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DOCUMENT RESUME ED 330 575 SE 052 085 TITLE The State of Mathematics Achievement in Ohio: 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 052 055-0c6. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solv%ng; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS Iitional Assessment of Educational Progress; *Numeracy; *Ohio; State Mathematics Assessments; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In Ohio, 2,673 students in 101 public schools were assessed. This report describes the mathematics proficiency of Ohio eighth-graders, compares their overall performance to students in the Central 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 commuirity, parents' educational level, and gender). To provide a context .!or 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, Ohio students had an average proficiency of 264 compared.to 261 nationwide. Many fewer students (0hio-12%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Ah ent in OHIO The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD POPY ITAPIRE U S DEPARTMENT Of EDUCATION On. P filut ReStnIU P and Irprovemeht I PU TIONAL RE SOURC ES INF OR MA T tON CENTFR tERIC1 hN do( ,,ment nas neer, frtlrOduCed as ms the pe,50h 'rgan.1111.0h nSu;shate beef% made to "prove ronts ot oe* opmonSstatec,h m'nEef g°17olt:',-%poctrcry" '"'eser" 'hfh" ;:i c5 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 represcntati.e and continuing assessment of what America's students know and can do in various subject areas. Since 1969. assessments have been conducted periodically in reading, mathematics. science, writing. history/geography. and other fields. By making objective information on student performance available to policymakers at the national, state, and local levels, NAEP is an integral part of our nation's evaluation of the condition and pmgress 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 Commissioner. who is also roponsible for providing continuing reviews, including validation studies and solicitation of public comment, on NAEP's conduct and usefulness. In 19814. Congress created the National Asseieiment Governing Board t NAGB) to formulate policy guidelines for NAEP. The board is responsible for selecting the subject areas to be assessed, which may include adding to those specified by Congress; identifying appropriate achievement goals for each age and grade; developing assessment objectives: developing test specifications: designing the assessment methodology; developing guidelines and standards for data analysis and for reporting and disseminating results; developing standards and procedures for interstate, regional, and national comparisons: improving the form and us: of the National Assessment; and ensuring that all items selected for use in the National Assessment are free frim racial, cultural, gender. or regional bias, The National Assessment Governing Board Richard A. Boyd. Chairman Executive Director Martha Holden Jennings Foundation Cleveland, Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.O.C.E.S. Saratoga Springs. New York Franck Alexauder Associate Superintendent California Department of Education Sacramento, California David P. Battini High School History Teacher Cairo-Durham High School Cairo, New York Parris C. Battle Teacher Horace Mann Elementary School Miami. Florida Mary R. Blanton Attorney Cromwell, Porter. Blanton & Blanton Salisbury. North Carolina Boyd W. BoehlJe Attorney Gaa.ss, Klyn, & Boehlic Pella. Iowa Linda R. Bryant Teacher Ureenway Middle School "kachcr Center Pittsburgh. Pennsylvania Honorabk Mkhael N. Castle Governor of Delaware ('arvel State Office Building Wilmington, Delawiue Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hartford. Connecticut Chester E. Finn. Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.('. Michael S. Glode Wyoming State Board of Education Saratoga, Wyoming Christine Johnson Principal Abraham Lincoln High School Denver. Colorado John Lindley Principal South Colby Elementary School Port Orchard. Washington Carl J. Mwer Director of Schools The Lutheran Church Missouri Synod International Center St. Louis. Missouri Mark D. Mu.sick President Southern Regional Education Board Atlanta. Georgia Honorabk 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.(7. Honorable Richard W. Riley Attorney Nelson. Mullins. Riley and Scarborough Columbia, South Carolina Thomas Toputes Attorney Law Offices of Frank Rogozienski Coronado. California Herbert J. Walberg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and Improvement (Ex-Officioi S. Department of Education Washington. D.C. Roy Truby Executive Director. NACB Washington, D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement in OHIO The Trial State Assessment at Grade Eight Report No: 2.; .ST-02 June 1991 Prepared by Educational Testing Service under Contra,A with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bnmo V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAM) Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Notion and all State participants, or for single copies of the Executive Summary while supplies last, write; Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jeisey Avenue, NW Washington, D.C. 20208-5641 or call 1-800424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Congress, Catalog Card Number: 91-61478 ISBN: 048683-14-9 The wad( upon which this publication is based was performed for the National Center for Education Statistics. Office of Educational Research and Improvement, by Educational Testing Service. Educational luting Service is an equal oppornmitylaffurtative action employer Educational Tatting Sdrvics, EFS, sad if.) are registered uademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of Ohio 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Ohio 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 Pareilts' Education Level 29 Gender 31 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 111 PART TWO Finding a Context for Understanding Stmdents' Mathematics Proficiency 37 Chapter 3. What Arc 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 ig Chapter 5. How Are Calculators Used" 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics? 67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Rtading 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 Ohio THE NATION'S REPORT CARO EXECUTIVE SUMMARY In 1988, Congress pasod new legislation for the National Assessment of Educational Progxess (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national essessv.ents that NAEP has conducted since its inception. As a result of the le3islation, the 19Q 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-gtade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully de6gned 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 mon'....ored 50 percent of the sessions As part of the quality assurance program designed to ensure that the sessions were being colducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT 1 Ohio In Ohio, 101 public schools participated in the assessment. The weighted school participation rate was 98 percent, which means that all of the eighth-grade students in this sample of schools were representative of 98 percent of the eighth-grade public-school students in Ohio. In each school, a random sample of students was selected to participate in the assessment. As estima.ed by the sample, 0 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 8 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a 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 6 percent of the population, respectively. In total, 2,673 eighth-grade Ohio 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 Ohio. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from Ohio on the NAEP mathematics scale is 264. This proficiency is no different from that of students across the nation (261). Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- en the NAEP scale. 9 2 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio In Ohio, 98 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in Ohio (12 percent) and 12 percent in the naiion appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementaty geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content arms -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in Ohio performed comparably to students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the Ohio eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In Ohio: White students had higher average mathematics proficiency than did Black or Hispanic students. Further, a greater percentage of White students than Black or Hispanic students attained level 300. The results by type of community indicate that the average mathematics performance of the Ohio students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural areas, or areas classified as "other". In Ohio, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 27 points higher than that of students whose parents did not graduate from high school. The results by gender show tkiat eighth-grade males in Ohio had a higher average mathematics proficiency than did eighth-grade females in Ohio. In addition, there was no difference between the percentages of males and females in Ohio who attained level 300. Compared to the national results, females in Ohio performed no differently from females across the country; males in Ohio performed no differently filom males across the country. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 3 Ohio A Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for imptoving instruction and setting policy when supplemented with contextual information about schools, teacheis, 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 wore asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the cutrent 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 Ohio are as follows: More than half of the students in Ohio (66 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 Ohio, 81 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in Ohio were taking eighth-grade mathematics (63 percent) than were taking a course in pre-algebra or algebra (36 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 Ohio spent 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 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 ASSESSMENT Ohio In Ohio, 12 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 34 percent of the students were taught by teachers who got only mate er none of the resourres they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Ohio, 27 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. In Ohio, 51 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, where 66 percent of students were taught by teachers who were certified at the highest level available 4,n their states. Students in Ohio who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of these materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. Some of the eighth-grade public-school students in Ohio (13 percent) watched one hour or less of television each day; 11 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 5 Ohio ME NATION'S REPORT CARD INTRODUCT ION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following paxticipants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Vffginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Ohio This report describes the performance of the eighth-grade public-school students in Ohio 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 stuucnts in Ohio. Part One describes the mathematics performance of the eighth-grade public-school students in Ohio, the Central region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Ohio, the Central region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment stovey 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)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(i))) As a result of the legislation, the 1990 NAEP program included a 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-schoc I students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 7 4 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and pattemee -fter the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council al Chief State School Officers in mid-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,1 the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-grade public-school students in Ohio, in the Central region, and for the nation. Results also are provided for gaups of students defmed by shared characteristics -- race/ethnicity, type of community, parents education level, and gender. Definitions of the subpopulations referred to in this report arz presented below. The results for Ohio 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 not guarantee representative national or regional results, since not every state participated in the program. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards _for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 9 Ohio RACE/ETHNICITY Results are presented for students of different racutl/ethnic groups based on the students' self-identification of their race/et:micity 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, thr data for all students, regardless of whether their racial/ethnic group was reported separately, were included m computing overall results for Ohio. 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. Disadvantgged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are on welfare or are not regularly employed. Extreme Rural: Students in this group live outside metropolitan statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indimte the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. :6 10 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio 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 ar-1 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 Washincon, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURE 1 J Regions of the Country NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Alabama Alaska Delaware Arkansas Indiana Arizona District of Columbia Florida Iowa California Maine Georgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana Now Jersey North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohio Oklahoma Rhode Island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT 11 Ohio 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 particularway. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of till relationships among combinations of these subpopulations or background questions. Because the proportions of st adents in these subpopulations ard their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. 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 strorg (i.e., the difference is statistically significant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) regardless of whether the sample means or sample propotions 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 pere nt confidence interval for the difference between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. When three or more groups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendix. n 12 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-aIgebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRJAL STATE ASSESSMENT 13 Ohio Profile of Ohio EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in Ohio, the Central region, and the nation. This profile is based on data collected from the students and schools participating in the Trial State Assessment. TABLE 1 I Profile of Ohio Eighth-Grade Public-School I Students PERCENTAGE OF STUDENTS 1090 NAEP TIUAL STATE ASSESSMENT Ohio Central Nation , .11111, DEMOGRAPHIC SUBGROUPS Percentage Peruentage Percentage Nace/Elleticity White 82 ( 0.9) 79 ( 2.8) 70 ( 0.5) Black 11 ( 0.8) 13 ( 3.2) 18 ( 0.3) Hispanic 3 ( 0.4) 6 ( 1.0) 10 ( 0.4) Asian 1 ( 0.3) ( 0.4) 2 ( 0$) American Indian ( 0.3) 1 ( 0.4) 2 ( 0.7) Type of Community Advantaged urban 14 ( 3.3) 3 ( 3.1) 10 ( 3.3) Disadvantaged urban 13 ( 1.7) 10 ( 42) 10 ( 2.8) Extreme , ural 10 ( 2.2) 8 ( 8.0) 10 ( 10) Other 03 ( 4.2) 79 ( 7.7) 70 ( 4.4) Parents Education Did not finish high school 7 ( 0.7) 7 ( 0.9) 10 ( 0.8) Graduated high school 32 ( 1.1) 33 ( 2.1) 25 ( 1.2) Some education after high school 20 ( 0.8) 19 ( 0.9) 17 ( 0.9) Graduated college 36 ( 1.7) 35 ( 1.8) 39 ( 1.9) Gender Male 53 ( 0.9) 50 ( 1.4) 51 ( 1.1) Female 47 0.9) 50 ( 1.4) 49 ( '1.1) a 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 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Ohio schools and students sampled for the 1990 Thal State Assessment. In Ohio, 101 public schools participated in the assessment. The weighted school participation rate was 98 percent, which means that all of the eighth-grade students in this samplo of schools were mpresentative of 98 percent of the eightL wade public-school students in Ohio. TABLE 2 I Profile of the Population Asaessed in Ohio EIGHTH-ORAN PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution Weighted school participation rate after substitution Number of schools ortginaily 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 105 2 ea 4 2 101 EIGHTWORAOF PUBLIC-1CHOOL 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 95% I 3,129 134 0% 0% 4% 0% 2.800 2.073 A.- I THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Ohio In each school, a random sample a 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 8 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a 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 6 percent of the population, respectively. In total, 2,673 eighth-grade Ohio public-school students were assessed. The weighted student participation tate 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 Ohio. 16 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Ohio Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall perfonmance 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 siudents in Ohio. Chapter 1 compares the overall mathematics performance of the students in Ohio to students in the Central 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 defmed by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 17 Ohio CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from Ohio on the NAEP mathematics scale is 264. This proficiency is no different from that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School Mathematics Proficiency NAEP Manama tics Scale 200 225 250 275 300 SOO Average Proficiency Ohio Central Nation 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 6-04). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difTerence in the average mathematics proficiency between the two populations of interest. 24 18 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio 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 denribe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are given in Figure 3. It is important to note that the defmitions of these levels arc 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 Ohio, 98 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in Ohio (12 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properiies, 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 Ohio, Central region, and national results for each content area. Students in Ohio performed comparably to students in the nation in all of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 Ohio FIGURE 3 f Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level hme some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and diVision problems. These students can identify solutions to one-step word problems and select the greatest four-digit number in a list. In measurement, these students can read a ruler as well as common weight and graduated scales. They also can make vOlume ComparisOns based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they ere able to reed simple bar graphs. In the algebra dimension, these students can recognize translations of word Problems to numerical sentences and extend simple pattern sequences. ILEVEL: 250 1 Simple Multiplicative Reasoning and Two-Step Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to 'other elementary two-Step word prOblerns. In these basic problem-solving situations, they can identify missing or extraneous information and have some knowledge of when to use computational estimation. They have a rudimentary understanding of such concepts as whole number place value, "even," "factor," and "multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and probability. In algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions. 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio FIGURE 3 I Levels of Mathematics Proficiency (continued) I LEVEL 300 .011 Aeasoning and Problem Solving involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations Students at this level are able to represent, interpret, and perform simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, and recognize the equivalerice between common fractions and decimals, Including pictorial representations. They can interpret the meaning of percentS leas than and greater than 100 and apply the concepts ot percentages to Solve simple problems. These students demonstrate some evidence of using mathematical notation to Interpret expressions, including those with exponents and negative integers. In measurement, these students can find trie perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, arid 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 3501 Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to include some properties of exponents. They can recognize scientific notation on a Calculator and make the transition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles to solve problems. They can find the circumferences of circles and the surface areas of solid figures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirect measurement. These students also can apply their knowledge of the properties of geometric figures to solve problems, such as determining the slope of a line. In data analysis, these students can compute means from quency 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. Tney cart determine the nth term of a sequence and give counterexamples to disprove art algebraic generalization. THE 1990 NAEP TRIAL STATE ASSESSMENT 21 Ohio FIGURE 4 I Levels of Eighth-Grade Public-School I Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation 0 20 40 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 1-1-I). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 26 22 THE 1990 NAEP TRIAL STATE ASSESSMENT Percentago 0 ( 0.0) 0 ( 0.2) 0 ( 0.2) 12 ( 0.9) 12 ( 2.5) 12 ( 1.2) 87 ( 1.3) 70 ( 3.2) 64 ( 1.6) 98 ( 0.3) 98 ( 0.9) 97 ( 0.7) Ohio FIGURE 5 I Eighth-Grade Public-School Mathematics I Content Area Performance State Region Nation State Region Nation State Regioo Nation State Region Nation State Region Nation , . 5 0 200 225 250 275 Average Proficiency 268 ( 1.0) 270 ( 2.7) 256 ( 1.4) 259 ( 1.2) 263 ( 3.4) 258 ( 1.7) 250 ( 1.1) 282 ( 3.1) 259 ( 1.4) 268 ( 1.2) 255 ( 3.2) 282 ( 1.8) 282 ( 1.0) 283 ( 2.1) 260 ( 1.3) 300 500 Mathematics Submit!. Proficiency The standard errors are presented in parentheses. With about 95 percent certamty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-0-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 0 CI 14. 4 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 23 CHAPTER 2 Ohio 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/ETILNICITY 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). Avelage mathematics performance results for White, Black, and Hispanic students from Ohio are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black or Hispanic students. Figure 7 presents mathematics performance by proficiency levels. Thf! figure shows that a greater percentage of White students than Black or Hispanic students attained level 300. 24 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio FIGURE 6 I Average Eighth-Grade Public-Scbool I Mathematics Proficiency by Race/Ethnicity MEP Mathemalks Seats 200 225 250 275 300 500 Mango Proficiency * *. tmliwq Foieso4 reamt Ps Ohlo White Black Hispanic Central WhIte Black Hispanic Nation White Black Hispanic The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 04-1). 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). tL THE 1990 NAEP TRIAL STATE ASSESSMENT 25 Ohio 111E NATION'S REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARO I Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Black Hispanic ROon White Black Hispanic Mallon White Black Hispanic LEVEL 250 State White Black Hispanic R9Ian White Black Hispanic Nation White Black Hispanic LEVEL 200 Stat White Black Hispanic Region White Black Hispanic Nation White Black Hispanic 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 1-44). 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). 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 14 ( 1.0) 1 ( 0.9) 2 ( 1.7) 14 ( 2.8) I ( 1.0)1 ( 15 ( 1.5) 2 ( 1.3) 3 ( 1.1; 74 ( 1.3) 24 ( 2.1) 33 ( 6.7) 79 ( 3.1) 23 ( 4.7)1 sax ( et* ) 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) ( 0.2) 90 ( 1.7) 93 ( 2.5) 100 ( 0.4) 111 ( 4.4)1 ( '") 1111 ( 0.4) 00 ( ) 93 ( 1.8) Ohio TYPE OF COMMUNII'Y Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, disadvantaged urban areaa, extreme rural arms, and areas elassifkd as "other". (These are the "type of community" groups in Ohio with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Ohio students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural amas, or areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community NAEP Mathematics Scale 200 225 250 275 300 500 Average Proficiency 1404 Ohio Advantaged urban 2.511, 1-404 Disadvantaged urban ( 3.43) P1111 Extreme rural 217 ( 2,5$ Other IN ( .14) Central Advantaged urban ( "") P-4+4 Disadvantaged urban 221 ( SA)l Extreme rural IPrI Other 3111 ( 3.4) Nation 1-4/1.1.4 Advantaged urban 351 ( 3.1)1 Disadvantaged urban $411 ( 3.5$ oPA4 Extreme rural 21$ ( 4.1$ t+i Other 201 ( 1.8) The standard errors are presented in parentheses. With about 95 peroent 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 1-1-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 27 Ohio FIGURE 9 LEVEL 300 State Adv. urban Disadv. urban Ext. rural Other Adv. urban Wady. urban Ext. rural Other Won Adv. urban Disadv. urban Ext. rural Other LEVEL 250 State Adv. urban Disadv. urban Ext. rural Other i tion Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban DIsadv. urban Ext. rural Other LEVEL 200 State Adv. urban Disadv. urban Ext. rural Other Region Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community 0 20 40 00 SO 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 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). 22 ( 2.8)1 5 ( 1.7) 10 ( 2.0)1 12 ( 1.2) ***) ( 1.0)1 mot ( 13 ( 2.9) 29 ( 4.8)1 7 ( 2.1)1 ( 2.3)1 12 ( 1.2) 97 ( 2.9)t 3S ( 5.1) 74 ( 4.7)1 67 ( 1.8) 31 ( 5.7)t lout 73 ( 4.2) 93 ( 4,8)1 49 ( 5.0)1 U ( 6.2)1 64 ( 2.3) 100 ( 0.5)1 92 ( 2.3) Oa ( 0.7)i 90 ( 0.3) ,,,, ..) 92 1 3.0)1 Ka* *.) 99 ( 0.9) 100 ( 0.0) 96 ( 1$)1 97 ( 2.8)1 97 ( 1.0) 100 3 4 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figuars 10 and 11). In Ohio, the average mathematics proficiency of eighth-grade public-school students havingat least one parent who graduated from college was approximately 27 points highes than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, about the same percentage of students in Ohio (36 percent) and in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 7 percent for Ohio and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School i Mathematics Proficiency by Parents' Education NAEP Mathematics $cale 200 225 250 275 300 SOO Average Proficiency it4 Ohio HS non-graduate $P ( 2:1) HS graduate :SP( 1.2) Some college 31*( College graduate t74( 41.1) Central HS non-graduate HS graduate Some college College graduate Nation 141 HS non-graduate HS graduate HI Some college tt4 College graduate mit ( 1744 1Lsig 07:41 Ost The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 nandard errors of the estimated mean (95 percent confidence interval, denoted by H-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difTerence between the populutions. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Ohio THE NMI= Ivor. FIGURE 11 I Levels of Eighth-Grade Public-School CAR0 1 Mathematics Proficiency by Parents' Education LEVEL 300 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 230 State HS non-grad. HS graduate Some college College grad. Region HS ncin-grsd. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 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. 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 14-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 3 ( 1.4) ( 0.9) 12 ( 1.7) 21 ( 1.9) ( *44) 9 ( 3.9) 4 ( 3.4) 17 ( 3.7) ( 0.9) 5 ( 1.5) 12 ( 14) 21 ( 1.9) 44 ( 4.9) 59 ( 2.3) 77 ( 1.9) 77 ( 15) mou ( 444) W ( 4.1) 75 ( 5.1) 79 ( 3.9) 37 ( 4.6) 55 ( 2.7) 71 ( 2.8) 78 ( 2.0) 95 ( 2.1) ( 0.8) 100 ( 0.2) 911 ( 05) Assi ( .44) 59 ( 1.2) 100 ( 0.0) 90 ( 0.9) 99 ( 1.9) 17 ( 0.8) ( 0.7) 90 ( 0.7) 100 30 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio GENDER As shown in Figure 12, eighth-grade males in Ohio had a higher average mathematics proficiency than did eighth-grade females in Ohio. Compared to the national resuhs, females in Ohio performed no diffesently from females across the country; males in Ohio performed no differently from males across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by I-1-1). If the confidence intervals for the populations do not overlap, there is a statistially significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in Ohio who attained level 200. The percentage of females in Ohio who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in Ohio who attained level 200 was similar to the percentage of males iv the nation who attained level 200. 3 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 31 Ohio FIGURE 13 I Levels of Eighth-Grade Public-School I Mathematics Proficiency by Gender LEVEL 300 State Male Female Reston 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 20 40 so 80 100 Percentage at or Above Proficiency Levels The standard errors are prelented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-1-4). 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. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 14 ( 1.3) 11 ( 1.1) 14 ( 4.8) 9 ( 2.3) 14 ( 1.7) 10 ( 1.3) 70 ( 1.7) 53 ( 1.9) OS ( 3.3) 71 ( 4.0) ( 2.0) 64 ( 1.8) 90 ( 0.4) 911 ( 0.6) 99 ( 0.6) 911 ( 1.2) 97 ( 0.9) 97 ( 0.8) Ohio In addition, there was no difference between the percentages of males and females in Ohio who attained level 300. The percentage of females in Ohio who attained level 300 was similar to the percentage of females in the nation who attained level 300. Also, the percentage of males in Ohio who attained level 300 was similar to the percentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. 3;) THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Ohio TABLE 3 I Eighth-Grade Public-School Mathematics i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1990 NAEP TRIAL STATE AS SESSMENT Numbers and Operations Measurement Geometry Data Malys's, Statistics, and Probability Algebra and Functions TOTAL proficiency Proficiency Proficiency PnificiencY PruficiwCY State 288 ( 10) 259 ( 12) 260 ( 1.1) 266 ( 1.2) 262 ( 1.0) Region 270 ( 2.7) 263 ( 3.4) 262 ( 3.1) 265 ( 3.2) 263 ( 2.1) Nation 206 ( 1.4) 258 ( 1.7) 259 ( 1.4) 262 ( 1.8) 260 ( 1.3) RACE/ETHNICITY White State 273 ( 1.0) 265 ( 1.2) 264 ( 1.1) 272 ( 1.3) 267 ( 1.0) Region 276 ( 2.9) 271 ( 3.7) 288 ( 3.0) 273 ( 3.1) 269 ( 2.3) Nation ac 273 1.6) ( 2.0) 267 ( 1.5) 272 ( 1.8) 26$ ( 1.4) State 240 ( 1.6) 226 ( 2.1) 231 ( 1.8) 227 ( 2.3) 215 ( 1.8) Region 241 ( 8.5)1 223 ( 3$)1 231 ( 42)1 225 ( 7.0)1 231 ( 1.9)1 Nation 244 ( 3.1) 227 ( 3.8) 234 ( 2.8) 231 ( 3.8) 237 ( 2.7) Hispanic State Region 44,41. 44.* 226 ( 5.5) **el 241 ( 3.9) *4.&) 235 ( 4.5) ,free ap,v) 238 ( HP* ( 3.7) *On Nation 248 ( 2.7) 238 ( 3.4) 243 ( 32) 239 ( 3.4) 243 ( 3.1) TYnE OF COMMI1NITY Advantaged urban State Region 283 ( 3.1)1 ity eirs) 276 ( 2.6)1 RS/ 277 *1M ( 2,8)1 ) 284 ( *ST ( 3.0)1 Ittlf 278 ( 2.5)1 Nation 283 ( 3.2)1 281 ( 3.2)1 277 ( 5.2)1 285 ( 4.8)1 277 ( 44)! Disadvantaged urban State 247 ( 3.3) 234 ( 4.9) 238 ( 3.7) 238 ( 5.0) 243 ( 3.7) Region 245 ( 2.2)1 228 ( 5.9)1 236 ( 6.7)1 231 ( 5.0)1 234 ( 4.7)1 Nation bdrame rural 255 ( 3.1)1 242 ( 4.9)1 24$ ( 3,7)1 247 ( 4.6)1 247 ( 32)1 State Region 272 ( 2.7)1 285 ( **. 3.9)1 262 ( ( 2.7)1 270 ( 3.7)1 285 ( 2.3)1 Nation 258 ( 4.3)1 254 ( 4.2)! 253 ( 4.5)1 257 ( 5.0)1 258 ( 4.8)/ Othsr State 269 ( 12) 260 ( 1.5) 260 ( 1.4) 267 ( 1.4) 262 ( 1.1) Region 273 ( 3.5) 266 ( 4.3) 264 ( 3.7) 267 ( 4.1) 265 ( 2.8) 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. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE 3 I Eighth-Grade ,Schooi Mathematics (cmtinued) I Content Area Performance by Subpopuiations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 11180 NAEP TRIAL STATE ASSESSMENT Numbers and OPITs4006 Measurement Geometry Date Analysis' Statistiml, 604 Probability Algebra end Functions TOTAL PreSciancy Prelldoncy Pretkiency PrOvisney State 266 ( 1.0) 250 ( 240 1.1) 260 ( 1.2) Region Nation 270 ( 266 ( 2.7) 1.4) 263 256 3.4 ( 1.7 202 ( 250 3.1) ( 14) 205 ( 262 ( 12) 1.6) PARENTS' EDUCATION NS non-graduate State 251 ( 22) 238 ( 3.5) 245 ( 2.3) '<ida 3.5) Region ( 04* ( 4011 ( **It) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) :1" 3.1) NO gradtude State 261 ( 1.2) 253 ( 1.0) 254 ( 1.4) 258 ( 1.5) Region 269 ( 23) 258 ( 3.8) 257 ( 3.4) 260 ( 3.2) Nation 259 ( 1.8) 243 ( 2.1) 252 ( 1.6) 253 ( 2.2) Sem college State 274 ( 1.3) 265 ( 22) 263 ( 1.6) 272 ( 1.6) Region 275 ( 32) 270 ( 5.7) 264 ( 4.9) 273 ( 4.7) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 24) College graduate State 279 ( 1.6) 270 ( 1.8) 270 ( 1.5) 277 ( 1.7) Region 277 ( 42) 270 ( 4.4) 270 ( 4.3) 273 ( 4.5) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 276 ( 2.2) GENDER Male State 271 ( 1.2) 265 ( 1.4) 263 ( 1.2) 200 ( 1.5) Region 271 ( 3.9) 267 ( 4.8) 264 ( 3.7) 285 ( 34) Nation 268 ( 2.0) 262 ( 2.3) 200 ( 1.7) 262 ( 2.1) Female State 288 ( 1.3) 253 ( 1.8) 257 ( 1.4) 263 ( 1.4) Region 270 ( 2.7) 250 ( 3.4) 280 ( 3.1) 265 ( 4.0) Nation 266 ( 1.4) 253 ( 1.6) 255 ( 1.5) 261 ( 1.3) Preadmit/ 262 263 2.1 260 13 243 ( 2.0) i 242 3.0) 256 1.4) 250 C 3.4) 253 2.0) 267 ( 1.7) 240 ( 3.7) 263 ( 22) 272 ( 1.4) 271 ( 3.1) 273 ( 1.7) 263 ( 11) 263 ( 2.2) 260 ( 1.6) 201 ( 14) 202 ( 2.1) 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 stands-. errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 1 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Ohio THE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participat:- the 1990 Trial State Assessment, their mathematics teachers, and the principals or oi.. iministrators 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 gratifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. t; THE 1990 NAEP TRIAL STATE ASSESSMENT 37 Ohio Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an enormous impact on future academic achievement. Yet, as shown in Cilapters 3 and 7, large proportions of students report having spent much more time each day watching television than doing mathematics homework. ?art Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 38 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio 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 refomn that are changing the direction of mathematics education. Recent reports have called for ftmdamental 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 Ohio public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffmg. Some of the salient results arc as follows: More than half of the eighth-grade students in Ohio (66 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. Schocq Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign, IL: Supes Publishing Company, 1987). 1.ynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Education (Washington, DC: National At-auemy Press, 1989), THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Ohio In Ohio, 81 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Almost all of the students in Ohio (90 percent) were taught mathematics by teachers who teach only one subject. More than half (68 percent) of the students in Ohio were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was equally prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in Ohio Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1906 NAEP TRIAL STATE ASSESSMENT Ohio Central Nation Percentage of eighth-grade students in public schools that Identified mathematics as receiving special emphasis In school-wide goals and objectives, Instruction, in-service training, etc. Percentage of eighth-grade public-school students who are offered a course in algebra for high school course placement or credit Percentage of eighth-grade students In public schools who are taught by teachers who teach Oft mathematics Percentage of elghth-grade students In public schoois who are assigned to a mathematics class by their ability In mathematics Percentage of eighth-grade students in public schools who receive far or more haws of mathematics kestniction per week Peroentage Percentage Percentage 00 ( 4.7) 79 (13.8) 03 ( 5.9) 81 ( 4.0) 09 (15.4) 78 ( 4.6) ( 3.0) 87 ( 7.8) 91 ( 3.3) 08 ( 3.0) 00 ( 5.7) 03 ( 4.0) 10 ( 2.2) 25 ( 8.6) 30 ( 4.4) The standard errors of the estimated stAilitiCs appear in 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. 4 5 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in Ohio are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in Ohio were taking eighth-grade mathematics (63 percent) than were taking a course in pre-algebra or algebra (36 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 Ohio who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who werT, 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 ., MO NAEP TRIAL STATE ASSESSMENT Ohio Central Nation - Percentage and Proficiency Perearga. and Prodchoncy Percentage end Proficiency What kind of mathematics class are you taking this year? Eighth-grade mathematics 63 ( 2.2) SiS ( 4.6) 62 ( 2,1) 254 ( 12) 255 ( 3.1) 251 ( 14) Proalgebra 20 C 2.0) 22 ( 4.3) 19 ( 1.9) 270 ( 1.9) 276 ( 272 ( 2.4) Algebra 16 ( 1.1) 15 ( 2.8) 1$ ( 1.2) 300 ( 1.5) 289 ( 5.4) 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. k f; TEX 1990 NAEP TRIAL STATE ASSESSMENT 41 Ohio Further, froin Table A5 in the Data Appendie About the same parentage of females (36 percent) and males (35 percent) in Ohio were enrolled in pre-algebra or algebra courses. In Ohio, 36 percent of White students, 30 percent of Black students, and 28 percent of Hispanic students were enrolled in pre-algebra or algebra courses. Similarly, 45 percent of students attending schools in advantaged urban areas, 42 percent in schools in disadvantaged urban areas, 31 percent in schools in extreme rural areas, and 33 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 amoum 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-gade students in public schools in Ohio spent 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent either 15 or 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 Ohio, 1 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 4 percent of the students in Ohio and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. 4 For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations race/ethnicity, type of community, parents' educauon level, and gender. 4 42 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio The results by race/ethnicity show that 3 percent of White students, 5 percent of Black students, and 2 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 1 percent of White students, 1 percent of Black students, and 2 percent of Hispanic students spent no time doing mathematics homework. In addition, 0 percent of students attending schools in advantaged urban areas, 3 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 5 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 0 percent of students attending schools in advantaged urban areas, 4 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme niral areas, and l percent in schools in areas classified as "othes" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE or STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1950 NAEP TRIAL STATE ASSESSMENT Ohio Central Nation Percentage and Proficiency Pommies* and Proficiency Percentage and Proficiency About how much time do students spend on mathematics homework each day? None 1 ( 0.4) ( .44) IHrft 1 ( 0,3) ( .44) 15 minutes 36 ( 3.8) 34 ( 7.1) 43 ( 4.2) 258 ( 2.4) 255 ( 4.7) 256 ( 2.3) 30 minutes 52 ( 3.7) 48 ( 9.6) 43 ( 4.3) 267 ( 1.5) 272 ( 3.5) 266 ( 2.6) 45 minutes 7 ( 1.4) 13 ( 6.0) 10 ( 1,9) 283 ( 5.2)1 2e1 (12.5)1 272 ( 5.7)1 An hour or more 4 ( 1,1) 285 ( Le)I 6 ( 2.3) «44) 4 ( 0.9) 278 ( 5.1)1 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 stanOdird errors of the esthnate for the sample. ! Interpret with caution the nature of the sample does not P.Viow accurate determination of the variability of this estimated mean profs, ,ency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Ohio TABLE 7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL. STATE ASSESSMENT , Ohio t Central , Nation . About how much bine do you usually spend each day on mathematics homework? 15 minutes 30 Mirages 45 minutes An hour or more Percents. and Pmadency 8 ( 0.7) 258 ( 22) 310: ( 1.1) 264 ( 1.0) 35 ( 1.1) 267 ( 1.4) 14 ( 0.7) 262 ( 2.3) 9 ( 0.6) 258 ( 2.5) Percentage Percestage and and Prelleisnay Pridlaway 7 ( 1.4) 34 ( 4.8) 289 ( 3.8) 32 ( 2.3) 294 ( 32) 15 ( 1.2) 265 ( 4.0) 12 ( 9.4) 262 ( 8.2)1 9 ( OA) 251 ( 2.8) 31 ( 2.0) 264 ( 12) 32 ( 12) 263 ( 12) 16 ( 1.0) 208 ( 1,9) 12 ( 1.1) 258 ( 3.1) The standard errors of the estimated statistics appear in parentheses, lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 4%** Sample size is insufficient to permit a reliable Cgtimate (fewer than 62 students). And, according to the studesits (Table 7 and Table A7 in the Data Appendix): In Ohio, relatively few of the students (6 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 9 percent of the students in Ohio 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 8 percent of White students, 14 percent of Black students, and 14 percent of Hispanic students spent an hour or more on mathematics homework each day. ln comparison, 7 percent of White students, 5 percent of Black students, and 3 percent of Hispanic students spent no time doing mathematics homework. 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio In addition, 6 percent of students attending schools in advantaged urban areas, 16 percent in schools in disadvantaged urban areas, 8 percent in schools in extreme rural areas, and 8 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 6 percent of students attending schools in advantaged urban areas, 10 percent in schools in disadvantaged urban areas, 4 percent in schools in extreme rural areas, and 6 percent in schools in areas classified as "other" spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurements Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to leam the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 5 THE 1990 NAEP TRIAL STATE ASSESSMENT 45 Ohio The responses of the assessed students' teachers to the topic emphasis questions for each content area were combined to create a new variable. For each question in a particular content area, a value of 3 was given to "heavy emphasis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 5 1 46 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT Ohio Central Nation - _ Teacher "emphasis" categories by content areas Plumbers and Operations Heavy emphasis 48 ( 3.7) 54 ( 72) 3.11 281 ( 1.8) 284 ( 4.3) 249 00 1.83 Little or no emphasis 14 ( 22) 13 ( 43) 15 ( 2.1) 294 ( 3.7) 285 ( 5.8)t 28? ( 3.4) MOSSUM41141111 Heavy emphasis 1? ( 2.8) 18 ( 5.7) 17 ( 3.0) 243 ( 4.2) 247 (12.5)1 250 ( 83) Uttle or no emphasis 33 ( 3.1) 42 ( 9.7) 33 ( 4.0) 275 ( 2.4) 270 ( 7.7)1 272 ( 4.0) Geometry Heavy emphasis 23 ( 3.1) 26 ( 7.0) 28 ( 3.8) 284 ( 2.7) 261 ( 7.9)1 260( 3.2) Little or no emphasis 27 ( 23) 35 ( 72) 24 ( 3.3) 284 ( 2.4) 261 ( 9.0)1 284 ( 54) Data Analysis, Statistics, and Probability Heavy emphasis 13 ( 2.3) 12 ( 2.5) 14 ( 2.2) 270 ( 4.4) 262 ( 7.5) 269 ( 4.3) Little or no emphasis 84 ( 3.2) 57 ( et) 33 ( 4.4) 266 ( 2.1) 264 ( 5,6)1 201 ( 2.9) Algebra and Functions Heavy emphasis 50 ( 3.0) 50 ( 78) 48 ( 3.8) 277 ( 1.8) 273 ( 3.8) 275 ( 2.5) Little or no emphasis 20 ( 2.8) 19 ( 3.9) 20 ( 3.0) 243 ( 2.0) 242 ( SS)! 243 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty ;hat, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 Ohio SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are tmlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: More than half of the eighth-grade students in Ohio (66 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Ohio, 81 percent of the students could take an algebra course in eigjith grade for high-school course placement or credit. A greater percentage of students in Ohio were taking eighth-grade mathematics (63 percent) than were taldng a course in pre-algebra or algebra (36 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 Ohio spent 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 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 Ohio, relatively few of the students (6 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 9 percent of the students in Ohio and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instnictional 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. 48 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio CHAPTER 4 yzxa-ax 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. 6 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Ohio From Table 9 and Table A9 in the Data Appendix: In Ohio, 12 pexcent of the eighth-grade students had mathematics teachers who reported getting all of the ntfMLITCS they needed, while 34 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figums were 13 percent and 31 percent, respectively. In Ohio, 18 percent of students attending schools in advantaged urban areas, 15 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 11 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in Ohio, 21 percent of students attending schools in advantaged urban areas, 51 percent in schools in disadvantaged urban aireas, 4 percent in schools in extreme rural areas, and 39 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 mathematics achievement levels similar to those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of i Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . 1990 PIMP TRIAL STATE ASSESSMENT Ohio Central Nation Which of the following statements is true about how welt supplied you are by your school system with the instructional materials and other resources you need to teach your class? I get eft the moron I need. I get most of the resources I need. I get some or none of the resources I need. Percentage Peroentage Percentage and and end Proaliciancy Preidency Prelideray 12 ( 26$ ( 2.5) 5.0)1 8 ( 2.4) 4,44) 13 245 ( 2.4) ( 4.2) 54 ( 4.4) 45 ( 7.0) 51 ( 4.0) 2S0 ( 1.8) 271 ( 24)1 265 ( 2.0) 34 ( 4.0) 47 ( 7.3) 31 ( 42) 259 ( 2.1) 259 ( 3.5) 261 ( 2.9) The standard errors of the er ated SlatiStiCs appear in parentheses. It can be said with about 95 percent certainty that, for each populativn of interest, the value for the entire population is within ± 2 standard errors of the estimate for th^ 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). 50 THE 2990 NAEP TRIAL STATE ASSESSMENT Ohio PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: Less than half of the students in Ohio (37 percent) worked mathematics problems in small groups at least once a week; some never worked mathematics problems in small groups (14 percent). The largest percentage of the students (80 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (6 percent). In Ohio, 69 percent of the students were assigned problems from a mathematics textbook almost every day; 5 percent worked textbook problems about once a week or less. Less than half of the students (38 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (30 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 Ohio TABLE 10 I Teachers' Reports on Patterns of Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL STATE ASSESSMENT Ohio Central Nation Paraamtage and illaraantsga and Parcantage and About how often do studeMs work problems In small groups? Predicioncy Medway Proticknay Al Most once a week 37 ( 3.4) SO ( 7.8) 50 ( 4.4) 286 ( 2.0) 258 ( 4.1) 280 ( 22) Less than once a week 49 ( 3.6) 43 ( 8.6) 43( 4.1) 265 ( 1.9) 206 ( 4.0)! 284 ( 2.3) Never 14 ( 2.6) 7 ( 4.3) 8 ( 2.0) 266 ( 3.9) ( 277 ( 5.4)i About how often do students use objects Percentage Percentage Percentage like rulers, counting blocks, or geometric and and and solids? Proficiency Proficiency Proficiency AI least once a week 14 ( 2.1) 15 ( 5.1) 22 ( 3. 259 ( 3.2) 255 ( 4.9)1 254 ( 32) Less than once a week 80 ( 2.8) 81 ( 6.0) 69 ( 3.9) 265 ( 1.5) 264 ( 3.3) 263 ( 1.9) Never 8 ( 1.5) 279 ( 9.0)1 4 ( 2.3) ***) ( 2.6) 282 ( 5.9)1 The standard errors of the estimated statist/Cs appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entre population is within ± 2 standard errors of the estimate for the sample. 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). r- 7 52 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE 11 1 Teachers' Reports on Materials for I Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT ado COWS! Nation Perm*. and Prof "dew Percentsge Ind Preliclasey Percentage and linsedancy About how often do students do problems from textbooks? Almost *my day 09 ( 3.8) 82 ( SA) 62 ( 34) 287 ( 1.8) 269 ( 3.8) 267 ( 1.8) Several linos a wank 27 ( 3.6) 32 ( 4.2) 31 ( 3.1) 262 ( 3.2) 252 ( 5.3) 254 ( 2.9) About once a wank or loss 5 ( 1.6) 251 ( 9.4)1 ( 2.7) ***) 7 ( 1.8) 250( 5.1)1 About how often do students do problems on worksheets? Percentage snd Percentage snd Percentage and Proliciency Proficiency Proficiency Al toast ~oral times a wash 38 ( 3.8) 38 ( 8.3) 34 ( 3.8) 261 ( 2.3) 252 ( 5.5)1 258 ( 2.3) About ono* a weak 32 ( 3.9) 23 ( 4.8) 33 ( 3.4) 259 ( 2.8) 261 ( 8.1) 200 ( 2.3) Loss than wasidy 30 ( 3.8) 39 ( 7.0) 32 ( 3.8) 277 ( 22) 278 ( 4.1) 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 Ohio COLLABORATING IN SMALL GROUPS In Ohio, 52 percent of the students reported never workin mathematics problems in small groups (see Table 12); 20 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 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT Ohio Cantral Nation How often do you work in small groups in your mathematics class? Ihmagigags and Preadoncy Pareantaga and Proficiency Percentage and ProliciencY At Mast once a wHk 20 ( 1.7) 23 ( 4.6) 28 ( 2.5) 262 ( 2.7) 266 ( 8.5) 258 ( 2.7) Lass than one. a weak 2$ ( 1.6) 32 ( 3.3) 28 ( 1.4) 268 ( 1.8) 266 ( 3.0) 287 ( 2.0) Now 52 ( 2.4) 45 ( 6.3) 44 ( 2.9) 262 ( 1.5) 284 ( 3.4) 281 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within i 2 standard errors of the estimate for the sample. Examiriing the subpopulations (Table Al2 in the Data Appendix): In Ohio, 20 percent of students attending schools in advantaged urban areas, 31 pement in schools in disadvantaged urban areas, 12 percent in schools in extreme rural areas, and 18 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 18 percent of White students, 27 percent of Black students, and 26 percent of Hispanic students worked mathematics problems in small groups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (19 percent and 20 percent, respectively). 54 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio USING MATHEMATICAL OBJECTS Students wore asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: About half of the students in Ohio (47 percent) never used mathematical objects; 2 1 percent used these objects at least once a week. Mathematical objects were used at least once a week by 21 percent of students attending schools in advantaged urban areas, 22 percent in schools in disadvantaged urban areas, 16 percent in schools in extreme rural areas, and 22 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 (25 percent and 18 percent, respectively). ln addition, 20 percent of White students, 27 percent of Black students, and 30 percent of Hispanic students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AN- AVERAGE MATHEMATICS PROFICIENLY 1900 NAEP TRIAL STATE ASSESSMENT How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Percentage Mod Proficiency Percentage and Prolidency Penaentage end Prolidnicy At lust once a week 21 ( 1.5) 23 ( 22) 28 ( 1.8) 262 ( 2.1) 260 ( 3.5) 25$ ( 2.15) Lass than once a wink 32 ( 1.3) 36 ( 2.5) 31 ( 1.2) 266 ( 1.6) 272 ( 2.9) 209 ( 1.5) MOW 47 ( 2.0) 41 ( 4.6) 41 ( 22) 262 ( 1.4) 262 ( 2.8) 25( 1.6) The standard errors of the estimated statistics appear in parentheses. It con 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. G o THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Ohio MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in Ohio who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teac.hing 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 Ohio (75 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 70 percent of students attending schools in advantaged urban areas, 69 pexcent in schools in disadvantaged urban areas, 82 percent in schools in extreme rural areas, and 76 percent in schools in anas classified as "other". TABLE 14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP fRIAL STATE ASSESSMENT Clio Central Nation How often do you do mathematics problems from textbooks in your mathematics class? Percentage and Proficiency Percentage and Pro Money Percentage and Proficiency Mufti every day 75 ( 22) 74 ( 4.7) 74 ( 1.9) 266 ( 1.1) 271 ( 22) 287 ( 12) Several times a week 17 ( 1.3) 15 ( 1.6) 14 ( 0.8) 257 ( 1.6) 250 ( 4.2) 252 ( 1.7) About once a week or less 7 ( 1.2) 11 ( 4.3) 12 ( 1.8) 253 ( 3.3) 250 ( 4.7)1 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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. Gi 56 THZ 1990 NAEP TRIAL STATE ASSESSMENT Ohio And, for the frequency of worksheet usage (Table 15 and Table Al5 in the Data Appendix): Less than half of the students in Ohio (38 percent) used worksheets at least several times a week, compared to 38 percent in the nation. Worksheets were used at least several times a week by 37 percent of students attending schools in advantaged urban areas, 45 percent in schools in disadvantaged urban areas, 22 percent in schools in extreme rural areas, and 39 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- 1980 NAEP TRIAL STATE ASSESSUENT Ohio How often do you do mathematics problems on worksheets In your mathematics class? At least several Urnes a week About once a week Less than moldy Percentage Percentage Percentage and and aid Prat:fenny Prveciancy Prof kiencli 38 ( 2.6) 257 ( 1S) 27 ( 1.4) 263 ( 1.9) 35 ( 2.3) 272 ( 1.5) 36 ( 6.0) 257 ( 4.9) 23 ( 2.3) 264 ( 2.8) 40 ( 5.6) 2Th ( 4.0) 38 ( 2.4) 253 ( 2.2) 25 ( 1.2) 281 ( 1.4) 37 ( 2$1 272 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each populatm of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. G THE 1990 NAEP TRIAL STATE ASSESSMENT 57 Ohio TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and MateriaLs for Mathematics Instruction PERCENTAGE OF STUDENTS 11410 NAEP TRIAL STATE ASSESSMENT Ohio Central elation Patterns of classroom instruction PerssallP SUM% Teachers Percentage Shatents Teachers Percentage Students Teachers Percentage of students sho work mathematics problems in Inuit groups At least once a week 20 ( 1.7) 37 ( 3.4) 23 ( 4.6) 50 ( 7.8) 28 ( 2.5) 50 ( 4.4) Less than once a week 28 ( 1.6) 49 ( 3.8) 32 ( 3.3) 43 ( 8.6) 28 ( 1.4) 43 ( 4.1) Never 52 ( 24) 14 ( 2.8) 45 ( 0.3) 7 ( 4.3) 44 ( 2.9) 8 ( 2.0) Percentage of students who use objects like riders, counting blocks, or geometric sande At least once a week 21 ( 1.5) 14 ( 2.1) 23 ( 2.9) 15 ( 5.1) 28 ( 1.8) 22 ( 3.7) LeSS than once a week 32 ( 1.3) 80 ( 2.8) 30 ( 2.5) 81 ( 6.0) 31 ( 12) 69 ( 3.9) Never 47 ( 2.0) 6 ( 1.5) 41 ( 4.8) 4 ( 2.3) 41 ( 22) 9 ( 2.6) Materials for mathematics instruction Percentage Students Teachers Percentage Students Teachers Percentage Students Teachers Percentage of students vale use a mathematics twdbook Almost every day 75 ( 2.2) 69 ( 39) 74 ( 4.7) 62 ( 5.6) 74 ( 1.9) 62 ( 3.4) Several times a week 17 ( 1.3) 27 ( 3.6) 15 ( 1.6) 32 ( 4.2) 14 ( 0.8) 31 ( 3.1) About once a week or ;ass 7 ( 1.2) 5 ( 1.8) 11 ( 4.3) 6 ( 2.7) 12 ( 1.8) 7 ( 1.8) Percentage of students who use a mathematics worksheet At least several times a week 38 ( 2.6) 38 ( 3.8) 36 ( 6.0) 38 ( 8.3) 38 ( 2.4) 34 ( 3.8) About once a week 27 ( 1.4) 32 ( 3.9) 23 ( 2.3) 23 ( 4.8) 25 ( 12) 33 ( 3.4) Less than weekly 35 ( 2.3) 30 ( 3.8) 40 ( 5.6) 39 ( 7.0) 37 ( 2.5) 32 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. pu 5S THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery practicesand 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 pratices are emerging, they are not yet commonplace. According to the students' mathematics teachers: Less than half of the students in Ohio (37 percent) worked mathematics problems in small groups at least once a week; some never worked in small groups (14 percent). The largest percentage of the students (80 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (6 percent). In Ohio, 69 percent of the students were assigned problems from a mathematics textbook almost every day; 5 percent worked textbook problems about once a week or less. Less than half of the students (38 percent) did problems from worksheets at 1.ast several times a week; about one-quarter did worksheet problems less than weekly (30 percent). Arid, according to the students: In Ohio, 52 percent of the students never worked mathematics problems in small groups; 20 percent of the students worked mathematics problems in small groups at least once a week. About half of the students in Ohio (47 percent) never used mathematical objects; 21 percent used these objects at least once a week. About three-quarters of the students in Ohio (75 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. Less than half of the students in Ohio (38 percent) used worksheets at least several times a week, compared to 38 percent in the nation. G 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Ohio CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to u.sz. 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 cf calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks.' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. a National Assessment of Educational Progress, Mathematics Objectives: 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for Schoo; Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 85 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio Table 17 provides a profile of Ohio eighth-grade public cchools' policies with regard to calculator use: In comparison to 33 percent across the nation, 33 percent of the students in Ohio had teachers who allowed calculators to be used for tests. About the same percentage of students in Ohio and in the nation had teachers who permitted unrestricted use of calculators (15 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of Ohio Policies on Calculator Use PERCENTAGE OF STUDENTS _ MO NAEP TRIAL STATE ASSESSMENT Ohio CI *al Nation Percentage ot eighth-grade students in public schools whose teachers permit the tivestricted UM of CaktiatOrs Percentage ot eighth-grade students in public schools whose teachers permit the use of calculators for togs Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators awned try tho school Percentage Percentage Percentage 15 ( 2.0) 27 ( 8.1) 18 ( 3.4) 33 ( 43) 44 ( 7.9) 33 ( 4.5) 51 ( 4.3) 55 ( 8.2) 58 ( 4.8) The standard errors of the estimated staustics appear in 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 61 Ohio THE AVAILABILFFY OF CALCULATORS In Ohio, most students or their families (98 percent) owned calculators (Table 18); however, fewer students (49 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In Ohio, 46 percent of White students, 69 percent of Black students, and 50 percent of Hispanic students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (47 percent and 50 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 1900 NAEP TRIAL STATE ASSESSMENT Ohio Central Nation Percentage and Proficiency ea ( 0.3) 264 ( 1.0) tim) Percentage and Proaciancy Percentage end Proficiency 96 ( 0.6) 266 ( 2.5) 2 ( 0.6) 444 Percentage and Proliciency Percentage and Proficiency 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( SA) Percentage and Prolidency Do you or your family own a calculator? Yes r--------- Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes 49 ( 2.1) 56 ( 4.9) 49 ( 2.3) 259 ( 1.3) 263 ( 3.0) 258 ( 1.7) No 51 ( 2.1) 44 ( 4.9) 51 ( 2.3) 269 ( 1.4) 269 ( 3.4) 266 ( 1.5) The standard errors of the estimrted statistics appear in 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 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio 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 sIdlls and content. As part of the Trial State Assessment, students were asked how frequently (never, sometimes, almost always) they used calculas ror working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In Ohio, 27 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. Some of the students (17 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 (36 t) never used a calculator to take quizzes or tests, while 25 percent Le r tnalways did. TABLE 19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . , 1000 NAEP TRIAL STATE ASSESSMENT Ohio Central Nation , How often do you use a calculator for the following tasks? Pan:engage and proficianoY Percantaao and Prolidency Percentage and Proficiency Working problems in class Almost always 45 ( 1.5) 51 ( 3.8) 48 ( 1.5) 255 ( 1.3) 280 ( 2.8) 254 ( 1.5) Never 27 ( 1.7) 14 ( 36) 23 ( 1.9) 275 ( 1.4) 270 ( 4.1)1 272 ( 1.4) Doing problems at home Almost always 29 ( 1.5) 35 ( 22) 30 ( 1.3) 259 ( 11) 266 ( 2.8) 284 1.8) Never 17 ( 11) 18 ( 2.1) ( 0.9) 270 ( 1.7) 263 ( 3.3) 283 ( 1.8) Taking quizzes or tests Almost always 25 ( 1.3) 29 ( 4.5) 27 ( 1.4) 253 ( 1.8) 280 ( 4.0) 253 ( 2.4) Never 30 ( 1.5) 22 ( 4.8) 30 ( 2.0) 275 ( 1.1) 271 ( 3.4)1 274 ( 1.3) The ittandard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. ! Interpret with caution the nature of the sainple does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 63 7 Ohio WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether studems know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students wen 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 item', 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, beause of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who use 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 thP time and indicated that they had used the calculator for at least half of the calculator-active itemsthey were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. G 64 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio The data presented in Table 20 and Table A20 in the Data Appendixare highlighted below: A smaller percentage of students in Ohio 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, 49 percent of White students, 31 percent of Black students, and 45 percent of Hispanic students were in the High group. TABLE 20 1 Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATEEMATICS PROFICIENCY 19610 NAEP TRIAL. STATE ASSESSMENT Oh lo Central Nation , "Catoulator-use" group Nigh Percentage and Prettoiency 47 ( 1.1) 271 ( 1.5) 53 ( 1.1) 255 ( 0.9) Prowls., Percents. and end Prolloterog Prellotenty 46 ( 1.8) 272 ( 3.4) 54 ( 1.$) 200 ( 2.7) 42 ( 1.3) 272 ( 1.15) 58 ( 12) 255 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 7t) THE 1990 NAEP TRIAL STATE ASSESSMENT 65 Ohio 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 wore instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The da'a related to calculators and their use show that: In comparison to 33 percent across the nation, 33 percent of the students in Ohio had teachers who allowed calculators to be used for tests. About the same percentage of students in Ohio and in the nation had teachers who permitwl unrestricted use of calculators (1$ percent and 18 percent, respectively). In Ohio, most students or their families (98 percent) owned calculators; however, fewer students (49 percent) had teachers who explained the use of calculators to them. In Ohio, 27 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. Some of the students (17 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 (36 percent) never used a calculator to take quizzes or tests, while 25 percent almost always did. 71 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has become an issue of increasing importance to federal, state, and local governments. As part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.9 Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In Ohio, 51 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 thc nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. About three-quarters of the students (75 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 '"..ston VA. National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 67 Ohio TABLE 21 I Profile of Eighth-Grade Public-School i Mathematics Teachers PERCENTAGE OF STUDENTS - MO NAEP TRIAL STATE ASSESSMENT Ohio CentrM Nation Percentage of studenb whose mathematics teachers reported having the following degrees Percentage Percuttage Percentsge Bachelor's degree 49 ( 42) 48 ( 11) SO ( Master's or specialist's degree 51 ( 4.2) 46 ( 8.6) 42 ( 4.2 Doctorate or professional degree 0 ( 0.0) 4 ( 2.7) 2 ( 1.4 Percentage of students whose mathematics teachers have the following types of teaching certificates that we recognized by Ohio No regular certification 17 ( 3.2) 4 ( 2.7) 4 ( 12) Regular certification but less than the highest available 34 ( 4.0) 25 ( 7.3) 29 ( 4.3) Highest certification available (permanent or long-term) 50 ( 45) 71 ( 7.3) 68 ( 4.3) Percentage of students whose mathematics teachers have the following types of teaching certificates that are recognized by Ohio Mathematics (middle school or secondary) 75 ( 3.5) 77 ( 4.5) 84 ( 2.2) Education (elementary or middle school) 25 ( 3.8) 17 ( 7.5) 12 ( 2.6) Other ( 0.3) 7 ( 4.8) 4 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. EDUCA11ONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. 68 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In Ohio, 39 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 Ohio (12 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and 1 Graduate Fields of Study PERCENTAGE OF STUDENTS 1000 NAEP TRIAL. STATE ASSESSMENT Ohio Central Nation What was your undergraduate major? Percentage Percentage Percentage Mathematics 39 ( 4.2) 57 ( 7.1) 43 ( 3.0) Education ( 4.1) 29 ( 8.4) 35 ( 3.8) Other 13 ( 2.8) 14 ( 5.4) 22 ( 3.3) ( What was your graduate major? Percentage Percentage Percentage Mathematics 12 ( 2.7) 34 ( 9.1) 22 ( 3.4) Education 49 ( 4.1) 34 ( 8.2) 38 ( 3.5) Other or no graduate level study 40 ( 4.2) 32 ( CS) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 69 Ohio Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In Ohio, 22 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-servicm education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Some of the students in Ohio (16 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT I Obio ellilitall _ Nation , During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? Nona Ono to 15 hours 15 hours or more Paroantago Parcontogo Pmvontago 16 ( 2.7) 1 ( 1.3) 11 ( 2.1) 83 ( 3.8) 71 ( 5.4) 51 ( 4.1) 22 ( 34) 28 ( 5.0) 39 ( 3.8) The standard errors of the estimated statistiCs appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 15 70 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio 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.1° 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.1' In curriculum areas requiring special attention and improvement, .such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and tenitories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and expenence do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In Ohio, 51 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 Ohio, 39 percent of the eighth-gxade 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 Ohio (12 percent) wtre 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. I° Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, .4 World of Differences An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1984 " Ina V.S. MuIhs, John A. Dossey. Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement NA Ers 1990 Assessment of the Vation and the Plat Assessment of the States (Princeton. NJ: National Assessment of Educational Progress, Educational Testing Service, 199 1 ). P-76 THE 1990 NAEP TRIAL STATE ASSESSMEN I 71 Ohio In Ohio, 22 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in- service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Some of the students in Ohio (16 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. 77 72 TUE 1940 NAEP TRIAL STATE ASSESSMENT Ohio CHAPTER 7 The Conditions Beyond School that Facilitate Mathematics Learning and Teaching Because students spend much more time out of school each day than they do in school, it is reasonable to expect that out-of-school factors greatly influence students' attitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, encouragement, and participation in student learning experiences are powerful influences. Together, teachers and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment and mathematics proficiency, students participating in the Trial State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education. obl r) 1 3 THE 1990 NAEP TRIAL STATE ASSESSMENT 73 1 Ohio AMOUNT OF READING MATERIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students participating in the Trial State Assessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports ov Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Oflio Central 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 twos Four typos Pareantag and Proficiency Parconteps * and Proficiency Percertege end Proficiency 16 ( 1.0) 19 ( 2.1) 21 ( 1.0) 247 ( 1.4) 250 ( 3.4) 244 ( 2.0) 30 ( 0,8) 31 ( 2.2) 30 ( 1.0) 260 ( 1.4) 265 ( 3.6) 258 ( 1.7) 54 ( 1.1) 50 ( 1.6) 46 ( 1.3) 271 ( 1.1) 272 ( 2.1) 272 ( 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 populabon is within ± 2 standard errors of the estimate for the sample. The data for Ohio reveal that: Students in Ohio 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. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio A smaller percentage of Black and Hispanic students had all four types of these reading materials in their homes than did White students. A greater percentage of students attending schools in advantawd urban areas than in disadvantaged urban areas, extreme rural areas, or areas classified as "other" had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Trial Stir Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Ohio Contra! Nation Parentage and Prellelancy Parentage and Prellolincy Pareentege and Pram:Wm How much television do you usually watch each day? One hour or loss 13 ( 0.7) 11 ( 1.6) 12 ( 0.8) 272 ( 1.0) 270 ( 3.5) 288( 2.2) Two hours 24 ( 1.0) 22 ( 1.7) 21 ( 0.9) 272 ( 1.5) 274 ( 3.2) 266 ( 1.8) Thrso hours 24 ( 0.9) 25 ( 2.4) 22 ( 0.8) 208 ( 1.4) 271 ( 4.0) 286 ( 1.7) Four to fiv. hours 28 ( 0.0) 27 ( 3.0) 28 ( 1.1) 259 ( 1.1) 261 ( 2.0) 200 ( 1.7) Slx hours or mars 11 ( 0.8) 14 ( 1.6) 10 ( 1.0) 244 ( 1.9) 247 ( 3.4) 245 ( 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 the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 75 Ohio From Table 25 and Table A25 in the Data Appendix: In Mio, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Some of the eig4th-grade public-school students in Ohio (13 percent) watched one hvur or less of television each day; 11 percent watched six hours or more. About the same percentage of males and females tended to watch six or more hours of television daily. However, a smaller percentage of males than females watched one hour or less per day. In addition, 8 potent of White students, 32 percent of Black students, and 19 percent of Hispanic students watched six hours or more of television each day. In comparison, 14 percent of White students, 5 percent of Black students, and 10 percent of Hispanic students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine Jae 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 Ohio, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in Ohio (42 percent) did not miss any school days in the month prior to the assessment, while 22 percent missed three days or more. In addition, 22 percent of White students, 27 percent of Black students, and 22 percent of Hispanic students missed three or more days of school. 81 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio Similarly, 16 percent of students attending schools in advantaged urban areas, 34 percent in schools in disadvantaged urban areas, 14 percent in schools in extreme rural areas, and 22 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 111110 NAEP TRIAL STATE V N NWENT Ohio Central Nation How many days of school dld you miss last month? One or two days rya, days or MOM and Proficiency 42 ( 12) 249 ( 1.2) 35 ( 1.1) 215 ( 1.2) 22 ( 011) 253 ( 9.4) Peroestege and end Preficienni Prolickney 47 ( 1.7) 21111( 24) 30 ( 2.0) 271 ( 3.4) 23 ( 2.0) 252 ( 3.3) 45 ( 1.1) 265 ( 14) 32 ( 04) 2S8 ( 1.5) 23 ( 1.1) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. (32 THE 1990 NAEP TRIAL STATE ASSESSMENT 77 Ohio STUDENTS' PERCEPTIONS OF MATHEMA TICS to the National Council of Teachers of Mathematics, :.vning mathematics should require students not only to master essential skills and concepts but also to develop confidence in their mathematical abilities and to value mathematics as a discipline.' 2 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; 1 am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Abnost all people we mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for solving everyday problems. A student "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly agree" were given a value of 1 (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's responses were averaged over the five statements. The students were then assigned'a perception index according to whether they tended to strongly agee with the statements (an index of 1), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with tho statements (an index of 3). Table 27 provides the data for the students' attitudes toward mathernat'cs as defined by their perceptien index. The following results were observed for Ohio: Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who we_ in the "undecided, disagree, strongly disagree" category. Less than half of the students (32 percent) were in the "strongly agree" category (perception index of 1). This compares to 27 percent across the nation. Some of the stu&nts in Ohio (20 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). 2 2 National Council of Teachers of Mathematics, Curricuhmi and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 63 75 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111S0 NAEP TRIAL STATE ASSESSMENT Student "perception index" groups Peroentage and Proficiency Percentage and Proficiency Percentase and Proficiency Strongly agree 32 ( 1.0) 25 ( 1.8) 27 1.3) ("perception index" of 1) 273 ( 1.3) 272 ( 3.5) 271 ( 1.9) Aare* 48 ( 1.0) 50 ( 1.8) 49 ( 1.0) ("perception index" of 2) 283 ( 1.1) 257 ( 3.1) 252 ( 1.7) Undecided, disagree, strongly diugree 20 ( 1.0) 25 ( 2.2) 24 ( 1.2) ("perception index" of 3) 253 ( 1.8) 258 ( 2.3) 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. The data related to out-of-school factors show that: Students in Ohio who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. THE 1990 NAEP TRIAL STATE ASSESSMENT 79 Ofrio Some of the eighth-grade public-school students in Ohio (13 percent) watched one hour or less of television each day; 11 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 Ohio (42 percent) did not miss any school days in the month prior to the assessment, while 22 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three 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 proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. 80 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio NE 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 based, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Educational Testing Service. The development of the Trial State Assessment Program benefitteJ frnm the involvement of hundreds of representatives from State Education Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the program. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The first step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. (.; 6 THE 1990 NAEP TRIAL STATE ASSESSMENT SI Ohio The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required approximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets were spiraled or interleaved in a systematic sequence so that each booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as descsibed in the introduction to this report.' The assessment framework ronsisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure A 1). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to aetermine 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 subpopuladons, even when all students do not answer the same set of questions. This common scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. National Assessment of Educational Progress, Mathematics ObJectives 1990 Assessment (Princeton, NJ: Educauonid Testing Service, 1988). E7 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio FIGURE Al I COntent Areas Assessed Numbers and Operations This cOntent area focuses on students' understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-world situations, as well as computational and estimation situations. Understanding numerical relationships as expressed In ratios, proportions, and percents is emphasized. Students' abilities In eStimation, mental computation, use of calculators, generalization of numerical patterns, and Verification of results are also included. IMeasurement A 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 eccuracy. Questions requiring estimation, measurements, and applications of measurements of length, time, money, temperature, maSsiweight, 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 ideas. In addition, students should be able to uSe informal reasoning to establish geometric relationships. Data Analysis, Statistics, and Probability This content area focuses on data representation and analysis across all disciplines and reflects the importance and prevalence of these activities in our sOCiety. Statistical knowledge and the ability to interpret data are necessary skills in the contemporary world. Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysts. Algebra and Functions This content area is broad in scope, covering algebraic and functional concepts In more informal, exploratory ways for the eighth-grade Trial State Assessment. Proficiency in this concept area requires both manipulative facility and conceptual understanding: it involves the ability to use algebra as a means of representation and algebraic processing as a problem-solving tool. Functions are viewed not only In terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 83 Ohio FIGURE A2 I Mathematical Abilities The following three categories of matftmatical abilities are not to be construed as hierarchical. For example, problem Solving involves interactions between conceptual knOWledge end :,ocedural skills, but what Is considered complex problem solving at one grade level may be , zidered conceptual understanding or procedural knowledge at another. Conceptual Understanding Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts; can use and interrelate models, diagrams, and varied representations of concepts; can Identify and apply principles; know and can apply facts and definitions; can compare, contrast, and integrate related concepts and principles; can recognize, interpret, and apply the signs, symbols, and terms used to represent concepts; and can interpret the assumptions and relations Involving concepts in mathematical settings. Such understandings are essential to performing procedures In a meaningful way and applying them in problem-solving situations. Procedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to select and apply appropriate procedures correctly, verity 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 noncomputational Skills such as rounding and ordering. [ Problem Solving In problem solving, students are required to use their reasoning and analytic abilities when they encounter new situations. Problem Solving includes the ability to recognize and formulate prot...oms: 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, D 84 THE 1990 NAEP TRIAL STATE ASSESSMENT A scale ranging from 0 to 500 was created to report performance for each content area. Each content-area scale was based on the distribution of student performance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing that is, by comparing students at a particular scale level to other students. In contrast, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 040-500 scale. Although proficiency levels bet 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics items from the 1990 assessment that discriminated well between adjacent levels. The criteria for rAecting these "benchmark" items were u follows: To define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 n 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. DO THE 1990 NAEP TRIAL STATE ASSESSMENT 85 Ohio Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a slImmAly of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.' Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students And to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and refotm, 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 itesative process that involved extensive development, field testing, and review by external advisory groups. MATHEMA11CS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as raze/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 the use of various instructional approaches. Because of the nature of the sampling for the 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 Smile there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the quesUons exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio FIGURE A3 1 Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers IR/ EXAMPLE 1 #4-7 Gov aba T40 Sob 0 Itnibet Sant 7. Luids bad atm kw Ws" all tit mad sire and duce &Omni kinds a be& is *era skew. i ake fine mob Sex wick do kied of ban shown. wind bad wil1 bate inrsot Wit in its CD The boa 1,44 the man %Ds 0 TM boa nub lbw pig We 0 Tim boo «kb dm tubber We 0 bat cda's Wt. EXAMPLE 2 IOUS OF MOT mono AT FAkAWAY MIMS No Thu Wad Urn Dino OtTli. Wok amen timmi ammalait 1 Ift 11. How ismay bozo oi mapswors Viand on Tbinsdoyt Qi) 55 CD 60 0 70 CD SO CD SO CID don't know. ret Grade 4 Overall Percentage Percentage Correct 222 85 91 Correct 73% for Anchor Lavels: 152 100 Grade 4 Overall Percentage Correct 80% Percentage Correct for Anchor Levels: ZQQ 222 75 91 100 Grade 8 Overall Percentage Percentage Correct Z22 IN 76 87 Correct: 89% for Anchor Levels: AQ 96 100 THE 1990 NAEP TRIAL SMTE ASSESSMENT 87 Level 250: Simple Multiplicative Rmening and Two-Step Problem Salving 1 Ohio FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) EXAMPLE 1 7. What is the value of n + 5 when n = 3 I Answer EXAMPLE 2 WA COLOR SURVEY MIMS Celetzt Kat ham. Taub 37 SO 23 Tim table Am shays she tanks of sway of bail cokti. On As dock below. mitt a click pip3e se gleams tin vim tba obit 1.4.1 sub pen ol the 4:431 otapb iota die meets bait OW. Dal you use glie salami so di* quitstiosi! C3 Yes ON. EXAMPLE 3 4. Kaddeatas packaq baschalle into bow Loch baz holds 6 booluils. has 24 balk. Wtich number unmet will bap kar towitmn howzuny hems she tea] sae& CD 24 CD 24 + c1:5 24 + - 0 02,4 xbCi (g) I kaow. 88 Grade 8 Overall Percentage Percentage Correct ala 25 89 Grade 8 Overall Percentage Percentage Correct 222 21Q 21 ea Commit 78% for Anchor Levels: MI MD 98 98 Correct 73% for Anchor Levels; 122 92 92 Grad. 8 Overall Percentage Correct 77% Percentage Correct for Anchor Levels; 222 21CI 37 71 95 100 ME 1990 NAEF TRIAL STATE ASSESSMENT FIGURE A3 I (continued) Ohio Example Items for Mathematics Proficiency Levels If. Wikh at the fottairtai skews die malt tait &Lava times ova the Lima t EXAMPLE 2 6 Oa ala Nam clam Ditilgiag. a cat Mai lats atfaciciad mask mottal Lido kw& U thu.. scala I rie d. haw n hat It* iratald be agitsrotad by a luta ask! haw may bakes Dif you ibe ialculatiir so 44 O. ONø THE 1990 NAEP TRIAL STATE ASSESSMENT Grade 8 Overall Percentage Correct 60% Percentage Correct for Anchor Levels: 2122 222 222 MI 33 49 77 90 Grade 12 Overall Percentage Correct 75% Percentap Correct for Anchor Levels: a2Q 22Q 222 48 79 95 Grad. 8 Overall Percentage Percentage Correct 22a &IQ 77 46 Correct: 59% for Anchor Levels: 212 86 99 BEST COPY AVAILABLY 89 Ohio FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) L Level 350: Rumming and Problem Solving Involving Geometric Relationships, Algebraic Equation% and Beginning Statistics and Probability EXAMPLE I Pt ()endow 16-17 mho to du Went tog I4$4* I bot-ttetwo. . . 2 1 16. II this mum o doc-limitto j coksatoi. bkr ow don w3I k in tito wstAtast JD 100 W 101 199 200 0201 EXAMPLE 2 17. E :plata how iota ktood your ammo to 'venial 1 6. Aratikr Grade 8 Overall Percentage Correct 34% Percentage Correct for Anchor Levels: 2Q2 ift2 2C2 114 13 19 53 88 Grade 12 Overall Percentage Correct 49% Percentage Correct for Mchor Levels: 242 2:02 ----- 22 48 90 Grade 8 Overall Percentage Correct: 15% Percentage Carect for Anchor Levels: 221 afgi 202 1 4 28 74 Grade 12 Overall Percentage Correct 27% Percentage Correct for AtIN1Of Levels: 2QQ 2§Q 22/ 2214 3 22 74 90 THE 1990 NAEP TRIAL STATE ASSE.i.iMENT Ohio 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, these were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when infotmation from the teaches or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to descsibe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective fmni that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEP's goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or teiritory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAEP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like almost all estimates based on assessment measures, NAEP's total group and subgroup proficiency estimates are subject to a second source of unce,sainty, in addition to sampling error. As previously noted, each student who participated in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropriate, set of the assessment questions -- or the entire set of questions -- somewhat different estimates of total group and subgroup proficiency might have been obtained. Thus, a second source of uncertainty arises because each student was administered a subset of thc total pool of questions. n6 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 Ohio 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 air called standard errors and ate 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 ra....ndard errors. Drawing Inferences from the Results One of the goals of the Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inferences about the population. The use of confidence intervc."7, hased on the standard errors, provides a way to make inferences about the population means and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 236 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 populat;on of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be construcred for percentages, provided that the percentages are not extreme& large (greater than 90 percent) or extremely small ( less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedtTes for obtaining accurate confidence intervals are quite complicated. 92 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the ovesall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usua140 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 hinutes 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 betweesa the two groups in the population because of the uncertainty associated with the estimated average proficiency of the groups in the sample. Remember that the intent is to make a statement about the entire population, not about the particular sample that was assessed The data from the sample are used to make inferences about the population as a whole. AI discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the manner in which the standard error for an individual group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups 2 standard errors of the difference represents an approxhnate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between groups in the population. If the interval does not contain zero, the difference between groups is statistically significant (different) at the .05 level. t THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Ohio 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: Grou p Average Proficiency Standard Error Female 259 2.0 Male 255 2.1 The difference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is V 2.02 + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference * 2 standard errors of the difference = 4 d: 2 (2.9) = 4 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value Zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a statistically significant difference in the population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. 3 The procedure described above (especially the estimation of the standard error of the difference) is, in a strict sense, only appropriate when the statistics being compared come from independent samples. For certain comparisons in the report, the groups were not independent. In those cases, a different (and more appropriate) estimaW of the standard error of the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significance is being performed. However, in each chapter of this report, many different groups are being compared (i.e., multiple sets of confiden= intervals are being analred). When one considers sets of confidence intavals, statistical theory indicates that the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. If one wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, tyyically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol "!". In such cases, the standard errors -- and any confidence intervals or significance tests involving these standard errors -- should be interpreted cautiously. Further details concerning procedures for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defined by race/ethnicity and type of school community, as well as by gender and parents' education level. NAI P collects data for f.ve racial/ethnic subgroups (White. Black, Hispanic, Asian/Pacific Islander, and A merican Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and/or background variable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined ty computing the sample size required to detect an effect size of .2 with a probability of .8 or greater. 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 Ohio The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or tenitory, divided by the standard deviation of the proficiency in the total population. If the true difference between subgroup and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical report. Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitraiy. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage Description ot 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 89 Many 89 < p < p = 100 100 Almost all All 90 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio ME 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 1990 NAEP TRIAL STATE ASSESSMENT 97 Ohio TABLE A5 I Students' Reports on the Mathematics Clam I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY L11190 NAEP TRIAL STATE ASSESSMENT Eighthirado kilathansatics TOTAL rerceniays and Pra Waxy 83 ( 22) 254 ( 12) 82 ( 2.1) 251 ( 1.4) 82 ( 2.4) 256 ( 12) 59 ( 2.5) 259 ( 1.6) 88 ( 4.0) 227 ( 1.9) 72 ( 4.7) 232 ( 34) 75 ( 4.4) 240 ( 2.4) 53 ( 8.0) 287 ( 3.1)1 55 ( 9.4) 289 ( 23)1 58 ( 8.8) 228 ( 32) 85 ( 8.0) 240 ( 4.0)1 88 ( 6.0) 257 ( 2.4)1 74 ( 4.5) 249 ( 3.1)1 85 ( 2.5) 255 ( 1.8) 81 ( 2.2) 251 ( 2.0) Percentage and 'radon 20 ( 2.0) 270 ( 1.9) 19 ( 1.9) 272 ( 2.4) 20 ( 2.0) 278 ( 1.8) 21 ( 2.4) 277 ( 2.2) 23 ( 3.5) 244 ( 3.2) 18 ( 3.0) 248 ( 0.4) 18 ( 5.4) 13 ( 3.9) 23 ( 8.0) 278 ( 2.7)1 22 ( 7.9) ..) 27 ( $.8) 251 ( 4.8)1 18 ( 4.1; ...) 8 ( 5.3) elr f+Ire) ( 2.4) 273 ( 2$) 20 ( 2.1) 272 ( 2.8) Percentaile and Proficiency 16 ( 1.1) 300 ( 1.5) 15 ( 12) 266 ( 24) 17 ( 1.3) ( 1.4) 17 ( 1$) 300 ( 2.3) ( 1.4) ...) 9 ( 22) ...) 10 ( 2.9) ...) 8 ( 1$) 1.44 22 ( 2.4) 313 ( 2,4)1 21 ( 4.4) 1111 15 ( 2.5) *44 ***) 14 ( 3.3) 287 ( 42)1 23 ( 6.1) 292 3.2)1 7 ( 2.2) ) 13 ( 12) 302 ( 1.8) 18 ( 1.4) 294 ( 2.7) State Nation RACE/ETHNICITY WNW State Nation Slack State Nation Hispanic State Nation TYPE OF COMMUNITY Ad Milord urban State Nation Diudvantaged urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. f Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 98 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE As Students' Reports on the Mathematics Class (continued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL EIghthirade STATE ASSESSMENT Mathematics Pre-algebra .1IMM, MINIIMINIIMMIIMII116=W pyral Paroentage and PraNciancy 114roantaga and PrvIldancy Paremia. Ilradlaioncy State 63 ( 22) 20 2.0) 16 ( 1.1) 264 ( 12) 210 1.9) ( 1.5) Nation 62 ( 2.1) 19 1.9) 15 ( 1.2) 261 ( 1.4) 272 ( 2.4) 295 ( 2A) PARENTS EDUCATION NS nen-graduate State 76 ( 243 ( 4.1) 2.6) 14 ( 3.1) es, ( van 7 ( 2.1) Nation 77 ( 241 ( 3.7) 2.1) 13 ( 3.4) 0. 3 ( NI* ( 1.1) IMO) HS graduate State 73 ( 2.4) 18 ( 2.2) 10 ( 250 ( 12) 268(3.0) 245 ( 1.9 Nation 70 ( 2.6) 18 ( 2.4) ( 1.1 249 ( 1.9) 268 ( 3.5) 277 ( 5.2) Seale coNage State 83 ( 2.6) 20 ( 22) 16 ( 1.7) 261 ( 1.7) 273 ( 2.7) 299 ( 2.8) Nation 80 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 278 ( 2.8) 295 ( 32) Co Nage gradual* State 49 ( ^ 9' 25 ( 2.8) 25 ( 1.7) 259 ( 7 t'i) 275 ( 2.4) 304 ( 1.6) Nation 53 21 ( 2.3) 24 ( 1.7) 2591 1,5) 27$ ( 2.8) 303 ( 23) GENDER Mat State 63 ( 2.1) 20 ( 2.2) 15 ( 1.3) 257 ( 1.4) 27", ( 2.0) 303 ( 1.2) Nation 83 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 290 ( 2.5) Female State 62 ( 2.7) 20 ( 2.1) 17 ( 1.5) 250 ( 1.4) 206 ( 2.3) 297 ( 1.7) Nation 81 ( 2.6) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Tht. percentages may not tots! 100 percent because a small number of students reported taking other mathematics courses. *** Sample size is insufficient to permit a reliable estimatr (fewer than 62 studentii). 1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Ohio TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT None 1$ M inutes 30 Mi oadn 45 Minutes An Hour or More TOTAL Percentage and Prodiciency 1 ( 0.4) 1 ( 0.3) ( 1 ( 0.4) ( 1 ( 0.3) ( 1 ( 1.0) ( 0.7) ( 2 ( 1.8) ( 1 ( 0.8) ( ** ) 0 ( 0.0) 1 ( 0.9) 4 ( 3.0) .44) 0 ( 0.0) ( "*) 0 ( 0.0) ( 0 ( 0.0) ( 4.4) ( ***) ( 0.4) ( Percentage end Proackncy 38 ( 3.8) 25$ ( 2.4) 43 ( 4.2) 250 ( 2.3) 30 ( 3.9) 283 ( 2.1) 39 ( 4.5) 286 ( 2.2) 43 ( 8.7) 227 ( SS ( 7.8) 232 ( 3.1) 38 ( 9.1) IP** 4/11 40 ( 7.8) 245 ( 3.0)1 31 (10.2) 274 ( 82)1 61 (11.3) 273 ( 3.1)1 31 ( 8.3) 233 ( 5.5)1 41 (12.6) 238 ( 2.1)1 29 (15.9) 267 ( 3.7)1 86 (14.9) 253 ( 5.4)1 40 ( 4.4) 258 ( 2.4) 37 ( 4.3) 256 ( 3.1) Percentage and Madam 62 ( 3.7) 267 ( 1.5) 43 ( 4.3) 200 ( 2.0) 53 ( 3.7) 271 ( 1.6) 45 ( F.1) 270 ( 2.7) 43 ( 8.3) 232 ( 2.7) 40 ( 8.7) 248 ( 5.3) 53 ( 92) ( .41 34 ( 6.8) 251 ( 42)1 55 ( 9.4) 280 ( 3.6)1 32 ( 8.6) 4,.*) 54 ( 7.2) 245 ( 5.9)! 36 ( 9.4) 253 ( 9.0)1 56 (18.4) 266 ( 6.7)1 14 (10.9) .4» ( *41 SO ( 4.3) 266 ( 1.6) 49 ( 5.1) 265 ( 2.5) Paroodage and Preatiency ( 1.4) 283 ( 5.2)1 10 ( 1.9) 272 ( 5.7)1 ( 1.4) 28$ ( 4.4)1 11 ( 2.4) 277 ( 7.8)1 8 ( 3.3) 3 ( 12) 4a4 ( *41 6 ( 3.2) 4.** 13 ( 2.9) 0.0. 13 ( 5.1) +.) 5 ( 3.4) *. .44) 8 ( 3.9) 12 ( 5.9) 13 ( 8.3) 4.4.1 4 ( 1.0) 279 ( 84)1 10 ( 2.4) 278 ( 8.6)1 Percentage and Prolkiency 4 ( 1.1) 285 ( 8.6)1 4 ( 0.9) 27$ ( 5.1)1 3 ( 1.1) 290 ( 92)1 4 ( 0.9) 279 ( 5.8)1 5 ( 2.9) .44(44*) 2 ( 0.8) ( *41 7 ( 2.1) ( of.) 0 ( 0.3) 3 ( 3.1) *** ( I*/ 1 0 ( 8.2) ( 4** 5 ( 1.7) 287 ( 9.4)1 4 ( 1.1) 282 (11.6)1 State Nation RACE/ETHNICITY Whit. State Nation Slack State Nation Hispanic State Nation TYPE Of COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State NAtion Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of' the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 115 100 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A6 Teachers' Reports on the Amount of Time (c4)ntinued) Studeuts Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP 'TRIAL STATE ASSESSMENT 15 Wages 30 Mimeos 46 Mktutos An Hair or Moro TOTAL livarantaga and Pralialina 1 OA) 1 *44 *01 1 ( 1.0) «be ( *01 1 ( OA) ( 1 ( 0.5) .44,) 1 ( 0.5) ( 4") I ( 0.5) 444 ( 444) 1 ( 0.9) ( 444) 1 ( 0.6) "4 ( "4) 0 ( 4") 1 ( 0.8) 1 ( 0.3) 1 ( 0.4) 4" ( 4") 1 ( 0.4) 4" ( 4") P4W0~ and Pralcianq 38 3.6) 266 2A) 43 4.2) 250 ( 2.9) 48 ( 8.7) 243 ( 3.3) 49 ( 6.3) 240 ( 2.8) 30 ( 4.5) 252 ( 2.9) 43 ( 52) 249 ( 3.1) 40 ( 4.6) 263 ( 2.2) 44 ( 5.4) 265 ( 2.6) 32 ( 3.8) 268 ( 3,6) 40 ( 4.7) 285 ( 24) 38 ( 3.8) 2$2 ( 2.6) 44 ( 4.4) 257 ( 2.9) 37 ( 4.1) 254 ( 2.8) 41 ( 4.4) 255 ( 2.3) Palmtop and 52 ( 3.7) 287 ( 43 ( 4.3 208 2.8 44. ( .ev 40 ( 8.1) 248 ( 3.7) 55 ( 4.4) 260( 1.7) 44 ( 5.8) 256 ( 2.7) 48 ( 4.6) 273 ( 2.0) 43 ( 5.8) 270 ( 3.6) 53 ( 3$) 275 ( 2.1) 44 ( 4.1) 277 ( 3,0) 54 ( 3.8) 270 ( 1.7) 43 ( 4.3) 26$ ( 2.9) 50 ( 4.0) 264 ( 1.7) 43 ( 4.7) 264 ( 2.8) Porcantage and PrelicioncY ( 1.4) 283 ( 52)1 10 ( 1.0) 272 t 5.70 7 ( 2.9) 0 (1.7) 5 ( 1.5) ( .41 9 ( 3.1) ***) 7 ( 1.8) ee. *el 7 ( 2.1) 1rf 9 ( 2.1) 295 ( 5.2)1 11 ( 2.3) 287 ( 0.1)1 a ( 1.2) 288 ( 82) 9 ( 1.9) 273 ( 7.3)1 8 ( 1.8) 279 ( 5.8)1 11 ( 2.0) 272 ( 5.7)1 Paraudap and tividencl? 4 ( 1 2115 ( 8 4 ( 278 ( 5.11 4 ( 2.4) 441 444 ( 444) 2 ( 1.3) 444 ( 444) 3 ( 1.0) 4" (. 444) 4 ( 1.3) HI* ( eon 4 ( 1.0) *gm, ( 44.) 5 ( 1.5) 5 ( 1.3) "4 ( 444) 3 ( 1.0) 4" ( 444) 5 ( 1.3) 279 ( 7.7)1 4 ( 1.5) 4 ( 0.9) ( 4.1 State Nation PARENTS EDUCATION HS non-graduate State Nation NO "Moat. State Nation Soma collage State Nation CoOgo graluate State Nation GENDER M. State Nation Fonate 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, Vic, value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret .1.ith 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 101 Ohio TABLE A7 I Students' Reports on the Amount uf Time They I Spent on Mathematia Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL ISTATE ASSESSMENT 15 Minutes 30 Minutes 45 Minutes An Hour or Moro TOTAL Percentage and Pro diciancy 0 ( 0.7) 258 ( 22) ( 0.8) 251 ( 2.8) 7 ( 0.7) 262 ( 2.3) 10 ( 1.0) 253 ( 3.4) 5 ( 1.3) ( «on 7 ( 15) 3 ( 2.1) 12 ( 1.6) ( ***) 6 ( 0.9) ( 2.5) 10 ( 2.1) ( '") 12 ( 3.7) *) 4 ( 0.8) ( ***) 6 ( 2.2) IND.) 6 ( 0.9) 280 ( 2.8) 9 ( 1.0) 250 ( 3.8) Percentage and Pro &dewy 38 ( 1.1) 264 ( 1.0) 31 ( 2.0) 264 ( 1.9) 37 ( 1.2) 288 ( 1.0) 33 ( 2.4) 270 ( 1.9) 30 ( 3.0) 234 ( 3.8) 28 ( 2.5) 241 ( 3.8) 29 ( 4.7) 0.04. 27 ( 3.0) 248 ( 3.6) 39 ( 2.5) 279 ( 2.1)1 41 (12.5) 278 ( 3.0)1 28 ( 2.2) 240 ( 4.5) 24 ( 3.3) 253 ( 4.9)1 40 ( 3.2) 267 ( 1.8)1 36 ( 4.6) 280 ( 3.5)1 38 ( 1.4) 264 ( 1.3) 30 ( 1.8) 263 ( 2.3) Percentage and Prolidetny 05 ( 1.1) 287 ( 1.4) 32 ( 1.2) 263 ( 1.9) 35 ( 1.3) 272 ( 1.3) 32 ( 1.3) 270 ( 2.1) 32 ( 3.9) 238 ( 2.0) 33 ( 2.7) 237 ( 3.5) 38 ( 5.2) 30 ( 2.8) 248 ( 3.4) 38 ( 1.8) 282 ( 3.8)1 31 ( 8.8) 280 ( 4.8)1 33 ( 3.1) 248 ( 5.6) 31 ( 3.0) 247 ( 4.7)1 35 ( 3.0) 272 ( 3.7)1 31 ( 2.9) 255 ( 5.1)1 35 ( 15) 287 ( 1,5) 32 ( 1.3) 264 ( 2.3) Percentap and Proaciency 14 ( 0.7) 262 ( 2.3) 16 ( 1.0) 2fr ( 1.4) 13 ( 0.8) 287 ( 2.2) 15 ( 0.9) 277 ( 2.2) we* ( 18 ( 2.3) 240 ( 3.6) 15 ( 4.8) 17 ( 2.1) 241 ( 4.3) 13 ( 1.9) 12 ( 3.3) 14 ( 2.0) 04* 20 ( 1.9) 250 ( 4.8)1 14 ( 2.8) 1, *se) 18 ( 3.8) *v. ( 15 ( 0.9) 263 ( 2.6) 15 ( 1.1) 267 ( 2.1) Percentage and Proficiency 0 ( OA) 258 ( 2.5) 12 ( 1.1) 258 ( 3.1) 8 ( 0.7) 285 ( 2.5) 11 ( 1.3) 288 ( 3.3) 14 ( 2.1) 11,44 18 ( 1.9) 232 ( 3.7) 14 ( 5.0) 14 1.7) .H.) 6 ( 1.1) 44,4) 7 ( 3.4) 16 ( 1.9) *4.* ( 14 ( 2.2) 8 ( 2.1) *44(04*) 7 ( 2.7) ( *ea) 8 ( 0.8) 281 ( 2.7) 13 ( 1.1) 258 ( 3.6) State Nation RACE/ETHNICITY Ifeitite State Nation Bieck State Nation Hispanic State Nation TYPE Of COMMUNITY Advantaged urban State Nation Disadvantaged State Nation Extreme rurai 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 accura': determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 82 students). 1 7 102 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A7 I Students' Reports on the Amount of Time They (continued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT - . None 15 Minutes- 30 Minutes 45 Minutes An Noir or] &bre TOTAL Percentage and Pteliciancy Panwitalle and PraNciancy Peroontaa. and ProNdancy ftramtagi and Pealldancy Parcatale and Peva:lam State ( 0.7) 36 ( 1.1) 35 ( 1.1) 14 ( 0.7) ( 0.6) 256 ( 2.2) 264 ( 1.0) 267 ( 1.4) 262 ( 2.3) 256 ( 2.5) Nation 9 ( 0.6) 31 ( 2.0) 32 ( 1.2) 16 ( 1.0) 12 ( 1.1) 251 ( 2.6) 264 ( 1.9) 263 ( 1.9) 266 ( 1.9) 256 ( 3.1) PARENTS' EDUCATION NS non-graduate State 12 ( 11) 30 ( 3.0) 32 ( 3.8) 17 ( 3.1) 10 ( 2.5) ( "4) 444 Nation 17 ( 3.0) 26 ( 3.3) 34 ( 4.4) 12 ( 23) 1C ( 2.2) *** ( ***) 248 ( 4.0) 246 ( 2.6) ` ( ***) ""' ( "") 146 graduate State 7 ( 1.3) 37 ( 1.9) 34 ( 1.8) 13 ( 1.2) 9 ( 1 1) 257 ( 1.4) 259 ( 1.8) 257 ( 3.8) 253 ( 3.9) Nation 10 ( 1.7) 33 ( 2.2) 31 ( 1.9) 16 ( 1.4) 11 ( 13) 246 ( 4.2) 259 ( 3.2) 254 ( 2.4) 258 ( 2.8) 244 ( 3.4) Some collage State 5 ( *** ( 1.0) ***) 36 ( 272 ( 2.3) 1.9) 37 ( 267 ( 2.4) 2.0) 13 ( 269 ( 1.6) 3.6) 6 ( *** ( 1.0) ***) Nation 9 ( 1-2) 30 ( 2.7) 36 ( 2.1) 14 ( 1.8) 11 ( 1.5) 266 ( 3.0) 266 ( 2.6) 274 ( 331 *** ( "4) Whip graduate State 5 ( 0.6) 34 ( 1.3) 37 ( 1.4) 15 ( 1.3) 9 ( 0.9) 272 ( 1.8) 260 ( 2.0) 270 ( 3.6) 268 ( 4.7) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Male State 7 ( 0.8) 39 ( 1.2) 33 ( 1.5) 13 ( 0.9) 7 ( 0.6) 259 ( 3.0) 267 ( 1.4) 271 ( 1.9) 263 ( 3.1) 262 ( 3.8) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 266 ( 2.4) 265 ( 3.0) 256 ( 4.1) Female S:ate 5 ( 0.8) 32 ( 1.3) 37 ( 1.5) 15 ( 1.2) 11 ( 1.0) 255 ( 3.0) 261 ( 1.4) 264 ( 1.7) 261 ( 3.0) 254 ( 3,4) Nation 7 ( 0.9) 26 ( 2.0) 15 ( 1.7) 17 ( 1.0) 13 ( 1.3) 248 ( 4.1) 263 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear M parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufricient to permit a reliable estimate (fewer than 62 students). 1 s THE 1990 NAEP TRIAL STATE ASSESSMENT 103 Ohio TABLE A8 I Teachers' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Numben and Operations Meastripment 04remetty Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation RACE/ETHNICITY Whit* State Nation Black State Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantapad urban State Nation Extreme rural State Nation Other State Nation Porondep Paneneses Porcentsge Pavente. Percentage Pereenteas and end SW and end Presidency Preiciency Pala:4mq Praidency Presidency Poidency 4$ ( 3.7) 14 2.2 17 33 ( 3.1 23 V 27 261 ( 1.8) 294 3.7 243 4.2 275 ( 2.4 284 22 MK 2.4 49 ( 3.8) 15 2.1 17 3.0 33 ( 4.0 20 al ) 21 3. 260 ( 14) 237 ( 3.4 250 ( s.a) 2rd. ( 4.0 260 3.2 ) as 5.4 48 ( 3.9) 15 ( 2.4) 15 ( 2.9) 38 ( 3.3) 24 3.3) 28 2.1 287 ( 1.7) 295 ( 3.7) 253 ( 3.5)1 277 ( 2.2) 208 2.8) 46 ( 3.7) 18 ( 2.4) 14 ( 3.4) 38 ( 4.7) 27 4.41 22 3.4) 267 ( 2.2) 289 ( 3.5) 259 ( 0.9y 277 ( 4.3) 285 3.3) 273 5.11) 04 ( 0.7) 5 ( 1.8) 34 ( 54) 13 ( 4.1) 21 1 4.51 15 1 2.7) 234 ( 2.5) ( e") 211 ( 5.3)1 e" ( "4) 4" ..... *II 54 ( 74) 11 ( 3.3) 25 ( 74) 23 ( 5.7) 33 ( 7.9) 24 ( 7.3) 243 ( 4.3) Ir" ( "") 226 ( 2.8)1 238 ( 8.1 )4 242 ( 54)4 233 f 4.7$ 54 ( 7.0) 8 ( 3.4) 22 ( 5.7) 24 ( 7.2) 19 ( 5.0) 21 ( 65) fili* ( .41 RIM ( ***) 41/4* V41 40 ( ***) M. ( *On ~ ( *On 47 ( 8.7) 6 ( 2.2) 23 ( 4.1) 34 ( 5.8) 240 ( 4.8) ( "*) *** ( "*) 255 ( 44)1 28 ( 7.8) 278 ( 5.0)1 2$ (13.0)( 59 ( 8.4) 240 ( 4.8) 46 (12.1) 255 ( top 24 (15.4) .44.) 53 (12.4) 257 ( 7.1)1 55 ( 4.2) 283 ( 2.0) 52 ( 4.1) 200 ( 2.3) 21 ( 5.9) 310 ( 42)1 16 ( 42) 14 ( 4.4) 9 ( 4.0) 18 (10.2) 41144 **11) 6 ( 3.0) 04.i) 12 ( 2.4) 292 ( 5.4)1 16 ( 2.7') 286 ( 3.8) 13 ( 4.9) *e 9 ( 7.0) *el 33 ( 7.3) 214 ( 5.3)1 39 (10.3) 238 ( 8.4)1 19 (12.2) ***) ( 4.9) 41111,1t ( tit* ) 15 ( 3.5) 24$ ( 34)4 18 ( 3.9) 253 ( 7.1)1 44 ( 7.9) 287 ( 3.9)1 40 ( 8.5) 25 (102) 261 ( 7.3)1 21 ( es) Mr* 414t) 44 (11.5) 277 ( 5.6)1 32 (11.7) 265 ( 9.1)1 30 ( 3.8) 272 ( 3.6) 34 ( 5.3) 270 ( 4.8) 27 ( 8.6) ( ") 29 ( 7.5) 277 ( 4.5)4 as ( 9.4) 267 4.9)1 12 ( 2.4) 33 (11.8) 24$ ( 8.2)1 13 (105) .4.41 9 ( 8.1) 9** /am) 28 ( 4.1) 262 ( 3.3) 26 ( 4.6) 280(34) 18 ( 5.5) ( ***) 23 ( 5.3) 289 ( 7.0r 13 ( 32) 4tr **at) 19( 31) 18 ( 7.6) in 23 (10.0) ( 115 ( 7.9) 441 30 ( 3.1) 259 ( 2.3) 24 ( 4.3) 285 ( 5.7) Thr 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. 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 accu-ate 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 Ohio TABLE A8 I Teachers' Reports on the Emphasis Given to (continued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11410 NAEP TRIAL STATE ASSESSMENT Numbers and Operations- Measurement Deoutetry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis AMMEIMINNIPOIMINO, TOTAL Percentage and Pro latency Percentage and Prelickatcy Percentage and *Mc Macy Percentage and Prone Macy Pacientase mid Pre Odom Pommies* and Prat:Macy State 43 ( 32) 14 ( 2.2) 17 ( 2.8) 33 3.1) 23 ( 3.1) 27 ( 2.6) 261 ( 1.8) 294 ( 3.7) 243 ( 4.2) 275 ( 2.4) 264 ( 2.7) 264 ( 2.4) Nation 40 ( 3.8) 15 ( 2.1) 17 ( 3.0) 33 4.0) 28 ( 3.8) 21 ( 3.3) 260 ( 1.8) 287 ( 3.4) 250 ( 5.6; 272 ( 4.0) 260 ( 3.2) 264 ( 5.4) PARENTS' EDUCATION Itti non-graduate State 63 ( 250 ( 5.8) 4.2) 10 ( ( 3.6) *IN) 22 ( se, 6.1) 26 ( 5.2) ( sits) 20 ( es, ( 5.4) 30 ( ( 5.0) 4pinal Nation 60 ( 251 ( 6.9) 3.4) 7 ( 2.3) .41 22 ( 5.3) sss ass.) 25 ( 5.3) so. ss.) 32 ( sss 6.3) 20 ( 44. 6.7) so.) H3 graduat State 54 ( 4.4) 10 ( 2.1) 19 ( 3.7) 29 ( 3.5) 24 ( 4.1) 26 ( 3.2) 255 ( 2.1) 278 ( 4.8)1 243 ( 5.2)1 282 ( 3.8) 261 ( 3.1) 254 ( 2.9) Nation 55 ( 250 ( 4.8) 2.9) sss ( sits) 17 ( 251 ( 3.9) 6.1)1 27 ( 253 ( 5.0) 4.7)1 27 ( 255 ( 4.5) 42) 24 ( 248 ( 5.1) 4.8)1 Some aglow Stste 47 ( 4.8) 12 ( 2.9) 19 ( 4.0) ( 4.3) 25 ( 3.9) 27 ( 3.3) 272 ( 2.3) 250 ( 5.3)1 280 ( 4.4) 263 ( 4.1) 206 ( 3.7) Nation 47 ( 205 ( 4.4) 2.0) 17 ( 284 ( 3.3) 4.1)! 12 ( se. ( 2.7) 0..) 39 ( 279 ( 5.5) 4.5) 27 ( 262 ( 5.0) 4.8)1 23 ( 270 ( 4.1) 4.7) College graduate State 40 ( 3.3) 20 ( 2.8) 13 ( 2.2) 39 ( 3.4) 24 ( 27 ( 2.9) 269 ( 2.7) 306 ( 2.7) 248 ( 7.3) 287 ( 2.2) 270 ( 3.6) 279 ( 3.3) Nation 44 ( 41) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 269 ( 2.6) 298 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 6.4) GENDER Mal* State 50 ( 3.8) 13 ( 2.2) 17 ( 2.9) 31 ( 3.3) 24 ( 3.2) 27 ( 2.8) 284 ( 2.1) 297 ( 4.3) 250 ( 4.6) 281 ( 2.8) 287 ( 2.9) 268 ( 2.8) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 261 ( 2.5) 287 ( 4.4) 258 ( 5.7) 275 ( 4.8) 263 ( :1.8) 266 ( 6.8) Female State 48 ( 4.1) 15 ( 2.5) 17 ( 3.0) 35 ( 3.3) 23 ( 3.3) 27 ( 2.9) 259 ( 2.3) 291 ( 3,$) 230 ( 5.2) 289 ( 3.2) 200 ( 3.2) 263 ( 3.0) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 260 ( 2.0) 286 ( 3.3) .41 ( 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, t.he value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 11 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Ohio TABLE A8 I Teachers' Reports on the Emphasis Given To (continued) i Specific Mathf :'natics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Data Analysts, Statistics, and Probability Algebra and Ftections Heavy Emphasis Little or No Emphasis Heavy Emphasis 'Ale or No Emphasis you4.. Percentage and Preficiency Porcenfaso and Prolkiency State 13 ( 2.3) 64 ( 3.2) 270 ( 4.4) 2611 ( 2.1) Nation 14 ( 2.2) 53 ( 44) 289 ( 4.3) 261 ( 2.9) RACE/ETHNICITY Wt. State 13 ( 2.4) 06 ( 3.2) 277 ( 4.3) 272 ( 1.7) Nation 14 ( 2.4) 53 ( 5.0) black 270 ( 4.1) 271 ( 3.1) State 17 ( 4.3) 53 ( 7.0) ( 1141 218 ( 5.7) Nation 14 ( 3.4) 53 225 ( 82) ( 4.3) Hispanic State 18 ( 5.8) ..**) 58 ( 8.9) Nation .041 56 248 ( 8.3) ( 4.4) TYPE Of COMMUNITY Advantaged urban State 19 ( 9.4) 58 (10.6) 283 ( 4.0)1 Nation 11 ( 6.6) 05 (19.4) 284 ( 7.4)! Disadvantaged urban State 17 ( 5.1) 45 (10.7) 231 (10.9)1 Nation 19 ( 9.4) 4.1 34 238 (11.4) ( 8.2)1 , Extreme rural State 3 ( 1.9) 88 (10.7) 274 ( 3.6)1 Nation 5 ( 5.4) 65 (16.9) 254 ( 6.7)1 Other State 13 ( 2.6) 69 ( 3A) 272 ( 4.8)1 266 ( 1.9) Nation 15 ( 2.9) 53 ( 5.2) 267 ( 4.7) 200 ( 3.4) Porcentago aid and Proiciency Proficiency 217°1 .6 11 46 IS) 275 2.5) 49 ( 3.2) 282 ( 1.7) 48 ( 4.2) 281 ( 3.0) 43 ( 5.6) 242 ( 4.3) 39 ( 7.1) 253 ( 8.3) 54 ( 6.8) 044 ( 46 ( 5.9) 257 ( 4.0)1 64 ( 6.7) 287 ( 3.0)1 41 ( 8.9) 296 ( 7.9)1 61 ( 4.9) 253 ( 5.7) 53 (11.8) 254 ( 8.3)1 36 ( 8.8) 280 ( 9.5)1 33 ( SA) 46 ( 4.2) 279 ( 2.3) 47 ( 4.3) 278 ( 2.8) 20 ( 2.8) 243 ( 2.0) 20 ( 3.0) 243 ( 3.0) 20 ( 2.6) 245 ( 22) 18 ( 2.8) 2*1 ( 3.3) 21 ( 5.5) 00. 27 ( 8.9) 226 ( 2.2)1 18 ( 8.4) ( «al 18 ( 4.2) 8 ( 3.6) (44 ( 18 ( 5.3) 12 ( 5.9) 20 ( 94) ( 4.1 21 ( 9.9) IP.O1P 42 (16.0) 241 ( 5.9)! 25 ( 4.0) 243 ( 2.4) 17 ( 3.3) 245 ( 4,4)1 The standard errors of the estimated statistics appear in parentheses. It can be said .7.h about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 106 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A8 I Teachers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRIAL STATE ASSESSMENT Data Ans lysis, Statistics, and Probability Algebra and Functions Heavy Emphasis Uttle or No Emphasis Heavy Emphasis , Little or No Emphasis Peroutap an* Proldency 13 ( 2.3) 270 ( 4A} 14 ( 2.2) 209 ( 4.3) ilanusage end Prellaleacy 64 3.2) 2.1) 53 4.4) 261 2.9) State Nation PARENTS' EDUCATION NS non-graduat State 7 ( vas ( 3.1) 441 73 248 ( 5.11) ( 4.2) Nation 9 ( 3.0) 53 ( 7.7) 240 ( 8.2) NS graduate State 13 ( 2e0 ( 2.1) 4.3)1 96 248 ( 3.8) ( 2.8) Nation 17 ( 3.7) 54 ( 5.4) 261 ( 8.0)1 247 ( 2.0) Some college State 12 ( 2.6) 64 ( 3.8) 274 ( 2.3) Nation 13 ( 2$).) 57 ( 270 ( 5.8) 3.7) College graduate State 16 ( 3.1) 81 ( 3.8) 261 ( 4.5)1 27$ ( 2.7) Nation 15 ( 2.4) 53 ( 4.4) 262 ( 4.5) 275 ( 3.8) GENDER Male State 13 ( 2.4) 83 ( 3$) 272 ( 5.4) 289 ( 2.4) Nation 13 ( 2.2) 54 ( 4.7) 275 ( 5.3) 290 ( 3$) Female State 13 ( 2.3) 85 ( 3.1) 266 ( 4.7) 264 ( 2.5) Nation 16 ( 2.4) 53 ( 4.5) 283 ( 4.4) 262 ( 2.8) Parositab. Perfards0 anti Praliciancy Prolicism 50 ( 3.0) 277 ( 1.6) 48 ( 3.6) 275 ( 2$) 31 ( 5.5) 78 *562) 41 ( 3.7) 268 ( 22) 44 ( 4.8) 245 ( 3.5) 52 ( 4.3) 277 ( 2.3) 48 ( 4.8) 278 ( 3.0) 81 ( 2.8) 288 ( 1.7) 50 ( 3.9) 28$ ( 3,0) 46 ( 3.4) 276 ( 22) 44 ( 4.1) 278 ( 3.2) ( 3.1) 276 ( 2.5) 48 ( 3.8) 274 ( 2.7) 20 ( 2.6) 243 ( 2.0) 20 ( 3.0) 243 ( 3.0) 32 ( 6.0) 29 ( 6.9) ( 441 25 ( 2.5) 240 ( 2.9) 23 ( 3.9) 239 ( 3.4) 20 ( 3.9) 250 ( 3.1)1 .7) 13 ( 22) 248 ( 3.5) 18 ( 2.4) 249 ( 4.0) 21 ( 3.2) 244 ( 2.6) 22 ( 3.6) 243 ( 3.0) 19 ( 2.6) 241 ( 2,8) 18 ( 2,9) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 9.5 percent certainty that, for /Bch population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. 1 Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 107 Ohio TABLE A9 I Teachers' Reports on the Availability of I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL I Gat AN the Resources I I Om Most of the I ON Same or Nano ot STATE ASSESSMENT Need Rmaustas I Med the Resources I Need TOTAL Percentage and PrePcioncy and Prelloiency Percentage and Proficiency State 12 ( 2.8) 54 ( 4.4) 94 ( 4.0) 266 ( 5.0)1 206 ( 1.8) 250 ( 2.1) Nation 13 ( 2.4) 56 ( 4.0) 31 ( 42) 265 ( 42) 265 ( 2.0) 261 ( 2.9) RACE/ETHNICITY State 12 ( 2.9) 56 ( 4.7) 32 ( 4.0) 273 ( 33)1 260 ( 1.4) 260 ( 11) Nation 11 ( 2.5) 58 ( 4.6) 90 ( 4.6) 275 ( 3.5)! 270 ( 2.3) 267 ( 3.3) Black State ( 5.8) 41 ( $.4) 50 ( 9.7) !he ( *41 235 ( 2.8); 231 ( 25)1 Nation 15 ( 4.2) 52 ( 6.0) 33 ( 72) 241 ( 5.3)1 242 ( 2.4) 235 ( 4.9) Hispanic State 11 ( SD) 48 ( $.6) 41 ( 8.6) ( 0+0) 044 44* ) Nation 23 ( TA) 44 ( 4.0) 34 ( '.T) 248 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 TYPE Of COMMUNITY Advantaged urban State 8 (11.0) 61 (12.4) 21 ( 8.0) 263 ( 4.2)1 277 ( 3.7)1 288 ( 3.8)1 Nation 36 ( 9.2) so ( 8.9) 3 ( 3.1) 2721 8.5)1 288 ( 1.3)1 IMO ( 4.04 10) Disadvantagad urban State 34 (10.7) 51 (13.4) 243 ( 8.1)1 240 ( 6.0)1 Nation 10 ( 6.8) 40 (13.1) ( 5.4)1 50 (145) 253 ( 5.5)1 Extrema rural State 96 ( 4.0) 4 ( 4.0) 287 ( 2.3)1 Nation ihkr. 54 (104) 280 ( 8.8)1 43 (10.3) 257 ( 5.0)1 Other State 11 ( 3.2) 50 ( 5.5) 39 ( 5.3) 269 ( 4.3)1 265 ( 1.8) 281 ( 1.8) Nation ( 2.9) 58 ( 5.4) ( 5.6) 265 ( 3.9)1 264 ( 2.1) 283 ( 42) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 3 10/1 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A9 I Teachers' Reports on the Availability of (contin I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MO NAEP TRIAL I Get All the Resources I I Get Most of the I Oitt Some or None of STATE ASSESSMENT Need Resources I Need the Ramiro/8 I Need TOTAL Paraoadafa awl Preficiency Perceds. ind lindiciancy Peramilegs tad Pralloisecy State 12 2e8 ( 2.6) ( 5.0)1 54 208 ( 44 1.1 34 259 2.1 Nation 13 ( 2.4) 56 4.01 31 4.2 285 ( 4.2) 265 2.0 261 (2.9) PARENTS' EDUCATION MI non-graduate State ( *41 51 247 ( ( 8.6) 3.5) 58 ( 248 Nation I ( 2.8) 54 244 ( 5.7) ( 2.7) 38 63 243 Id graduate State ( 2.4) 55 t 4.8) 37 ( 261 ( 5.6)1 259 ( 1.6) 253 ( 2.5 Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.9 253 ( 4.8)1 256 ( 1.9) 258 ( 2.6) Soma college State 10 ( 2.6) .41 59 ( 270 ( 4.9) 1.0) 32 4.2) 268 ( 2.6) Nation 13 ( 3.3) ow* ( «al 62 ( 289 ( 4.3) 2.5) 25 ( 4.1 287 ( 3.6) College graduate State 15 ( 4.2) 53 ( 5.3) 32 ( 4.0 280 ( 3.8)1 278 ( 22) 288 ( 2.9) Nation 15 ( 2.9) 56 ( 4.9) 30 ( 5.1 278 ( 5.4)1 276 ( 2.2) 273 ( 3.7 GENDER Male State 11 ( 2.7) 54 ( 4.4) 35 ( 4.0) 272 ( 4.9)1 266 ( 2.2) 262 22) Nation 13 ( 2.6) 57 ( 4.0) 30 4.0) 264 ( 5.0)1 265 ( 2.6) 264 3.3) Female State 12 2.9) 54 ( 4.6) 34 ( 4.2) 284 ( 51)1 263 ( 1.6) 256 ( 2.5) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 208 ( 3.9) 264 ( 2.0) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each populigtion of interest, the value for the entire population is *.ithin * 2 standard errors of the estimate for tht 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). 1 7 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 Ohio TABLE Alth I Teachers' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Lass Than Once a Weak Now - TOTAL. Paroentaga and PTO/klitfiCy PoroOft. and Proikkoncy Pieventage and Prsildena State 37 ( 3.4) 49 ( 3.0) 2.8) 206 ( 2.0) 285 ( 1.9) 200 3.9) Nation 50 ( 4.4) 43 ( 4.1) 8 2.0) 200 ( 2.2) 264 ( 2.3) 277 ( 5.4)t RACE/ETHNWITY White State 36 ( 3.6) 49 ( 3.9) 1$ ( 3.1) 270 ( 1.7) 270 ( 1.5) 287 ( 3.9)1 Nation 49 ( 4.6) 43 ( 4.5) 8 ( 2.3) 265 ( 2.7) 271 ( 2.2) 285 ( 4.1))1 Black State 36 ( 0.5) 54 ( 5.7) 10 ( 2.5) 236 ( 4.1)! 227 ( 2.8) Nation 47 240 ( 8.1) ( 3.4) 45 ( 238 ( 7.0) 4.0) 9 ( *44 ( 4.1) Hispanic State 34 44rIt ( 7.1) ***) 4$ ( 7 .4) (4.0.1 21 (( 7.6) *el Nation 64 ( 7.2) 32 ( RA) 248 ( 2.5) 247 ( 8.3)1 ( 4") TYPE Of COMMUNITY Advantaged urban State 45 (10.3) 45 ( 7.3) 250 ( 4.4)1 252 ( 4.7)1 Nation 39 (220) 41 (17.9) 20 (12.2) ( 273 ( 6.0)1 Disadvantaged urban State 39 ( 9.8) 49 ( 7.8) 12 ( 8.0) 250 ( 7.6)1 235 ( 4.4) IV* ( Ain Nation 70 248 (11.7) ( 4.8)1 21 ( 249 ( 9.0) 5.7)1 9 ( ( 8.5) **al Extreme rural State 12 ( 5.4) 68 (13,4) 20 (13.0) INF* ( MO) 289 ( 3.7)1 Nation 35 (14.0) 58 (17.1) 9 ( 9.6) 255 ( 5,5)1 258 ( 5.9)1 ( ***) Other State 30 ( 4.8) 47 ( 4.7) 15 ( 3.5) 285 ( 1.8) 206 ( 2.0) 265 ( 5.1)1 Nation 50 4.4) 44 ( 4.5) ( 1.8) 260 ( 2.4) 284 ( 29) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 110 115 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE AlOa I Teaches' Reports on the Frequency of Small (ccntinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 NAEP TRIAL STATE ASSESSMENT At Laast Once a %Wei( Less Than Once a Week Never TOTAI Prolloisacy am0 IIVW1dimay Pareasdaga and Pnglidencif State 37 ( 3.4) 49 ( 3.6) 14 2.0) 200 2.0) 205 ( 1.9) 200 *9) Nation 50 4.4) 43 ( 4,1) 2.0) 200 2.2) 264 ( 2.3) 277 SAY PARENTS' EDUCATION NS non-wading* State 30 ( 5.8) 49 ( 249 ( 6.8) 5.0) 15 (( 4.8) Nation BO ( 6.4) 244 ( 3.2) 39 ( 244 ( 6.5) 3.2)1 ( 1A) «01 HS graduate State 35 ( 3.8) 49 ( 4.1) ( 3.3) 258 ( 2.6) 25a ( 2.1) 256 ( 3.9)1 Nation 49 ( 4.8) 252 ( 2.8) 45 ( 257 ( 5.1) 2.7) ( 2.5) Soule coNege State 38 ( 3,8) 49 ( 4.0) 13 ( 3.1) 272 ( 1.6) 269 ( 2.1) Nation Si ( 52) 42 ( 5.1) 268 ( 3.1) 268 ( 3.2) IN* ( *44 ) Colter graduate State 37 ( 4.6) 48 ( 4.0) 15 ( 3.2) 276 ( 2.4) 274 ( 2.8) 277 ( 3.6)1 Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.0) 278 ( 3.0) 265 ( 4.9)1 GENDER Male State 36 ( 35) 49 ( 3.7) 15 ( 2.9) 28$ ( 2.3) 286 ( 2.3) 268 ( 3.9) Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 285 ( 3.1) 278 ( 5.3)1 Female State 38 ( 3.6) 48 ( 3.8) 14 ( 2.8) 264 2.4) 261 ( 2.1) 282 ( 4.7)1 Nation 50 ( 4.7) 43 ( 4.7) ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.8)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each pcpulation 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). THE 1990 NAEP TRIAL STATE ASSESSMENT 111 Ohio TABLE MOb I Teachers' Reports on the Use of Mathematical I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT At Least Once a Week Loss Than Once a Week _ Never TOTAL State Nation RACE/ETHNICITY White State Nation Mack State Nation Hispank State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Wren* mind State Nation i Other State Nation and Prodialaney 14 2.4) 259 3.2) 22 3.7) 254 3.2) 13 ( 2.2) 284 ( 2.7) 17 ( 4.0) 261 ( 3.8)1 15 ( 4.3) 044 ( 22 ( 5.9) 233 ( SA)' 18 ( 5.3) wire ( 39 ( 7.5) 247 ( 3.8) 17 ( 5.8) 111.4MI ( *IN) 23 (14.4) ( ( 5.8) *IMO ( 0+1 39 (11.4) 247 ( 7.5)1 11 ( 9.7) 27 (14.9) 12 ( 2.4) 259 ( 3.7)1 19 ( 4.3) 253 ( 3.9)1 Percellbls and Pnallidancy SO ( 23) Percentage and Prefteiency ( 14) 285 ( 1.5) 219 9.011 69(3.9 ) ( 2.6) 263 ( 1.9) 282 ( 5.9)1 81 ( 2.5) ( 1.4) aes ( 1.4) 290 ( 8.0)! 72 ( 4.2) 10 ( 2.7) 269 ( 2.1) 288 ( 6211 74 ( 233 ( 8.9) 2.5) (( 5.5) 441 70 ( 6.3) ( 3.9) 241 ( 2.9) ( ***) 80 ( 8.0) 2 ( 1.8) ( ( ***) 55 ( 7.3) 7 ( 2.6) . 245 ( 3.8)1 75 ( 6.6) 282 ( 2.9)I ( "") 63 (11.5) 278 ( 5.8)i ( ***) 69 ( 247 ( 8.0) 5.7)1 11 ( 5.9) ***) 59 (12.1) 2 ( 1.8) 253 ( 7.0)1 ( 89 ( 9.7) 206 ( 3.0)1 ( ***) 85 (14.8) ( 3.9) 262 ( 2.8)1 ( 82 ( 3.0) ( 1.8) 266 ( 1.6) 288 ( 9.8)1 72 ( 5.0) 9 ( 3.3) 263 ( 2.2) 281 ( 7.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE AlOb Teachers' Reports on the Use of Mathematical (continued) i Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1990 NAEP TRIAL STATE ASSESSMENT At Wan Once a Wm* Loss Than Once a Was& Now , TOTAL Parentage and Midway Pansantage and !Widow Parowdasa and RraNdancy State 14 ( 2.1) *3 ( 2.0) 0 ( 1.5) 259 ( 3.2) 26S ( 1.5) 279 9.0)1 Nation 22 ( 3.7) 09 ( 3.9) 9 2.13) 254 ( 3,2) 263 ( 1.9) 282 5.9)1 KS noniraduat State ( 72 ( 244 ( 5.7) 2.6) 6 ( 2.0) ( 041 Nation 25 ( ay. 5.6) 88 ( 243 ( 7.2) 2.2) 143 graduate State 15 ( 253 ( 2.6) 4.1) 81 ( 258 ( 3.0) 1.8) 4 ( 1-2) 41 Nation 23 ( 248 ( 4.6) 4.0)1 70 ( 255 ( 5.3) 2.2) .441, ( 2.8) Soma college State 14 ( 2$) 82 ( 2.8) 4 ( 12) ( 271 ( 1.8) ( Nation 18 ( 4.0) 73 ( 4.3) 9 ( 2.4) 261 ( 4.4)1 269 ( 2.3) College graduate State 12 ( 2,1) 79 ( 3.1) 9 ( 2.8) 285 ( 4.2) 276 ( 2.0) 292 ( 82)1 Nation 20 ( 3.9) 69 ( 3.7) 11 ( 2$) 286 ( 3.5)1 274 ( 2.2) 297 ( 42)1 GENDER M. State 14 ( 2.1) $0 ( 2.6) 6 ( 1.5) 261 ( 3.8) 266 ( 1.7) 282 ( 9.7)1 Nation 22 ( 4.1) 69 ( 4.1) ( 2.0) 255 ( 4.1) 265 ( 2.1) 287 ( 7.2)1 Female State 14 ( 2.3) 80 ( 2.7) 6 ( 1.6) 256 ( 3.5) 262 ( 1.7) 276 (10.0)1 Nation 21 ( 3.6) 69 ( 4.2) 10 ( 3.3) 254 ( 3.3) 282 ( 1.9) 278 ( 0.0)! The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Ohio TABLE Al la I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Lass TOTAI, and Praidency Paraantaga and fordicionst 1Parcanlion and Poiciaacy State % L81.6 SA) 5 ( 1.0) 257 202 3.2) 251 ( Nation 62 ( SAS Si SA) 7 ( 1,11 267 ( 1.8) 254 2.9) 200 ( 5.1 RAcEirniNtegY Whit State 70 ( 4.0) 25 ( 3.7) 4 ( 1.4) 271 ( 1.3) 267 ( 2.7) 263 ( Nation 64 ( 5.7) 20 ( 3.2) 8 ( 2.3 272 ( 1.9) 254 ( 3.4) 264 ( 5.4 I Slack State 59 ( 9.1) 235 ( 3.0) 32 ( el) 230 ( 4.4)I 10 ( 5.5) IN* in Nation 51 ( 7.7) 244 ( 4.0) 41 ( 7.9) 233 ( 3.9)I 2 1A) ..- ( «in Hispanic State 50 ( 7.5) *** 26 ( 6.0 ( 15 ( 8.0) Nation 61 ( 6.6) 251 ( 3.1) 32 ( 5.3 240 ( 4.3 8 ( 2.3) ( .4.1 TYPE OF COMMUNITY Advantaged urban State 00 (12.0) 40 (12.6) 0 ( 0.0) 281 ( 3.5)1 281 ( 4.0)1 Nation 63 (15.9) 283 ( 7.3)1 23 ( 5.2) 14 (14.6) is** 44.) Disadvantaged urban State 54 (11.6) 33 (10.6) 13 ( 6.9) 246 ( 6.6)1 244 ( 8.1)1 Nation OF (10.7) 252 ( 4.7)1 31 (11.1) 243 ( 8.0)1 4 ( 2.2) ion Extreme rival State 91 ( 7.6) 266 ( 3.1)1 ( 7.6) ( +.1 0 ( 0.0) Nation 50 (10.6) 268 ( 4.0)1 40 (10.0) 247 ( 7,6)1 10 ( 72) 4.44. °thaw State 70 ( 4.4) 25 ( 3.9) 5 ( 1.9) 267 ( 1.7) 259 ( 3.1) 200 ( 6.8)1 Nation 63 ( 3.9) Si ( 3.5) 8 ( 1i) 207 ( 22) 2$5 ( 3.1) 257 ( 5.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size IS insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE Al la I Teachers' Reports on the Frequency of (emitinued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Loos TOTAL Percentage an/ Proficiency 09 ( 3.0) 287 ( 02 ( 3.4) 207 ( 1.8) 67 ( 5.8) 248 ( 2.9) 67 ( 5.5) 245 ( 3.2) 68 ( 4.4) 258 ( 1.9) 61 ( 4.4) 257 ( 2.5) 70 ( 4.1) 273 ( 1.8) 68 ( 4.2) 272 ( 2.7) 70 ( 4$) 278 ( 2.0) 61 ( 4.0) 281 ( 2.2) 69 ( 4.0) 270 ( 1$) 80 ( 3.7) 269 ( 2.1) 69 ( 4.0) 265 ( 1.8) 65 ( 3.8) 265 ( 1.8) and Proficiency 27 ( 32) 262 ( 3.2) 311 3.1) 254 ( 2.9) 23 ( 4.6) ( 27 ( 5.2) ( 29 ( 4.3) 255 ( 2.9) 34 ( 3.7) 250 ( 2.9) 28( 32) 206 ( 3.2) 26 ( 3.7) 258 ( 5.2) 25 ( 42) 274 ( 4.0) 31 ( 3.9) 265 ( 3.1) 27 ( 3.7) 264 ( 3$) 33 ( 3.4) 256 ( 3.6) 28 ( 3.8) 259 ( 3.4) 28 ( 3.3) 253 ( 2.5) peroenlege and Prelidency 5 ( 1.6) 251 ( 9.4)1 7 ( 12) 200 ( 5.1)1 10 ( 4.9) 61 2.1) ( *el 3 ( 12) 41, 8 ( 1.5) *** ( ".) 4 ( 1.4) G") 6 ( 1.9) *** ***) 5 ( 1.8) 0441, 11411 8 ( 3.1) *** 4,44,) 4 ( 1.6) 7 ( 1.9) 281 ( 8.7)1 *IP* 11-11 7 ( 22) "44 State Nation PARENTS EDUCATION KS non-graduate State Nation NS graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent altainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 115 Ohio TABLE Al lb I Teachers' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111110 tiAEP TRIAL STATE ASSESSMENT At Lam! Several Times a Weak About Once a Week Lass than Weekly TOTAL State Nation Peramdags and Preadantal 36 3.6) 261 2.3) 34 3...8) 250 ( 2.3) RACE/ETHNICITY Mite State 38 ( 3.6) 280 ( 2.1) Nation 32 ( 4.1) 264 ( 2.7) Black State 43 ( 3.6) 233 ( 4.5)1 Nation 45 ( 7.5) 232 ( 3.1)1 Hispanic State 42 ( 7.7) Nation 41 ( 7.7) 242 ( 3.2)1 TYPE OF COMMUNITY Advantaged urban State 4$ ( 7.9) 275 ( 2.9)1 Nation 59 (13.9) 273 ( 3.4)! Disadvantaged urban State 49 (11.8) 242 ( 8.7)1 Nation 50 (13.9) 237 ( 2.4)1 Extreme rural State 10 ( 9.0) Nation 27 (14.3) ( *IV Other State 38 ( 5.3) 282 ( 3.0) Nation 30 ( 4.4) 256 ( 3.3) pervonlaga amd Pradialincv Paroasiage and PrefIckancy 32 ( 31) 30 ( 250 ( 2.8) 277 ( 2.2 33 ( 3.4) 32 ( 3.0 260(2.3) 274 ( 2.7 31 ( 4.2) 32 ( 4.0) 264 ( 2.3) 2$0 ( 1.7) 33 ( 3.5) 35 ( 3.8) 284 ( 2.7) 279 ( 2.9) 37 ( 6.3) 20 ( 5.3) 220 ( 3.8)1 .44 ( aim 31 ( 7.8) 23 ( 3.3 243 ( 2.3)1 243 ( 7.0)1 30 ( 6.8) 28 ( 74) 26 ( 5.3) 33 ( 7.5) 244 ( 5.1)1 257 ( 2.3)1 28 ( 9.8) 23 (10.0) 285 ( 6.5)1 288 ( 2.8)1 20 ( 6.0) 21 ( 8.2) ... ( .....) .4' ( 44') 24 ( 7.1) 27 ( 8.8) ,p.... t ,...) 280 (12.2)1 22 (11.2) 28 (10.7) 258 ( 8.3)1 263 ( 4.1)1 53 (15.3) 38 (18.9) 271 ( 7.3)1 271 ( 2.2)1 49 (12.7) 258 ( 6.7)1 24 (10.1) ( .41 31 ( 4.9) 31 ( 4.1) 255 ( 2.1) 278 ( 2.3) 3.5 ( 4.3) 313 ( 4.2) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE Al lb Teachers' Reports on the Frequency of (continued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1100 NAEP TRIAL At Lint Swint Timis STATE ASSESSMENT a Womb About Once a Week Less than Wieldy 1 TOTAL Praidsaiy 311 3.8) 261 2.3) 34 3.8) 256 ( 2.3) liwoantaila and Prilidancy $2 ( 3.9) 250 ( 2.8) 33 ( 34) 260( 2.3) Iliaraanino and PrdikdonN 30 3.8) 277 2.2) 32 SS) 274 ( 2.7) State Nation PAI_ANMENSAIM liS non-graduate State 38 ( 8.1) *imp ( sin 27 ( 5.2) .41 35 ( 6-3) ( Nation 35 ( 239 ( 6.0) 3.5) 29 ( 4.04. ( 8-3) v.) 38 250 ( 6.9) ( 4.5)I NS walla% State 40 ( 4.4) 34 ( 4.6) 25 ( 3.9) 255 ( 2.7) 252 ( 3.0) 26$ ( 2.8) Nation 35( 5.3) 36 ( 4.5) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 2E3 ( 3.4) Some masa State 37 ( 4.3) 31 ( 4.7) 32 ( 4.5) 267 ( 2.6) 265 ( 2.3) 280 ( 2.5) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) colliga graduate 200 ( 2.8) 266 ( 42) 278 ( 2.6). State 36 ( 4.1) 30 ( 4.3) 34 ( 4.3) 272 ( 2.7) 270 ( 4.2) 286 1 2.2) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER M. State 39 ( 3.6) 33 ( 4.1) 28 ( 3.8) 264 ( 2.6) 262 ( 3.3) 280 1 2.3) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 251 ( 2.8) 275 ( 3.2) Female State 37 ( 4.1) 31 1 4.0) 33 ( 4.0) 258 ( 2.5) 256 ( 3.0) 273 1 2.7) Nation 341 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 ± 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 A THE 1990 NAEP TRIAL STATE ASSESSMENT 117 Ohio TABLE Al2 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Lust Once a Week Less Than Once a Week Never TOTAL Percentage and Prot !chancy Percentage and Praidency Percialage and Prolidency State 20 ( 1.7) 28 ( 1.6) 52 ( 2.4) 262 ( 2.7) 208 ( 1.8) 262 ( 1$) Nation 28 ( 2$) 28 ( 1.4) 44 ( 2.9) 25$ ( 2.7) 287 ( 2.0) 261 ( 1.6) RACE/ETHNICITY MOW State 18 ( 1.6) 30 ( 1.8) 52 ( 2.5) 271 ( 2.4) 271 ( 1.6) 267 ( 1.4) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 288 ( 3.1) 272 ( 1.9) 270 ( 1.7) Black State 27 ( 4.7) 22 ( 2.3) 51 ( 5.9) 230 ( 3.4)1 It4- .) 234 ( 3.2) Nation 28 ( 3.0) 24 ( 3.6) 48 ( 4.7) 234 ( 3.0) 245 ( 4.6) 234 ( 3.1) Hispanic State 28 ( 7.2) .44) 19 ( 4.7) .4* ( SS ( 7.1) Nation 37 ( 52) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) TYPE OF COMMUNITY Advantaged urban State 20 ( 5.5) S5 ( 8.3) 45 ( 6.8) 283 ( 3.0)1 283 ( 4.8)1 276 ( 2.3)1 Nation 27 (13.9) 33 ( 4.5) 40 (13.4) ( 286 ( 5.4)1 279 ( 3$)I Disadvantaged urban State 31 ( 8.3) 20 ( 2.9) 49 ( 8.4) 244 ( 8.4)1 248 ( 6.9)i 238 ( 5.0) Nation 31 ( 5.7) 20 ( 2.8) 49 ( 8.3) 245 ( 4.0)1 267 ( 8.4)1 245 ( 3.7)1 Extreme rural State 12 ( 1 .9) 4144 ( *IN ) 21 ( 5.0)) 87 ( 5.6) 265 ( 2.1)1 Nation 34 (10.8) 27 ( 3.8) 39 (11.6) 249 ( 5.2)1 284 ( 3.5)1 258 ( 8.2)1 Other State 18 ( 2.1) 30 ( 2.0) 52 ( 3.0) 262 ( 3.3) 286 ( 1$) 264 ( 1.8) Nation 27 ( 2.0) 28 ( 1.7) 45 ( 3.3) 260 ( 3.31 204 ( 262 ( 22) he 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. 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). 118 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE Al2 I Students' Reports on the Frequency of Small (cantinued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1060 NAEP TRIAL STATE ASSESSUENT At UMW Once a Week Less Than Once a Weak Never TOTAL Parventr moi Preliviency 20 ( 1.7) 262 ( 2.7) 26 ( 2.5 258 ( 2.1) 23 ( 3.0) ips ( 044) State Nation PARENTS' EDUCATION NS non-graduata State Nation 29 ( 4.5) 242 ( 3.4) Id graduate State 18 ( 21) 266 ( 2.9) Nation 28 ( 3.0) 251 ( al) Sons, collagot State 17 ( 1.9) 270 ( 3.1) Nation 27 ( 19) 26$ ( 3.5) Collage graduate State 21 ( 2.2) 272 ( 3.6) Nation 28 ( 3.0) 270 ( 2.7) GENDER Mal State 20 ( 1.9) 263 ( 3.3) Nation 31 ( 2.9) 250 ( 3.3) Famate State 19 ( 2.0) 262 ( 2.9) Nation 20 ( 2.4) 257 ( 2.8) PorcsabNp Proildiecy Percastage anil Preisleacv 28 1.6) S2 ( 2.5 1.8) 262 26 1.4) 44 ( 2.0 267 2.0) 261 ( 1.8) 24 ( 3.5) 53 ( 5.0) 0411, ( 441 240 ( 2.6) 29 ( 3.0) 42 ( 4.5) 244 ( 3.0) 242 ( 23) 26 ( 2.1) 64 ( 262 ( 2.1) 235 ( 1.6 28 ( 1.6 43 ( 3.4 261 ( 2.6) 252 ( 12) 29 ( 2.7 54 ( 3.3) 273 ( 2.1) 267 ( 1.9) 27 ( 2.4) 411 ( 3.6) 263 ( 3.3) NO ( 2.1) 30 ( 2.0) 49 ( 2.111) 276 ( 2.5) 274 ( 1.8) 28 ( 1.9) 44 ( 3.6) 278 ( 2.8) 275 ( 2.2) 28 ( 12) 52 ( 2.4) 272 ( 2.2) 26$ ( 1.4) 2$ ( 1.7) 41 ( 2.9) 203 ( 2.8) 262 ( 1.8) 29 ( 2.2) 52 ( 2.7) 284 ( 2.0) 259 ( 1.9) 27 ( 1.8) 47 ( 3.2) 266 ( 1.7) 200 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estImate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Ohio TABLE A13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE AMMO' Al Least Once a Week Less Than Once a Week Never TOTAL. Percentage and Pneciency Percentage and Preadoncar Percentage and Prelidenry State 21 ( 1.5) 32 ( 1.3) 47 ( 2.0) 2tM ( 2.1) 268 ( 1.6) 262 ( 1.4) Nation 2$ ( 1.6) 31 ( 1.2) 41 ( 2.2) 25$ ( 2.6) 209 ( 1.5) 259 ( 1.6) RACE/ETHNICITY White State 20 ( 1.6) 34 ( 1.4) 48 ( 2.0) Nation 267 ( 1.6) 27 ( 1.9) 271 ( 1.5) 33 ( 1.6) 266 ( 1.4) 40 ( 2.5) 206 ( 2.6) 275 ( 1.6) 268 ( 15) Black State 27 ( 3.5) 238 ( 3.0) 19 ( 2.5) ( *in 54 ( 4.5) 230 ( 2.5) Nation 27 ( 3.3) 27 ( 3.2) 46 ( 4.5) 234 ( 3.7) 248 ( 4$) 232 ( 2.6) Hispanic State 30 ( 6.6) ( .01 .res. 45 ( 52) ..**) Nation 3$ ( 4.2) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) TYPE OF COMMUNITY Advantaged urban State 21 ( 4.6) 36 ( 3.5) 43 ( 5.8) 274 ( 5.2)! 284 ( 3.6)1 279 ( 2.6)1 Nation 98 0031 33 ( 4.8) 32 (11.1) 27$ ( 6.1)1 2$4 ( 3.2)1 281 ( 5.9)1 Disadvantaged urban State 22 ( 5.4) 25 ( 35) 53 ( 5.7) 238 ( 55)1 252 ( 5.1)! 236 ( 5.1) Nation 35 ( 6.6) 19 ( 2.1) 46 ( 6.4) 249 ( 5.3)1 256 ( 5.7)1 248 ( 4.5)1 Eafreme rural State 16 ( 3.7) ( 5.3) 46 ( 8.3) 265 ( 3.7)1 270 ( 2.1)1 Nation 21 ( 3.1) 37 ( 4.7) 43 ( 5.0) 262 ( 4.7)1 251 5.2)1 Other State 22 ( 1.8) 31 ( 1.6) 47 ( 2.3) 264 ( 2.4) 207 ( 1.7) 263 ( 1.7) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 256 ( 2.9) 270 ( 1.8) 200 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample Si2e is insufficient to permit a reliable estimate (fewer than 62 students). 120 125 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A 13 I Students' Reports On the Use of Mathematics (cmitinucd) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MO NAEP TRIAL STATE ASSESSMENT At Least Once a Week Lass Than Ones a Weak Now _ TOTAL Peraantaga and fradicloncy Pinengell. and lordiaisney Passamine and Pnalialancy State 21 ( 2e2 ( 1.5) 2.1) 32 ( 205 ( 1.3) 1.6) 47 ( 262 ( 2.0) 1.4) Nation 24 ( 1.1) 111 ( 12) 41 ( 2.2) 25$ ( 2.8) 209 1.5) 25S ( 1.6) PARENTS' EDUCATION NS non-graduata State 19 ( 3.2) 26 ( 2.4) 54 ( 4.1) ( Itern 244 ( 2.8) Nation 27 ( 4.2) 20 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) 145 graduate State 21 ( 2.8) 30 ( 2.3) 49 ( 2.7) 250 ( 2.7) 261 ( 2.0) 254 ( 1.9) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some college State 20 ( 2.0) 32 ( 22) 43 ( 2.5) 266 ( 2.7) 271 ( 2.3) 270 ( 1.9) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.8) 281 ( 3.5) 274 ( 2.2) 263 ( 2.1) College gradate State 23 ( 1.9) 31 ; 1.9) 43 ( 2.8) 271 ( 3.0) 276 ( 2.3) 274 ( 1.7) Nation 30 ( 2.5) 32 ( 2.0) 3$ ( 2.6) 289 ( 3.0) 27$ ( 2.0) 275 ( 2.0) GENDER Maio State 25 ( 1.8) 32 ( 1.5) 44 ( 2.0) 263 ( 2.4) 271 ( 1.8) 265 ( 1.6) Nation 32 ( 2.0) 30 ( 1.5) 3$ ( 2.2) 258 ( 2.9) 271 1 2.1) 260 ( 1.8) Female State 14 ( 1.6) 31 ( 1.7) 51 ( 2.3) 200 ( 2.9) 265 ( 1.9) 259 ( 1.6, Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 26$ ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. *** Sample size is insuMcient to permit a reliable estimate (fewer than 62 students). 1 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Ohio TABLE A14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT Moos* Every Day Several Times a Weak About Ono* a Week or Less _ - TOTAL and Praliakany and Pralidanay State 75 2.2) 17 1.3) 200 1.1) 257 1.0) Nation 74 1.9) 14 0.6) Vi7 11) 252 ( 1.7) RACE/EMNICITY 1111hite State 70 ( 2.3) 17 ( 1.4) 271 ( 1.1) 261 ( 14) Nation 70 ( 2.5) 13 ( 04) 274 ( 1.3) 250 ( 21) Black State 73 ( 42) 17 ( 2.3) 235 1.5) Nation 71 2.8) 15 ( 1.7) 240 2.9) 232 ( 3.1) Hispanic State 75 ( 52) 19 ( 4.3) 240 ( 3.3) Nation 61 ( 3.7) 21 ( 2.9) 249 ( 2.3) 242 ( 5.1) TYPE Of COMMUNITY Advantaged urban State 70 ( 8.8) 22 ( 4.5) 283 ( 2.5)1 273 ( 3.1)1 Nation 73(11.1) 286 ( 4.6)1 Disadvantaged urtan State 89 ( 5.6) 19 ( 3.0) 245 ( 4.4) **Al Nation 09 ( 22) 15 ( 2.5) 253 ( 32)1 243 ( 44)1 E/drarne nral State 82 ( 271 ( 6.3) 2.5)1 14 ( 44. ( 3.8) .41 Nation 69 (11.3) 15 ( 3.6) 263 ( 4.2)1 *No Other State 76 ( 2.7) 17 ( 1.5) 266 ( 1.2) 257 ( 1.9) Nation 75 ( 2.2) 14 ( 1.0) 287 ( 1.6) 252 ( 2.6) Paroaninie an. Prelialancy ( 1.2) 253 ( 3.3 12 ( 1.11 242 ( 4.5) ( 2ao 3.1) 11 ( 2.2) 252 ( 5.1)1 10 ( 3.3) OM. frirl 14 ( 3.2) 223 ( 6.1)1 ( 2.7) ( 17 ( 2.7) 224 ( 3.4) 3.1) 14 (10.4) 12 3.3) Or** 441 15 2.2) 235 6.5)1 4 ( 2.5) 4.411 17 8.2) .44 ( .441 7 ( 1.5) 257 ( 3.2)1 10 ( 1.9) 239 ( 4.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Mterest, 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 7 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A14 I Students' Reports on the Frequency of (wntinued) I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Less _ TOTAL Peroantage mid Midway 15 22) 203 1.1) 74 1,9) 267 ( 1.2) 79 ( 3.4) 249 ( 2.1) 64 ( 3.4) 245 ( 2.3) 73 ( 2.7) 259 ( 1.4) 71 ( 3.6) 258 ( 1.6) 72 ( 3.0) 272 ( 1.4) 80 ( 2.0) 270 ( 1.9) 79 ( 2.1) 277 ( 1.5) 77 ( 2.7) 279 ( 1.6) 74 ( 2.4) 270 ( 1.4) 72 ( 2.4) 288 ( 1.6) 77 ( 2.3) 283 ( 1.4) 76 ( 1.8) 265 ( 1.3) Pereeniage and PrelIchney 17 ( 1.3) 257 ( 1.6) 14 ( 0.6) 252 ( 1.7) 11 ( 2.5) dweal 18 ( 2.0) ( «pi 20 ( 1.7) 250( 2.2) 16 ( 1.8) 249( 32) 19 ( 2.1) 262 ( 2.8) 11 ( 1.2) It HP ( 16 ( 1.4) 266( 2.0) 13 ( 0.9) 280 ( 2.8) 19( 1.6) 259 ( 1.8) 16 ( 12) 252 ( 2.5) 16 ( 1.4) 254 ( 2.5) 13 ( 1.0) 250( 2.5) Percentage and Prifichiscq 7 ( 253 12 ( 242 9 18 13 239 9 9 444. 10( 257 257 12 242 7 250 11 242 12) ( 3.3) 1.8) ( 4.5) ( 2.8) ( 3.1) ( 1.4) ( **e) ( 2.6) ( 3.4)! ( 1.6) ..41 ( 1.7) ( .91 ( 1.2) ( 11114 ) 2.3) ( 6.4)1 ( 1.3) ( 4.0) ( 2.1) ( 6.1) ( 1.3) ( 3.9) ( 1.6) ( 3.8) State Nation PARENTS EDUCATION NS non-graduate State Nation MS graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest., the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Ohio TABLE AIS Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY I1900 NAEP TRIAL STATE ASSESSMENT 1 At Least Several Tinto, a Weak About Ono* a Weak Less Than Waskly TOTAL floraanlaga and Prallaimay Pareamtais Mid Preficisacy State S8 2 27 ( 257 121 209 ( Natior 3124 25 ( 1.2 253 ( 2.2) 281 ( 1.4) RIMMETHNICITY White State 37 ( 2.6) 28 ( 263 ( 1.3) 267(1.9 Nation 35 ( 2.9) 24 ( 1.3 262 ( 2$) 219 ( 1$) Madc State 47 ( 4.5) 23 ( 2.9) 230 ( 2.7) 239 ( 3.0) Nation 48 ( 36) 32 ( 2.7) 232 ( 4.3) 241 ( 2,9) Hispanic State 41 ( 5.8) ( 441 28 1144' ( 4.0) *41 Nation 44 ( 4.1) 25 3.4) 238 ( 3.9) 247 ( 3.3) TYPE OF COMMUNITY Advantaged urban State 37 ( 5.8) 30 ( 2.5) 272 ( 2.7)1 283 ( 3.9)1 Nation 50 ( 9.0) 271 ( 3.3)1 19 it** ( 4.9) ( 4.1 Disadvantaged urban State 45 ( 0.5) 25 3.5) 235 ( 3.8) 245 8.4)I Nation 37 ( 5.8) 23 ( 3.0) 240 ( 4,8)1 253 ( 4.1)1 Extreme neat State 22 ( 4.1) 041 30 266 4.3) 5.3)1 Nation 42 (10.1) 30 ( 44) 249 ( 4.0)t 258 3.4)1 Other State 3C ( 34) 27 2.0) 259 ( 1.9) 261 1.8) Nation 36 ( 2.9) 26 ( 1.2) 252 3.0) 261 ( 2.1) Poroaalap and Otaliakmay 55 1.5 ST 2.5 272 fa) Se ( 24) 278 ( 1.4) 41 ( 3.0) 277 2.0) 31 ( 46) 236 4.2) 20 3.1) 241 4.4) 31 ( NA) et* .04) 32 ( 4.3) 240 3-3) 32 5.11) 286 3.4)1 31 9.3) 299 ( 5.3)1 30 5.1) 2411 5.5)1 41 0.7) 255 4.2)1 49 ( 0.0) 270 ( 2.2)1 28 ( 7.5) 267 ( 7.3)1 34 1 3.0) 273 ( 1 36 ( 2.9 272 ( 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. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. I"' Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 1 47 ;) THE 1990 NAE.P TRIAL STATE ASSESSMENT Ohio TABLE AlS I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1190 NAEP TRIAL STATE AtiESSMENT At Lust Several Times a Week - About Ottsa a Weak , Lass Then Weekly TOTAL Porosednie and Puideasy 36 ( 2.6) 257 ( 145) 36 2.4) 25:. ( 2.2) State Nation y_larATIMTS" 1910 non-graduate State 40 ( 45) 243 ( 3.0) Nation 41 ( 4.5) 235 ( 3.1) MS gradua te State 40 ( 3.2) 252 ( 2.1) Nation 40 ( 3.2) 247 ( 2.7) Sem college State 34 ( 3.5) 265 ( 2.4) Nation 34 ( 3A) 259 ( 2.3) CoNege graduate State 37 ( 2.6) 285 ( 1.9) Nation 38 ( 221 264 ( 2.6) GENDER maw State 41 ( 2.7) 280 ( 1.9) Nation 39 ( 2.7) 253 ( 2.7) Female State 35 ( 21) 254 ( 1.6) Nation 37 ( 2.5) 253 ( 2.1) PeraNdaiN and Padding 27 ( 1.4) 12) 25 1.2) 281 1A) 27 3.1) 41 30 2.7) 243 2.7) 26 ( 2.0) 254 ( 2.3) 29 ( 2.2) 256 ( 2.5) 31 ( 2.4) 207 ( 2.0) 213 ( 2.2) 209 ( 2.6) 26 ( 1.7) 275 ( 3.0) 22 ( 12) 273 ( 2.5) 26 ( 1.7) 286 ( 2.3) 25 ( 1.8) 283 ( 2.3) 26 ( 1.7) 256 ( 22) 23 ( 1.5) 250 ( 1.6) PeriaNtaia and Prollideva 35 23 272 1.5?i 27 2.5 272 ( 1.9) 33 ( 32) 251 9.7) 25 4.0) 253 2.6) 34 ( 264 1 32 3.8 262 ( 2.2) 35 ( 3.0) 275 ( 2.0) 40 ( 32) 271 ( 2.6) 30 ( 2.7) 263 ( 2.0) 41 ( 22) 265 ( 2.3) 31 ( 2.3) 275 ( 1.6) 35 ( 2.7) 274 ( 2.4) 39 ( 2.1) ( 2.1) 36 ( 2.0) 289 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each popu/ation of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 125 Ohio TABLE AIS Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AHD AVERAGE. MATHEMATICS PROFICIENCY 11190 MEP TRIAL STATE ASSESSMENT Ow a Calculator ' - Teacher Waits Cala lahw Me Yes No Yes No TOTAL, and foralciancy OS ( 0.3) 214 (1.0) ST 0.4) State Nation 213 1.3) NAE1ETM$I1TV White State 09 ( 02) 202 ( 1.0) Nation 96 ( 0.3) 270 ( 1.5) Ma& State 94 ( 11) 234 ( 1.5) Nation 93 ( 1.5) 237 ( 2.8) Hispanic State 96 ( 2.0) 240 ( 3.4) Notion 92 ( 1.2) 245 ( 2.7) TYPE OF COMMUNITY Advantaged urban State 99 ( 0.4) 280 ( 2.7)i Nation 29 ( 1.0) 281 ( 3.8)1 Disadvantaged State 96 ( 1.8) 242 ( 3.9) Nation 94 ( 1.2) 250 ( 3.5)1 Extrenw rural State 99 ( 0.5) 267 ( 2.5)1 Nation 96( 1.3) 257 ( 3.9)1 Other State 98 ( 0.3) 265 ( 1.1) Nation 97 ( 0.5) 263 ( 1.7) Pertondass Parosadap Pannaday and and and Prallalency Pralalinq Prillokany 2 3 234 ( 0.3) 40 ( ( 251 ( ( 0.4) 40 ( ( 3.6) 251( 1 ( 1.0) "1' ( ***) 4 ( 1.6) 6 ( 12) 44.4, I ( 0.5) ( 4 ( 1.3) ( "") 2 ( 0.3) 3 ( 0.5) 233 ( 5.4) 2.1) 1.3) 2.3) 1.7) 48 ( 2.3) 206 ( 12) 48 ( 2.6) 200 ( 1.8) 09 ( 4.4) 231 ( 1.6) 53 ( 4.9) 235 ( 3.6) 50 ( 64) ( 63 ( 4.3) 243 ( 3.4) 4$ ( 5.5) 275 ( 3.7)1 45 (122) 276 ( 2.5)1 69 ( 5.1) 238 ( 4.5) 53 ( TS) 247 ( 4.1)1 36 ( 4.7) 263 ( 3.5)1 42 ( 8.7) 251 ( 4.8)1 47 ( 2.9) 261 ( 1,6) 50 ( 2.7) 258 ( 2.1) 51 2.1 209 1.4 51 231 206 15) 54 ( 2.3) 271 ( 1.3) 54 ( 2.0) 273 ( 1.6) 31 ( 4.4) 240 ( 3.9) 47 ( 4.9) 239 ( 2.7) 50 ( 6.6) flet ( .41 37 ( 4.3) 245 ( 2.9) $2 ( 5.5) 285 ( 3.4)1 55 (12.2) 285 ( 6.4)1 31 ( 5.1) 250 ( 5.3)1 47 ( 7.5) 251 ( 3.6)1 64 ( 4.7) 270 ( 2.2)1 58 ( 8.7) 2151 ( 4.4)1 S3 ( 2.9) 267 ( 1.6) 50 ( 2.7) 206 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 1 126 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A18 (continued) Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1810 KW TRIAL STATE lISSEINIIENT - Own a Calculator Teacher Bp Mine Calculator Use Yes I No _ Yes No MI& State Nation PARENTS EDUCATION Rerdentage and Pre Ildency 98 ( 204 ( 1.0 97 ( 0.4 283 ( 1.3) 94(1.9) 247 ( 2.2) 92 ( 1.8) 243 ( 2.0) N ( 0.5) 257 ( 1.2) 97 ( 0.6) 255 ( 1.5) 99 ( 0.5) 269 ( 1.3) 90 ( 0.9) 2Sa ( 1.8) 99 ( 0.3) 274 ( 1.3) 99 ( 02) 275 ( 1.6) 98 ( 0.4) 257 ( 12) 97 ( 0.5) 264 ( 1.7) 96 ( 0.4) 261 ( 1.3) 97 ( 0.5) 262 ( 1.3) Percentage aW Pralkiency 2 ( 03) 234 SA) 8 ( 1.9) ( 0.1 1.8) 2 ( 0.5) ( "el ( I ( 0.5) ( «4) 4 ( 0.9) ( 44 ( 03) *** (( 0.2) ( 2 ( 0.4) 3 ( 0.5) *e. 2 ( 0.4) ( *01 ( Pereentige Percentage and and PreNdestey Prelidency 49 ( 2.1) 51 ( 2.1) 209 ( 49 2.3 51 ( 2.3 258 1.7 296 ( 44 ( 4.5 58 ( 4.5) 248 ( 3.1) 248 ( 53 ( 4. 47 ( 4.6) 242 ( 2.9 243 ( 2.5) 50 ( 2.7 50 ( 2.7) 253 ( 1.7) 261 ( 1.6) 54 ( 3.0) 46 ( 3.0) 252 ( 1.9) 258 ( 2.0) 47 ( 3.2) 53 ( 3.2) 264 ( 1.9) 274 ( 1.8) 48 ( 3.2) 52 ( 3.2) zes ( 2.4) 268 ( 22) 4$ ( 2.8) 52 ( 2.8) 267 ( 1.9) 281 ( 1.8) 46 ( 2.6) 54 ( 2.6) ( 2.2) 280 ( 1.9) 50 ( 2.4) 50 ( 2.4) 261 ( 1.6) 272 ( 1.4) 51 ( 2.6) 49 ( 2.6) 258 ( 2.1) 209 ( 2.1) 47 ( 2.4) 53 ( 2.4) 256 ( 1.5) 265 ( 1.7) 47 ( 2.5) 53 ( 2.5) 258 ( 1.7) 263 ( 1.6) 011 non-greduate State Nation NS graduate State Nation Some college State Nation College graduate Stets Nation OENDER M. State Nation Female State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. * Sample size is insufficient to permit a reliable estimate (fewer than 62 students), THE 1 940 NAEP TRIAL STATE ASSESSMENT 127 Ohio 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 MAEP TRIAL STATE ASSESSMENT ioddng Problems in Clan Doing Problems at Nome Taking QUIZ:1M or Tens Almost Always Never Almost Always Never Almost Always Never .001111M, TOTAL. Parentage and Proficiency Percentage and Proficiency Parrontage and Mildewy Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 45 ( 1.5) 27 ( 1.7) 29 ( 1.5) ( 1.1) 25 ( 1.3) 36 ( 13) 255 ( 1.3) 275 ( 1.4) 259 ( 1.7) 270 ( 1.7) 253 275 ( 1.1) Nation 4$ ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 1.4 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.6) 263 ( 1.3) 253 2.4 274 ( 1.3) NACEIETNNICITY 1011ite State 43 ( 1.7) 29 ( 2.0) 2$ ( 1.7) 18 ( 1.3) 22 ( 1.0) 39 ( 1.8) 261 ( 12) 277 ( t3) 254 ( 1.6) 272 ( 1.6) 261 ( 1.8) 277 ( 1.1 Nation 48 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 12) 25 ( 1.8) 32 ( 2.3) 262 ( 1.7) 278 ( 1.3) 270 ( 1.7) 26( 2.3) 263 ( 2.6) 279 ( 1.2) Mad/ State 80 ( 230 ( 4.0) 2.0) 12 ( .4. 2.6) ( ...) 37 ( 231 ( 2.9) 3.4) 10 ( ( 1.8) ...) 44 ( 228 ( 2.4) 2.1) 19 ( 2.1) Nation ( 32) 20 ( 3.9) 31 ( 2.9) 16 ( 1.9) 38 ( 3.3) 24 ( 3.1) 232 ( 2.4) 249 ( 4.0) 233 ( 3.3) 248 ( 5$) 230 ( 3.0) 251 ( 4.1) Hispanic State es ( 5.8) 15 ( *4 3.8) ft** ) ( ...) 14 ( ( 3.7) ...) *** ( *44) Nation 51 ( 2.9) 18 3.5) 26 ( 32) 21 ( 2.1) 26 ( 2.7) 22 ( 3.1) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1) 237 ( 3.2) 258 ( 4.2) TYPE OF COMMUNITY Advantaged urban State 45 ( 3.9) 23 ( 4.5) 34 ( 4.1) 20 ( 3.2) 34 ( 4.4) 271 ( 2.8)1 287 ( 4.1)1 275 ( 3.2)1 ( 271 ( 2.7)1 288 ( 4.4) Nation 51 ( 270 ( 5.4) 4.7)f 23 (10.7) .44 ( 4..) 32 ( 274 ( 8.1) 4.9)1 15 ( 2.4) 31 ( 281 ( 3.8) 7.6)1 28 ( 285 ( 9.8) 42)1 Disadvantaged State 51 ( 235 ( 3.8) 4.8) 13 ( 4.1) 29 ( 239 ( 3.8) 5.6) 10 ( ( 2.2) ...) 33 ( 231 ( 3.1) 4.2) 23 ( 255 ( 3.7) 5.2)1 Nation 52 ( 3.1) 22 ( 4.5) 30 ( 3,3) 24 ( 2.3) 27 ( 2.9) 27 ( 4.8) 241 ( 3.8)1 259 ( 5.4)1 248 ( 5.2)1 254 ( 4.8)1 240 ( 4.9)1 263 ( 5.0)1 Extrerrut rural State 40 ( 259 ( 2.7) 3.5)1 38 ( 274 ( 4.0) 2.8)1 19 ( 2.3) 21 ( 2.0) 14 ( 4.. ( 3.4) ...) 47 ( 275 ( 2.8) 2.8)1 Nation 46 ( 246 ( 7.4) 4.3)1 29 ( 288 ( 85) 8.1)1 20 ( 4.4 ( 2.5) ...) 23 ( 263 ( 3.9) 4.4)1 24 ( 04* ( 6.6) MR) 37 ( 270 ( 8.3) 4.0)1 Other State 45 ( 2.0) 29 ( 2.2) 30 ( 1.9) 1$ ( 1.5) 26 ( 1.8) 38 ( 2.2) 256 ( 1.5) 275 ( 1.6) 258 ( 2.0) 271 ( 1.9) 255 ( 2.3) 275 ( 1.3) Nation 4$ ( 1.9) 22 ( 2.0) 32 ( 1.1) 18 ( 1.1) 27 ( 1.8) 29 ( 2.1) 254 ( 2.1) 272 ( 1.8) 263 ( 2.3) 263 ( 2.8) 253 ( 2.7) 275 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. 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). 128 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio 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 1900 NAEP TRIAL STATE ASSESSMENT Worldng Problems in Class Doing Problems at Noma Salting Quizzes or Tests Almost Alwaye Never , Almost Always Never . i IMOSt Always Never ICSAL State Nation PARENTS' EDUCATIOR NS non-graduate State Nation NS graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Femal State Nation Pencentage Percentage Peroentage and and and Proficiency ProliciancY ProadencY 45 ( 1.5) 27 1.7) 29 ( 1.5 255 ( 1.3) 275 259 ( 1.7 46 ( 1.5) 23 1.9 30 ( 1.3 254 ( 1.5) 272 14 261 ( 1.8 53 ( 3.6) 23 ( 24) 2$ ( 3.5) 241 ( 2.3) ( eg. ( ) 54 ( 3.3) 10 ( 3.8) 26 ( 3.1) 240 ( 2.3) e"' ( ***) 244 ( 3.8) 47 ( 1.9) 28 ( 2.0) 28 ( 2.0) 250 ( 1.7) ( 1.9) 251 ( 2.2) 52 ( 2.5) 20 ( 2.4) 29 ( 1.9) 249 ( 1.4) 265 ( 2.7) 250 ( 2.4) 42 ( 2.8) 31 ( 2.7) 27 ( 2.2) 261 ( 1.7) 278 ( 1.8) 263 ( 2.0) 46 ( 2.8) 26 ( 2.8) 20 ( 2.0) 258 ( 2.1) 272 ( 2,5) 267 ( 3.0) 43 ( 1.9) 28 ( 2.4) 32 ( 2.2) 264 ( 2.0) 284 ( 2.0) 208 ( 2.3) 4.5 ( 1.9) 25 ( 2.4) 33 ( 2.0) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 4$ ( 1.6) 25 ( 1.8) 28 ( 1.6) 258 ( 1.5) 280 ( 1.6) 202 ( 1.7) 50 ( 1.7) 20 ( 2.0) 29 ( 1.8) 255 ( 1.9) 275 ( 2.2) 264 ( 2.8) 43 ( 2.0) 20 ( 2.1) 31 ( 2.0) 252 ( 1.7) 271 ( 1.9) 255 ( 2.2) 46 ( 2.0) 26 ( 2.1) 32 ( 1.6) 252 ( 1.7) 20 ( 1.8) 259 ( 11) Penentage and PrIPIthligtv 17 ( 1.1) 270 ( 1.7) 19 ( 0.0) 263 ( 11) Parcentage and Prefidengr 25 ( 1.3 1.11 27 1.4 255 2.4 25 ( 2.7) 441 3.7) ***) 22 ( 2.6) 32 3.6) 244 4.2) 237 ( 2.3) 17 ( 14) 25 ( '1.5) 261 ( 24) 242 ( 2.3) 18 ( 1.5) 20 ( 1.8) 256 ( 2.4) 246 ( 2.0) 18 ( 1.8) 23 ( 23) 277 ( 2.8) 256 ( 24) 20 ( 11) 26 ( 2.4) 203 ( 3.2) 255 ( 3.6) 16 ( 1.0) 24 ( 1.7) 284 ( 2.2) 265 ( 3.2) 16 ( 1.4) 28 ( 1.6) 278 ( 2.8) 268 ( 2.8) 18 ( 1.5) 24 ( 1.6) 274 ( 2.0) 256 ( 2.1) 19 ( 1.3) 27 ( 1.5) 263 ( 2.5) 256 ( 3.0) 17 ( 1.2) 27 ( 1.8) 266 ( 2.3) 251 ( 2.2) 18 ( 1.2) 27 ( 1.8) 263 ( '1.1) 251 ( 2.4) Pereentage and Pragemot 30 1.5 275 1.1 30 2 274 1.3 301 2.9) In* 0.1 24 ( 3.2) 251 ( 4.6) 33 ( 208 1 1.3 27 ( 2.2) 265 ( 2.0) 42 ( 2.8) 277 ( 1.8) 35 ( 2.5) 275 ( 2.0) 30 ( 2.2) 234 ( 1.7) 33 ( 2.7) 265 ( 2.0) 34 ( 1.8) 279 ( 1.0) 28 ( 2.1) 277 ( 1.9) 39 ( 1.8) 271 ( 1.3) 33 ( 2.1) 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 Ohio TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111110 NAEP TRIAL "Calm "Calculator-Use" STATE ASSESSMENT Nigh lator-Use" Group Other Oros* , TOTAL. Percantage and Pr. "dam Percentage and PrciakonCY State 47 ( 1.1) 53 ( 1.1) 271 ( 1.5) 258 ( 0.9) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACE/ETHNICITY, Whit* State 49 ( 1.1) 51 ( 1.1) 274 ( 1.5) 264 ( 1.0) Nation 44 ( 1.4) 58 ( 1.4) 277 ( 1.7) 283 ( 1.7) Black State 31 ( 5.0) 89 ( 230 ( 5.0) 2.2) Nation 37 ( 3.4) 63 ( 3.4) 248 ( 3.9) 231 ( 3.0) Hispanic State 45 ( 6.5) Mit ( Mit ) Nation 30 ( 4.2) 84 ( 4.2) 254 ( 4.6) 238 ( 3.0) TYPE OF COMMUNITY Advantaged titan State 55 ( 2.9) 45 ( 2.9) 287 ( 3.4)1 278 ( 21)1 Nation 50 ( 3.8) 50 ( 3.8) 286 ( 4.9)1 275 ( 4.4)1 Disadvantaged urban State 36 ( 3.2) 64 ( 3.2) 252 ( 5.5) 237 ( 3.8) Nation 38 ( 4.2) 62 ( 4.2) 202 ( 5.6)1 244 ( 3.9)1 Extreme nsral State 41 ( 3.8) 59 ( 3.8) 272 ( 3.4)1 264 ( 3.1)1 Nation 39 ( 5.6) 61 ( 5.8) 269 ( 4.4)1 244 ( 4.3)1 Other State 48 ( 1.3) 52 ( 1.3) 270 ( 1.6) 2$8 ( 12) Nation 42 ( 1.4) ( 1.4) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of Ow sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 130 1 13 5 THE 1990 NAEP TRIAL STAT E ASSESSMENT Ohio TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT _. Nigh "Calor later-Use Group "Calculator-We" Group TOTAL Pennon Inge and Proficiency PerceniliP and Proficiency State 47 ( 1.1) 5$ I 1.1 271 ( 1.5) 25$ ( 041 Nation 42 ( 13) 5$ ( 272 ( 1.6) 255 ( 1.5) PARENTS' EDUCATION te non-graduate State 44 ( 4..5) 56 ( 4.5) ( 244 ( 3.0) Nation 34 ( 3.3) 66 ( 3.3) 248 ( 4.4) 242 ( 2.4) HI 9-actuat State 47 ( 1.9) 53 ( 1.9) 263 ( 1.8) 251 ( 1.4) Nation 40 ( 2.2) 60 ( 22) 263 ( 2.0) 249 ( 1.8) Some college State 48 ( 2.3) 52 ( 2.3) 275 ( 2.0) 264 ( 2.1) Nation 48 ( 2.2) 52 ( 22) 277 ( 2.6) 258 ( 2.5) Co Sege graduate State 49 ( 2.1) 51 ( 2.1) 283 ( 2.1) 268 ( 1.5) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER M. State 44 ( 1.4) 56 ( 1.4) 276 ( 1.9) 260 ( 1.2) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 50 ( 1.7) 50 ( 1.7) 257 ( 2.0) 255 ( 1.8) Nation 45 ( 1.8) 5$ ( 1.8) 269 ( 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 Ohio TABLE A24 I Students' Reports on Types of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1180 NAEP TRIAL STATE ASSESSMENT Zwo to Two Types Throe Types Fear Types TOTAL Poramtap NNI Po Wow Porsentsge and Pratiokoncy PoreoRtago and Pralloisney State le ( 1.0) SO ( OA) 54 ( 1.1) 247 t 1.4) 210 ( 1.4) 271 ( 1.1) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) EfigangniM White State 14 ( 1.1) 30 ( 1.0) 57 ( 1.1) 254 ( 1.7) 265 ( 1.5) 274 ( 1.1) Nation 18 ( 1.1) 29 ( 1.3) 56 ( 1.5) 251 ( 2.2) 268 ( 1.5) 278 ( 1.7) Made State 23 ( 3.3) 34 ( 2.5) 38 ( 2.9) 230 ( 2.6) 228 ( 2.9) 240 ( 2.4) Nation 31 ( 1.9) 38 ( 2.2) 33 ( 2.4) 232 ( 32) 233 ( 19) 245 ( 3.3) NIspenic State 30 ( 6.2) ( .01 ( 41 ( ( 6.3) Nation 44 ( 3.0) 30 ( 2.4) 26 ( 2.3). 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) TYPE OF COMMUELLY Advantaged urban State ( 1.4) .44) 24 ( 2.8) 277 ( 4.3)1 70 ( 253 ( 1.9) 2.7)1 Nation 13 ( 3.8) ( 81 ( 287 ( 4.9) 3.6)1 Digadvantaged urban State 2$ ( 3.9) 37 ( 3.2) 30 ( 4.3) . 227 ( 3,3) 242 ( 3.6) 251 ( 8.5)1 Nation 32 ( 3,9) 31 ( 2.3) 37 ( 16) 243 ( 2.9)1 247 ( 3.7)1 257 ( 4.9)1 Extreme nazi State 11 ( 2.5) 34 ( 3.1) 56 ( 4.1) 259 ( 4.3)1 274 ( 2.8)1 Nation 17 ( 4,9) 33(3.2) 50 ( 8.1) T ( 4,1 253 ( 4.3)1 283 ( 5.8)1 Other State 16 ( 1.2) 30 ( 1.0) 53 ( 1.2) 252 ( 1.6) 261 ( 1.9) 270 ( 1.0) Nation 22( 15) 30 ( 1.3) 48 ( 1.5) 244 ( 2.8) 259 ( 2.2) 272 ( 1.7) The standard errors of te estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each p-*,pulation 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 t#4-nination of the variability of this estimated mean proficiency, *** Sample size is insufficient to permit a rehaole estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A24 I Students' Reports on Types of Reading (continued) Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL STATE ASSESSMENT Zwo to Two Types Three Typos Four Typos TOTAL Pernentage and Pr* lokinqf Perosntsge and Proficiency Percentage and Prodkiency State 18 ( 1.0) ao ( mei) 54 ( 1.1) 247 ( 1.4) 280 ( 14) 271 ( 1.1) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.1) 272 ( 1.5) PARENTS' EDUCATION NS non-graduate State 34 ( 4.1) 97 ( 3.8) 29 ( 3.8) 237 ( 3.4) 250 ( 3.0) 4144 ( ***) Nation ( 4.0) 2$ ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 246 ( 3.3) IM graduate State 18 ( 1.9) 34 ( 1.7) 48 ( 2.0) 250 ( 2.7) 255 ( 1.7) 281 ( 1.5) Nation 26 ( 2.2) 33 ( 1.9) 40 ( 1.7) 248 ( 2.2) 253 ( 2.7) 260 ( 2.1) Some college State 14 ( 1.4) 28 ( 1.9) 58 ( 2.2) 258 ( 3.7) 266 ( 2.3) 274 ( 1.7) Nation 17 ( 1.5) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.8) 274 ( 1.9) College graduate State 8 ( 0.9) 28 ( 1.6) 65 ( 1.8) 251 ( 42) 269 ( 2.8) 279 ( 1.5) Nation 10 ( 0.8) 28 ( 1.8) 02 ( 2.0) 254 ( 2.8) 269 ( 2.5) 260 ( 1.8) GENDER Male State ,15 ( 1.2) 1.2) 54 ( 1.4) 249 ( 2.2) 261 ( 1.9) 274 ( 1.3) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 t 2.3) 259 ( 2.1) 273 ( 2.0) Female State 17 ( 1.4) 30 ( 1.4) 53 ( 1.6) 245 ( 1.9) 258 ( 1.8) 267 ( 1.6) Nation 22 ( 1.2) 29 ( 1.4) 49 ( 1.9) 244 ( 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. *** Sample tize is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 133 Ohio TABLE A25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL One Notr or Two Hours TTwse Hours Four to Five SIN Hours or STATE ASSESSMENT Less Hours Moro . TOTAL State Nation NACE/ETHNICITY Whitt State Nation Mack State Nation Hispanic State Nation TYPE OF COMMUNITY Advantagod urban State Nation Disadvantaged urban State Nation Extrome neal State Nation Other State Nation Peoventage Peovenat. and and Praddency firadolancy 13 ( 0.7) 272 ( 1.9) 12 ( 0.8) 269 ( 22) 14 ( 0.9) 274 ( 2.0) 13 ( 14) 278 ( 2.5) 5 ( 1.3) 6 ( 0.8) ( «an 1NP NM) 14 ( 2.4) *** 1$ ( 22) 2843 ( 3.4)1 8 ( 1.4) ( ( 1.2) ( ( .41 14 ( 3.3) 13 ( 0.8) 269 ( 22) 12 ( 1.0) 268 ( 2.6) 24 1.0) 272 21 ad 2611 1.11 26 ( 1.1) 2/4 ( 1.5) 23 ( 1.2) 275 ( 2.2) 13 ( 1.7) 239 ( 7.0) 16 ( 4.11) 20 ( 2.5) 245 ( 3.2) 28 ( 3.2) 283 ( 3.3)1 25 ( 4.3) **4. 18 ( 2.5) 17 ( 3.1) 250 ( 4.0)1 20 ( 1.9) ( 441 19 ( 2 A) IN* ( 26 ( 1.4) 270 ( 2.0) 21 ( 1.0) 269 ( 2.3) Paraantap and !relabel* Pereordap and Itradelancy 24 ( 0,9) 24 ( 203 ( 14) 2$9 ( 1.1 22 ( 0.6) 28 ( 1.1 205 ( 1.7) 200 ( 1.7 24 ( 1.0) 27 ( 1.0) 270 ( 1.4) 264 ( 12) 24 ( 1.1) 27 ( 1.4) 272 ( 1.0) 2.7 ( 1.7) 19 ( 2.0) 34 ( 2.5) ( 234 ( 2.2) 17 ( 2.1) 32 ( 1.8) 239 ( 5.0) 239 ( 4.0) 23 ( 4.8) 32 ( 5.1) 41.41 19 ( 2.1) ( 3.1) 242 ( 5.6) 247 ( 3.5) 30 ( 3.4) 19( 1.9) 279 ( 3.3)1 275 ( 5.0)1 21 ( 1.8) 30 ( *4.4. 4.3) 18 ( 1.8) 35 ( 2.5) ( 241 ( 3.2) 19 ( 2.1) 34 ( 2.4) 255 ( 5.0)1 251 ( 4.7)1 20 ( 2.1) 26 ( 2.4) ( 3.0)1 265 ( 3.7)1 26 ( 2.7) 256 ( 3.0)1 23 ( 1.0) 28 ( 1.3) 266 ( 1.5) 261 ( 1.1) 23 ( 1.2) 27 ( 1.2) 265 ( 2.1) 259 ( 2.2) Peessodap and Prallidenty 11 0.4) 244 11 16 1.0 245 1.7 8 ( 0.7) 254 ( 12 ( 12 253 ( 2.0 32 ( 2.6) 227 ( 2.9) 32 ( 2.2) 233 ( 2.5) 19 ( I** ( *an 17 ( 1.7) 236 ( 3.8) 4 ( 1.1) ( 2.0) *01 24 ( 2.9) 228 ( 3.9) 20 ( 3.2) 238 ( 4.5)1 10 ( 1.9) OM* ( 441 19 ( 3.8) **1 11 ( 1.0) 249 ( 2,4) 17 ( 1.4) 246 ( 2.5) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Oido TABLE A25 1 Students' Reports on the Amount of Time Spent (wntinued) I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One Hour or LOU Two Hors Three Hours Four to Flye Hours Vat Hours or More TOTAL Pavan laga and Po Waxy Parneranga and Po edam Parnantaga and Pro Pereantaga and *al Mew Rwandans and Prat Mom State 13 ( 0.7) 24( tO) 24 ( 0.9) 28 ( 0.9) 11 ( OS) 272 ( 1.9) 272 ( 1.5) 266 ( 1.4) 259 ( 1.1) 244 ( 1.9) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 ( 1.1) 16 ( 1.0) 269 ( 2.2) 28$ ( 1.8) 205 ( 1.7) 200 ( 1.7) 245 ( 1.7) PARENTS' EDUCATION HS non-graduate State 12 ( 2.3) 18 ( 2.2) 24 ( 2.7) e..) 10 ( 2.5) op, ( Nation 12 ( 22) fro* ( ***) 20 ( 3.1) If ( 21 ( 2.8) oi4o, ( ion 28 ( 2.9) 244 ( 32) 20 ( 24) too,. upon HS graduate State 11 ( 1.3) 20 ( 1.4) 24 ( 1.6) 31 ( 14) 14 ( 1.3) 260 ( 2.8) 262 ( 2.2) 25$ ( 2.1) 257 ( 1.5) 244 ( 2.3) Nation ( 1.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 19 ( 1.6) ( 4.7) 257 ( 2.8) 259 ( 3.2) 253 ( 2.5) 24a (10) Same college State 12 ( 1.3) 26 ( 2.1) 26 ( 1.8) 28 ( 1.9) 8 ( 1.4) 280 ( 3.6) 272 ( 2.3) 272 ( 2.3) 264 ( 2.8) frerh ) Nation 10 ( 1.4) *oho ( oleo) 25 ( 2.4) 275 ( 2.7) 23 ( 2.6) 269 ( 34) 28 ( 22) 267 ( 2.5) 14 ( 1.5) 242 ( 3.4) College graduat State 16 ( 1.1) 30 ( 14) 22 ( 12) 24 ( 1.4) 8 ( 1.1) 282 ( 2,4) 281 ( 1.9) 276 ( 2.2) 266 ( 2.5) 250 ( 42) Nation 17 ( 1.3) 22 ( 1.8) 23 ( 1.1) 25 ( 1.5) 12 ( 1.1) 282 ( 2.6) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 12) GENDER Mal* State 11 ( 0.9) 24 ( 1.3) 24 ( 1.2) 29 ( 1.3) 11 ( 1.1) 275 ( 3.4) 274 ( 2.2) 269 ( 1.7) 202 ( 1.3) 246 ( 2.9) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 28 ( 1.3) 17 ( 1.5) 269 ( 3.3) 267 ( 2.0) 267 ( 2.2) 262 ( 2.1) 248 ( 2.5) Female State 16 ( 1.0) 24 ( 1.5) 23 ( 1.3) 26 ( 1.4) 12( 1.1) 270 ( 2.3) 270 ( 1.8) 263 ( 1.7) 258 ( 1.7) 23$ ( 2.7) Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 1.6) 15 ( 1.2) 269 ( 2.8) 269 ( 2.2) 264 ( 1.8) 256 ( 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). THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Ohio TABLE A26 I Students' Reports on the Number of Days of 1 School Mined PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL E ASSSM STAT I. ENT - None Ono ar Two Days _ - Woo Don or More TOTAL Parentage and alniledaaay Illenneds. and Prallaiway Piartne$9. and Pralkdoncy State 42 ( 1.2) $5 ( 1.1) 22 ( OS) 260 ( 1.2) 265 ( 1.2) 2f4 ( 1.4) Nation 45 4.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 266 ( 1.5) 250 ( 1.9) EAMMIICITY Whits State 42 ( 1.2) 37( 1.0) 22 ( 1.0) 273 ( 1.0) 270 ( 1.2) 258 ( 1.5) Nation 43 ( 1.2) 34 ( 1.2) 23( 1.2) 273 ( 1.8) 272 ( 13) 258 ( 2.1) Black State 40 ( 4.1) 27 ( 3.9) 27 ( 2.5) 239 ( 2.3) 234 ( 3.9) 223 ( 3.0) Nation 50 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 41 ( 444 ( 5.8) 37 ( 6.5) 22 (( 5.4) 041 Nation ( 3.3) 32 ( 2.2) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) TYPE OF COMMUNITY Advantaged urban State 43 ( 3.5) 41 ( 3.9) 16 ( 1.9) 284 ( 2,7)1 280 ( 3.1)1 Nation 47 ( 284 ( 2.3) 4.4)1 38 ( 279 ( 2.6) 4.5)1 15 ( ( 3.7) 444) Disadvantagad urtan State 35 ( 3.3) 31 ( 4.0) 34 ( 3.4) 244 ( 4.3) 247 ( 5.4)1 234 ( 4.2) Nation 42 ( 3.3) 28 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 256 ( 4.2)1 238 ( 6.3)1 Extreme rural State 47 ( 2.5) 40( 1.8) 14 ( 2.2) 272 ( 2.4)1 266( 4.1)1 Nation 43 ( 4.4) 32 ( 4.2) 25 ( 3.9) 257 ( 4.1)1 264 ( 5.8)1 Other State 43 ( 1.5) 34 ( 12) 22 ( 1.0) 269 ( 1.4) 265 ( 1.3) 256 ( 1.6) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 286 ( 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 Ohio TABLE A26 I Students' Reports on the Number of Days of (cmtinued) i School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . _ 1990 NAEP TRIAL STATE ASSESSMENT None _ Ono or Two Days . Throe Days or Moro Pardantass and Predidanoy kroonlage dad Pralkdancy TOTAI State 1.2) 35 ( 209 1.2) 205 ( 1.2 Nation 45 1.1) 32 ( 01) 255 ( 1.6) 208 ( 14) PARENTS' EDUCATION MS non-graduato State 29 (( 3.7) 411 32 ( 34) 414* Nation 30 ( 32) 26 ( 3.1 245 ( 3.0) 249 1 3.3) NS graduato State 40 ( 11) 36 ( 261 ( 1.0) 256 ( 1.6 Nation 43 ( 2.1) $1 ( 1.9 255 ( 2.0) 257 ( 2.6) Soma collage State 43 ( 2.1) 36 ( 2.4) 274 ( 11) 209 ( 1.6) Nation 40 ( 1.6) 37 ( 1.6) 270 ( 3.0) 271 ( 2.5) Collage graduate State 47 ( 1.7) 3e ( 1.7) 278 ( 1.6) 278 ( 1.9) Nation 51 ( 1.6) 93 ( 12) 275 ( 2.1) 277 ( 1.7) GENDER M. State 46 ( 1.3) 34 ( 1.3) 271 ( 1.6) 268 ( 1.5) Nation 47 ( 1.6) 31 ( 1.4) 206 ( 2.0) 287 ( 2.1) Female State 39 ( 1.7) 37 ( 1.7) 206 ( 1.5) 262 ( 2.1) Nation 43 ( 1.4) 32 ( 1.1) 264 ( 2.3) 208 ( 1.7) Panama. PUfliiif 22 ( AO) 263 ( 1.4) 23( 1.1) WO( 1,9) 39 I S. 38 ( 237 ( 3.1 24 ( 1.7) 27 241(2.3 249 ( 2.4) 21 ( 1.7) 260 ( 2.0) 23 ( 1.6) 253 ( 3.1) 17 ( 0.9) 265 ( 3.3) 16 ( 1.9) 265 ( 3.1) 20 ( 1.1) 255 ( 1.9) 22 ( 14) 250 ( 2.6) 25 ( 1.2) 251 ( 250 ( 1.6 25 ( 1.3 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 Ohio TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT , SPxmilly Mrs* , Agree Undecided, Disagree, Strongly Wain. - TOTAL Perwordaya and Pre *Amy Peroonlapre and Proficiency Petunias and Preliciancy State 32 ( 1.0) 48 ( 1.0) 20 ( tO) 273 ( 1.3) 263 ( 1.1) 253 ( 1.6) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 12) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) fflKrAE:WL_4ICIT_Y Witits State 32 ( 1.1) 48 ( 1.1) 20 ( 1.1) 2M ( 1.4) 268 1.1) 257 ( 1.5) Nation 26 ( 1.6) 48 ( 1.3) 26 ( 1.5) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Black State 32 ( 3.2) 49 ( 2.9) 18 2.3) 242 ( 2.7) 233 ( 2.5) Mat II*1 Nation 32 ( 2.5) 52 ( 2.3) 10 ( 1.9) 247 ( 4.1) 233 ( 3.3) 227 ( 4.2) HispatOe State 33 ( 6.0) 441 49 (( 5.6) .44) 19 ( 4.8) 441 Nation 24 ( 2.5) 48 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 236 ( 3.8) TYPE Of COMMUNITY Advantaged trban State 34 ( 3.1) 48 ( 2.3) 18 ( 2.5) 286 ( 2.8)1 280 ( 3.0)1 269 ( 4.0)1 Nation 17 ( 3.2) 55 ( 2.4) 28 ( 42) 280 ( 4.1)1 A** ( 1141 Disadvantaged urban State 31 ( 4.1) 49 ( 3.6) 20 ( 3.6) 252 ( 4.4) 241 ( 3.9) 228 ( 4.7)1 Nation 26 ( 2.9) 48 ( 2.9) 26 32) 260 ( 5.6)1 249 ( 4.6)1 240 ( 4.5)1 Extreme rural State 31 ( 2.6) 48 ( 3.1) 21 ( 3.8) 278 ( 3.1)1 266 ( 3.1)1 Nation 34 ( 270 ( 2.8) 3,9)1 49 ( 252 ( 2.2) 4.1)1 17 ( ( 1.4) .41 Other State 33 ( 1.3) 47 ( 1.2) 20 ( 1.2) 273 ( 1.5) 263 ( 1.4) 254 ( 1.6) Nation 27 ( 1.4) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of intenst, 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). 138 1 " THE 1990 NAEP TRIAL STATE ASSESSMENT Ohio TABLE A27 I Students' Perceptions of Mathematics (continued) 1 PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10410 NAP, TRIAL STATE ASSESSMENT , &Ton* Aire* .. *Imo Undecided, Disagree, Strongly Disagree TOTAL Percentage and Proficiency Percentage end PfaCifilM Percentage and Proficiency State 32 ( 1.0) 48 ( 1.0) 20 ( 1.0) 273 ( 1.3) 263 ( 1.1) 253 ( 1.6) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 202 ( 1.7) 251 ( 1.8) PARENTS' EDUCATION MS non-graduate State 30 ( *** ( 4.1) *el 43 ( 245 ( 3.7) 3.6) 27 ( 3.1) .84,*) Nation 20 ( 2.6) 50 ( 3.3) 30 ( 3.6) 243 ( 2.6) 238 ( 4.3) NS graduste State 31 ( 1.8) 47 ( 1.9) 22 ( 1.8) 200 ( 21) 255 ( 1.4) 247 ( 2.4) Nation 27 ( 2.1) 47 ( 2.3) 28 ( 2.0) 282 ( 2.7) 255 ( 23) 245 ( 2.4) $ome college State 31 ( 1.8) 50 ( 2.1) 19 ( 1.7) 279 ( 1.9) 267 ( 2.1) 259 ( 2.3) Nation 28 ( 2$) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 258 ( 3.2) College graduate State 36 ( 12) 47 ( 1.5) 17 ( 1.3) 282 ( 2.1) 273 ( 1.6) 263 ( 2.4) Nation 30 ( 2.3) 51 ( 16) 19 ( 1.8) 280 ( 2.4) 274 ( 22) 266 ( 2.5) GENDER Male State 34 ( 1.3) 47 ( 1.3) 19 ( 1.3) 275 ( 1.6) 265 ( 1.4) 257 ( 1.9) Nation 28 ( 1.5) 48 ( 1.2) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Female State 30 ( 1$) 49 ( 1.4) 21 ( 1.3) 271 ( 1.8) 260 ( 1.4) 248 ( 2.0) Nation 28 ( 1.7) 50 ( 1.7) 25 ( 1.9) 269 ( 2.1) 262 ( 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 I 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 9. 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 contributions of hundreds of individuals at the state and local levels Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Fmally, and most importantly, NAE? is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (CCSSO) for its considerable contributions to the program, especially its management of the National Assessment Planning Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In particular, we note the significant contrileutions of Ramsay Se lden, Director of the State Education Assessment C.mter 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 hrongh NCES, in the Office of Educational Research and Improvement of the U.S. Department of Educatit.g. 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 El'S, Westat, and NCS staff and playa a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve czedit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematks 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 lcd 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 Korner, 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, distaution, 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 tort 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 McCamley, 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. 1 4 5 UK GOVERNMENT PRINTING OFFICE : IMI () 293-275 QL S (BK. SO) 1 46