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) '