3) .14111 Nation 37 ( 5.2) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) American Indian State 22 ( 6.0) .p,pe 53 (12.5) Nation 31 ( 5.1) 35 ( 5.5) 44 ( 33 ( 5.0) ( gm.) TYPE OF COMMUNITY Advantaged urban State 63 (10.6) ( MEI ) 286 ( 4.7)1 Nation 27 (13.9) 33 ( 4,5) 40 (13.4) 286 ( 5.4)1 279 ( 35)1 Disadvantaged urban State 37 ( $.4) 31 (10.2) 4,114 Nation 31 ( 5.7) 20 ( 2.8) 49 ( 13.3) 245 ( 4.0)1 267 ( 5.4)! 245 ( 3.7)1 Extreme rural State 20 ( 3.0) 26 ( 2.8) 55 ( 4.7) 241 ( 4.4)1 251 ( 32)1 241 ( 2.7)1 Nation 34 (10.8) 27 ( 3.13) 39 (11.6) 249 ( 5.2)1 264 ( 35)1 256 ( 6.2)! Other State 23 ( 1.7) 28 ( 1.7) 49 ( 2.3) 245 ( 2.2) 258 ( 2.1) 250 ( 1.4) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 264 ( 2.1) 262 ( 2.2) The standard errors of the estimated stausucs appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reiable estimate (fewer than 62 students). 118 li THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE Al2 I Students' Reports on the Frequency of Small (ccultinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Meek Never j -AMY TOTAL Rarcentage and Proficiency State 23 ( 1.4) 245 ( 1.9) Nation 2$ ( 2.5) 256 ( 2.7) PARENTS' EDUCATION NS neograduate State 23 ( 2.6) 225 ( 3.6) Nation 29 ( 4.5) 242 ( 3.4) NO graduate State 21 ( 1.9) 236 ( 2.5) Nation 26 ( 3.0) 251 ( 3.7) Some college State 24 ( 2.3) 253 ( 3.1) Nation 27 ( 32) 265 ( 3.0) College graduate State 22 ( 1.8) 260 ( 3.4) Nation 28 ( 3.0) 270 ( 2.7) GENDER Male State 24 ( 1.5) 243 2.3) Nation 31 ( 2.9) 259 ( 33) Female State 21 ( 1.8) 247 ( 2.2) Nation 26 ( 2.4) 257 ( 2.8) Percesioye and Proliciency Pesosidepr and Proficiency 23 1.3) 49 ( 2,1 257 14) 246 ( 13 23 1.4) 44 ( 2.91 267 2.0) 261 ( 1.6) 24 ( 2.4) 239 ( 3.3) 29 ( 3.0) 244 ( 3.0) 27 ( 1.8) 247 ( 2.2) 28 ( 1.8) 291 ( 2.6) 32 ( 2.0) 202 ( 2.2) 27 ( 2.4) 2845 C 3.3) 30 ( 2.1) 272 ( 2.8) 2$ ( 1.9) 278 ( 2.8) 28 ( 1.3) 25$ ( 1.9) 2$ ( 1.7) 208 ( 2.6) 30 ( 1.8) 256 ( 2.1) 27 ( 1.8) 265(1.7) 53 ( 2.9) 233 ( 2.1) 42 ( 4.5) 242 ( 2.7) 51 ( 2.3) 241 ( 1,6) 43 ( 3.4) 252 ( 1.7) 44 ( 32) 258 ( 2.1) 46 ( 3.8) 206 ( 2,1) 48 ( 2.9) 211 ( 2.3) 44 ( 3.6) 275 ( 2.2) 49 ( 2.1) 249 ( 1.6) 41 ( 2.9) 202 ( 1.8) 49 ( 2.4) 246 ( 1.5) 47 ( 3.2) 280 ( 1.6) The standard errors of the estitnated 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 2 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 North Carolina TABLE A13 I Students' Reports on the Use of Mathematics 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT , At Least Once a weak Loss Than Ones a Weak Never TOTAL Parcantage and Proficiency Percontsge and Madam Porcartaga Prolidency State 28 ( 1.7) 31 ( 1.3) 43 ( 2.1) 241 ( 1.5) 256 ( 1.8) 251 ( 1.4) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.6) 209 ( 1.5) 259 ( 1.6) RACE/ETHNICITY White State 22 ( 1.9) 35 ( 1.6) 43 ( 2.3) 253 ( 1.7) 264 ( 12) 263 ( 1.7) Nation 27 ( 1.9) 33 ( 1.6) 40 ( 25) 2es ( 2.8) 275 ( 1.6) 268 ( 1.8) Slack State 33 ( 251 23 ( 1.8) 43 ( 2.8) 228( 1:4 236 ( 2.0) 232 ( 1.6) Nation 27 ( 3.3) 27 ( 3.2) 48 ( 4.5) 234 ( 3.7) 248 ( 4.5) 232 ( 2.0) Hispanic State 32 ( 4.1) 26 ( 4.9) ..**) 42 ( 5.3) Nation 38 ( 4.2) 2`.1( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) Amorican Indian State 30 ( 7.3) 044 ( MI* ) 29 ( 5.3) Hirt ( It*/ 411 7.1) 444(444) Nation 3$ ( 3.4) 37 ( 8.2) 28 ( 8.8) ***) TYPE OF COMMUNITY Advantaged urban State 10 ( 3.1) 32 (12.5) 58 (13.3) *44(44*) Nation 36 (10.3) 33 ( 4.8) 32 (14 1) 273 ( 6.1)1 284 ( 3.2)1 281 ( 5.9)1 Disadvantaged urban State 35 (10.5) 44 ( 9.1) dhilY 444) Nation 35 ( 6.6) 19 ( 2.1) 46 ( 6.4) 249 ( 5.3)1 256 ( 5.7)1 246 ( 4.8)1 Estrum niral State 30 ( 4.2) 30 ( 3.8) 40 ( SA) 239 ( 3.6)1 250 ( 4.1)1 241 ( 3.0)1 Nation 21 ( 3.1) 37 ( 4.7) 43 ( 5.0) 202 ( 4.7)1 251 ( 5.2)1 Mbar State 26 ( 1.9) 31 ( 1.5) 43 ( 2.4) 243 ( 1.7) 256 ( 1.6) 252 ( 1.6) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 256 ( 2.9) 270 ( 1.8) 260 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A13 I Students' Reports on the Use of Mathematics ("Intinued) i Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19610 NAEP TANK STATE ASSESSMENT Al Least Once a Wank Leas Than Once a Week Never TOTAL and Pfallokow 20 ( 241 15 1.8 258 (2.6) Varemalage amd Pralideacv SI ( 256 ( 14 31 ( 12 206) ( 14) Psommesp and Prolicienqf 43 ( 2.1) 251 ( 1A) 41 ( 2.2) 259 ( 14) State Nation PARENTS' EDUCATION NS non-graduate State 28 ( 2.8) 2? ( 3.3) 45 ( 3.5) 225 ( 3,1) 240 ( 2.9) n3 ( 2.1) Nation 27 ( 4.2) 25 2.7) 4? 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) HS graduate State 27 ( 2.3) 30 ( 2.1) 43 ( 2.8) 236 ( 2.2) 245 ( 1.9) 242 ( 1.9) Nation 2? ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( :.1) Some college State 22 ( 2.4) 36 ( 2.8) 41 ( 32) 248 ( 2.7) 262 ( 2.5) 260 ( 2.3) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 24) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) CoNege graduate State 26 ( 2.0) 32 ( 1.9) 42 ( 25) 252 ( 2.4) 269 ( 2.1) 287 ( 2.4) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.8) 262 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Male State 29 ( 1.7) 30 ( 1.4) 42 ( 2.1) 242 ( 2.1) 255 ( 1.8) 251 ( 1.7) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 22) 258 ( 2.9) 271 ( 2.1) 280 ( 1.8) Renal* State 23 ( 2.0) 33 ( 1.7) 44 ( 24) 241 ( 1.9) 258 ( 2.0) 251 ( 1.7) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 288 ( 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 v 2 standard errors of the estimate for the sample. 1 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 North Carolina TABLE A14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1NO NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week Abod Once a Week or Less TOTAL Percentage and Preidenny and Prodidency Percents's and Proficiency State 77 ( 14) 15 ( 1A) 8 ( 0.7) 254 ( 1.1) 258 ( 1.8) 230 ( 3.0) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) gmaimpiaac 267 ( 1.2) 252 ( 1.7) 242 ( 4.5) White State 81 ( 1.6) 12 ( 1.1) 7 ( OA) 264 ( 1.3) 251 ( 2.9) 240 ( 3.4) Nation 76 ( 2.5) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 22) 252 ( 5.1)1 Slack State 70 ( 2.1) 19 ( 1.9) 11 ( 12) 23$ ( 1.4) 227 ( 2.0) 219 ( 3.0) Nation 71 ( 2.8) 15 ( 1.7) 14 ( 12) 240 ( 2.9) 232 ( 3.1) 223 ( 5.1)1 Hispanic State 65 ( 5.0) ( 3.2) 23 ( 42) et, ( 12 ( 2.9) Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) American Indian State 73 ( 5.5) AN. 12 ( 3$) 15 ( 4.4) ( .41 Nation 61 ( 4.4) 4i ( 11411) 22 ( 3.6) 17 ( 4.0) *** TYPE OF COMMUNITY Advantaged urban State 74 ( 6.1) 18 ( 6.6) ( 1.7) 278 ( 6.0)1 Nation 73 (11.1) 266 ( 4.6)1 13 ( 1.7) *4* ( «HI 14 (104) 4.4. Disadvanteged urban State 63 ( 5.5) 251 (15.0)1 23 ( 4.2) ( «b.) 13 1 32) ( ***) Nation do ( 2.11) 15 ( 2.5) 15 ( 2.2) 253 ( 3.7)1 243 ( 4.4)1 235 ( 6.5)1 Extreme nazi State 83( 3.2) 247 ( 2.4) 11 ( 2.0) ( *44) 8 ( 1.6) IP, 11411 Nation 68 (11.3) 263 ( 4.2)1 15 ( 3.6) 444, 17 ( 82) eq.) Other State 77 ( 1.7) 15 ( 1.2) 9 ( 0.9) 255 ( 1.3) 240 ( 2.1) 232 ( 3.7) Nation 75 ( 2.2) 14 ( 1.0) 10 ( 1.0) 267 ( 1.6) 252 ( 2.6) 239 ( 42)1 The standard errors of the estimated stafistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! 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). 1C7 122 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A14 I Students' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP MAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Less TOTAL Pirantage and Proficiency Plordentein and 'radon Pennalaile and PradidencY State 77 ( 1.4) 15 ( 1.0) 8 ( 0.7) 254 ( 1.1) 236 ( 1.6) 230 ( 3.0) NatIon 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 4.5) PARENTS EDUCATION HS non-graduate State 75 ( 2.9) 14 ( 2.2) 10 ( 1.9) 235 ( 1.6) ( *41 Nation 64 ( 245 ( 3.4) 2.3) 18 ( 2.0) 44.) 18 ( 3.1) .44) M9 graduate State 74 ( 2.0) 17 ( 1.5) 10 ( 1.1) 245 ( 1.3) 233 ( 2.3) 225 ( 3.4) NatIon 71 ( 34) 16 ( 1.8) 13 ( 2.8) 258 ( 1.6) 249 ( 3.2) 239 ( 3.4)! Some college State 78 ( 2.2) 15 ( ( 12) 2e1 13) 248 ( 42) 4rk *el Nation so ( 2.0) 11 (1.2) 9 ( 1.7) 270 ( 1.9) Co keg* graduat State 81 ( 1.8) 12 ( 1.5) 7 ( 0.9) 269 ( 14) 247 ( 3.7) 237 ( 4.5) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 23) 279 ( 1.6) 260 ( 2.8) 257 ( 6.4)1 GENDER Maio State 75 ( 1.6) 16 ( 1.2) 10 ( 0,9) 254 ( 1.4) 240 ( 1.7) 231 ( 3,4) Nation 72 ( 2.4) 16 ( 12) 12 ( 2.1) 268 ( 1.6) 252 ( 24) 242 ( 8.1) Female State 79 ( 1.6) 14 ( 1.2) 7 ( 0.9) 255 ( 1.2) 238 ( 3.1) 229 ( 3.5) Nation re ( 1.8) 13 ( 1.0) 11 ( 1.6) 265 ( 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 North Carolina TABLE A15 I Students' Reports On the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Lust Several Times STATE ASSESSMENT a *sok Abate Once a Weak Less Tban Weeidy _ TOTAL Persentap perventsge and mid Pralkiency Prallialoncy Peronista and Plciency State 45 ( 29 ( 1.3) 27 ( 13 ) 244 ( 1.7 252 ( 1.5) 258 ( 1.8 ) Nation 38 ( 2.4 25 ( 1.2) 37 ( 2.5) 253 ( 2.2) 2/51 ( 14) 212 ( 1.9) RACE/ETHNICITY Mite State 40 ( 2.5 2Sf 1.5) 30 ( 2.4) 257 ( 2.0) 262 ( 1.9) 2.o Nation 35 ( 2.9 24 ( 1.3) 41 3.0) 262 ( 2.5 209 ( 1.5) 277 2.0) Black State 51 ( 2$ ( 1.9) 20 ( 227 ( 1.6 235 ( 2.0) 239 ( 2.4 Nation 42 ( 3.8 32 ( 2.7) 20 ( 3.1 232 ( 43) 241 ( 2.9) 241 ( 4.4) Hispanic State 63 217 ( 5.0) ( 24 4.2 13 ( 3.0) 444. ( 44.9 Nation 44 ( 4.1 25 3.4 32 ( 4.3) 238 ( 3.9 247 ( 3.3) 24$ ( 3.3) Amedcan hidian State ( *44 ) 26 ( 6.1) 41,641 ( *01 31 ( 5.9) 444 444) Nation 41 ( 4.2 4,44) 30 (11.3) 444 ( 449 26 (12.5) 6+. ( 41 TYPE OF COMMUNITY Advantaged urban State 37 ( 6.2) 33 (10.1) ,64.fr 29 (11.2) «kit ( Nation 50 271 ( 9.0) ( 3.3)1 19 ( 4.9) 444 ( 4 31 ( 9.3) 229 ( 5.3)1 Disadvantaged urban State 58 (11.0) 4.4.) 26 ( 6.0) 111.** 1141 16 ANHO 5.6) 411.11 Nation 37 ( 5.8) 23 ( 3.6) 41 6.7) 240 ( 4.0)t 253 ( 4.1)1 255 ( 4.2)1 Extreme rural State 44 ( 5.5) 34 ( 3.8) 22 ( 3.8) 239 ( 3.4)1 243 ( 2.9)1 253 ( 5.0)1 Nation 42 (101) 30 ( 44) 28 ( 7.5) 249 ( 4.0)! 256 ( 34)1 207 ( 7.3)1 Other State 44 ( 2.4) 28 ( 1.4) 28 ( 2.0) 245 ( 1.9) 253 ( 1.7) 258 ( 2.1) Nation 36 ( 2.9) 28 ( 1.2) 36 ( 2.9) 252 ( 3.0) 281 ( 2.1) 272 ( 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. ! 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). 124 1 el Ci f I THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE MS I Students' Reports on the Frequency of (continUed) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1000 NAEP TRIAL At Least Several Tknes STATE ASSESSMENT a Week About Once a Weak Leis Than Weekly _ TOTAL Peroontege and Proficiency POWN111.0 owl Proficiency Penentane and Proficiency State 45 ( 2.1) 29 ( 13) 27 ( 12) 244 ( 1.7) 252 ( 1.5) 255 ( 12) Nation 38 ( 2.4) 25 ( 1.2) 37' ( 2.5) 253 ( 2.2) 261 ( 1.4) 272 ( 12) PARENTS' EDUCATION NS non-graduate State 43 ( 3.4) 31 ( 2.5) 28 ( 24) 225 ( 2.6) 238 ( 24) 241 ( 2.9) Nation 41 ( 4.5) 30 ( 2.7) 22 ( 4.0) gracksata 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) State 43 ( 2.5) ( 2.1) 27 ( 2.2) 235 ( 1.7) 243 ( 2.1) 251 ( 23) Nation 40 ( 32) 29 ( 2.2) 32 ( 3.6) 247 ( 2.7) 250 ( 2.5) 262 ( 22) Som college State 43 ( 2.9) 29 ( 2.3) 28 ( 2.5) 255 ( 1.9) 256 ( 2$) 265 ( 2.5) Nation 34 ( 3.4) 26 ( 22) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) College graduate State 46 ( 2.6) 2$ ( 2.0) 26 ( 24) 257 ( 2.6) 269 ( 2.8) 271 ( 2.6) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.8) 264 ( 2.6) 273 ( 2.5) 255 ( 2.3) GENDER Mak§ State 47 ( 2.2) 27 ( 1.6) 25 ( 2.0) 243 ( 1.9) 253 ( 2.1) 2sa ( 1.9) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 263 ( 2.3) 274 ( 2.4) Female State 42 ( 2.4) 30 ( 1.5) 28 ( 2.0) 245 ( 2.0) 252 ( 2.1) 258 ( 22) Nation 37 ( 2.5) 25 ( 1.5) 38 ( 2.6) 253 C 2.1) 259 ( 1.8) 269 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 North Carolina TABLE AB Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Me MEP TRIAL STATE ASSESSMENT Cakulator Teacher Detains Calculator Use Yes No Yes No TOTAL Ilanuntago and Pralaiency Percentage and Praidency Pereentap Pertenlage and and Proadancy Pralakincy State 90 ( 0.3) 4 ( 0.3) 53 ( 47 2.4) 251 ( 1.0) 2244 2.9) 245 ( 255 14 Nation 97 ( 0.4) 3 ( 0.4) 49 ( 2.3 51 2.3) 263 ( 1.3) 234 ( 3.6) 25$ ( 1.7) 208 ( 1.5) RACEMINNWATY White State 96 ( 0.3) 50 ( 2.8) 50 ( 2.8) 262 ( 1.3) 257 ( 1.6) 200 ( 14) Nation 90 ( 270 ( 0.3) 1.5) 2 ( *I* ( 0.3) 46 ( 2.61 266 ( 1.8) 54 273 ( 2.0) ( 1.8) Black State 94 ( 0.8) 6 ( 0.8) 55 ( 32) 45 ( 3.2) 233 ( 1.1) ( 229 ( 1.4) 235 ( 1.7) Nation 93 ( 1,5) 53 ( 4.9) 47 ( 4.9) 237 ( 2.8) *** ( 235 ( 3,6) 239 ( 2.7) Hispanic State 90 ( 222 ( 2.6) 2.7) 10 ( 2.6) 70 ( 4.3) 218 ( 2.9) 30 ( 4.3) elm Nation 92 ( 12) 8 ( 12) 83 ( 4.3) 37 ( 4,3) 245 ( 2.7) ( "") 243 ( 3.4) 245 ( 2.9) American Indian State 93 ( 237 ( 2.3) 3.7)1 e3 7.0 ...) 37 ( 7.0) 11.04 .01 Nation 94 ( HP* ( 3.1) *41 ( ( 3.1) 71 (18.7) el") 29 (113.7) ( *4.) TYPE Of COMMUNITY Advantaged urban State 96 ( 273 ( 0.1) 6.4)1 4 ( ( 0.1) *44) 37 ( 4.3) 63 ( 4.3) 271 ( 5.9)1 Nation 99 ( 1.0) 1 ( 1.0) 45 (12.2) 55 (12.2) 281 ( 3.8)1 276 ( 2.5)1 285 ( 64)1 Disadvantaged urban State 97 ( 2.1) 243 (10.9)1 3 ( 2.1) 48 (15.0) 01. 52 (15.0) Nation 94 ( 1.2) 53 ( 74) 47 ( 7.5) 250 ( 3.5)1 ( .") 247 ( 4.1)1 251 ( 3.6)1 Extreme rural State 95 ( 1.1) 53 ( 54) 47 ( 5.4) 24.5 ( 2.3) 241 ( 2.1)1 246 ( 3,5)1 Nation 96 ( 1.3) 42 ( 8.7) 58 ( 8.7) 257 ( 3.9)1 251 ( 4.8)1 261 ( 4.4)1 OtHer State 97 ( 0.4) 4 ( 0.4) 53 ( 2.8) 47 ( 2.8) 252 ( 1.1) 22$ ( 3.7) 246 ( 1.5) 257 ( 1.6) Nation 97 ( 0.5) 3 ( 0.5) 50 ( 2.7) SO ( 2.7) 263 ( 1.7) 233 ( 5.4) 258 ( 2.1) 266 ( 2.0) The standard errors of the estimated statictics 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 te) permit a reliable estimate (fewer than 62 students). 126 131 THE 1990 NAFP TRIAL STATE ASSESSMENT North Carolina TABLE A18 (continued) Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL STATE ASSESSMENT . Own a Calculator . Teacher Explains Calculator Use Yes No Yes No I . TOTAL Perm lase and lira licking Parcantaga and Prelkeency Persentane an0 Proficiency Peraenfane and leralidency State 90 ( 0.3) 4 ( 0.3) 53 ( 2.4) 47 ( 2.4) 251 ( 1.0) 224 ( 245 ( 1.2) 25$ ( 1.4) Nation 97 ( 0A) 3 ( 0.4 4. ( 2.3) 51 ( 2.3) 283 ( 1.3) 234 3.8 258 ( 1.7) 208 ( 1.5) PARENTS' EDUCATION non-graduats State 91 ( 1.7) 9 ( 1.7) 59 ( 3.7) 41 ( 3.7) 234 ( 1.6) 230 ( 2.3) 236 ( 2.5) Nation 92 ( 1.6) 243 ( 2.0) 6 1.6) 4.) 53 ( 242 ( 4.8) 2.9) 47 ( 243 ( 4.8) 2.5) NS graduate State 95 ( 0.7) 5 ( 0.7) 54 ( 2.7) 48 ( 2.7) 243 ( 1.3) ( 238 ( 1.6) 248 ( 1.7) Nation 97 ( 0.6) 255 ( 1.5) 3 ( 0.8) ( .41 S4 ( 2S2 ( 3.0) 1.9) 48 ( 25$ ( 3.0) 2.0) Solna college State 98 ( 0.6) 258 ( 1.4) 2 ( 1,0* 0.6) ( $2 ( 254 ( 33) 2.2) 48 ( 262 ( 3.8) 1.7) Nation 98 ( 0.9) 4 ( 0.9) 48 ( 32) 52,( 3.2) 208 ( 1.8) "# "1 265 ( 2,4) 268 ( 2.2) College gretkiate State 99 ( 0.3) 1 ( 0.3) 49 ( 2.6) 51 ( 2.8) 265 ( 1.6) 259 ( 1.9) 269 ( 2.4) Nation 99 ( 0.2) 275 ( 1.8) 1 ( *** 02) ( ***) 46 ( 26$ ( 2.8) 22) 54 ( 280 ( 2.6) 1.9) GENDER, Male State 90 ( 04) 251 ( 1.2) 4 ( «hi 0.5) $3 ( 248 ( 2.7) 1.5) 47 ( 2.34 ( 2.7) 1.8) Nation 97 ( 0.5) 264 ( 1.7) 3 ( *0. 0.5) .1.) 51 ( 256 ( 2.6) 2.1) 49 ( 26a ( 2,6) 2.1) Female State 97 ( 0.4) 252( 1.1) 3 ( 0.4) ***) 52 ( 244 ( 24) 1.4) 4$ ( 257 ( 2.5) 1.13) Nation 97 ( 0.5) 3 ( 0.5) 47 ( 2.5) 53 ( 2.5) 262 ( 1.3) ( ***) 258 ( 1.7) 263 ( 1.6) The standard errors of the estimated Statistics appear in parentheses. It can be said With about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 10* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 North Carolina TABLE A19 I Students' Reports on the Use of a Calculator i for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL. STATE ASSESSMENT Wgirking Pr@blems in Doing Probkms at Home Class Almost Always Never Almdst Always Never Taking Quizzes or Tests Almost Always Never Percentage Percentage Percentage Percentage Percentage Percentage end and and and TOTAL Proficiency Proliciency Proficiency Proficiency end Proficiency and Proficiency State 45 ( 1.2) 26 ( 1.8) 29 ( 1.2) 18 ( 0.9) 24 ( 1.0) 38 ( 1.4) 238 ( 1.0) 263 ( 1.5) 245 ( 1.3) 280 ( 1.9) 238 ( 1.4) 204 ( 1.4) Nation 441 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.8) 283 ( 1.8) 253 ( 2.4) 274( 1.3) RACE/ETHNICITY whits State 39 ( 1.3) 29 ( 2.0) 27 ( 1.2) 20 ( 1.3) 19 ( 1.2) 44 ( 1.7) 250 ( 1.5) 271 ( 1.8) 258 ( 1.7) 267 ( 2.1) 252 ( 1.7) 271 ( 1.4) Nation 46 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 25 ( 1.6) 32 ( 2.3) 262 ( 1.7) 278 ( 1.3) 270 ( 1.7) 200 ( 2.3) 263 ( 2.6) 279 ( 1.2) Black State 55 ( 1.8) 21 ( 2.1) 31 ( 1.9) 15 ( 1.4) 33 ( 2.0) 30 ( 1.8) 225 ( 1.2) 243 ( 2.9) 230 ( 1.9) 243 ( 3.5) 225 ( 1.5) 245 ( 2.3) Nation 57 ( 3.2) 20 ( 3,9) 31 ( 2.9) 15 ( 1.9) 38 ( 3.3) 24 ( 3.1) 232 ( 2.4) 249 ( 4.0) 233 ( 3.3) 24$ ( 5.5) 230 ( 3.6) 251 ( 4.1) Hispanic State 54 ( 4.8) 13 ( 3.1) 38 ( 4.3) 13 ( 3.1) 32 ( 4.4) 18 ( 3.8) 212 ( 2.5) 4.4.4, ( 04e) "...A, /A. ( NH. ( *4) ( *4) Nation 51 ( 2.9) 18 ( 3.5) 26 ( 3.2) 21 ( 2.1) 28 ( 2.7) 22 ( 3,1) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1) 237 ( 3.2) 256 ( 4.2) American Indian State 67 ( ( 8.3) *44) 10 ( *a* ( 5.7) *41 42 ( 7.5) «H.) 10 ( ( 3,8) ***) 29 ( ( 4.1) *49 ) 21 ( II1** 6.1) *Al Nation 33 ( *** 9.8) ***) 23 ( 4.9) 15 ( 4.9) .4*) 32 (10.1) ( *di 20 ( ( 6.2) *41 21 ( *MI ( 7.8) TYPE Of COMMUNITY Advantaged urban State 29 ( 2.8) 38 ( 8.0) 26 ( 4.2) 24 ( 6.4) 14 ( 3.5) 55 ( 4.8) .44 1144 ( 4144 *** ( *04 ) *411 *** ( 44* ) Oh! ( 14* ) Nation 51 ( 5.4) 23 (10.7) 32 ( 8.1) 15 ( 2.4) 31 ( 3.8) 28 ( 9.8) 270 ( 4.7)1 "9 ( ***) 274 ( 4.9)1 *** ( ""') 281 ( 7.8)1 285 ( 4.2)1 Disadvantaged urban State 42 ( 8.8) 33 ( 4.8) ( es.) 30 ( 44-* ( 3.1) 23 ( 1.2) 18 ( 5.2) ..**) 40 ( ( 8.5) *61 Nation 52 ( 3.1) 22 ( 4.5) 30 ( 3.3) 24 ( 2.3) 27 ( 2.9) 27 ( 4.8) 241 ( 3.8)1 259 ( 5.4)1 246 ( 5.2)1 254 ( 4.8)1 240 ( 4.9)1 263 ( 5.0)1 Extreme rural State 48 ( 2.4) 22 ( 2.7) 31 ( 1.9) 14 ( 1.9) 25 ( 2.6) 36 ( 2.2) 233 ( 2.7) 252 ( 3.3)1 240 ( 3.2) 251 ( 23), 236 ( 4.5)1 280 ( 3.1)1 Nation 46 ( 7.4) 29 ( OS) 20 ( 2.5) 23 ( 3.9) 24 ( 8.6) 37 ( 8.3) 246 ( 4.3)1 288 ( 8.1)1 *** ( "-*) 283 ( 4.4)1 ( "") 270 ( 4.0p Other State ( 1$) 26 ( 2.2) 28 ( 1.6) 18 ( 1.1) 24 ( 1.3) 38 ( 1.6) 240 ( 1.4) 264 ( 1.4) 246 ( 1.7) 200 ( 1.9) 238 ( 1.6) 264 ( 1.5) Nation 48 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1,8) 29 ( 2.1) 254 ( 2.1) 272 ( 1.8) 263 ( 2.3) 203 ( 2.8) 253 ( 2.7) 276 ( 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 "Sometime? category is not included, Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 128 TH E 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A19 I Students' Reports on the Use of a Calculator (continued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENcY 1980 NAEP TRIAL. STATE ASSESSMENT Woddng Problims in Class Doing Problem at Nom Taking QUIZSIS ar Tests Almost Always Never Almost Alwys a Never .. Almost Always Never _ TOTAL Parosnew and Praidency Parcentags ani Odom Porcentop and Madam State 45 ( 1.2) 28 ( 11) 29 ( 1.2) 238 ( 1.0) 263 ( 1.5) 243 ( Nation 43 ( 1.5) 23 ( 1.9) 90 ( 1.3 254 ( 1.5) 272 ( 1.4) 261 ( 1.8 PARENTS EDUCATION 145 non.graduato State 33 ( 3.0) 23 ( 22) 23 ( 3.0) 227 ( 1.8) 244 ( 3.0) 231 ( 2.8) Nation 34 ( $.3) 19 ( 3.8) 28 ( 3.1) 240 ( 2.3) "4' ( '1") 244 ( 3.8) NS graduate State 49 ( 1.7) 22 ( 1.8) 26 ( 1.7) 232 ( 1.5) 256 ( 2.1) 237 ( 1.9) Nation 52 ( 2.5) 20 ( 24) 29 ( 1.9) 249 ( 1.4) 265 2.7) 250 ( 2.4) Soma cottage State 37 ( 2.3) 31 ( 2.7) 28 ( 2.0 246 ( 2.1) 268 ( 1.8) 232 ( 3.1) Nation 46 ( 2.8) 26 ( 24) 26 ( 2.0 238 ( 2.1) 272 ( 2.5) 26? ( 3.0) Coils** graduat State 40 ( 1.8) 29 ( 21) 30 ( 1.7) 230 ( 1.9) 274 ( 25) 258 ( 2,4) Nation 4$ ( 1.9) 25 ( 2.4) 33 ( 2.0) 285 ( 1.7) 284 ( 1.8) 274 ( 2.2) GENDER Male State 50 ( 11) 23 ( 1.8) 29 ( 1.5) 239 ( 1.3) 264 ( 1.7) 246 ( 1.8) Nation 30 ( 1.7) 20 ( 2.0) 29 ( 1.8) 255 ( 1.9) 275 ( 22) 264 ( 2.8) Foliat State 40 ( 1.5) 28 ( 2.0) 29 ( 1.6) 237 ( 1.3) 232 ( 11) 244 ( 1.8) Nation 48 ( 2.0) 28 ( 2.1) 32 ( 1.6) 252 ( 1.7) 209 ( 1.8) 2.99 ( 1.7) Paroaft. renisidage 998 and and Preaciam Pripkiamy Prolkdansy 11 Di 24 ( 1.0 30 1.4 NO 1.9 238 1.4 294 14 19 0.9 2? 14 30 2.0 20$ 11 252 2.4 274 1.3 18 ( 2.8) 2.8) 32 21 *** .) 228 3.0) 243 2.2 22 21) 32 3.6) 244 4.2) 23? ( 2.3) 251 4.6 16 ( 13) 21 ( 14) 32 ( 1.5) 251 ( 2.3) 232 ( 2.3) 25? ( 1.9) 18 ( 1.5) 26 ( 11) 21 ( 2.2) 256 ( 24) 246 ( 21) 265 ( 2.0) 19 ( 2.0) 20 ( 1.7) 48 ( 2.3) 209 ( 2.6) 244 ( 21) 2212 ( 11) 20 ( 1.9) 28 ( 2.4) 35 ( 25) 268 ( 3.2) 235 ( 3,8) 275 ( 2.0) 19 ( 1.4) 21 ( 1.4) 42 ( 2,3) 273 ( 3.0) 249 ( 2.8) 276 ( 2.0) 16 ( 1.4) 26 ( 1.6) 33 ( 2.7) 276 ( 2.8) 284 ( 2.0) 285 ( 2.0) 18 ( 1.1 25 ( 1.3 34 ( 11) 261 ( 2.2 239 ( 2.0) 285 ( 11 19 ( 1.3 27 ( 11) 26 ( 2.1 263 ( 21) 236( 3.0) 277 ( 11 17 ( 1.1) 23 ( 1.3) 42 ( 1.7) 280 ( 2.4) 237 ( 1.8) 283 ( 1.8) 18 ( 1.2) 27 ( 11) 33 ( 2.1) 283 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students), 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 North Carolina TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT High "Calculator.Uss" Group Other "Calcu later-Use" Group TOTAL end Pro Schwa Rareantogs and Pralkdancaf State 44 ( 0.9) 56 ( 0.9) 200 ( 1.4) 243 ( 12) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.8) 255 ( 1.5) RACE/ETHNICITy Whits State 48 ( 12) 52 ( 1.2) 268 ( 1.8) 255 ( 1.7) Nation 44 ( 1.4) SO ( 1.4) 277 ( 1.7) 263 ( 1.7) Black State 37 ( 2.1) 63 ( 2.1) 240 ( 2.0) 22$ ( 1.7) Nation 37 ( 3.4) 63 ( 3.4) 248 ( 3.9) 231 ( 3.0) Hispanic State 27 ( 4.4) ( 441 73 ( 4.4) 216 ( 3.2) Nation 38 ( 42) ( 4.2) 254 ( 4.6) 238 ( 3.0) Anstrican Indian State 45 ( 5.4) 55 ( 5.4) ete) Nation 29 (12.0) ( 71 (12.0) op** ( TYPE Of COMMUNITY Advantagad urban State 61 ( 8.0) 39 ( 8.0) 04. V** ) Nation 50 ( 3.8) 50 ( 3.8) 28$ ( 4.9)1 27$ ( 4.4)1 Disadvantaged urban State 38 ( 4.1) 64 ( 4.1) ( ***) Nation 38 ( 42) 62 ( 4.2) 262 ( 5.6)1 244 ( 3.9)1 Extreme rural State 41 ( 2.1) 59 ( 253 ( 2.6)1 238 ( 2.8) Nation 39 5.5) 61 ( 5.8) 269 ( 4.4)1 24$ ( 4.3)1 Other State 44 ( 1.1) 58 ( 1.1) 260 ( 1.5) 244 ( 1.5) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) Nmmlmm' 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 msuflicient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMEJ'TT North Carolina TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11100 NAEP TRIAL. STATE ASSESSMENT Nigh "Calculator-Use" Group Othoi "Calculator-Use" Group TOTAL and Pro Ramsey Pinverdase and Proficiency State 44 ( 58 ( 0.9) ZOO ( 1.4 243 ( 1.2) Nation 42 ( 1.3 58 ( 1.3) 272 ( 1.8) 2$5 ( 1.5) PARENTS' EDUCATION NS noniraduato State 37 ( 3.0) 83 ( 3.0) 245 ( 3.0) 225 ( 2.2) Nation 34 ( 3.3) GO ( 3.3) 246 ( 4.4) 242 ( 2.4) HS graduat State 42 ( 2.0) 58 ( 2.0) 249 ( 1.6) 235 ( 1.8) Nation 40 ( 2.2) 80 ( 2.2) 283 ( 2.0) 248 ( 1.6) Some cottage State 45 ( 2.7) 55 ( 2.7) 282 ( 2.1) 252 ( 2.2) Nation 43 ( 22) 52 ( 2.2) 277 ( 2.8) 258 ( 2.5) Collin* graduate State 48 ( 1.7) 52 ( 1.7) 275 ( 22) 256 ( 1.6) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 289 ( 1.9) GENDER Mat State 39 ( 1.6) 61 ( 1.6) 200 ( 1.6) 243 ( 1.5) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Firnale State 46 ( 1.5) 52 ( 1.5) 259 ( 1.8) 243 ( 1.4) Nation 45 ( 1.8) 55 ( 1.8) 289 ( 1.7) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 131 North Carolina TABLE A24 I Students' Reports on Types Ading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11100 NW TRIAL STATE ASSESSMENT Zero to Two Types Three Types Far Types MI& Parsentap and and Prollaboacy Praideng Parcodolla and Prallakincy State 22 ( 03) 32 ( 0.11) 46 ( 1.1) 234( 1.3) 245 ( 12) 261 (1.4) Nation 21( 1.0 30 ( 1.0) 46 ( 1.3) 244 j 2.0 258 ( 1.7) 272 ( 1.5) RACVETHNICITY Whits State 17 ( 1.0 30 ( 1.0) 53 ( 1.4, 24$ ( 257 ( 1.6) 269 ( 1A) Nation 16 ( 1.1 29 ( 1.3) 56 ( 1.5) 251 ( 2.2 26$ ( 1.5) 276 ( 1.7) Mack State 28 ( 1.5) 35 ( 1.3) 37 ( 1.6) 22$ ( 1.5) 229 ( 1.9) 239 ( 1.7) Nation 31 ( 1,9) 38 ( 2.2) 33 ( 2.4) 232 ( 3.2) 233 ( 3.9) 245 ( 3.3) Hispanic State 34 43) 39 ( 4.7) 27 ( 3.8) ) ( ft* ) Nation 44 ( 3.0) 30 ( 2.4) 29 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) American Indian State 31 ( 7.2) 4144 ( Mb* ) ( 5.8) f4.* ( 37 ( 6.0) elm ( es* ) Nation 29(11.1) .41 40 ( 4.9) 31 ( 9.2) TYPE OF COMMUNITY Advantaged urban Ste.;e5 55 ( 9.4) ( INN ) Nation 13 ( 3.8) 26 ( 2.1) 0.**) 61 ( 4.9) 287 ( 3.6)1 Disadvantaged urban State 29 ( 4.0) ,1.4* 0-.4) Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.6) 243 ( 2.9)1 2417 ( 3.7)1 257 ( 4.9)1 Extreme rural State 23 ( 1.8) 35 ( 2.0) 42 ( 1.9) 230 ( 3.4) 238 ( 2.6)1 254 ( 34)1 Nation 17 ( 4.9) 33 ( 3.2) 50 (. 5.1) ( 11..11 253 ( 4.3)1 263 ( 5.6)1 Other State 22 ( 0.9) 31 ( 1.0) 47 ( 1,3) 238 ( 1.7) 245 ( 1.4) 261 ( 1.5) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 1,5) 244 ( 259 ( 2.2) 272 ( 1.7) 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 t.he 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 sire is insufficient to permit a reliable estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A24 I Students' Reports on Types of Reading (continued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MO NAEP TRIAL - STATE ASSESSMENT Zero to Two Typos Throe Types Few Typos IDTAL Percentage and Proficiency Percentage and Proficiency Percentage and Preaching State 22 ( 0.8) 32 ( 0.0) 48 ( 1.1) 234 ( 1.3) 245 ( 1.2) 261 ( 1A) Nation 21 ( 1.0) 30 ( 1.0) 46 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) PARENTS' EDUCATION MS non-gradiat State 44 ( 3.1) 31 ( 2.7) 26 ( 2.8) 230 ( 2.9) 232 ( 2.6) 237 ( 3.9) Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) graduate 240 ( 3.4) 243 ( 3,3) 246 ( 3.3) State 27 ( 1.5) 37 ( 14) 38 ( 1.8) 232 ( 2.1) 239 ( 1.6) 251 ( 1.6) Nation 219 ( 2.2) 33 ( 1.9) 40 ( 1.7) 248 ( 22) 253 ( 2.7) 260 ( 2.1) Sam college State 17 ( 1.9) 32 ( 2.3) 51 ( 22) 247 ( 2.8) 258 ( 2.8) 263 ( 1.6) Nation 17 ( 1.5) 22 ( 1 7) 51 ( 2.0) 251 ( 4,0) 262 ( 2.6) 274 ( 1.9) College graduate State 10 ( 1.0) 26 ( 1.7) 64 ( 1.7) 243 ( 3.8) 257 ( 2.6) 270 ( 1.8) Nation 10 ( 0.8) 28 ( 1.8) 62 ( 2.0) 254 ( 2.8) 289 ( 2.5) 280 ( 1.8) GENDER Mao State 23 ( 1.0) 34 ( 1.'. 43 ( 1.4) 235 ( 1.8) 244 ( 1. 281 ( 1.8) Nation 21 ( 1.5) 31 ( 1.5, 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Female State 21 ( 1.2) 30 ( 1.2) 49 ( 1.4) 233 ( 1.7) 246 ( 1.8) 260 ( 1.6) Nation 22 ( 1.2) 29 ( 1.4) 49 ( 1.9) 24.4 ( 2.2) 258 ( 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. 1 38 THE 1990 NAEP TRIAL STATE ASSESSMENT 133 North Caro Una TABLE A2.5 1 Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 MEP TRIAL STATE ASSESSMENT Ono Hotr or Loss Two Hours Throe Hours FON tO Five Hours Six Houn or Mors TOTAL. Potentags and !roadway 10 ( 0.0) 259 ( 3.1) 12 ( 0.8) 209 ( 2.2) 12 ( 0.8) 270 ( 2.9) 13 ( 1.0) 270 ( 2.5) ( 0.9) IMP* 41 6 ( 0.8) 4.1. ( .11 8 ( 2.3) ( 441 14 ( 2.4) ( *es) 10 ( 2.7) ( 13 ( 5.0) ( «H.) 19 ( 4.1) 18 ( 1.4) ** 44P11 ( 1 .8) *** 9 ( 1.2) ( 1.1) 14 ( 3.3) 10 ( 0.7) 259 ( 3.7) 12 ( 1.0) 268 ( 2.6) Peroantaga and Pro Idiocy 18 ( 0.7) 258 ( 1.6) 21 ( 0.9) 266 ( ta) 22 ( 1.0) 263 ( 13) 23 ( 1.2) 275 ( 22) 10 ( 12) 233 ( 3.4) 13 ( 1.7) 239 ( 7.0) 16 ( 3.2) 20 ( 2.5) 245 ( 3.2) 13 ( 3.1) 01,1 17 ( 8.4) 24 ( 4.4) *In 25 ( 4.3) .44 ( 17 ( 3.1) 250 ( 4.0)1 18 ( 1.2) 249 ( 3.8)1 19 ( 2.6) 44. 1 8 ( 0.7) 258 ( 2.1) 21 ( 1.0) 269 ( 2.3) Rattaitsp and linecteacy 20 ( 0.8) 25a ( 1.5) 22 ( 0.8) 265 22 ( 1.0) 264 ( 1.91 24 ( 1.1) 272 ( 1.9) 10 ( 1.4) 238 ( 2.3) 17 ( 2.1) 239 ( 5.0) 10 ( 2.6) 19 ( 2.1) 242 ( 5.8) 26 ( 5.9) 111k ( 21 (10$) *** 18 ( 3.9) 21 ( 1i) 17 ( 5.1) 19 ( 2.1) 255 ( 5.0)1 19 ( 1.8) 250 ( 2.6)1 23 ( 2.0) 4144 ( 20 ( 1.0) 257 ( 1.7) 23 ( 1.2) 265 ( 2.1) Pamela,* and Praia Macy 32 ( tO) 248 1.3) 28 1.1) 260 ( 1.7) 30 ( 1.2) 258 ( 1.3) 27 ( 1.4) 267 ( 1.7) 30 ( 1.5) 23$ ( 1.8) 32 ( 1.8) 239 ( 4.0) 35 ( 4.3) 444 ( ..**) 31 ( 3.1) 247 ( 3.5) 23 ( 4.1) *** ( 28 ( 5.7) **it ( 24 ( 5.6) 30 ( 4.3) *4.* ( 31 ( 4.8) 34 ( 2.4) 251 ( 4.7)1 35 ( 2.6) 242 ( 3.1) 28 ( 2.7) 25$ ( 3.6)1 32 ( 1.1) 250 ( 1.5) 27 ( 12) 259 ( 2.2) lierasatasa ant Pralialmic:y 21 ( 1 235 ( 1 10 ( 245 ( IS) 14 ( 0.9) 248 ( 2.3) 12 ( 1.2) 253 ( 2.6) 32 ( 1.9) 227 ( 1.0) 32 ( 2,2) 233 ( 2.5) 32 ( 3.7) 04.1 17 ( 1.7) 230 ( 3.8) 28 ( 52) 22 ( 8.4) v.* 15 ( 0.4) **4,) ( 2.0) *04(44*) 28 (11.4) 4.4,41 20 ( 32) 238 ( 4.5)I 20 ( 22) 234 ( 3.8)1 19 ( 3.8) IMO ( **41 20 ( 1.0) 237 ( 1.7) 17 ( 4.4) 24$ ( 2$) State Nation RACE/ETHNICITY White Stat., Nation Flack State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extol.* rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 1 elk ( i g I THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A25 I Students' Reports on the Amount of Time Spent (continued) I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 14100 NW TRIM. STATE ASSESSMENT Ono Hour or Loss TWO HOOFS , Throe Hors Fos to Fly* Noun Six Notts or Moro TOTAL Peroaniage and Plialciancy 110 ( 0.6) 250 ( Si) 12 ( 0,6) 269 ( 2,2) normality and Pralicioncy 18 ( 0.7) 258 ( 14) 21 ( 0.0) 265(1.8) State Nation PARENTS' EDUCATION t45 non-gractusto State 10 ( 1.7) 15 ( 2.3) ( NO. ( Nation 12 ( 22) 20 ( 3.1) **a ( ( HS graduate State ( 1.0) 10 ( 1.3) 247 ( 4.0) 245 ( 2.5) Nation ( 1.0) 17 ( 1.4) 249 ( 4.7) 257 ( 2.8) Some ooNogo State 7 ( 1.3) 19 ( 13) 200 ( 2.6) Nation 10 ( 1.4) int) 25 2.4) 275 ( 2.7) Co Mtg. graduat State 14 ( 1.5) 21 ( 1.4) 277 ( 3,5) 273 ( 2.7) Nation 17 ( 1,3) 22 ( IA) 282 ( 2.8) 280 ( 2.5) GENDER M. State 10 ( 0.6) 17 ( 1.1) 257 ( 4.1) 255 ( 2.3) Nation 11 ( 0.9) 22 ( 1.2) 209 ( 3.3) 207 ( 2.0) Font** State 10 ( 04) 18 ( 1.0) 261 ( 3.7) 257 ( 2.2) Nation 14 ( 1.1) 20 ( 1.3) 209 ( 2.8) 209 ( 2.2) Parcentap Pannatage Paraintaga and and and Pinlidestcy Pro &fancy Praidancy 11 22 205 18 (( 21 ( 19 ( 249 ( 23 ( 259 ( 24 ( 262 ( 23 ( 209 ( 20 ( 255 ( 23 ( 277 ( 19( 255 ( 22 ( 267 ( 20 ( 258 ( 23 ( 264 ( ( 1.0) 21 ( tO) 1.51 248 ( 1.3) 235 ( 1.0) 04) 28 ( 1.1) 10 ( 1.0) 1.7) 200 ( 1.7) 246 ( 1.7) 2.2) *41 29 ( 229 ( 2.5) 3.3) 27 ( 229 ( 2.4) 2.6) 2.8) 2$ ( 24) 20 ( 2.4) 244 ( 3.2) 1.4) 35 ( 1.5) 23 ( 1.2 2.4) 243 ( IA) 230 ( 2.1 2.0) 32 ( 2.3) 19 ( 1.61 3.2) 253 ( 2.5) 248 ( 3.0) 14) 35 ( 2.2) 15 ( 1.5) 3.1) 250 ( 2.0) 248 ( 32) 211) 28 ( 2.2) 14 ( 1.5) 3.5) 267 ( 2.5) 242 ( 3.4) 1.5) 26 ( 1.9) 15 ( 1.7) 2.7) 260 ( 22) 246 ( 3.4) 1.1) 25 ( 1.5) 12 ( 1.1) 2.2) 270 ( 2.4) 255 ( 32) 1.1) 32 ( 1.3) 22 ( 12) 2.1) 249 ( 1.6) 236 ( 2.1) 1.0) 28 ( 1.3) 17 ( 1.5) 2.2) 202 ( 2.1) 248 ( 2.5) 1.1) 32 ( 1.1) /9 ( 1.3) 1.7) 247 ( 1.7) 235 ( 2.1) 1.4) 28 ( 1.6) 15 ( 12) 1.8) 258 ( 1.9) 241 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 North Carolina TABLE A26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT None One or Two Days Three Days or More TOTAL Pereentapt and Pelagic:dewy Percentage and Prolkiency Per01111111.0 and Proidency State 42 ( 1.1) S2 ( 0.0) 25 0.9) 252 ( 1.4) 254 ( 1.1) 242 1.4) Nation 45 ( 1.1) 32 ( 0,9) 23 1.1) 265 ( 13) 260 f 1.5) 250 ( 4.9) RACVETHNICITY White State 38 ( 1.4) 35 f 1.1) 27 ( 1.3) 2tZ ( 1.5) 263 ( 1.5) 2$3 ( 1.5) Nation 43 ( 12) 34 ( 1.2) 23 ( 12) 273 ( 1.8) 272 ( 1.7) 258 ( 2.1) Black State 50 ( 2.0) 27 ( 1.6) 2$ ( 1.7) 235 ( 1.6) 234 ( 1.9) 222 ( 22) Nation 56 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 3.2) 240 ( 4.1) 2.24 ( 3.5) Hispanic State 42 ( 42) 3.9) es* ( «HI 30 ( 45) 044 ( Nation 41 ( 3.3) 32 ( 22) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) American Indian State 43 ( 6A) 33 ( 6.5) 24 ( 5.0) ( e") 11.* ( *411 Nation 23 ( 6.6) ( !pee) 39 ( 5.1) ( 38 ( 5.2) ***) TYPE OF COMMUNITY Advantaged urban State 41 ( 2.6) *44) 31 ( 4.4) *14 ( <44) 2G ( 6.1) 4.1.) Nation 47 ( 2.3) 284 ( 4.4)1 38 ( 2.6) 279 ( 43)1 15 ( 3.7) 444) Disadvantaged urban State 48 ( 1.6) 23 ( 6.0) 29 ( 4.7) *14(4*4) Nation 42 ( 3.3) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 256 ( 4.2)1 238 ( 6.3)1 Extreme nral State 40 ( 2.6) 32 ( 2.4) 27 ( 2.0) 243 ( 2.9)1 246 ( 3,1) 241 ( 3.3)1 Nation 43 ( 4.4) 257 ( 4.1)1 32 ( 4.2) 264 ( 5.8)1 25 ( 3.9) 4.44) Other :-ttate 43 ( 1.2) 33 ( 1.0) 24 ( 1.1) 254 ( 1.5) 255 ( 1.4) 243 ( 1.8) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 266 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of 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 North Carolina TABLE A26 I Students' Reports on the Number of Days of (cIantinued) School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL. STATE ASSESSMENT Nene One or Two Days Three Days or More TOTAL Pereilltale and Prolidency Pardintass and Pralidenay Parcedain and Prolkiasei State 42 ( 1.1) $2 ( 0.9) 25 ( 0.9) 252 ( 14) 2$4 ( 1.1 242 ( 14) Nation 45 ( 1.1) aa1.51 23 ( 1.1) 265 ( 1.8) 21111$2 250 ( 1.9) PARENTS' EDUCATION HS non-graduate State 36 ( 2.5) 31 ( 2.6) 33 ( 2.6) 234 ( 2.9) 236 ( 2.3) 229 ( 3.1) Nation 38 ( 32) 20 ( 3.1) 38 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) N3 graduata State 42 ( 1.7) 32 ( 1.3) 27 ( 1.7) 245 ( 1.8) 244 ( 1.5) 235 ( 2.1) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.6) 249 ( 24) Sam coilesp State 41 ( 2.0) 38 ( 2.2) 23 ( 2.1) 258 ( 1.9) 262 ( 1.9) 258 ( 3.3) Nation 40 ( 1.8) 37 ( 1.6) 23 ( 1.6) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) College graduate State 46 ( 1.5) 33 ( 1.4) 21 ( 12) 265 ( 2.3) 269 ( 1.9) 255 ( 2.0) Nation 51 ( 1.6) 33 ( 1.2) 18 ( 1.3) 275 ( 2.1) 277 ( 1.7) 205 ( 3.1) GENDER Mato State 45 ( 1.4) 31 ( 1.2) 25 ( 1.0) 251 ( 1.6) 254 ( 1.5) 243 ( 1.9) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 14) 268 ( 2.0) 287 ( 2.1) 250 ( 2.6) Rotate State 40 ( f .5) 34 ( 1.2) 26 ( 1.2) 253 ( 1.8) 254 ( 14) 242 1.6) Nation 43 ( 1.4) 32 ( 1.1) 25 (1.3) 264 ( 2.3) 256 ( 1.7) 250 1.8) The standard errors of the estirnated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 c72 THE 1990 NAEP TRIAL .il'ATE ASSESSMENT 137 North Carolina TABLE A27 1 Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Stranin Ain* AVM* Undecided, Disagree, Shan* Disagree TOTAL. and Pieliciancy Parcentags and Proadancy Percentage and Praticiancy State 32(1.0) 48 ( 1.0) 20 0.9) 250 ( 1.3) 250 ( 1.3) 241 1,4) Nation 27 ( 1.3) 49 ( 1.0) 24 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) RACE/ETHNICITY Obit* State ( 1.0) 48 ( 1.3) 22 ( 1.2) 269 ( 1.8) 262 ( 1.5) 250 ( 1.9) Nation 26 ( 1-5) 48 ( 1.3) 20 ( 1.5) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Wade State 39 ( 1.8) 40 ( 1.5) 15 ( 1.1) 240 ( 1.6) 228 ( 1.6) 222 ( 2.3) Nation 32 ( 2.5) 52 ( 2.3) 16 ( 1.9) 247 ( 4.1) 233 ( 3.3) 227 ( 4.2) Hispanic State 26 ( 3.6) 50 ( 44) 24 4.9) ( IN* eel Nation 24 ( 2.5) 48 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 236 ( 3.8) American Indian State 29 ( 7.6) 57 ( ( 8.4) "") 14 ( 2.9) ( «el Nation 23 ( *** 7.4) ***) 4$ (14.9) ( `") 29 ( 9.5) TYPE OF COMMUNITY Advantaged urban State 28 ( 5.6) 53 ( 3.9) 19 ( 1.8) ( ( G111 Nation 17 ( 3.2) 55 ( 2.4) 25 ( 4.2) 280 ( Disadvantaged urban State 33 ( 5.7) ***) 46 ( 1.4) 19 ( MP* ( 4.6) 44.1 ) Nation 26 ( 2.9) 4$ ( 2.9) 26 ( 3.2) 260 ( 5.6)1 249 ( 4.6); 240 ( 4.5)1 Extrem rural State 34 ( 2.5) 47 ( 2.0) 19 ( 2.7) 248 ( 3.4)1 241 ( 2,8) 242 ( 3.0)1 Nation 34 ( 2.8) 49 ( 2.2) 17 ( 1.4) 270 ( 3.9)1 252 ( 4.1)1 11. Other State 32 ( 1.1) 47 ( 1.2) 20 ( 1.1) 25$ ( 1.6) 251 ( 1.5) 240 ( 1.5) Nation 27 ( 1.4) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 250 ( 1,9) The sulnclard 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 rehable estimate (fewer than 62 students). 138 THE 1990 NAEP TRIAL STATE ASSESSMENT North Carolina TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT ,_ .. _ Wrap* kiln Agree Undecided, Disagree, Strongly Minim =wiwommlNONNINNINMENI.4111111111011=1.101=11141001111.110P, TOTAL Percentage sed Proddincy loorcontago ind Proliciancy Paroonlay and State 32 ( 1.0) 48 ( 1.0) 20 ( 03) 2510 ( 1.3) 250 ( 1.3) 241 ( 1.4) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) PARENTS EDUCATION KS non-graduate State 29 ( 2.?) 48 ( 2.9) 23 ( 2.8) 2381 3.5) 222 ( 2.1) 227 ( 3.3) Nation 20 ( 2.6) ..**) 50 ( 243 ( 3.3) 2.6) 30 ( 235 ( 3.8) 4.3) S graduate State 30 ( 1.6) 48 ( 1.6) 22 ( 1.5) 249 ( 2.0) 241 ( 1.9) 233 ( 2.2) Nation 27 ( 2.1) 47 ( 2.3) 26 1 2.0) 282 ( 2.7) 255 ( 2.3) 245 ( 2.4) Some coNego State 33 ( 2.3) 47 ( 2.2) 20 ( 1.8) 261 ( 1.9) 259 ( 1.9) 252 ( 3.0) Nation 28 ( 2.5) 47 ( 2.4) 2$ ( 16) 274 ( 3.1) 267 ( 1.9) 258 ( 12) Capp graduate State 38 ( 1.7) 47 ( 1.7) 17 ( 1.1) 268 ( 2.2) 264 ( 1.9) 254 ( 3.1) Nation 30 ( 2.3) 51 ( 1.8) 19 ( 1.8) 280 ( 2.4) 274 ( 2.2) 260 ( 2.5) GENDER M. State 32 ( 1.2) 48 ( 1.5) 20 ( 1.2) 258 ( 1.7) 249 ( 1.6) 243 ( 2.0) Nation 28 ( 1.5) 48 ( 1.2) 24 ( 14) 273 ( 2.3) 203 ( 2.0) 251 ( 2.4) Female State 32 ( 1.4) 47 ( 1.2) 20 ( 1.1) 256 ( 1.8) 251 ( 1.4) 239 ( 1.7) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 269 ( 2.1) 202 ( 1.8) 252 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 ,1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing Service (ETS), Westat, and National Computer Systems (NCS). The program benefitted from the contrthutions of hundreds of individuals at the state and local levels GovernorS, Chid State School Officers, State and District Test Directors, State Coordinators, and district administrators -- who tirelessly provided their wisdom, experieace, and hard work. Maly, and most importantly, NAEP is Fateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (CCSSO) for its considerable contautions to the program, especially its management of the National Assessment Planning Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In particular, we note the significant contautions of Ramsay Selden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering. Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the US. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the Natio Lal Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a geat deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people from school districts, colleges and universities, and State Education Agencies worked tirelessly to help ETS staff develop the assessment and a framework for interpreting the results. Under the NAEP contract to ETS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mazzeo, with consultation from Eugene Johnson and Donald Rock John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koff ler, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zaback, The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Ku lick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCain ley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koff ler wrote the text for the report. Kent Ashworth was responsible for coordinating the cover design and final printing of this report. Special thanks are also due to many individuals for their invaluable assistance in reviewing the reports, especially the editors who improved the text and the analysts who checked the data. 145 MR GOVERNMENT PRINTING OFF1CS : 1991 0 - 293475 QL 3 (BK 28) 146