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ED 330 571 SE 052 081 TITLE The State of Mathematics Achievement in New Mexico: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.:.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-C-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessmew.; Family Environment; *Grade 8; Homework; Junior Hign Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS National Assessment of Educational Progress; *New Mexir:o; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAM)) 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 New Mexico, 2,643 students in 106 public schools were assessed. This report describes the mathematics proficiency of New Mexico eighth-graders, compares their overall performance to students in the West 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 svmmarizes the performance of subpopulations (race/ethnicity, type of community, parents' educational level, and gender). To provide a context for the assessment data, participating students, their mathematics teachers, and principals completed questionnaires Which focused on: instructional content (curriculum coverage, amount of homework); delivery of math instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, New Mexico students had an average proficiency of 256 compared to 261 nationwide. Many fewer students (New Mexico-8%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathema' Aele in NEW MEXICO The Trial State Akeiteseateat at Grade Eight PCST MPY itULABLE U.S DEPARTMENT Of EDUCATION Oft, ef. of f ducal,onar Rese Arch ancl Imprcwerhen` IIEC CATIONAL RESOURCES INFORMATrON CENTER IERIC; ument has been ,pc roducni as rec e,verd from ffle person or orgamtahort (),,glnal,ng I C` SA.nor changes havP heeo made 10 anprove repioduct.on Quamy Pomis ot ,re* or oo,,,,ons ;124.0 0 thrs docu rheht do riot hecenarory ferroesrm oftrcrIr OE RI DOSotion of poltry Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvermsnt U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD, the National Assessment of Educational Progress (NAEP). is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1969, assessments have been conducted periodically in reading, mathematics, science. writing, history/geography. and other fields. By making objective information on student performance available to policymakers at the national, state, and local levels. NAEP is an integral part of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics. the U.S. Department of Education. The Commissioner of Education Statistk:; is responsible, by law, for canying out the NAEP project through competitive awards to qualified organirations. NAF.P reports directly to the Commissioner, who is also responsible for providing continuing reviews. including validation studies and solicitation oi public comment. on NAEP's conduct and usefulness. In 1988, Congress created the National Assessment Chwerning Board (NAGB) to formulate policy guidelines for NAEP. The board is responsible for seluting 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; doveloping standards and procedures for interstate, regional, and national comparisons; improving the form and use of the National Assessment; and ensuring that all items selected for use in the National Assessment are free from racial, cultural, gender. or regional bias. The National Assessment Governine Board Richard A. Boyd, Chairman Executive Director Martha Holden Jennings Foundation Cleveland, Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren 13.0,C.E.S. Saratoga Springs. New York Francie Alexander Associate Superintendent California Department of Education Sacramento, Ca:ifornia David P. Battini High School History Teacher Cran,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 Gaass. Klyn. & Bochlje Pella, Iowa Linda R. Bryant Teacher Oreenway Middle School Teacher Center Pittsburgh, Pennsylvania Honorable Michael N. Castle Governor of Delaware Carvel State Office Building Wilmington. Delaware Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hanford. Connecticut Chester 1. Film, Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.C. 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 0,--hard. Washington Carl J. Moser Director of Sehools The Lutheran Church International Center St. Louis, Missouri Missouri Synod Mark D. Musick Pwsident Southern Regional Education Board Atlanta, Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith, Arkansas Matthew W. Prophet. Jr. Superintendent Portland Oregon Sehool District Portland, Oregon Honorable William T. Randall Commissioner of Education State Department of Education Denver, Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington. D.C, Honorable Richard W. Riley Attorney Nelson. Mullins, Riley and Scarborough Columbia. South Carolina Thomas Toputes Attorney Law Offices of Frank Rogoiienski Coronado. California Herbert J. Wa !berg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and Improvement (Ex-Officio) U.S. Department of Education Washington, D.C. Roy Truby Executive Director, NAGB Washington. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement in NEW MEXICO The Trial State Assessment at Grade Might Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the. National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education L.; US. Department of Education Lamar Alexander Secretary Office of Educatiwal Research and Improvement Bmno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. kitiott Acting Commissioner FOR MORE LNFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, orfor single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Resauch and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). library of Congress, Catalog Card Number: 91-61478 ISBN: 0-88685-14-9 The work upon which this publication is based was performed for the National Caner for Educaticn Statistics, Office of Educational Research and Improvement, by Educational Testing Service. Educational Testing Service is an equal opportunity/affirmative action employer. aucasiasal Testing Service, ATS, and 0. are registered trademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY INTRODUCTION Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis Profile of New Mexico 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in New Mexico Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 Levels of Mathematics Proficiency Content Arca Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race/Ethnicity 24 Type of Community 27 Parents' Education Level 29 Gender 31 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics/ 39 Cuniculum Coveragt 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Delivered/ 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used/ 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics? 67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX S I DATA APPENDIX Q7 iv THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessine:nt, on a trial basis, in addition to continuing its primary mission, the national assessment that NAEP has conducted since its inception. As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel admitistered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT 1 New Mexico In New Mexico, 106 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in New Mexico. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 2 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 9 percent had an Individualized Education Plan (IEP). An IEP is a plan, 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 partic;pating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP =presented 1 percent and 6 percent of the population, respectively. In total, 2,643 eighth-grade New Mexico public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligible eighth-grade public-school student population in New Mexico. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from New Mexico on the NAEP mathematics scale is 256. This proficiency is lower than that of students across the nation (261). Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students' prcficiency 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. 2 THE I99t) NAEP TRIAL STATE ASSESSMENT New Mexico In New Mexico, 98 percent of the eighth graders, ..ompared 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 New Mexico (8 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimais, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in New Mexico performed lower than students in the nation in Numbers and Operations and Data Analysis, Statistics, and Probability. Students in New Mexico performed comparably to students in the nation in Measurement, Geometry, and Algebra aad Functions. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the New Mexico eighth-grade student population defmed by race/ethnicity, type of community, parents' education level, and gender. In New Mexico: White students had higher average mathematics proficiency than did Hispanic or American Indian students. Further, a greater percentage of White students than I lispanic or American Indian Audents attained level 300. The results by type of community indicate that the average mathematics performance of the New Mexico students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, exlreme rural areas, or areas classified as "other". In New Mexico, the average matbanatics proficiency of eighth-grade public-school students having at leo3t one parent who graduated from college was approximately 32 points higher than that of students whose parents did not graduate from high school. The results by gender show that eighth-grade males in New Mexico had a higher average mathematics proficiency than did eighth-grade females in New Mexico. In addition, a greater percentage of males than females in New Mexico attained level 300. Compared to the national results, females in New Mexico performed lower than females across the country; males in New Mexico performed no differently from males across the country. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 3 New Mexico 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 instmction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the piincipals or other administrators in their schools were . asked to complete questionnaires on policies, instniction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information about student achievement. Some of the salient results for the public-school students in New Mexico are as follows: More than half of the students in New Mexico (61 percem) 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 New Mexico, 60 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 New Mexico were taking eighth-grade mathematics (62 percent) than were taking a course in pre-algebra or algebra (34 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 New Mexico 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. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico In New Mexico, 11 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 39 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In New Mexico, 27 percent of the students never used a calculator to work problems in class, while 44 percent almost always did. In New Mexico, 46 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 (53 percent) had teachers who had the highest level of teaching certification available. This is different from the figure for the nation, wheie 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in New Mexico who had four types of reading materials (an encyclopedia, newspapers, maga7ines, 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-gyade public-school students in New Mexico (14 percent) watched one hour or less of television each day; 11 percent watched six hours or more. Avelage mathematics proficiency was lowest for students who spent six hours or more watching television each day. ME 1990 NAEP ill1AL STATE ASSESSMENT 5 New Mexico THE NATION'S REPORT CARO INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Asse3sment was conducted in February 1990 with the following participants: 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 Virginia 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 m=1, New Mexico This report describes the performance of the eighth-grade public-school students in New Mexim and consists of three sections: This Introduction provides background information about the Trial State Assessment and this report. It also provides a profile of the eighth-grade public-school students in New Mexico. Part One describes the mathematics performance of the eighth-grade public-school students in New Mexico, the West region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in New Mexico, the West 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 survey instrument for the eighth grade and shall conduct a demonstration of the instrument in 1990 in States which wish to participate, with the purpose of determining whether such an assessment yields valid, reliable State representative data. (Section 406 (i) (2)(C)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 1221e-1(i)(2)(C)(i))) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent 'he 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 assesment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance progam designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 1 4 8 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patten .01 after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council of Chief State School Officers in mid-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,' the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (A PC), 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 sokly 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 New Mexico, in the West region, and for the nation. Results also are provided for groups of students defined by shared characteristics -- race/ethnicity, type of community, parents education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for New Mexico 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 prop.= 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 New Mexico RACE/ElliNICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Procedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for New Mexico. TYPE OF COMMUNITY Results are provided for four mutually exclusive community types -- advantaged urban, disadvantaged urban, extreme rural, and other -- as defined below: Advantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are in professional or managerial positions. Disadvantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are on welfare or are not regularly employed. Extreme Rural: Students in this group live outside metropoLan statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. 10 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico GLNDER 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 1..sion are shown in Figure I. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the rtmainder 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. TN NATION'S REPORT CARO FIGURE 1 I Regions of the Country NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Alabama Illinois 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 New 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 WashingOn Wyoming 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 11 New Mexico Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistically sigmficant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) -- regardless of whether the sample means or sample proportions appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the difference is not statistically significant), the means or proportions are desc-a-ibed as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the apparent magnitude of the difference between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. When three or more goups are being compared, a Bonferroni Procedure is also used. The statistical tests 4.,..nd Bonferroni procedure are discussed An greater detail in the Procedural Appendix. S 12 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent ccnfidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests arc based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT 13 New Mexico Profile of New Mexico EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISlICS Table l provides a profile of the demographic characteristics of the eighth-grade public-school students in New Mexico, the West region, and the nation. This profile is based on data collected from the students and schools participating in the Trial State Assessment. TABLE I I Profile of New Mexico Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS MO MEP TRIAL STATE ASSESSMENT Wm Mexico West Nation , DEMOGRAPHIC SUBGROUPS Percentage Percentage Percentage Raceattinicity White 40 ( 1.3) 63 ( 1.9) 70 ( 0.5) Black 2 ( 0.4) ( 2.0) 16 ( 0.3) Hispanic 45 ( 1.3) 21 ( 1.5) 10 ( 0.4) Asian 1 ( 0.3) 4 ( 1.3) 2 ( 0.5) American Indian 11 ( 0.) 4 ( 2.3) 2 ( 0.7) Type of Community Advantaged urban 5 ( 0.1) 14 ( 8.5) 10 ( 3.3) Disadvantaged urban 7 ( 0.1) 19 ( 7.5) 10 ( 2.8) Extreme rural 18 ( 0.9) 10 ( 3.8) 10 ( 3.0) Other 70 ( 0.9) 58 (10.1) 70 ( 4.4) Parents' Education Did not finish high school 11 ( 0.8) 10 ( 1.3) 10 ( 0.8) Graduated high school 27 ( 1.1) 19 ( 2.5) 25 ( 1.2) Some education after high school 16 ( 0.8) 16 ( 1.2) 17 ( 0.9) Graduated college 33 ( 1.0) 42 ( 4.0) 39 ( 1.9) Gender Male SO ( 1.2) 55 ( 2.1) 51 ( 1.1) Female 50 ( 1.2) 45 ( 2.1) 49 ( 1.1) ..,11=1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. The percentages for Race Ethnicity may not add to 100 percent because some siudents categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "1 don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for New Mexico schools and students sampled for the 1990 Trial State Assessment. In New Mexico, 106 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in New Mexico, TABLE 2 I Profile of the Population Assessed in I New Mexico EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution Weighted school participation rate after substitution Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating Schools 100% 100% 108 2 106 0 0 106 0 THE 1990 NAEP TRIAL STATE ASSESSMENT EIGHTH-GRADE PUBLIC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students selected to participate in the assessment Number of students withdrawn from the assessment Percentage of students who were of umited 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 94% 3,213 236 2% 1% 9% 6% 2,792 2,643 15 New Mexico In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 2 percent of the eighth-grade public-school population was classified as limited English Proficient (LEP), while 9 percent had an Individualized Education Plan (IEP). An IEP is a plan, 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 1 percent and 6 percent of the population, respectively. in total, 2,643 eighth-grade New Mexico public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligible eighth-grade public-school student population in New Mexico. 22 16 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico NE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in New Mexico Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAFP mathematics scale, which ranges from 0 to 500. This part of the report contain:, two chapters that describe the mathematics proficiency of eighth-grade public-school students in New Mexico. Chapter 1 compares the overall mathematics performance of the students in New Mexico to students in the West region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chaptcr 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 New Mexico CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from New Mexico on the NAEP mathematics scale is 256. This proficiency is lower than that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency MEP Mathematics Scale o 200 225 250 275 300 SOO Average Proficiency New Mexico 256 ( 0.8) 1-10-1 West 201 ( 2.8) 1.4 Nation 251 ( 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. a Differences reported arc statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 18 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico LEVELS OF MATHEMATICS PROFICIENCY .1.111110 Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to defme the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- en the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are given in Figure 3. It is important to note that the definitions of these levels are based solely on student performance on the 1990 mathematics assessment. The levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In New Mexico, 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 New Mexico (8 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). CONTENT AREA PERFORMANCE As previously indicated, the questions comprising the Trial State Assessment covered five ccintent areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Figure 5 provides the New Mexico, West region, and national results for each content area. Students in New Mexico polormed lower than students in the nation in Numbers and Operations and Data Analysis, Statistics, and Probability. Students in New Mexico performed comparably to students in the nation in Measurement, Geometry, and Algebra and Functions. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 New Mexico FIGURE 3 I Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify Solutions to one-step word problems and select the greatest four-digit number in a list. In measurement, these students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numerical Sentences and extend simple pattern sequences. LEVEL 250 { Simple Multiplicative Reasoning and Two-Step Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to other elementary two-step word problems. In these basic problem-solving situations, they can identify missing or extraneous Information and have some knowledge of when to use computational estimation. They have a rudimentary understanding of such concepts as whole number place value, "even," "factor," and "multiple." In measurement, these students can use a ruler to measure objects, convert units Within a system when the conversions require multiplication, and recognize a numencal 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. 26 20 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico FIGURE 3 I Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasoning and Problem Solving involving Fractions, Decimals, Percents, Elementary Geomebic Properties, and Simple Algebraic Manipulations Students at this level are able to represent, interpret, and perform simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, and recognize the equivalence between common fractions and decimals, including pictorial representations. They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expressions, including these With expOnentS and negative integers. In measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to Solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and Solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open linear sentences and inequalities by substitution, and checking and graphing an interval representing a compound inequality when it is described in words. They Can determine and apply a rule for simple functional relations and extend a numerical pattern. LEVEL 350 Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to include some properties of exponents. They can recognize scientific ilotation 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 trial, s to solve problems. They can find the circumferences of circles and the surface areas of sotto .ires. In geometry, they can apply the Pythagorean theorem to solve problems involving indirect measurement. These students also can apply their knowledge of the properties of geometric figures to solve problems, such as determining the slope of a line. in data analysis, these students can compute means from frequency tables and determine the probability ot a simple event, in algebra, they can identity 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 ot linear functions and their graphs, as well as functional notation, including the composition of functions. They can determine the ntri term of a sequence and give counterexamples to disprove an algebraic generalization. 2 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 New Mexico FIGURE 4 I Levels of Eighth-Grade Public-School 1 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 Percentage 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 I.+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 22 THE 1990 NAEP TRIAL STATE ASSE.SSMENT o ( 0.0) 0 ( 0.4) o ( 0.2) 8 ( 0.8) 12 ( 2.4) 12 ( 1,2) 58 ( 1.3) 63 ( 2.8) 64 ( 1.8) 98 ( 0.5) 97 ( 1.0) 97 ( 0.7) New Mexico FIGURE 5 I Eighth-Grade Public-School Mathematics I Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation NUMBERS AND OPERATIONS MEASUREMENT GEOINTRY PM 14841 DATA ANALYSIS, STATISTICS, AND PROBABILITY ALGEBRA AND FUNCTIONS limmAy 1.44 Imporamw4 h4-1 200 225 250 275 moray* Proacioncy 258 ( 0.8) 204 ( 2.6) 206 ( 1.4) 253 ( 0.8) 258 ( 3.0) 258 ( 1.7) 257 ( 0.9) 280 ( 2.6) 259 ( 1.4) 253 ( 1.1) 282 ( 3.6) 262 ( 1.8) 258 ( 1.0) 259 ( 2.4) 260 ( 1.3) 300 500 Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-1-1). If the ambience intervals for the populations do no: overlap, there is a statistically significant difference between the populations. 21 TH E 1990 NAEP TRIAL STATE ASSESSMENT 23 New Mexico CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY The Trial State Assessment results can be compared according to the different racial/ethnic groups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Hispanic, and American Indian students from New Mexico are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Hispanic or American Indian students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Hispanic or American Indian students attained level 300. 3 24 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico FIGURE 6 I Average Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity NAEP Mathematics Scale 0 200 225 250 275 300 500 Average Proficiency NI NI 1+1 11.-40004 104 Now Moxico White 1.1) Hispanic 247 j aa) American Indian 227 ( 1.0) Wellt White .0 3.2) Hispanic 2414 3.7) American Indian ( ) Nation White 2fie ( 1.5) Hispanic 243 ( LS) American Indian 240 ( 5.3)1 The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-4-4). 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). TH 1990 NAEP TRIAL STATE ASSESSMENT 25 New Mexico NATIOWS REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARD I Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Hispanic Amer. Indian Region White Hispanic Amer. Indian Nation White Hispanic Amer. Indian LEVEL 250 State White Hispanic Amer. Indian Region Whfte Hispanic Amer. Indian Nation White Hispanic Amer. Indian LEVEL 200 State White Hispanic Amer. Indian Region White Hispanic Amer. Indian Nation White Hispanic Amer. Indian Mune 144 4emees4 P-11011 1410114MMIIMIii P44IMISIONNI.1 4 Percentage 17 ( 1.8) 2 ( 0.6) 1 ( 0.7) IS ( 3.2) 3 ( 1.6) mut *.) 16 ( 1.5) 3 ( 1.1) ( 2.3)1 7$ ( 1.6) 44 ( 1.6) 30 ( 3.5) 74 ( 3.3) 41 ( 5.4) olas 74 ( 1.8) 41 ( 4.5) 45 (16.0)I 4 100 ( 0.3) 1-4,4 97 ' 1 ,0) 1."4.4 93 ( 2.1) 94 ( 0.8) 11,-40 93 ( 2.0) It" ( ***) 00 ( 0.4) 93 ( 1.6) 97 ( 6.7)1 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 1 2 standard errors of the estimated percentage (95 percent confidenoe interval, denoted by I-+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 3 26 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban area, disadvantaged urban areas, extreme rural areas, and areas clanified as "other". (These are the "type of community" groups in New Mexico with student samples large enough to be reliably reported.) The eesults indicate that the average mathematics performance of the New Mexico 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". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community 0 200 NAEP Mathematics Scale 225 250 275 300 500 Average Pfeil/dewy P-001 P""Powl New Mexico Advantaged urban Disadvantaged urban 295 IN ( 3.5) f 249) Extreme rural 3 ( 1.0 Other west 221 0.9) Advantaged urban Disadvantaged urban 2416 5.6)I Extreme rural 263 ( 7.3)1 PPPoll Other 10 ( 3.6) Nation Advantaged urban 3.1$ I,""4 Disadvantaged urban 35)1 1P-1,11 Extreme rural 2116 4.1$ 1141 Other 261 ( 14) 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 P-H). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 New Mexico FIGURE 9 LEVEL 300 State Adv. urban Di &tidy. urban Ext. rural Other Regien Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban Dlsadv. urban Ext. rural Other LEVEL 250 State Adv. urban Disadv. urban Ext. rural Other Region Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other LEVEL 200 State Adv. urban DIsadv. urban Ext. rural Other Region Adv. urban Mac Iv. urban Ext. rural Other Nation Adv. urban Dtsadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community THE NATION'S REPORT CARD 31 (12.6) 7 ( 2.7) 144 3 ( 0.9) Polo 8 ( 0.8) 31 ( 3.1)1 9 ( 3.5)1 6 ( 4.8)1 ptowail 10 ( 1.8) 26 ( 4.8)1 1.-11.04 7 ( 2.1)1 6 ( 2.3)1 12 ( 1.2) 92 ( 4.8) 51 ( 6.4) ( 3.6) 54 ( 1.5) 63 ( 3.3)1 57 ( CO)' lo6- .4 52 (12.8)1 82 ( 5.0) 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each pcpulation of interest is within 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 14.4), lf 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 attamed that level. interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 83 ( 4.6)1 401 ( 5,0)1 64 ( 2.3) 100 ( 0.0) 97 ( 1.2) 97 ( 1.0) 97 ( 0.6) 100 ( 0.0) 96 ( 2.0)1 0. ( 1.3)1 96 ( 1.7) 100 ( 0.0) 95 ( 1.5)1 97 ( 2.8)1 0.401 97 ( 1.0) 100 3 4 28 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better edumted tend to have higher mathematics proficiency (see Figures 10 and I I). In New Mexico, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 32 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, a smaller percentage of students in New Mexico (33 percent) than in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 11 percent for New Mexico and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School Mathematics Proficiency by Parents' Education IMP Mathematics Scat* 200 225 250 275 300 500 Average Proficiency New Mexico t44 HS non-graduate 240 ( 14) MI HS graduate 247 ( 1.3) el Some college 2111 i 1.2) College graduate 02 ( IS) West HS non-graduate 240 ( 4.4) P4.1 MS graduate 240 ( 2.2) Some college 2111 ( 3.0) P-11.1 College graduate 2/3 ( 2.6) Nation 141 HS non-graduate 243 ( 2.0) HS graduate 264 ( 1.5) PH Some college 210 ( 1.7) PM College graduate 274 ( 1.6) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population a interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by HA). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 3 5 THE 1990 NAEP TRIAL STATE ASSESSMENT 29 New Mexico ME NA: REPORT FIGURE 1 1 I Levels of Eighth-Grade Public-School CARD Mathematics Proficiency by Parents' Education LEVEL 300 State HS non-grad. HS graduate Some college College grad. Regkal HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 Stat. HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad, Nation HS non-grad. HS graduate Some college College grad. 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the valu2 for each population of interest is within et: 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1+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. 100 30 THE 1990 NAEP TRIAL STATE ASSESSMENT 2 ( 1.1) 2 ( 0.9) 1 ( 1.2) 11 ( 2.2) 2 ( 2.3) 2 ( 1.3) 15 ( 2.8) 21 ( 3$) ( 0.9) ( 1.5) 12 ( 1.4) 21 ( 1.9) 33 ( 2.7) 46 ( 2.5) 06 ( 3.0) 77 ( 2.2) 44 ( 6.8) 51 ( 4.4) 75 ( 41) 78 ( 3.6) 37 ( 4.6) 58 ( 2.7) 71 ( 2.6) 78 ( 2.0) 98 ( 1.8) 98 ( 1.1) ( 0.4) 100 ( 0.0) 91 ( 3.2) 97 ( 1.8) DO ( 0.7) 99 ( 0.7) 91 ( 1.9) 97 ( 0.8) ( 0.7) 99 ( 0.7) New Mexico GENDER As shown in Fig= 12, eighth-grade males in New Mexico had a higher average mathematics proficiency than did eighth-grade females in New Mexico. Compared to the national results, females in New Mexico performed lower than females across the country; males in New Mexico performed no differently from males across the country. FIGURE 12 I Average Eighth-Grade Public-School i Mathematics Proficiency by Gender MEP Mathematics Scale 0 200 225 250 275 300 500 IM14 Averaoe Proficiency NI Now MIMICS Male 2W ( 1.1) Female wee 23 ( 1.0) 1441 Male 181 ( 3.5) 11-4N4 Female 210 ( 219 Nation pI Male 202 ( 1.8) 144 Female ISO ( 13) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by Hi). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in New Mexico who attained level 200. The percentage of females in New Mexico who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in New Mexico who attained level 200 was similar to the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASSESSMENT 31 New Mexico FIGURE 13 I Levels of Eighth-Grade Public-School i Mathematics Proficiency by Gender LEVEL 300 State Male Female Region Male Female Nation Male Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female 0 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 I-1-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not preented in this figure because so few students attained that level. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 10 ( 1.1) 6 ( 1.0) 13 ( 31) 11 ( 2.2) 14 ( 1.7) 10 ( 1.3) 110 ( 2.0) 53 ( 15) 85 ( 4.1) 61 ( 32) 64 ( 2.0) 64 ( 1.8) ( 0.6) 97 ( 0,8) 97 ( 1.2) 98 ( 1.0) 97 ( 0.9) 97 ( 0.8) New Mexico In addition, a greater percentage of males than females in New Mexico attained level 300. The percentage of females in New Mexico who attained level 300 was smaller than the percentage of females in the nation who attained level 300. Also, the percentage of males in New Mexico who attained level 300 was smaller than the percentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. 3 ;) THE 1990 NAEP TRIAL STATE ASSESSMENT 33 New Mexico TABLE 3 I Eighth-Grade Public-School Mathematics i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS liM0 MEP TRIAL STATE ASSESSMENT Numbers and Operations Measurement Geometry Data Analysis, Sint' Iltial, and Probability , 47m:ix= TOTAL Proficiency Proficiency Proficiency Proficiency Proficiency State 258 ( 0.8) 253 ( 0.8) 257 ( 0.9) 253 ( 1.1) 256 ( 1.0) Region 264 ( 2.6) 258 ( 3.0) 260 ( 2.6) 262 ( 3.6) 259 ( 2.4) Nation 266 ( 1.4) 258 ( 1.7) 259 ( 1.4) 262 ( 1.8) 260 ( 1.3) RACE/ETHNICITY White State 273 ( 1.3) 271 ( 1.4) 269 ( 1.3) 273 ( 1.4) 272 ( 1.6) Region 271 ( 32) 267 ( 3.9) 267 ( 3.0) 272 ( 4.4) 287 ( 2.8) Nation 273 ( 1.6) 267 ( 2.0) 267 ( 1.5) 272 ( 1.8) 268 ( 1.4) Hispanic State 250 ( 1.1) 241 ( 1.2) 248 ( 12) : 42 ( 1.4) 248 ( 1.2) Region 248 ( 33) 239 ( 42) 245 ( 4.4) 240 ( 4.7) 243 ( CO) Nation 248 ( 2.7) 238 ( 3.4) 243 ( 32) 239 ( 3.4) 243 ( 3.1) American Indian State Region 238 ( ( 2.0) 444) ) 226 ( 2.2) 235 ( 1.8) Nation 249 ( 7.8)1 247 ( 6.8)1 2a ( 8.6)1 242 ( 5.2)1 242 ( 4.9)1 TYPE OF COMMUNITY Advantaged urban State 285 ( 4.7) 289 ( 52) 281 ( 3.6) 287 ( 4.9) 284 ( 4.5) Region 284 ( 3.6)1 283 ( 2.7)1 279 ( 8.9)1 288 ( 4.1)1 279 ( 2.9)1 Nation 283 ( 3.2)1 281 ( 3.2)1 277 ( 5.2)1 285 ( 4.8)1 277 ( 4.8)1 Disadvantaged urban State 258 ( 2.7) 255 ( 5.4) 258 ( 2.8) 249 ( 4.6) 256 ( 3.9) Region 260 ( 5.4)1 250 ( 6.9)1 256 ( 4.5)1 255 ( 8.3)1 254 ( 4.6)! Nation 255 ( 3.1)1 242 ( 4.9)1 248 ( 3.7)1 247 ( 4.6)1 247 ( 3.2)1 Extreme rural State 254 ( 2.2) 250 ( 2.6) 256 ( 1.5) 248 ( 2.7) 252 ( 2.1) Region 254 ( 8.6)1 254 ( 4.6)1 252 ( 9.4)1 253 ( 8.8)1 251 ( 8.5)1 Nation 258 ( 4.3)1 254 ( 42)1 253 ( 4.5)1 257 ( 5.0)1 256 ( 4.8)1 Other State 257 ( 1.0) 251 ( 1.0) 255 ( 1.3) 251 ( 1.3) 255 ( 1.1) Revon 262 ( 3.5) 255 ( 4.2) 258 ( 3.4) 259 ( 4.2) 258 ( 3.5) Nation 266 ( 1.9) 257 ( 2.4) 259 ( 1.7) 261 ( 2.2) 2131 ( 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 esnmated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 0 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Ne xico TABLE 3 I Eighth-Grade Public-School Mathematics (continued) i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT , Numbers and Operation. Illeasureinent Geometry _ Data Analysis' Statistics, and Probability Algebra and Funtwos S. TOTAL ProOdency Prollolmloy Prollcieney Proficiency Proliciency State 258 ( 0.8) 253 ( 0.8) 257 ( 0.9) 253 ( 1.4) 256 ( 1.0) Region 264 ( 2.6) 258 ( 3.0) 200 ( 2.6) 262 259 ( 2.4) Nation 266 ( 1.4) 258 ( 1.7) 259 ( 1.4) 262 1 2' 260 ( 1.3) PARENTS EDUCATION KS noniraduate State 245 ( 1.6) 233 ( 32) 243 ( 2.3) 232 ( 2.2) 242 ( 1.9) Region 248 ( 4.2) 242 ( 8.2) 246 ( 4.9) 246 ( 6.2) 245 ( 5.1) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) 240 ( 3.1) 242 ( 3.0) KS graduate state 249 ( 14) 246 ( 2.1) 250 ( 1.4) 242 ( 1.8) 247 ( 1.7) Region 254 ( 2.5) 245 ( 3.0) 251 ( 3.6) 249 ( 3.2) 250 ( 2.4) Nation 259 ( 1.8) 248 ( 2.1) 252 ( 1.6) 253 ( 2.2) 253 ( 2.0) Some college State 265 ( 1.3) 256 ( 1.5) 260(1.3) 263 ( 14) 263 ( 1.7) Region 272 ( 2.7) 268 ( 5.3) 264 ( 3.9) 271 ( 4.9) 264 ( 3.2) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 263 ( 22) College graduate State 274 ( 1.7) 271 ( 1.9) 270 ( 1.5) 273 ( 2.0) 271 ( 1.9) Region 27$ ( 2.7) 271 ( 3.0) 271 ( 2.3) 276 ( 4.3) 272 ( 2.6) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 276 ( 2.2) 273 ( 1.7) GENDER Male State 260 ( 1.1) 260 ( 1$) 260 ( 1.1) 256 ( 1.7) 257 ( 1.2) Region 264 ( 3.8) 263 ( 3$) 261 ( 3.4) 264 ( 4.1) 260 ( 3.3) Nation 266 ( 2.0) 262 ( 2.3) 260 ( 1.7) 262 ( 2.1) 260 ( 1.R1 Female State 256 ( 1.1) 246 ( 1.3) 254 ( 1.1) 249 ( 1.5) 255 ( 1.2) Region 263 ( 2.5) 252 ( 2.9) 259 ( 2.9) 260 ( 4.0) 259 ( 2.8) Nation 266 ( 1.4) 253 ( 1.6) 258 ( 1.5) 261 ( 1.9) 260 ( 1.4) The standard errors of the estimated staustics appear in parentheses. II can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 35 New Mexico THE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is vaNRble in and of itself, but it becomes more useful for improving instruction and st policy when supplemented with contextual information about schools, teachers. and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade publie-school students' proficiency in the subject, and provide an educational context for understanding information on student acliievement. It is important to note that the NAEP data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning aid instruction -- fundamental aspects of the educational process in the countiy. 2 THE 1990 NAEP TRIAL STATE ASSESSME 37 New Mexico 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 , xtbooks or worksheets. Also, it is widely recognized that home environment has an --.innous impact on future academic achievement. Yet, as shown in Chapters 3 and 7, large proportions of students report having spent much more time each day watching television than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 38 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction ofmathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.3 This chapter focuses on curricular and instructional content issues in New Mexico public schools and their relationship to students' proficienc). Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: More than half of the eighth-grade students in New Mexico (61 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 Underachir ,g Currkulum Assessing U.S. School Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign. IL: Stipes Publishing Company, 1987). Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Educatifm (Wastungton, DC: National Academy Press, 1989). 4 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 New Mexico In New Mexico, 60 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Many of the students in New Mexico (88 percent) were taught mathematics by teachers who teach only one subject. More than half (65 percent) of the students in New Mexico were typicAlly taught mathematics in a class that was grouped by mathematics ability. Ability gimping was equally prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in New Mexico Eighth-Grade Public Schools PERCENTAGE OF STUDENTS MO NAEP TRIAL STATE ASSESSMENT New Mexico West 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 ofkred 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 only mathematics Percentage of eighth-grade students in public schooIs who are assigned to a mathematics dub by mob abllity in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics instnaction per week Percentags Percentage Percentage 61 ( 1.2) 81 ( 6.6) 63 ( 5.9) 60 ( 1.0) 92 4.7) 78 ( 4.6) 88 ( 0.9) 98 ( '.6) 91 ( 3.3) 85 ( 1.1) 84 ( 8.3) 63 ( 4.0) 30 ( 1.3) 25 ( 5.9) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 4 0 40 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in New Mexico are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in New Mexico were taking eighth-grade mathematics (62 percent) than were taking a course in pre-algebra or algebra (34 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 New Mexico who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 1 Students' Reports on the Mathematics Class 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1900 NAEP TRIAL STATE ASSESSMENT New Mexico West Nation [ What kind of mathematics class are you taking this year? Eighth-grade mathematics Pre-algetwo Ngebra Percentage and Proficiency Percantags and Proficiency Percentage and Proficiency 62 ( 1.2) 83 ( 2.7) 82 ( 2.1) 247 ( 0.7) 252 ( 2.4) 251 ( 1.4) 23 ( 1.1) 15 ( 2.7) 19 ( 1.9) 265 ( 1,5) 286 ( 3.6) 272 ( 2.4) 11 ( 0.6) 17 ( 1.8) 15 ( 1.2) 288 ( 1.9) 299 ( 4.5) 296 1 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 takmg other mathematics courses. THE 1990 NAEP TRIAL STATE ASSESSMENT 41 tykl New Mexico Further., from Table AS in the Data Appendix:' A greater percentage of females (37 percent) than males (31 percent) in New Mexico were enrolled in pre-algebra or algebra courses. In New Mexico, 40 percent of White students, 31 percent of Hispanic students, and 23 percent of American Indian students were enrolled in pre-algebra or algebra courses. Similarly, 26 percent of students attending schools in advantaged urban areas, 38 percent in schools in disadvantaged urban areas, 42 percent in schools in extreme rural areas, and 32 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 pmficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in New Mexico 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 New Mexico, 3 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 7 percent of the students in New Mexico and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations -- race/ethnicity, type of community, parents' education level, and gender. 42 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico The results by race/ethnicity show that 9 percent of White students, 6 percent of Hispanic students, and 6 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 2 percent of White students, 3 percent of Hispanic students, and 7 percent of American Indian students spent no time doing mathematics homework. In addition, 3 percent of students attending schools in advantaged urban areas, 18 percent in schools in disadvantaged urban areas, 10 percent in schools in extreme rural areas, and 6 percent in schools in areas classified as "other" spent an llour or more on mathematics homework daily. In comparison, 0 percent of students mending schools in advantaged urban areas, 13 percent in schools in disadvantaged urban areas, 6 percent in schools in extreme rural areas, and 2 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT New Mexico West Nation About how much time do students spend I on mathematics homework each day? None 15 minutes 30 minutes 45 minutes An hour or more Percentage and Pftlidency Percentage and Pronclancy Percentage and Proficiency 3 ( 240 ( 0.5) 3.5) 1 ( 0.3) 1 ( ( 0.3) .44) 33 ( 1.1) 42 ( 6.7) 43 ( 42) 255 ( 1.0) 258 ( 4.2) 258 ( 2.3) 44 ( 1-5) 43 ( 8.2) 43 ( 4.3) 253 ( 1.1) 264 ( 4.7) 268 ( 2.6) 12 ( 1.0) 9 ( 2.3) 10 ( 1.9) 268 ( 2.8) 270 ( 8.5)1 272 ( 5.7)1 7 ( 0.8) 4 ( 0.9) 27'3 ( 2.6) ") 278 ( 5.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, fur each population or interest, the value for the entire population is within ± 2 standard errors of the esumate 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). S THE 1990 NAEP TRIAL STATE ASSESSMENT 43 New Mexico 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 1960 NAEP TRIAL STATE ASSESSMENT New Mexico West Nation About how much time do you usually spend each day on mathematics homework? Percentage end Proficiency Percentage and ProPciency Percentage and Proficiency None 9 ( 0.6) 12 ( 1.7) 9 ( 0.8) 259 ( 2.7) 254 ( 4.2) 251 ( 2.8) 15 minutes 26 ( 1.1) 31 ( 4.5) 31 ( 2.0) 2.57 ( 1.3) 263 ( 3.8) 264 ( 1.9) 30 minutes 29 ( 1 0) 28 ( 1.7) 32 ( 1.2) 255 ( 1.2) 261 ( 2.9) 263 ( 1.9) 45 mintdiA 18 ( 0.9) 15 ( 1.6) 16 ( 1.0) 257 ( 1.7) 267 ( 4.2) 266 ( 1.9) An hour or more 18 ( 0.9) 14 ( 1.7) 12 ( 1.1) 255 ( 2.1) 261 ( 4.3) 258 ( 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 populauon is within ± 2 standard errors of the estimate for the sample. And, according to the students (Table 7 and Table A7 in the Data Appendix): In New Mexico, relatively few of the students (9 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 18 percent of the students in New Mexico 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 18 percent of White students, 18 percent of Hispanic students, and 20 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 12 percent of White students, 8 percent of Hispanic students, and 8 percent of American Indian students spent no time doing mathematics homework. 4 44 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico In addition, 18 percent of students attending schools in advantaged urban areas, 17 percent in schools in disadvantaged urban areas, 17 percent in schools in extreme rural areas, and 19 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 10 percent of students attending schools in advantaged urban areas, 6 percent in schools in disadvantaged urban areas, 11 percent in schools in extreme rural areas, and 9 percent in schools in areas classified as "other" spent no time doing mathematics homework. LNSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement.5 Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathem.atics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. 5 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: NaUonal Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 45 New Mexico 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. 46 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . 19110 NAEP TICAL STATE ASSESSMENT 1 New Mexico , _ West Nation Pwcentage and Ifteddancy Percentage and Preectency Percentage and Pnaliatency Teacher "emphasis" categories by content areas Numbers and Operations Heavy emphasis 54 ( 1.2) 42 ( 7.4) 49 ( 3.8) 254 ( 1.0) 257 ( 3.6) 260(1.8) Little or no emphasis 12 ( 0.7) 13 ( 2.1) 15 ( 2.1) 280 ( 3.2) 291 ( 8.6) 287 ( 3.4) Measurement Heavy emphasis 18 ( 1.1) 11 ( 2.8) 17 ( 3.0) 245 ( 3.1) 251 ( 7.7)1 250 ( 5.6) Little or no emphasis 33 ( 1.5) 36 ( 5.3) 33 ( 4.0) 200 ( 1.7) 275 ( 8.3) 272 ( 4.0) Geometry Heavy emphasis 25 ( 1.1) 24 ( 6.3) 28 ( 3.8) 258 ( 2.0) 260 ( 2.8)1 260 ( 32) Little or no emphasis 33 ( 1.3) 16 ( 4.5) 21 ( 3.3) 258 ( 1,3) 277 (11.4)1 284 ( 54) Data Analysis, Statistics, and Probability Heavy emphasis 14 ( 0.9) 14 ( 3.7) 14 ( 22) 255 ( 3.3) 264 (10.6)1 269 ( 4.3) Little or no emphasis 56 ( 1.3) 54 ( 6.3) 53 ( 4.4) 249 ( 1.3) 262 ( 4.9) 261 ( 2.9) Algebra and Functions Heavy emphasis 53 ( 12) 43 ( 5.6) 48 ( 3.8) 267 ( 1.4) 277 ( 52) 275 ( 2.5) Utt le or no emphasis 15 ( 1.0) 23 ( 5.1) 20 ( 3.0) 236 ( 1.6) 243 ( 4.2)1 243 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 pment 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 New Mexico SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: More than half of the eighth-grade students in New Mexico (61 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In New Mexico, 60 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 New Mexico were taking eighth-grade mathematics (62 percent) than were taking a course in pre-algebra or algebra (34 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 New Mexico 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 New Mexico, relatively few of the students (9 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 18 percent of the students in New Mexico and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. t." 48 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico CHAPTER 4 yeXA-Ax-49 On 11-11-12 Ii 111112151113112/ Ea MEE 2 EN In EIREILTE MUM OE 111EntiEll011111 111111111E11111i1111 12211111 1475E1111012U1111 IMMINI11 111111111.11?..1111 111211111111 AEI111111111111 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 instniction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. National Council of Teachers of Mathematics. Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). r THE 1990 NAEP TRIAL STATE ASSESSMENT 49 New Mexico From Table 9 and Table A9 in the Data Appendix: In New Mexico, 11 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 39 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In New Mexico, 0 percent of students attending schools in advantaged urban areas, 0 percent in schools in disadvantaged urban areas, 20 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 New Mexico, 42 percent of students attending schools in advantaged urban areas, 64 percent in schools in disadvantaged urben areas, 32 percent in schools in extreme rural areas, and 37 percent in schools in areas classified as "other" were in classrooms where only some or no resources wen 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 MO NAEP TRIAL STATE ASSESSMENT New Mexico West Nation _ Which of the following statementi is true about how well supplied you are by your school system with the Instructional materials and other resources you need to teach your class? I get ail the resoirces I need. I get most of the resources I need. t ipt some or none of the resources I mod. 7 Percentage Peremtage Percentage and and and Proficiency Proficiency Proficiency 11 ( 0.7) 15 ( 5.2) 13 ( 2.4) 254 ( 2.7) 261 ( 5.91? 285 ( 4.2) 50 ( 12) 02 ( 3.8) 58 ( 4.0) 258 ( 0.8) 288 ( 4.1) 265 ( 2.0) 39 ( 1.1) 23 ( $.1) 31 ( 4.2) 2S8 ( 1$) 257 ( 3.7)I 281 ( 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. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico PATTERNS LN 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 infomiation on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: About half of the students in New Mexico (51 percent) worked mathematics problems in small groups at least once a week; some never worked mathematics problems in small groups (11 percent). The largest percentage of the students (73 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; -elatively few never used such objects (8 percent). In New Mexico, 69 percent of the students were assigned problems from a mathematics textbook almost every day; 6 percent worked textbook problems about once a week or less. Less than half of the students (33 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (38 percent). Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Curriculum. Eighty-second Yearbook of the National Society for the Study of Edwation (Chicago. IL: University of Chicago Press, 1983). 5G THE 1990 NAEP TRIAL STATE ASSESSMENT 51 New Mexico TABLE 10 I Teachers' Reports on Patterns of Mathematics I Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENcv .. 1990 NAEP TRIAL STATE ASSESSMENT New Mexico West Nation - Percentage and Percentage and Percentage and About how often do students work problems in small groups? Proficiency Proficiency Prdetioxy At least once a week 51 ( 1.4) 57 ( 8.9) 50 ( 4.4) 257 ( 1.1) 262 ( 42)I 260(2.2) Less dun once a week 36 ( 1.4) 39 ( 1.8) 43 ( 4.1) 256 ( 1.2) 286(4.5) 264 ( 2.3) Never 11 ( 0.7) 25$ ( 2.0) 3 ( 22) 8 ( 2.0) 277 ( 5.4)1 About how often do students use objects Percentage Percentage Percentage like rulers, counting blocks, or geometric and and and solids? Profickincy Proficiency Proficiency At least once a week 19 ( 1.0) 34 ( 82) 22 ( 3.7) 252 ( 1.5) 256 ( 4.9)1 254 ( 3.2) Less than once a week 73 ( 1.1) 57 ( 6,4) 69 ( 3.9) 256 ( 0.9) 265 ( 4.0) 263( 1.9) New 8 ( 0.0) 9 ( 2.0) 269 ( 2,4) *** ( 282 ( 5.9)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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 52 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE 11 I Teachers' Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT New Miodco West Nation Percentage Percentage Percentage About how often do students do problems and and and from textbooks? Prediction)/ Pmeiciency Proficiency. Almost every day 69 ( 12) 55 ( 6.0) 62 ( 3.4) 258 ( 0.9) 270 ( 3.3) 267 ( 1.8) Several times a week 25 ( 1.2) 36 ( 5.1) 31 ( 3.1) 253 ( 1.4) 256 ( 52) 254 ( 2.9) About once a week or kris 6 ( 0.3) 7 ( 1.8) 247 ( 3.0) 260 ( 5.1)t About how often do students do problems Percentage Percentage Percentage on worksheets? and and and Proficiency Proddency Proficiency At least several times a week 33 ( 1.0) 25 ( 52) 34 ( 3.8) 248 ( 1.1) 258 ( 4.3)1 258 ( 2.3) About once a week 29 ( 1.2) 34 ( 4.6) 33 ( 3.4) 259 ( 1.4) 258 ( 4.1) 260 ( 2.3) Less than weekly 38 ( 1.4) 41 ( 5.6) 32 ( 3.6) 261 ( 1.3) 274 ( 4.2) 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 New Mexico COLLABORATING IN SMALL GROUPS In New Mexico, 52 percent of the students reported never working mathematics problems in small groups (see Table 12); 24 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 1000 NAEP TRIAL STATE ASSESSMENT New Mexico West Nation How often do you work in small groups in your mathematics class? Percentage and Proadency Percentage and Prolidency Percentage and Proficiency At least once a week 24 ( 0.9) 35 ( 4.8) 28 ( 2.5) 256 ( 1.6) 258 ( 4.2) 258 ( 2.7) Less thall 0040 a week 24 ( 0.9) 29 ( 2.8) 28 ( 1.4) 263 ( 1.6) 271 ( 3.1) 287 ( 2.0) Never 52 ( 1.0) 36 ( 4.8) 44 ( 2.9) 253 ( 1.0) 258 ( 2.0) 261 ( 1.6) 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. Examining the subpopulations (Table Al2 in the Data Appendix): In New Mexico, 22 percent of students attending schools in advantaged urban areas, 29 percent in schools in disadvantaged urban areas, 26 percent in schools in extreme rural areas, ani 22 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 23 percent of White students, 22 percent of Hispanic students, and 32 percent of American Indian 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 (24 percent and 24 percent, respectively). 54 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: About half of the students in New Mexico (47 percent) never used mathematical objects; 22 percent used these objects at least once a week. Mathematical objects were used at least once a week by 18 percent of students attending schools in advantaged urban areas, 29 percent in schools in disadvantaged urban areas, 23 percent in schools in extreme rural areas, and 21 percent in schools in areas classified as "other". Males were as likely as females to use mathematical objects in their mathematics classes at least once a week (23 percent and 21 percent, respectively). In addition, 20 percent of White students, 21 percent of Hispanic students, and 36 percent of American Indian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL. STATE ASSESSMENT New Miudco West Nation - How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency At least once a week 22 ( 1.1) 36 ( 3.5) 28 ( 1.8) 251 ( 1.4) 260 ( 4.0) 258 ( 2.6) Lass Irian once a week 31 ( 1.2) 28 ( 1.8) 31 ( 1.2) 261 ( 1.4) 269 ( 2.7) 269 ( 1.5) Now 47 ( 1.2) 36 ( 3.3) 41 ( 2.2) 256 ( 1.0) 256 ( 2.8) 259 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. C() THE 1990 NAEP TRIAL STATE ASSESSMENT 55 New Mexico MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in New Mexico who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table A14 in the Data Appendix): About three-quarters of the students in New Mexico (78 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 72 percent of students attending schools in advantaged urban areas, 68 percent in schools in disadvantaged urban areas, 82 parent in schools in extreme rural areas, and 78 percent in schools in areas classified as "other". TABLE 14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO MEP TRIAL STATE ASSESSMENT New Mexico West Nation How often do you do mathematics problems from textbooks in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Almost every day 78 ( 0.9) 71 ( 3.5) 74 ( 1,9) 259 ( 0.9) 267 ( 2.4) 267 ( 12) Several times a weak 13 ( 0.9) 15 ( 1$) 14 ( 0.8) 249 ( 2.4) 251 ( 2.4) 252 ( 1.7) Abad once a week or less 9 ( 0.6) 14 ( 3.1) 12 ( 1.8) 245 ( 1.4) 242 (11.2)I 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 61 55 THE 1990 NAEP TkIAL STAT E ASSESSMENT New Mexico And, for the frequency of worksheet usage (Table 15 and Table Al5 in the Data Appendix): Less than half of the students in New Mexico (34 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 45 percent of students attending schools in advantaged urban areas, 55 percent in schools in disadvantaged urban areas, 30 percent in schools in extreme rural areas, and 33 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 MO NAEP TRIAL STATE ASSESSMENT New i&exico West Nation How often do you do mathematics problems on worksheets in your , mathematics class? Percentage mid Proficiency Percentage and Proficiency Percaniage and Proficiency At least several Dines a week 34 ( 12) 35 ( 4.0) 38 ( 2.4) 250 ( 1.4) 250 ( 41) 253 ( 2.2) About once a week 25 ( 0.9) 23 ( 2.8) 25 ( 1.2) 254 ( 1.3) 282 ( 2.1) 261 ( 1.4) Less than weekly 41 ( 1.1) 41 ( 4.1) 37 ( 2.5) 283 ( 1.2) 270 ( 3.4) 272 ( 1.9) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 pert; . certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. 62 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 New Mexico TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT New Mexico West Nation Patterns of classroom instruction Percentage Students Teachers Percentage Students Teachers Pmenhige Students Teachers Percentage of students who work mathematics problems in small groups At least once a week 24 ( 0.9) 51 ( 1,4) 35 ( 4.8) 57 ( 8.9) 28 ( 2.5) 50 ( 4.4) Less than once a week 24 ( 0.9) 38 ( 1.4) 29 ( 2.8) 39 ( 7.6) 28 ( 1.4) 43 ( 4.1) Never 52 ( 1.0) 11 ( 0.7) 38 ( 4.8) 3 ( 2.2) 44 ( 2.9) 6 ( 2.0) Percentage of students who use objects like rulers, counting blocks, or geometric solids At least once a week 22 ( 1.1) 19 ( 1.0) 36 ( 3.5) 34 ( 82) 28 ( 1.8) 22 ( 3.7) Le Ss than once a week 31 ( 1.2) 73 ( 1.1) 28 ( 1.8) ST ( 6,4) 31 ( 1.2) 69 ( 3.9) Never 47 ( 1.2) 8 ( 0.6) 36 ( 3.3) t ( 3,0) 41 ( 2.2) 9 ( 2.6) Materials for mathematics Percentage Percentage Percentage instruction Students Teachers Students Teachers Student* Teachers Pwcantage of students who use a mathematics textbook Almost every day 78 ( 0.9) 69 ( 12) 71 ( 3.5) 55 ( 6.0) 74 ( 1.9) 62 ( 34) Several times a week 13 ( 0.9) 25 ( 1.2) 15 ( 1,5) 36 ( 5.1) 14 ( 0.8) 31 3.1) About once a week or less 9 ( 0.6) 6 ( 0.3) 14 ( 3.1) 9 ( 4.9) 12 ( 1.8) 7 ( 1.8) Percentage of students who use a mathematics worksheet At least several times a week 34 ( 1.2) 33 ( 1.0) 35 ( 4.0) 25 ( 52) 38 ( 2,4) 34 ( 3.8) About once a week 25 ( 0.9) 29 ( 1.2) 23 ( 2.6) 34 ( 4.6) 25 ( 1.2) 33 ( 3.4) Less than weekly 41 ( 1.1) 38 ( 1.4) 41 ( 4.1) 41 ( 5.6) 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. 133 58 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery practices and resources. It appears that mathematics textbooks and worksheets continue to play a major role in mathemat. :s teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachers: About half of the students in New Mexico (51 percent) worked mathematics problems in small groups at least once a week; some never worked in %mall groups (11 percent). The largest percentage of the students (73 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (8 percent). In New Mexico, 69 percent of the students were assigned problems from a mathematics textbook almost every day; 6 percent worked textbook problems about once a week or less. Less ulan half of the students (33 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (38 percent). And, according to the students: In New Mexico, 52 percent of the students never worked mathematics problems in small groups; 24 percent of the students worked mathematics problems in small groups at least once a week. About half of the students in New Mexico (47 percent) never used mathematical objects; 22 percent used these objects at least once a week. About three-quarters of the students in New Mexico (78 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 New Mexico (34 percent) used worksheets at least several times a week, compared to 38 percent in the nation. THE 1990 NAEP TRIAL STATE ASSESSMENT 59 New Mexico CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks.° The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. a National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, NJ: Educauonal Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evaluation .Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 60 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico Table 17 provides a profile of New Mexico eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 20 percent of the students in New Mexico had teachers who allowed calculators to be used for tests. About the same percentage of students in New Mexico and in the nation had teachers who permitted unrestricted use of calculators (18 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of New Mexico Policies on Calculator Use PERCENTAGE OF STUDENTS 10 NAEP TRIAL STATE ASSESSMENT New Mexico West Nation Percentage of eighth-grade students In public schools whose teachers permit the unreshicted use of calculators Percentage of eighth-grade students in public sChOOls whose teachers permit the use of calculators tor tests Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned .;$ the school Percentage Percentage Percentage 18 ( 0.8) 20 ( 4.9) 18 ( 3.4) 20 ( 1.1) 48 ( 8.8) 33 ( 4.5) 56( 1.1) 72 ( 7.4) 56 ( 4.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. 6 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 61 New Mexico ME AVAILABILITY OF CALCULATORS In New Mexico, most students or their families (97 percent) owned calculators (Table 18); however, fewer students (47 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In New Mexico, 44 percent of White students, 47 percent of Hispanic students, and 59 percent of American Indian students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (48 percent and 47 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NW TRIAL STATE ASSESSMENT New Mexico West Nation Do you or your family own a Calculator? Yes No Does your mathematics teacher explain how to use a calculator for mathematics 1 1 problems? Yes No Percentage and Protidency Percentage Percentage and and Wolkiency Proficiency 97 ( 257 ( 3 ( 231 ( 0.3) 0.8) 0.3) 3.8) 96 ( 283 ( 4 ( ( 0.8) 2.6) 0.6) 0.4) 97 ( 283 ( 3 ( 234 ( 0.4) 1.3) 0.4) 3.8) Percentage Percentage RIWW.Flage and and and Proaciency Proficiency Proficiency 47 ( 1.2) 59 ( 3.4) 49 ( 2.3) 252 ( 1.1) 260 ( 2.7) 258 ( 1.7) 53 ( 1.2) 44 ( 3.4) 51 ( 2.3) 260 ( 1.1) 265 ( 3.0) 266 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 THE 1990 NAEP TRIAL STATE ASSESSMENT THE USE OF CALCULATORS New Mexico As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment, students asked how frequently (never, sometimes, almost always) they used calculators for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In New Mexico, 27 percent of the students never used a calculator to work problems in class, while 44 percent almost always did. Some of the students (17 percent) never used a calculator to work problems at home, compared to 24 percent who almost always used one. Less than half of the students (38 percent) never used a calculator to take quizzes or tests, while 19 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT New Mexico West Nation r How often do you use a calculator for the Lfollowung tasks? Working problems in class Almost always Never Doing problems at home Almost always Never Taking quizzes or tests Almost always Never Percentage and Proficiency Percentage Percontaip and and Proficiency Proficiency 44 ( 1.2) 53 ( 2.1) 48 ( 15) 248 ( 1.0) 255 ( 2.6) 254 ( 1.5) 27 ( 1.1) 14 ( 2.4) 23 ( 1.9) 288 ( 1.5) 285 ( 3.0) 272 ( 1,4) 24 ( 0.9) 29 ( 1.7) 30 255 ( 1.4) 263 ( 3.3) 281 ( 1.8) 17 ( 0.8) 19 ( 1.8) 19 ( 0.9) 262 ( 2.0) 258 ( 3.7) 263 ( 1.8) 19 ( 0.8) 25 ( 1.6) 27 ( 1,4) 245 ( 1.5) 259 ( 3,9) 253 ( 2,4) 38 ( 1.0) 22 ( 3.0) 30 ( 2.0) 270 ( 1.3) 270 ( 3.3) 274 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. THE 1990 NAEP TRIAL STATE ASSESSMENT 63 New Mexico WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calrulator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defmed a.. "calculator-inactive" items items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of sty '.ents who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in New Mexico wtre in the High group than were in the Other group. About the same percentage of males and females were in the High group. In addition, 51 percent of White students, 42 percent of Hispanic students, and 36 percent of American Indian students were in the High group. TABLE 20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MOO NAEP TRIAL STATE ASSESSMENT New Mexico West Nation "Carculator-use" group Percentage awl Proficiency Percentage and Proficiency Percentage and Proficiency High 45 ( 1.3) 38 ( 2.6) 42 ( 1.3) 263 ( 12) 273 ( 2.7) 272 ( 1.6) Other 55 ( 1.3) 82 ( 2.6) 5. ( 1.3) 250 ( 1.0) 253 ( 2.8) 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 stanthad errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 New Mexico 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 praform routine calculations by hand. Using calculators to replace this time-consuming process would mate more instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 20 percent of the students in New Mexico had teachers who allowed calculators to be used for tests. About the same percentage of students in New Mexico and in the nation had teachers who permitted unrestricted use of calculators (18 percent and 18 percent, respectively). In New Mexico, most students or their families (97 percent) owned calculators; however, fewer students (47 percent) had teachers who explained the usn of calculators to them. In New Mexico, 27 percent of the students never used a calculator to work problems in class, while 44 percent almost always did. Some of the students (17 percent) nevet used a calculator to work problems at home, compared to 24 percent who almost always used one. Less than half of the students (38 percent) never used a calculator to take quizzes or tests, while 19 percent almost always did. 66 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has become an issue of increasing importance to federal, state, and local governments. As part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.' Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In New Mexico, 46 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 (53 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. About three-quarters of the students (71 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathernatics, 1991). 7 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 New Mexico TABLE 21 I Profile of Eighth-Grade Public-School 1 Mathematics Teachers PERCENTAGE OF STUDENTS 19110 MEP TRIAL STATE ASSESSMENT New Mexico West Nation , Percentage of students *tics* mathematics teachers reportsd having the following dogrsos Percentage Percentage Percentage Bachelor's degree 54 ( 1.2) 68 ( 5.2) 56 ( 4.2) Master's or specialist's degree 46 ( 12) 32 ( 5.2) 42 ( 42) Doctorate or professional degree 0 ( 0.0) 0 ( 0.0) 2 ( 1.4) Percentage of students whose mathematics teachers have this following types of teaching certificates that are recognized by New Mexico No regular certification 2 ( 0.4) 6 ( 2.4) 4 ( 1.2) Regular certification but less than the highest available 45 ( 1.1) 20 ( 3,3) 26 ( 4.3) Highest certification available (permanent or long-term) 33 ( 1.2) 74 ( 3.3) 66 ( 4.3) Percontago of students whose mathematics teachers have the fallowing typos of teaching certificates that are recognized by New Mexico Mathematics (middle school or secondary) 71 ( 1.3) 83 ( 3.0) 84 ( 2.2) Education (elementary or middle school) 28 ( 1.3) 9 ( 2.8) 12 ( 2.6) Other 1 ( 0.1) 2 ( 1.3) 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. EDUCATIONAL BACKGROUND Mthough 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. 73 65 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In New Mexico, 34 percent of the eighth-gradepublic-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 New Mexico (15 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and i Graduate Fields of Study PERCENTAGE OF STUDENTS _ . 1900 kAEP TRIAL STATE ASSESSMENT New Mexico West Nation [What was your undergraduate major? 1 Mathematics Education Other 1 What was your graduate major'? Mathematics Education Other or no graduate level study Percentage Parcantage Porcsatage 34 ( 1.4) 31 ( 5.9) 43 ( 3.9) 46 ( 1.3) 34 ( 6.6) 35 ( 3.8) 20 ( 0.8) 35 ( 6.6) 22 ( 3.3) Percentage Percentage Percentage 15 ( 0.9) 19 ( 4.7) 22 ( 3.4) 37 ( 1.4) 36 ( 4.5) 38 ( 3.5) 4$ ( 1.3) 45 ( 5.4) 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 619 New Mexico Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In New Mexico, 19 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. Less than half of the students in New Mexico (36 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, II 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 MO NAEP TRIAL STATE ASSESSMENT Now Mexico West Nation L. During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? None One to 15 hours 18 hours or more Percentage Percentage Percentage 36 ( 1.2) 11 ( 3.0) 11 ( 2.1) 45 ( 1.2) 45 ( 7.0) 51 ( 41) 19( 1.1) 44 ( 6.9) 39 ( 3.8) The standard errors et the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within 2 standard errors of the estimate for the sample. Pitr) 70 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement.' Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences acmss states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In New Mexico, 46 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 (53 percent) had mathematics teachers who had the highest level of teaching certification available. This is dfferent 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 New Mexico, 34 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Some of the eighth-gade public-school studen:s in New Mexico (15 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. '° Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips. A World of Differences. An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). 11 Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State ofMathematics Ach1evement NAEP's 1990 Assessment of the Nation and the Trial Assessment of the States (Princeton, NJ; National Assessment of Educational Progress, Educational Testing Service, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 71 New Mexico In New Mexico, 19 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, 3 9 percent of the students had teachers who spent at least that much time on similar types of in-service training. Less than half of the students in New Mexico (36 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 similor in-service training. 72 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico 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. 7S THE 1990 NAEP TRIAL STATE ASSESSMENT 73 New Mexico 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 on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT New Mexico West Nation Does your family have, or receive on a regular basis, any of the following items: more than 25 books, an encyclopedia, newspapers, magazines? Zito to two types Three types Four types Percentage Percentage Percentage and Ind and Proeldency Pro Odom Pro Wow 28 ( 1.1) 24 ( 1.6) 21 ( 1.0) 243 ( 1.4) 245 ( 4.1) 244 ( 2,0) 31 ( 0.9) 31 ( 1.4) 30 ( 1.0) 256 ( 1.1) 258 ( 2.4) 258 ( 1.7) 40 ( 1.1) 45 ( 1.9) ( 1.3) 286 ( 1.3) 273 ( 3.2) 272 ( 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 data for New Mexico reveal that: Students in New Mexico 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. r) 411 74 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico A smaller percentage of Hispanic and Mnerican Indian students had all four types of these reading materials in their homes than did White students. About the same percentage of students attending schools in advantaged urban areas as in disadvantaged urban areas, extreme rural areas, and areas classified as "other" had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER IAIT Excessive television watching is generally seen as aetracting from time spent on educational pursuits. Students participating in the Thal State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT New Mode* West Nation - _ Parcentaie and Preficiwcy Percentage and Proficiency Percentage and Proficiency How much televrslon do you usually watch each day? One hour or less 14 ( 0.6) 14 ( 1.8) 12 ( 0.8) 261 ( 2.0) 269 ( 3.6) 289 ( 2.2) Two hours 24 ( 1.0) 20 ( 1.6) 21 ( 0.9) 263 ( 11) 265 ( 3.6) 268 ( 1.8) Uwe* haunt 24 ( 0.9) 20 ( 12) 22 ( 0.8) 257 ( 1.3) 262 ( 3.2) 265 ( 1.7) Four to nye hours 27 ( 1.2) 29 ( 1.7) 28 ( 1.1) 252 ( 1.2) 263 ( 2.9) 280 ( 1.7) Six hews or more 11 ( 0.7) 10 ( 2.0) 16 ( 1.0) 243 ( 2.0) 248 ( 2.6) 245 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 8 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 75 Arty Mexico From Table 25 and Table A25 in the Data Appendix: In New Mexico, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Some of the eighth-grade public-school students in New Mexico (14 percent) wattled one hour 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. Similarly, about the same percentage of males and females watched one hour or less per day. In addition, 8 percent of White students, 12 percent of Hispanic students, and 14 percent of American Indian students watched six hours or more of television each day. In comparison, 16 percent of White students, 12 percent of Hispanic students, and 15 percent of American Indian students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix: In New Mexico, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in New Mexico (36 percent) did not miss any school days in the month prior to the assessment, while 27 percent missed three days or more. In addition, 24 percent of White students, 30 percent of Hispanic students, and 32 percent of American Indian students missed three or more days of school. 76 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico Similarly, 18 percent of students attending schools in advantaged urban areas, 30 percent in schools in disadvantaged urban areas, 28 percent in schools in extreme rural areas, and 27 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 i School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO MAEP TRIAL STAT 1.7SSISENT Now Maxim Pimento. and Petecioney 30 ( 1.0) 262 ( 1.0) S7 ( 1.1) 250 ( 14) 27 ( 1.0) 245 ( 1.2) Pow loge Pm* 43 21 200 3.5 30 ( 1A) 255 ( 3.0) 27 ( 1i) 250 ( 3.1) Poreente. and Pallitsoce 45 ( 1.1) 2951 1.3) 32 ( 0.11) ,1205 (.1.5) 23 ( 1.1) 250 ( How many days of school did you miss last month? Ono or two days Uwe' days or mon The standard errors of the estimated stillistia 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 77 MN!" New Mexico STUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not only to master essential skills and concepts but also to develop confidenct 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; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Abnost all people we mathematics in their fobs; 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 proHems. A student "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For earh of the five statements, students who responded "strongly agree" were given a value of 1 (indicating very positive attitudes about the srbject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception index according to whether they tended to strongly agree with the latements (an index of 1), tended to agree with the statements (an index of 2), o: tended to be undecided, to disagrtv, or to strongly disagree with the statements (an index of 3). Table 27 provides the data for the students' attitudes toward mathematics 4*5 defined by their perception index. The following results were observed for New Mexico: Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undeeided, disagree, strongly disagree" category. About one-quarter of the students (26 prcent) were in the "strongly agree" category (perception index of I). This compares to 27 percent across the nation. About one-quarter of the students in New Mexico (23 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). 12 National Council of Teachers of Mathematics, alum and Evaluation Standards for School Mathematics (Reston, VA: National Colincil of Teachers of MathernaUcs, 1989). 7g THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TNIAL STATE ASSESSMENT New Macice Nation Student "perception Index* groups Siren* agree ("perception index" of 1) AW** ("perception Index" of 2) Undecided, Aurae, strongly disagree ("perception index" of 3) IM1!1 Illaramlage Stereseisga aid aml owl arefisimacy Prditimay Pisray 112 27 ( 1.9) 71 248114 273 ( 99) v2 51 ( 1.3) ( 1.5) 49 ( 250 ( 1.1) 202 ( 2.4) 202 ( 23 ( 0.9) 25 ( 2.1) 24 ( 243 ( 1.2) 249 (2.9) 251 ( 11 s.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. 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 New Mexico 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 simibs to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had ero to two types. THE 1990 NAEP TRIAL STATE ASSESSMENT 84 79 New Mexico Some of the eighth-grade public-school students in New Mexico (14 t) watched one hour or less of television each day; 11 percent watched six hours or more. Avenge mathematics proficiency was lowest for students who spent six hours or more watching television each day. Less than half of the students in New Mexico (36 percent) did not miss any school days in the month prior to the assessment, while 27 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. About one-quaner of the students (26 percent) were in the "strongly agree" category relring to students' perceptions of mathematics. Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who wese in the "undecided, disagree, strongly disagree" ategory. 80 THE 1990 NAEP TRIAL STATE ASSESSMENT ;7, New Mexico THE NATION'S REPORT CARO PROCEDV,RAL 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 %cr.- 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 benefitted from the involvemcnt 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 stucent. 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. SC THE 1990 NAEP TRIAL STATE ASSESSMENT 81 New Mexico The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general backgronnd 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 evesy other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets were spiraled or intesleaved in a systematic sequence so that each booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as described in the inttoduction to this report.' The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure A 1). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales a.ce the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on students' performance on the set of mathematics items they received. IRT provides a common sae on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This common scale makes it possible to mood 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 (Princetc.., NJ: Educational Testing Service, 1988). re 82 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico 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 compth mons1 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 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 emprasis on precision and accuracy. 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. Geornetry Thls 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. IData Analysis, Statistics, and Probability This content area focuses on data representation and analysis across all disciplines and reflects the importance and prevalence of these activities in our society. Statistical knowledge and the ability to interpret data are necessary skills in the contemporary world. Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysis. IAlgebra and Functions alMMMI.M.M1 This content area is broad in scope, covering algebraic and functional concopts In more informai, 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 vieweLi not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. THE 1990 NAEP TRIAL STATE ASSESSMENT $3 New Mexico FIGURE A2 I Mathematical Abilities The following three categories of mathematical abilities are not to be construed a. hierarchical. For example, problem solving Invokes interactions between conceptual knowledge and procedural skills, but what is considered coMplex problem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. IConceptual Understanding Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts; can use and interrelate models, diagrams, 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 probicrn-solving sitations. IProcedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to seed and apply appropriate procedures correctly, verify and justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors inherent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have been created as tools to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce graphs and tables, axeCUte geomeeric constructions, and perform noncomputational skills such as rounding and ordering. IProblem Solving In problem solving, students are required to use their reasoning and analy, abilities when they encounter new situations. Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency ot data: use strategies, data, models, and relevant mathematics: generate. extend, and modify procedures: use reasoning (i.e., spatial, inductive, deductive, statistical, and proportional): and judge the reasonableness and correctness of solutions. 84 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico A scale ranging from 0 to 500 was mated to report performance for each content area. Each content-area scale was based oft 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, Ire NAEP scale anchoring is accomplished by describing what students at selected lev:As know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define pciforma e at each of the four levels on the scale, NAEP analyzed sets of mathematics items :lam the 1990 assessment that discriminated well between adjacent levels. The criteria for selecting these "benchmark" items were as follows: To define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To define performance at each of the higher levels on the scale, items were chosen that were: a) answered correctly by at least 65 percent of students whose proficiency was at or near that level; and b) answered incorrectly by a majority (at least 50 percent) of the students performing at or near the next lower level. The percentage of students at a level who answered the item correctly had to be at least 30 points higher than the percentage of students at the next lower level who answered it correctly. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 85 New Mexico 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 pmficiency levels was defined by descrling the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.2 Questionnaires for Teachers and Schools As part of the Trial 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 questionmires focused on six educational areas: curriculuzn, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. hi 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 matkinatical topics, and the 'AC of various instructional approaches. Because of the nature of the sampling for ti e Trial State Assessment, the responses to the mathematics teacher questionnaire not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 86 THE 1990 NAEP TRIAL CTATE ASSESSMENT New Mexico FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 ritab a Teals Cat bib 0 betel Seth 7. Link bed thole leap beam 41 the roe thie eel Wee Merest bete el bah as theme these. KA. fille eeth box with the bad of belle them whig bee have the tenet bate in it? 00 The box loth the UM* bah 0 The bee ma the pal lib 0 The boa with the 'Ohm bats 0 the cool wit EXAMPLE 2 111074511 OF FAIT 110:1D AT FAIIAWAT ?Ana Mis 1Wal athi Ulm Daps OM Wet *ma !Amor Chopobsii t. How ow bathe 01 omen wen peeked cm Thunder, CP 55 0 60 0 70 0 10 0 90 0 1 deet bow. Grade 4 Overall Percentage Correct 73% Peroentage Correct for Anchor Levels: 292 244 214 as 91 100 Grade 4 Overall Percentage Percntage Correct 292 214 75 91 Grade 8 Overall Percentage Percentage Correct Correct for Anchor Levels: 2i12 Correct: 89% for Anchor Levels: 242 214 244 224 78 87 96 100 ILevel 250: Simple Multiplicative Reasoning and Two-Stop Problem Solving 1 New Mexico FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) EXAMPLE 1 T. What is the value of a + 5 when a 3 Answer EXAMPLE 2 NAM COLON SLUM 112SULTS Grade 8 Conrail Percentage Percentage Coned 222 212 28 69 Correct: 76% for Anchor Levels: 202 95 98 14* renomeg Grade 8 Overall Percentage Percentage Correct CiOffKlt 73% for Anchor Levels: Shell Wes% Pak 10 Task The Oa* *bow shows dal main of army allots cake. On At &de Wawa mkt * cirdaspb tit ikons* dm dosil J*141014. LAW 1*h pan ol the Was de soma Ws mks. rid von use ese calCsAuse Ia1 lib ftwalic** 0 Vs ON. EXAMPLE 3 6. Koalas is what; baseballs into bola. Each box hail 6 baseballs. She hos 24 talk. Whicb number Macaw will blip ha Iird oda how Amy box* she win wadi OP 24 - 6 - 4 + 6 0 CD 24 +6 O (V 24 le 6 OD I don't know. ZC12 21 68 M2 252 92 92 Grade 8 Overall Percentage Percentage Correct Zflg ZS/ 37 71 Correct: 77% for Anchor Levels: 222 95 100 THE 1990 NAN' TRIAL STATE ASSESSMENT 'Or New Mexico FIGURE A3 f Example Items for Mathematics Proficiency Levels (continued) Level 300: Reasoning and Problem Solving involving Fractions, Dec Image, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE 1 WIWI of doe fo1i****4 Aare the nage at Rapt* do *gm* awes ova she Lae it EXAMPLE 2 la Ike need soma *it s dile a ea If as bag a apasalaid Inf Jule sage) 3 lacha }ay. II dm saw ea& * we. a Immo 33 Oa keg wage etptssamad ky Kale saki bong assy Ada high? CD V wee she eatuaksa pe aka gveseisa! YIN CT No Grade 8 Overall PeleVelen$01/ Correct 80% Percentege Correct for Anchor Levels: Ell CR 33 49 77 90 Grade 12 Overall Percentage Correct 75% Percentage Correct for Mchor Levels: 241/ 21211 46 79 95 Grade 8 Overall Percentage Correct 59% Percentage Correct for Anchor Levels: 322 Zig SI2 17 48 ee 99 BEST COPY AVAILABLE New Maim FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Lintel 350: Reasoning and Problem Solving involving Geometric Relationships Algebraic Equational and Boi tinning Statistics and Probability EXAMPLE 1 Q*attior 16- IT Mot to thsiolitypott ousts of douf loom. e a e a e 4. I 1 2 I. III Wu rigl. el dot-11.aws w unft w gied. how ay dots k ;be 01100 02 101 199 011100 45101 EXAMPLE 2 IT. ILsoloia kow yew latod your soma to questios 16. Grade 5 Overall Percentage Correct 34% Percentage Correct for Anchor Levels: 222 202 222 2fa 13 19 53 85 Grade 12 Overall Percentage Correct: 49% Percentage Correct for Anchor Levels: 2212 n2 202 212 22 45 90 Grade Overall Percentage Correct 15% PlIfeentiae Correct for Mawr Levels: CO 2/2 224 122 1 4 25 74 Grade 12 Overall Percentage Correct 27% Percentage Wrect for Anchor Lows: 222 2/2 alTa 3 22 74 90 ME 1990 NAEP TRIAL STATE ASSESSMENT New Mexico SCHOOL CHARACTERISTICS AND POUCIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administsalors in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with 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 territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAEP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like almost all estimates based on assessment measures, NA.SP's total group and subgroup proficiency estimates arc subject to a second source of uncenainty, in addition to sampling error. As previously noted, each student who participated ir. 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 eztimates of total group and subgroup proficiency might have been obtained. Thus, a second source of uncertainty arises because es-ich student was administered a subset of the total pool of questions. 9 THE 3990 NAEP TRIAL STATE ASSESSMENT 91 New Mexico 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 meaStires of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a background question in a certain way or the proportion of students in certain racial/ethnic groups) reflect only sampling error. NAEP uses a methodology called the jackknife procedure to estimate these standard errors. Drawing Inferences from the Results One of the goals of the Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inkrences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the popu; lion means and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 * 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar conEdence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. C. s.. 92 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defined by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As sn example, one might be interested in answering the question: Do students who reported spending 45 minutes or more doirg mathematics homework each day exhibit higher average mathematics proficiency than students who reported spendirkg IS 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 poup does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in performance between the two groups in the population because of the uncertainty associated with the estimated average proficiency of the groups in the sample. Remember that the intent is to incie a statement about the entire population, not about the particular sample that was assegai. The data from the sample are used to make inferences about the population as a whole. As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent set of questions, the performances of various groups would have been different. Thus, to determine whether there is a 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 erk-or 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 hell, determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups ± 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between groups in the population. If the interval does not contain zero, the difference between groups is statistkally significant (different) at the .05 level. S THE 1990 NAEP TRIAL STATE ASSESSMENT 93 New Mexico As an example, suppose that one were interested in determining whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard errors for females and males were as follows: Group Average Protickoney Standard Error Female 259 2.0 Male , i 255 2.1 The difference netween the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard eiror of this difference is + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., 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.3 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 mapitude 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 etandard error of the difference) is, in a strict sense, only appropriate when the Stang= being compared come from independent samples. For certain comparisons in the report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico The procedutes 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 confidence intervals are being analyzed). When one considers sets of confidence intervals, statistical theory indicates that the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. If one wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure -- the Bonferroni method was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the, previous pages. A more detailed 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 deg.= of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol 1". 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. NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or tenitories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and/or background variable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probabilit: of .8 or greater. 10 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 New Mexico The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or territory, divided by the standard deviation of the proficiency in the total population. If the true difference between subgroup and total group mean is .2 total-group standard deviation units, then a sample ize 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 percuitages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage [Ascription of Text in Report p = 0 None 0 < p 10 Relatively few 10 < p 20 Some 20 < p lc 30 About one-quarter 30 < p ...s. 44 Less than half 44 < p 55 About half 55 < p 5. 69 More than half 69 < p 5. 79 About three-quarters 79 < p S 89 Many 89 < p < 100 Almost all p = 100 All , 191 96 THE 1990 NAEP TRIAL STATE ASSESSMENT NE NATION'S REPORT CARO DATA APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains corresponding data for each level of the four reporting subpopulations -- race/ethnicity, type of community, parents' education level, and gender. 102 THE 1990 NAEP TRIAL STATE ASSESSMENT 97 New Mexico TABLE A5 I Students' Reports OD the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MD NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pre-algebra Algebra TOTAL Parowesp and Pro edam Peroadap awl Preideivw State 62 1.2) 1.1) 247 02) 205 1.5) Nation 62 2.1) 19 1.9) 251 ( 1.4) 272 f 2.4) RACE/ETHNICITY White State 55 ( 2.1) 26 ( 1.8) 262 ( 1.0) 277 ( 2.2) Nation 59 ( 2.5) 21 ( 2.4) 252 ( 1.6) 277 ( 22) Hispanic State 86 ( 1.7) 22 ( 1.4) 240 ( 1.0) 254 ( 1.8) Nation 75 ( 4.4) 13 ( 34) 240 ( 2.4) American Wien State 71 ( 3.2) 20 ( 2.8) 230 ( 1.8) 25$ ( 4.0) Nation 64 ( ( 5.7) ( 72) ..**) TYPE OF COMMUNITY Advantaged urban State 86 f 8.4) 17 ( 3.5) 1144 ***) Nation 55 ( 9.4) 269 ( 2.5)1 Disadvantaged urban State 54 ( 5.0) 247 ( 3.0) Nation 65 ( 6.0) 16 ( 4.1) 240 ( 4.0)t Extreme nral State 54 ( 4.0) 33 ( 4.2) 241 ( 2.6) 285 ( 2.0) Nation 74 ( 4.5) 249 ( 3.1)1 Other State 64 ( 1.1) 20 ( 0.9) 248 ( 0.8) 263 ( 22) Nation 81 ( 2.2) 20 ( 2.1) 251 ( 2.0) 272 ( 2.8) Pareentage and Pndlolenqf 11 0 208 1.111 15 1.2 200 2.4) 14 ( 1.1) 296 ( 2.3) 17 ( 1.5) 300 ( 2.3) ( 1.0) 277 ( 2 4) ( 1.5) Se* ( erg) 4 ( 0.9) 5 ( 2.7) .4* ( 1.7) 1111-* 14 ( 3.3) 287 ( 4.2)1 IN* 7 ( 2.2) ( 12 ( 0.5) 289 ( 2.1) 18 ( 1.4) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 98 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE AS I Students' Reports on the Mathematics Class (continued) i They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19610 NAEP TRIAL STATE ASSESSMENT EIghth-grade Mathematics Pm-algebra Algebra TOTAL and Madam 02 ( 1.2) and Proficiency 23 ( 1.1) PerCitgaill and Proficiency 11 ( 0.6) state 247 ( 205 ( 1.5) 288 ( 1.9) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 296 ( 2.4) PARENTS' EDUCATION NS non-graduate State 70 ( 3.1) 21 ( 3.1) 6( 1.1) 235 ( 1.5) 254 ( 3.4) ( 11111 Nation 77 ( 241 ( 3.7) 2.1) 13 .44 (( 3.4) 3 (* 1.1) ..**) N3 gracile. State 09 ( 241 ( 2.0) 1.3) 21 256 ( 2.2) ( 3.2) 6 ( 0.9) Nation 70 ( 2.6) 18 ( 2.t) 8 ( 1.1) 249 ( 1.9) 266( 3.5) 277 ( 5.2) Some college State 55 ( 3.0) 27 ( 2.9) 13 ( 1.9) 253 ( 1.7) 268 ( 2.1) Nation 60 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 27$ ( 2.8) 295 ( 32) College vaduate State 54 24 ( 14) 16 ( 1.3) 261 1.4) 276 ( 2.3) 299 ( 2.3) Nation t 2.7) 21 ( 2.3) 24 ( 1.7) 25 ( 1.5) 27$ ( 2.8) 303 ( 2.3) GENDER MI* State 65 ( 1.6) 21 ( 1.6) 10 ( 0.8) 250 ( 12) 270 ( 2.2) 295 2.9) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 2.5) Female State 58 ( 1.7) 24 ( 1.8) 12 ( 0.8) 243 ( 1.0) 261 ( 2.1) 282 ( 2.5) Nation 61 ( 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. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 New Mexico TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 15 Mint utes 30 Minues 45 Mi meos An Hour or Mors TOTAL Percentage and Proficiency 3 ( 0.5) 240 ( 3.5) ( .41 2 ( 0.4) 1 ( 0.3) ( 0.6) ir* 7 ( 2.5) ee. .**) 0 ( 0.0) 44,4) 0 ( 0.0) *** ( "4) 1 ( 0.9) ( 13 ( '2.1) *** ( ***) 0 ( 0.0) 6 ( 0.9) ( 0 ( 0.0) .** ( **.) 2 ( 0.6) .44(444) ( 0.4) *** ( Percentage and Proficiency 33 ( 1.1) 255 ( 1.0) 43 ( 4.2) 258 ( 2.3) 34 ( 1.7) 267 ( 1.4) 39 ( 4.5) 266 ( 22) 33 ( 1.6) 247 ( 1.7) 46 ( 7.8) 245 ( 3.0)1 26 ( 3.3) 239 ( 2.9) 74 (31.9) ..**) 29 ( 5.9) 61 (11.3) 273 ( 3.1)1 26 ( 5.4) 41 (12.6) 236 ( 2.1 17 ( 3.0) 246 ( 3.4) 68 (14.9) 253 ( 5.4)1 38 ( 1.3) 253 ( 1.2) 37 ( 4.3) 256 ( 3.1) Percentage and Proficiency 44 ( 1.5) 253( 1.1) 43 ( 4.3) 288 ( 2.8) 42 ( 2.1) 270 ( 1.5) 4,5 ( 5.1) 270 ( 2.7) 44 ( 1.8) 245 ( 1.3) 34 ( 8.8) 251 ( 4.2)1 55 ( 3.4) 233 ( 2.3) 22 (282) 44* ( ) 47 ( 9.5) *** ( ***) 35 ( 4.2) ( 4.1 38 ( 9.4) 253 ( 9.0)1 48 ( 5.4) 251 ( 2.4) 14 (10.9) ( *I") 44 ( 1.4) 250 ( 1.2) 49 ( 5.1) 265 ( 2.5) Percentage and Proficiency 12 ( 1.0) 208 ( 24) 10 ( 1.9) 272 ( 5.7)1 14 ( 1.5) 288 ( 3.2) 11 ( 2.4) 277 ( 7.8)1 13 ( 1.7) 253 ( 2.8) 13 ( 2.9) *4. ( 1 4 ( .7) ( *dm) 0 ( 0.0) vim) 21 ( 5.6) 8 ( 2.3) .1.111 12 ( 5.9) *el 19 ( 4.2) 255 ( 5.2)1 8 ( 5.6) 10 ( 0.8) 272 ( 3.3) 10 ( 2,4) 278 ( 8.8)1 Percentage and Proficiency 7 0.8) 273 2.8) 4 ( 0.9) 378 ( 5.1)1 9 ( 1.7) 290 ( 5.6)1 4 ( 0.9) 279 ( 5.8)1 ( 0.8) 7 ( 2.1) 41 6 ( 1.3) 4 ( 4.6) wh.) 3 ( 3.3) 44..) 0 ( 0.0) 18 ( 3.6) ( 10 ( 6.2) 10 ( 3.9) «4. ( 10 ( 7.3) 4.4,1 6 ( 0.5) 276 ( 4.0) 4 ( 1.1) 282 (11 .0)! State Nation RACE/ETHNICITY Mite State Nation Hispanic State Nation Arnadcan hictian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extrome rural State Nation Other State Nation The standard errors of the estimated statistacs appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the tntire 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), 100 THE 1990 NAEP TRIAL STATE ASSESSMENT 'New Mexico TABLE A6 Teachers' Reports on the Amount of Time (continued) Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT None 15 Mintdes 30 Minutes 45 &amass An Nour or More TOTAl. Poroontage and Praciency 3 ( 0.5) 240 ( 15) 1 ( 0.3) ( *el 3 ( 0.8) 1 ( 0.8) ( 0.7) ime.) ( 0.5) ( .41 3 ( 1.1) qt4re ( 1 ( 02) ( 1 ( 0.8) 0 ( 0.3) ( "") 3 ( 0.5) ( ( 0.3) ( ***) 4 ( 0.5) 1 ( 0.4) Poonowdaita and Madam 33 ( 1.1) 255 ( 1.0) 43 ( 4.2) 256 ( 2.3) 35 ( 3.3) 242 ( 2.9) 49 ( 8.3) 240 ( 24) 30 ( 22) 247 ( 22) 43 ( 52) 249 ( 3.1) 33 ( 2.4) 250 ( 1.8) 44 ( 5.4) 285 ( 2.8) 34 ( 1.8) 288 ( 1.8) 40 ( 4.7) 285 ( 2.5) 35 ( 1.8) 259 ( 1.8) 44 ( 4.4) 257 ( 2.9) 31 ( 1.8) 250 ( 1.5) 41 ( 4.4) 255 ( 2.3) Poem lage and Pie Mona 44 ( 14) 253 ( 1.1) 43 ( 4.3) 205 ( 2.0) 43 ( 3.6) 237 ( 2.0) 40 ( 8.1) 248 ( 3.7) 48 ( 2.4) 24$ ( 1.5) 44 ( 5.8) 2$8 ( 2.7) 43 ( 3.2) 281 ( 2.4) 43 ( 5.8) 270 ( 3.8) 42 ( 2.2) 288 ( 2.1) 44 ( 4.1) 277 ( 3.0) 45 ( 2.3) 258 ( 2.0) 43 ( 42) 268 ( 2.9) 44 ( A) 250 ( 1.3) 43 ( 4.7) 284 ( 2.6) Lege and Pro Odom 12 ( 1.0) 206 (2.e) 10 ( 1.9) 272 ( 5.7)1 13( 3.3) 1.7) .4,1 11 ( 1.4) 257 ( 3.5) 0 ( 3.1) 14 ( 2.0) 271 ( 4.2) 7 ( 2.1) 44* ( *In 13 ( 1.2) 288 ( 3.9) 11 ( 2.3) 287 ( 8.1)1 12 ( 1.1) 270 ( 34) 9 ( 1,9) 273 ( 7.3)1 13 ( 1.3) 287 ( 3.7) 11 ( 2.0) 272 ( 5.7)1 PIM WAlle and Pm/ding 7 0A 273 2.01 4 0.9 230 5 ( 1.5) I** 4 0 ( 1.1) - 3 1 .0) ( **111 7 ( 1.8) ( wen 4 ( 1.0) ( 9 ( 1.3) ( 5 ( 1.3) ( ( 1.4) 276 ( 4.111)1 5 ( 1.3) 279 ( 7.7)1 8 ( 1.3) 289 ( 4.7) 4 ( 0.9) State Nation PARENTS EDUCATIO4 HS non-graduate State Nation NS graduat State Nation Some college State Nation coftge graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statisti:A 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 estiriiated mtan proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 (I 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 101 New Mexico TABLE A7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 15 Minutes A 32 Minutes 45 Minutes An NOUr or Mare TOTAL 11410101118 and Preecientgi Pertiettage and Prodigality Percentage mid Proficiency Percentage and Proficiency Percentage and kaiak/my State 9 ( 0.8) 28 ( 1.1) 29 ( 1.0) 18 ( 0.9) 16 ( 0.9) 259 ( 2.7) 2$7 ( 1.3) 255 ( 12) 257 ( 1.7) 255 ( 2.1) Nation 0 ( 0.8) 31 ( 2.0) 32 ( 12) 16 ( 1.0) 12 ( 1.1) 251 ( 2.6) 264 ( 1.9) 263 ( 1.9) 266 ( 1.9) 250 ( 3.1) RUE/ETHNICITY MOW State 12 ( 1.1) 27 ( 1.5) 27 ( 1.5) 17 ( 1.1) 18 ( 1.4) 274 ( 3.8) 273 ( 2.3) 270 ( 1.8) 273 ( 2.4) 270 ( 3.2) Nation 10 ( 1.0) 33 ( 2.4) 32 ( 1.3) 15 ( 0.9) 11 ( 13) 258 ( 3.4) 270 ( 1.9) 270 ( 2.1) 277 ( 2.2) 288 ( 3.3) Hispanic State 8 ( 0.9) 23 ( 1.4) 30 ( 1.7) 18 ( 12) 18 ( 1.5) 243 ( 3.5) 247 ( 1.7) 246 ( 1.13) 249 ( 2.2) 246 ( 2.5) Nation 12 ( 1.8) 27 ( 248 ( 3.0) 3.6) 30 ( 248 ( 2.8) 3.4) 17 ( 241 ( 2.1) 4.3) 14 (. 1.7) American WW1 State 8 ( 1.9) ( «he) 20 ( 238 ( 1.8) 3.3) 29 ( 240 ( 2.9) 4,3) 24 ( 237 ( 22) 3.3) 20 ( 235 ( 2.1) 2.7) Nation 13 ( 5.3) 0.**) 30 (10.0) 27 ( **4 6.7)) 24 (14.2) 6 ( 6.4) TYPE Of COMMUNITY Advantaged urban State 10 ( ( 3.7) ***) 27 ( 2.4).) 27 ( 44. 1.0) 18 ( 4.9) 4.) 18 ( 4.9) Nation 8 ( 2.5) 41 (12.5) 31 ( 6.6) 12 ( 3.3) 7 ( 3.4) *** ( 275 ( 3.0)1 280 ( 4.8)1 Disadirantaged State 6 ( ( 2.0) ***) 32 ( ( 5.6) *to ) 33 ( 5.9) ***) 12 ( 2.1) 41+11 ) 17 ( 2.5) Nation 12 ( 3.7) 24 ( 3.3) 31 ( 3.0) 20 ( 1.9) 14 2.2) ( 253 ( 4.9)1 247 ( 4.7)1 250 ( 48)1 Extreme rtwal State 11 ( 1.6) 22 ( 1.8) 20 ( 2.4) 21 ( 1.7) 17 ( 1.9) ( "") 254 ( 2.3) 25$ ( 2.8) 252 ( 4.9) 246 ( 2.4) Nation 8 ( 2.3) ( t") 38 ( 200 ( 4.6) 3.5)1 31 ( 255 ( 2.9) 5.1)1 id ( 38) *44 ( 2.7) Other State 0 ( 0.7) 26 ( 1.4) 28 ( 1.2) 16 ( 1.1) 10( 1.1) 25$ ( 2.8) 255 ( 1.5) 254 ( 1.4) 258 ( 1.7) 255 ( 2.5) Nation 9 ( 1.0) 30 ( 18) 32 ( 1.3) 15 ( 1.1) 13( 1.1) 250 ( 3.9) 263 ( 2.3) 264 ( 2.3) 247 ( 2.1) 258 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of' interest, the value for the entire population is within ± 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. **0 Sample size is insufEcient to permit a reliable estimate (fewer than 62 students). 1 102 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A7 I Students' Reports on the Amount of Time They ("inued) Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT 15 Mintage 30 Minutes 45 Minutes An Heir or More TOTAL Psrolsols. and *Wiwi Parcentage and Proficiency Parssalsos and Preaciency Pirosolags and Prodiciency PerOiNtsge and ProSsIancy State 9 ( 0.6) 26 ( 1.1) 29 ( 1.0) 1$ ( 0.9) 18 ( 0.0) 259 ( 2.7) 257 i 1.3) 255 ( 1.2) 257 ( 1.7) 255 ( 2.1) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 16 ( 1.0) 12 ( 1.1) 251 ( 2.8) 284 ( 1.9) 2e3 ( 1.9) 246 ( 1.9) 258 ( 3.1) PARENTS EDUCATION noniraduate State 10 ( .44 2.3) 41 25 ( 238 ( 2.8) 32) 28 ( 241 ( 3.3) 3.2) 19 ( 3.1) 18 ( 240 ( 2.8) 3.9) Natton 17 ( se* 3.0) 26 ( 248 ( 32) 4.0) 34 ( 240 ( 4.4) 2.8) Ihht ( 4111 10 ( vim ( 22) 11 NS graduate State 10 ( 1.1) 27 ( 1.8) 30 ( 1.9) 17 ( 1.5) 18 ( 1.8) 250 ( 4.0) 247 ( 2.5) 248 ( 2.0) 250 ( 3.0) 243 ( 3.3) Nation 10 ( 1.7) 33 ( 2.2) 31 ( 1.9) 18 ( 1.4) 11 ( 1,5) 240 ( 42) 250 ( 32) 254 ( 2.4) 2$8 ( 2.8) 244 ( 3,4) Same coNego State 10 ( 1.3) 23 ( 22) 30 ( 2$) 18 ( 1.8) 21 ( 2.5) 261 ( 3.1) 261 ( 2.1) 285 ( 32) 258 ( 3.3) Nation ( 12) 30 ( 2.7) 38 ( 2.1) 14 ( 1.8) 11 ( 1,5) ( 4+1 200 ( 3.0) 268 ( 2.8) 274 ( 3$) College graduate State ( 1.1) 25 ( 1.5) 27 ( 1.5) 18 ( 1.4) 1 a ( 1.6) 273 ( 5.9) 275 ( 2.5) 269 ( 22) 271 ( 3.3) 272 ( 3.3) Nation ( 0,9) 31 ( 3.4) 31 ( 2.0) 1$ ( 12) 14 ( 1,9) 265 ( 3.8) 275 ( 2.0) 275 ( 2$) 27$ ( 32) 271 ( 2.8) GENDER Mate State 10 ( 0.8) 29 ( 1,4) 29 ( 1.4) 17 ( 1.0) 18 ( 0.9) 281 ( 3$) 282 ( 1.9) 260 ( 1.8) 257 ( 2.3) 255 ( 1,9) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 286 ( 2.4) 26.5 ( 3.0) 258 ( 4,1) 7smate State 9 ( 0.9) 23 ( 1.7) 29 ( 1.5) 20 ( 1.3) 20 ( 1.5) 256 ( 4.2) 251 ( 2.1) 251 ( 1.3) 257 ( 2 1) 255 ( 3.4) Nation ( 0.9) 2$ ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 248 ( 4.1) 283 ( 1$) 280 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). ns ME 1990 NAEP TRIAL STATE ASSESSMENT 103 New Mexico TABLE A8 I Teachers' Reports on the Emphasis Given To 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE AS3ESSMENT Numbers and Operations Meastrement Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Pomo MP and Pre Odom, 54 ( 254 ( 1.0 49 ( 3.8 200 ( 1.8) 49 ( 2.1) 208 ( 1.4) 48 ( 3.7) 207 ( 2.2) se ( 247 ( 1.2) 47 ( 8.7) 248 ( 4.8) 53 ( 3.4) 235 ( 2.7) 84 (184) ***) 50 (10.6) 111 28 (13.0) ( 43 ( 4.7) Mr* ( 4441 48 (12.1) 255 ( 8.3)1 82 ( 33) 253 ( 2.1) 53 (12.4) 257 ( 7.1)1 54 ( 1.2) 252 ( 1.1) 52 ( 4.1) 200 ( 2.3) Percentage Percentage Percentage and and and Pradenty MI Idiocy !Moloney 0.7) 230 3.2) 245 3.1 200 15 2.1) 17 3.0 33 287 ( 3.4) 250 ( 5.5) 072 18 ( 1.1) 13 ( 1.4) 39 285 ( 52) 260 ( 4.3) 277 ( 16 ( 2.4) 14 ( 34) 90 239 ( 3.5) 259 ( 6.9)1 277 ( ( 1.1) is ( 1.9) 270 ( 4.7) 238 ( 4.4) 243 5 ( 2.2) 23 ( 4.1) 94 *** ( ***) *** ( ***) 255 ( 4 ( 1.9) 20 ( 3.2) 17 ( ( "4) *** ( ***) '1** 8 ( 0.9) 7 ( 8.7) 13 ( 44) 22 ( 8.4) 11 ( 8.4) 39 (12.7) .. 16 ( 4.2) 9 ( 7.0) 40 ( **) 9 ( 2.8) 50 ( ( 4.0) 39 (10.3) 21 ( .4* ( 238 ( 8.4)1 ( 11 ( 1.8) 28 ( 3.4) 24 ( 4.01 240 ( 3.1) 263 ( ( 3.6) 6 ( 4.9) 32 (11.7) **a ( ( pi.) 205 ( 12 ( 0.0) 15 ( 1.1) 33 ( 281 ( 3.9) 243 ( 3.5) 258 ( 18 ( 2.7) 16 ( 3.9) 34 ( 280 ( 3.0) 253 ( 7.1)1 270 ( Paventage and Pro Gamy 1.1) 1.7 256 P.0) 4.0 2e 33) 4.0 200 ( 3.2) ( 22) 22 ( 2.1) 2.8) 271 ( 24) ( 4.7) 27 ( 44) 4.3) 205 ( 3.3) ( ten 28 ( 1.7) ( 2.6) 247 ( 2.6) ( 5.8) 27 ( 6.8) 44)1 ( ***) 2.5) 21 ( 3.3) ( "11 247 ( 5.0) (15.5) 18 (49.7) elm) «fr. 39(115) 8S) 38 ( 9.4) imp.) 287 ( 4.9)1 8.4) 20 ( 3.8) ...) 6.5) 33 (11.8) 248 ( 6.2)1 3.8) 33 ( 3.9) 3.7) 253 ( 2.0) 9 ( 6.1) 9.1 )1 1.3) 22 ( 1.1) 2.0) 252 ( 2.3) 5.3) 2$ ( 4.6) 4.5) 200 ( 3.9) Parcentep Xid Pre Odom 33 ( 13) 258 ( 4.3) 21 ( 33) 264 ( 5.4) 35 ( 2.4) 289 ( 1.7) 22 ( 3.4) 273 ( 5.8) 32 (115) 249 ( 2.0) 10 ( 5.5) ( ***) 22 ( 2.21 249 ( 4.1) 8 (10.4) *4. ( 26 ( 9.8) IHMOr 11111 13 ( 3.2) 46 ( 4.6) 1111M 18 ( 7.8) ( 33 ( 4.4) 261 ( 2.8) 16 ( 7.8) 32 ( 1.1) 257 ( 1.8) 24 ( 4.3) ( 5.7) State Nation RACE/ETHNICITY Wilts State Nation Mew* State Nation Marken Indian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Cludvimlaged urtan State Nation Samna rural State Nation Other State Nation The aanclard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included, 1 Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A8 I Teachers' Reports on the Emphasis Given to (contimled) i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSW NT Numbers and Oporations Uaitrsmsnt Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Pententsge and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage end Proficiency Percentage and PooSciency Percentage and Proficiency State 54 ( 1.2) 12 ( 0.7) 18 ( 1.1) 33 ( 1.5) 25 ( 1.1) 33 ( 1.3) 254 ( 1.0) 280 ( 3.2) 245 ( 3.1) 260 ( 1.7) 256 ( 2.0) 258 ( 1.3) Nation 49 ( 3.8) 15 ( 2.1) 17 ( 3.0) 33 ( 4.0) 28 ( 3.8) 21 ( 3.3) 2e0 ( Lb) 287 ( 3.4) 250 ( 5.6) 272 ( 4.0) 260 ( 3.7) 264 ( 5.4) PARENTS EDUCATIOR NS nonipadoat State 58 ( 3.1) 4 ( 1.8) 21 ( 2.9) 27 ( 3.5) 25 ( 3.9) 29 ( 2.8) 243 ( 2.4) 229 ( 5.7) 238 ( 5.0) 240 ( 4.5) 243 ( 3.1) Nation 00 ( 251 ( 0.9) 3.4) ( .") 25 ( 44 5.3) M ) 4.111* 1141 20 ( 6.7) ( *el NS graduate State 80 ( 247 ( 2.0) 1.9) 9 ( *** ( 1.3) ***) 1S ( 241 ( 1.7) 5.5) 34 ( 250 ( 2.4) 2.8) 24 ( 248 ( 1.8) 2.7) 33 ( 2.2) 252 ( 2.2) Nation 55 ( 4.8) 11 ( 2.8) 17 ( 3.9) 27 ( 5.0) 27 ( 4.5) 24 ( 5.1) 259 ( 2.9) 251 ( 6.1)1 253( 4.7)1 255 ( 4.2) 248 ( 4.8)1 Sesm college State 53 ( 2.6) 13 ( 2.1) 19 ( 2.5) 29 ( 2.9) 22 ( 2.2) 29 ( 2.8) 263 ( 2.1) 248 ( 4.4) 264 ( 3.9) 259 ( 3.9) 261 ( 2.8) Nation 47 ( 265 ( 4.4) 2.8) 17 ( 284 ( 3.3) 4.1)1 et* 39 ( 279 ( 5.5) 4.5) 27 ( 262 ( 5.0) 4.8)1 23 ( 270 ( 4.1) 4.7) College graduate State 48 ( 267 ( 1.9) 2.3) 18 ( 23 ( 1.7) 3.3) 12 ( 268 ( 1.5) 7.2) 37 ( 278 ( 2.2) 2.8) 26 ( 268 ( 1.9) 3.3) 33 ( 272 ( 2.1) 1.9) Nation 44 ( 4.1) 10 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 269 ( 2.8) 298 ( 3.4) 284 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 8.4) GENDER Maio State 54( 1.8) 12 ( 1.1) 17 ( 1.3) 32 ( 22) 24 ( 1.4) 32 ( 2.0) 258 ( 1.6) 282 ( 42) 251 ( 3.4) 289 ( '32) 260 ( 2.6) 260 ( 2.1) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 281 ( 2.5) 287 ( 4.4) 258 ( 81) 275 ( 4.8) 263 / 3.8) 286 ( 8.8) Female State 53 ( 1.7) 12 ( 1.1) 18 ( 1.5) 34 ( 1.6) 25 ( 1.7) 33 ( 1.6) 253 ( 1.5) 277 ( 5.3) 238 ( 3.7) 251 ( 2.7) 252 ( 2.7) 258 ( 2.0) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 280 ( 2.0) 286 ( 3.3) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 283 ( 5.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurst: determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 I THE 1990 NAEP TRIAL STATE ASSESSMENT 105 New Mexico TABLE A8 I Teachers' Reports on the Emphasis Given To ("mlinued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra and Functions Hea,....y Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Peroartage and Proficiency Percontego and Prendency Percentage and Prefidanc$ Pertoniapr and Peedideacy State 14 ( 0.9) SO ( 1.3) 53 ( 15 ( 1.0) 255 ( 3.3) 249 ( 13) 207 ( 1.4 230 1.8) Nation 14 ( 2.2) 53 ( 4.4) 48(3.5 20 3.0) 200 ( 4.3) 261 ( 2-9) 275 ( 2.5) 243 ( 3.0) RACE/ETHNICITY Whits' State 12 ( 1.1) 55 ( 1.7) 80 ( 2.0) 11 ( 1.1) 277 ( 5.2) 271 ( 1.5) 281 ( 2.0) 24$ ( 3.1) Nation 14 ( 2.4) 53 ( 5.0) 48 ( 4.2) 1$ ( 2.8) 278 ( 4.1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) Hispanic State 15 ( 1.4) 57 ( 2.0) 51 ( 1.0) 17 ( 14) 245 ( 3.2) 239 ( 1.7) 257 ( 1.8) 235 ( 24) Nation 15 ( ( 4.1) ...) 58 248 ( 6.3) ( 4.4) 46 ( 257 ( 5.9) 4.0)1 18 ( 4.2) ( 061 Amorican Indian State 13 ( 2.4) sa ( 3.8) 37 ( 3,4) 23 ( 2.3) 222 ( 3.0) 245 ( 3.5) 222 ( 2.5) Nation 3 ( ( 42) ...) 82 (29.1) ( ...) 16 (21.5) ( .4.) 67 (51.6) D. ( .4.) TYPE OF COMMUNITY Advantaged urban State ( ...) ( 2 ( 1.7) **4 ( ***) Nation 11 ( 6.6) 65 (19.4) 41 ( 8.9) 18 ( 5.3) *** e") 284 ( 7.4)1 296 ( 7.9)1 ( Disadvantaged urtan State 80 ( 4.8) 06 ( 5.9) 12 ( 0.4) 247 ( 3.1) 208 ( 4.1) Nation 19 ( !MO ( 9.4) IN) 34 236 (11.4) ( 8.2)1 53 (11.8) 254 ( 6.3)1 209.4) .4. ( 4..) Erdrorna rural State 13 ( 2.7) 50 ( 2.7) 48 ( 3.0) 18 2.9) 251 ( 7.4) 248 ( 4.3) 265 ( 2.4) 229 ( 2.7) Nation 5 ( .44 ( 5.4) *..) 85 254 (18.9) ( 6.7)1 33 (( 8.1) 4 ) 42 (16.0) 241 ( 5.9)1 Othor State 15 ( 1.0) 55 ( 1.0) 53 ( 1.4) 18 ( 1.3) 252 ( 3.8) 248 ( 1.8) 265 ( 1.5) 221 ( 1.13) Nation 15 ( 2,9) 53 ( 52) 47 ( 4.3) 17 ( 3.3) 267 ( 4.7) 200 ( 3.4) 276 ( 2.8) 245 ( 4.4)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because i "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 New Mexico TABLE AS I Teachers' Reports on the Emphasis Given To ("mitinued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Analysis, Statistics, and Probability .. Algebra and Rinctione Heavy Emphasis Little or No Emphasis Heay v Emphasis I Little or No Emphasis TOTAL Percentage and Pro Selena Percentage and Proficiency Perowitage and Proficiency Percentage and Proticiency State 14 ( 0.9) 56 ( 1.3) 53 ( 12) 15 ( 1.0) 256 ( 3.3) 249 ( 1.3) 267 ( 1.4) 230 ( 1.8) Nation 14 ( 2.2) 53 ( 4.4) 48 ( 3.6) 20 ( 3.0) 201 ( 4.3) 241 ( 2.9) 275 ( 2.5) 243 ( 3.0) PARENTS EDUCATION HS non-graduate State 14 ( 2.3) 59 ( 228 ( 3.5) 3.5) 46 ( 253 ( 3.5) 3.2) 23 ( era. 3.4) Nation 9 ( 444. 3.0) 53 ( 240 ( 7.7) 8.2) 25 ( 5.2) ..**) 29 ( 6.9) 0*n NS graduate State 12 ( 1.2) 60 ( 2.1) 46 ( 2.1) 16 ( 2.1) 244 ( 4.6) 239 ( 2,2) 256 ( 2.3) 232 ( 5.0) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 261 ( 6.0)I 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Some co4lege State /5 ( 2.2) 52 ( 2.5) 59 ( 2.7) 13 ( 1.7) 264 ( 5.9) 260 ( 2.8) 271 ( 1.1) IMHt ) Nation 13 ( *0,4, ( 2.5) 57 ( 270 ( 5.8) 3.7) 48 ( 278 ( 4.8) 3.0) 17 ( 3.1) College graduate State 15 ( 1.4) 52 ( 2.3) 60 ( 1.9) 10 ( 1.3) 270 ( 5.8) 270 ( 2.4) 281 ( 2.4) 248 ( 4.3) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 18 ( 2.4) 252 ( 4.5) 275 ( 3.8) 288 ( 3.0) 249 ( 4.0) GENDER Male State 13 ( 1.3) 59 ( 2.0) 50 ( 1.7) 16 ( 1.3) 256 ( 5.6) 254 ( 1.9) 270 ( 1.5) 237 ( 2.7) Nation 13 ( 22) 54 ( 4.7) 44 ( 4.1) ( 36) 275 ( 5.8) 260 ( 3.5) 276 ( 3.2) 243 ( 3.0) Female State 14 ( 1.1) 53 ( 1.8) 57 ( 1.6) 14 ( 1.3) 254 ( 3.4) 244 ( 2.4) 265 ( 2.0) 235 ( 3.0) Nation 16 ( 2.4) 53 ( 4.5) 4$ ( 3.6) 18 ( 2.9) 263 ( 4.4) 262 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2. standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature 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 107 New Mexico TABLE A9 I Teachers' Reports on the Availability of 1 Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL I Sot Al the Resources I I OM MOM of the I Get Some or None of STATE ASSESSMENT Nood Resources I Nosid the Resources I Need _ TOTAL Peraentage and Programa Parasatage and Prallaiaacy Pettontap Sod Pndlaisacy State 11 ( 0.7) 50 ( 1.2) 1.1) 254 ( 2.7) 258 ( 08) 258 'LS) Nation 13 ( 2.4) 58 ( 4.0) SI 42) 265 ( 4.2) 285 ( 2.0) 2S1 2.9) RACE/ETHNICITY Wt. State 13 ( 1.0) 51 ( 1.8) 38 ( 1.6) 261 ( 5.8) 272 ( 1.3) 276 ( 1.7) Nation 11 ( 2.5) 58 ( 4.8) 30 ( 4.6) 275 ( 3.5)1 270 ( 2.3) 267 ( 33) Hispanic State 9 ( 1.1) 51 ( 1.7) 39 ( 1.8) 247 ( 3.7) 248 ( 1.2) 245 ( 1.4) Nation 23 ( 7.6) 44 ( 4.9) 34 ( 7.7) 246 ( 7.7)4 250 ( 2.9) 244 ( 3.0)4 Amalie= Indian State 13 ( 22) ( 441 46 ( 33) 238 ( 2.3) 41 ( 4.0) 233 ( 3.1) Nation ( 7.4) 1. 72 (26.8) 41 22 (20.7) «el TYPE OF COMMUNITY Advantaged urban State O ( 0.0) 4.4.) 58 (102) 04* 42 (102) 11. ( MN) Nation 38 ( 92) 59 ( 8.9) 3 ( 3.1) 272 ( 84)1 286 ( 1.3)4 444 Disadvantaged urban State 0 ( 0.0) 38 ( 42) 64 ( 4.2) 258 ( 3.9) Nation 10 ( 6.8) 40 (13.1) 50 (14.5) 251 ( 5.4)1 253 ( 5.5)1 Extreme mad State 20 ( 2.7) 49 ( 4.2) 32 ( 4.0) 260 ( 2.8) 253 ( 1.9) 24$ ( 3.6) Nation 2 ( 2.6) 54 (10.4) 43 (10.3) IMP* ( *** ) 260 ( 8.8)! 257 ( 5.0)4 Other State 11 ( 08) 53 ( 1.2) 37 ( 1.1) 251 ( 3.6) 256 ( 1.1) 2$3 ( 1.7) Nation 11 ( 2.9) 58 ( 5.4) 31 ( 5.8) 265 ( 3.9)1 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A9 I Teachers' Reports on the Availability of (contiPued) i Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 116O NAEP TRIAL I Old Ail the Remarees 1 I Oat Meet of the I Oet Sam or Nene of STATE ASSESSMENT Need Resources I Reed the Resources I Need TOTAL Porsermage and Prolialow it 0.7) 254 21) 13 2.4) 205 4.2) Illercerdap and Pesikriancy SOf 1.2) 25e ( 0.8) 56( 4.0) 265 ( 2.0) Pareardage arid Praldancy ( 1.1) 258( 1,5) 31 ( 4.2) 261 ( 2A) State Naton gangmmomm nen-graduate State 11 ( *a* ( 2.2) 45 ( 242 ( 3.1) 2.0) 44 ( 238 ( 3.5) 2.4) Nation ( 2.8) 54 ( 5.7) 38 ( 8.3) 244 ( 2.7) 243 ( 3.5)i RS 'Mode State 12 ( 1.5) 52 ( 1.6) 36 ( 14) 251 ( 24) 249 ( 1.7) 244 ( 2.1) Nation 10 ( 2.5) 54 ( 4A) 35 ( 4.9) 253 ( 4.8)I 256 ( 1.9) 256 ( 2.8) Sem ceilege State 43 ( ( 2.0) 641 51 ( 293 ( 3.2) 1.8) 37 ( 259 ( 3.0) 2.7) Nation 13 ( 3.3) 62 ( 4.3) 25 ( 4.1) &OM ( 111.1111 269 ( 2.5) 267 ( 3.8) College graduate State 9 ( 1.5) 51 ( 270 ( 1.9) 1.8) 40 ( 278 ( 1.8) 1.9) Nation 15 ( 2.9) 56 ( 4.9) 30 ( 5.1) 278 ( 5.4)t 278 ( 2.2) 273 ( 3.7) GENDER Maio State 11 ( 1.0) 50 ( 14) 39 ( 1.7) 257 ( 2.9) 259 ( 1.5) 259 ( 2.0) Nation 13 ( 2.0) 57 ( 4.0) 30 ( 4.0) 204 ( 5.0)I 285 ( 2.6) 264 ( 3.3) Female State 11 ( 0.9) 51 ( 1.7) 38 ( 1.7) 251 ( 3.6) 254 ( 1.0) 252 ( 2.0) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 266 ( 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 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). 1.14 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 New Mexico TABLE Al Oa I Teachers' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1 1990 NAEP TRIAL STATE ASSESSMENT At Lust Onco a Weak LIM Than Once a Wm* Navar TOTAL Percentage and Pre Sciency Pardentwp and Proidancy Percentage and Rreacketta State 51 ( 1.4) 38 ( 1A) 11 ( 0.7) 257 ( 1.1) 258 ( 1.2) 258 ( 2.0) Nation 50 ( 4.4) 43 ( 4.1) $ ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 5.4)1 RACE/ETHNICITY Mita State 48 ( 1.7) 41 ( 1.7) 11 ( 0.9) 274 ( 2.0) 270 ( 1.4) 278 ( 2.4) Nation 49 ( 4.8) 43 ( 44) ( 2.3) 265 ( 2.7) 271 ( 2.2) 285 ( 4.9)1 Hispanic State 4$ ( 2.1) 39 ( 22) 12 ( 1.1) 249 ( 1.3) 245 ( 1.5) 248 ( 2.5) Nation 84 ( 7 2) 248 ( 2.5) 32 ( 6.9) 247 ( 6.3)1 4 ( 1.4) *el &nark= Minn State 69 ( 3.6) 24 ( 3.7) ( 1.2) 235 ( 2.1) 242 ( 3.8) Nation 18 (24.3) 80 (27.2) ( 2 ( 3.7) ysi) TYPE OF COMMUNITY Advantaged urban State 52 (11.9) ( 444 48 (11.9) ( 0 ( 0.0) de* ( Nation 39 (22.9) 41 (17.9) 20 (12.2) 273 ( 8.0)1 DIsadvantaged urban State 72 ( 42) 18 ( 4.4) 10 ( 0.6) 257 ( 3.5) Nation 70 (11.7) 248 ( 4.8)1 21 ( 9.0) 249 ( 8.7)1 9 ( 8.5) ( *41 Extrema rural State 61 ( 4.6) 25( 4-3) 14 ( 2.5) 255 ( 2.2) 250 ( 2.3) 247 ( 5.5) Nation 35 (14.8) 255 ( 5.5)1 56 (17.1) 256 ( 5.9)1 9 ( 9.8) *44. Other State 48 ( 1.5) 43 ( 1.6) 11 ( 0.7) 255 ( 1.4) 253 ( 1.2) 262 ( 2.3) Nation 50 ( 4.4) 44 ( 4$) 8 ( 1.8) 260 ( 2.4) 264 ( 2.6) 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. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 11" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 110 1 5 THE 1990 AEP TRIAL STATE ASSESSMENT New Mexico TABLE AlOa I Teachers' Reports on the Frequency of Small ("mtinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MOO NAEP TRIAL STATE ASSESSMENT At Least Ones a Wash Less Than Ones a Week Never TOTAL a n Proistlency Poreirs$410 sal Prificioncy Persaalles and Pirollolamay State 51 ( 1.4) 11 ( 01) 257 ( 1.1 250 12) 25$ 2.0) Nation 50 ( 4.4 43 4.1) 2.0) 240 ( 22) 244 ( 2.3) 277 5.4)1 PARENTS' EDUCATION Ifs nowgraduats State 52 ( 241 ( 4.3) 2.2) 97 ( 234 ( 3.7) 2.5) 10 ( 3.5) Nation 80 ( 244 ( 6.4) 3.2) 99 ( 244 ( 6.5) 3.2)1 ( 1.4) *dm ( 441 NS graduate State 50 ( 1.6) 99 ( 1.9) 11 ( 1.4) 249 ( 1.9) 248 ( 1.6) 247 ( 5.1 Nation 49 ( 252 ( 4.8) 2.8) 45 ( 257 ( 5.1) 2.7) (( se. Some coilege State 51 ( 202 ( 3.0) 2.2) 39 ( 263 ( 2.8) 2.5) 11 ( 1.4) .441 Nation 51 ( 52) 42 ( 5.1) ( 2.3) 208 ( 3.1) 269 ( 32) ( College graduate State 51 ( 2.0) 38 ( 2.1) 11 ( 12) 272 ( 1.9) 272 ( 2.5) 274 ( 3.7) Nation 48 ( 52) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 278 ( 3.0) 285 ( 4.9)1 GENDER M. State 49 ( 1.9) 39 ( 1.9) 12 ( 1.2) 260 ( 1.5) 259 ( 1.9) 280 ( 3.7) Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 281 ( 3.0) 285 ( 3.1) 278 ( 5.3)1 RIPM1110 State 53 ( 1.9) 37 ( 2.0) 10 ( 1.1) 254 ( 1.7) 252 ( 1.3) 256 ( 3.8) Nation 50 ( 4.7) 43 ( 4.7) ( 2.1) 259 ( 22) 283 ( 2.1) 275 ( 6.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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). liC THE 1990 NAEP TRIAL STATE ASSESSMENT 111 New Mexico TABLE AlOb I Teachers' Reports on the Use of Mathematical I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT , At Lust Once a Week Less Than Once a Week Never 1 TOTAL State Nation RACVETHNICITY White State Nation Hispanic State Nation Modem Indian State Nation TYPE OF COMMUNITY Advantageti urtan State Nation Disadvantaged urban State Nation Extreme neat State Nation Other State Nation Percentage and Proficiency Peraentap and Pralleircy Percentage and Proficiency 10 ( 1.0) 73 ( 1.1) 8 ( OA) 252 ( 1.5) 258 ( 0.9) 269 ( 2.4) 22 ( 3.7) 9 ( 2.8) 254 ( 3.2) 263 ( 1.9) 262 ( 5.9)1 14 ( 2.0) TB ( 2.2) 10 ( 0.9) 272 ( 2.5) 272 ( 1.0) 270 ( 4.3) 17 ( 4.0) 72 ( 42) 10 ( 2.7) 261 ( 3.8)1 269 ( 2.1) 288 ( 6.2)1 22 ( 1.4) 70 ( 1.7) 8 ( 1.0) 246 ( 1.9) 246 ( 1.1) 263 ( 3.1) 39 ( 7.5) SS ( 7.3) 7 ( 2.6) 247 ( 3.8) 245 ( 3.8)1 30 ( 3.0) 69 ( 3.1) ( 0.5) 233 ( 3.2) 239 ( 2.0) 7$ (34.6) 22 (34.6) ( 27 4..p (11.0) 73 (11.0) 0 ( 0.0) 23 *** (14.4) 63 27$ (11.6) ( 5.6)1 15 ( 9.3) 16 ( 4.6) ( *44) 68 259 ( 4.0) ( 3.4) 39 247 (11.4) ( 7.5)1 50 253 (12.1) ( 7.0)! **.i) 16 ( 2.5) 82 ( 2.5) 2 ( 0.6) 252 ( 3.5) 252 ( 2.0) 4Mre 27 (14.9) 65 (14.6) 8 ( 3.9) ( 262 ( 2.8)! 4-41. 20 ( 1.0) 70 ( 1.2) ( 0.7) 249 ( 1.8) 255 ( 1.0) 270 ( 2$) 19 ( 4.3) 72 ( 5.0) ( 3.3) 253 ( 3.9)1 263 ( 2.2) 281 ( 7.1)1 S. The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "4' Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A 10b I Teachers' Reports on the Use of Mathematical (mntinued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT Al Least Om* a Week Less Than Once a Week Never TOTAL Proonlapi an0 Prolcbmit Parasniage and Prtichancy Pervade. and Pralkiangf State 10 ( 73 ( 1.1) ( OA) 262 ( 250 ( 0.9) 20a ( 2.4) Nation 22 ( 09 ( 34) ( 2.6) 254 ( &a) 263 ( 1.9) 262 ( 5.9)1 PARENTS EDUCATION 148 non-graduate State 2. 242 ( 2.3) ( 2.7) 70 ( 240 ( 3.4) 2.1) 5 ( 444 ( 2.5) 441 Nation 25 44* ( 5.6) 444) 06 ( 243 ( 7.2) 2.2) 9 ( ( 64) HS graduate State 18 245 ( 1.3) ( 2.2) 74 ( 247 ( 2.2) 1.5) 9 ( .44 1.8) 441 Nation 23 248 ( 49) ( 4.0)1 70 ( 255 ( 5.3) 2.2) ( 444 ( 2.8) 441 Same conga State 18 255 ( 14) ( 3.7) 73 ( 263 ( 2.2) 1.7) 9 ( 2.1) 444) Nation 18 ( 4.0) 73 ( 4.3) 9 ( 2.4) 261 ( 4.4)1 269 ( 2.3) College graduate State 19 ( 1.7) 72 ( 1.8) 9 ( 0.8) 266 ( 3.5) 272 ( 1.6) I** ( 411 Nation 20 ( 3.9) 69 ( 3.7) 11 ( 2.5) 206 ( 3.5)1 274 ( 2.2) 297 ( 4,2)1 GENDER Male State 19 ( 1.8) 73 ( 2.0) 8 ( 1.2) 252 ( 2.5) 260 ( 1.3) 272 ( 4.3) Nation 22 ( 4.1) 89 ( 4.1) 8 ( 2.0) 255 ( 4.1) 265 ( 2.1) 287 ( 7.2)1 Female State 20 ( 1.7) 72 ( 1.8) 7 ( 0.8) 252 ( 2.3) 252 ( 1.3) 265 ( 3.5) Nation 21 ( 3.6) 69 ( 4.2) 10 ( 3.3) 254 ( 3.3) 262 ( 1.9) 278 ( 6.0)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. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 113 New Mexico TABLE Al la Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STuDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL About Once a Wu* or STATE ASSESSMENT Almost Every Day Several Tknes a Week Less TOTAL Percentage and Prolictincy Percentage and Pm/Wow Parosnlas and Praidency State 89 ( 12) 25 1.2) 0 ( 0.3) 258 ( 0.9) 253 1.4) 247 ( 3.0) Nation 02 ( 3.4) 267 ( 12) 31 3.1) 254 ( 2.9) 7 ( 12) 260( Mcvtmrncrrv White State 73 ( 1.9) 23 ( 2.0) 4 ( 0.5) 274 ( 1.5) 268 ( 2.1) Oa* VII Nation 64 ( 3.7) 28 ( 3.2) 3 ( 2.3) 272 ( 1.9) 264 ( 3.4) 264 ( 5.4)1 Hispanic State ISS ( 1.9) 28 ( 12) ( 0.5) 249 ( 12) 24$ ( 1.5) 244 ( 3.0) Nation 61 ( 6.8) 32 ( 5.3) ( 2.3) 251 ( 3.1) 240 ( 4.3)I American Indian State 66 ( 3.3) 24 ( 3.2) 10 ( 02) 238 ( 1.8) 239 ( 3.9) WSW ( 1.11 Nation 15 (25.9) ( 83 (283) eye 2 ( 3.0) ( **) TYPE Of COMMUNITY Advantaged urban State 100 ( 0.0) 285 ( 4.8) 0 ( 0.0) ,HH,) 0 ( 0.0) 11111,^ ..1411 Nation 63 (15.9) 23 ( 5.2) 14 (14.8) 263 ( 7.3)! Disadvantagod urban State 341 4.2) 18 ( 0.8) elhl ( **it ) seit ( Nation 08 (10.7) 252 ( 4.7)! 31 (11.1) 243 ( 8.0)1 4 ( 2.2) .44 Extrisne rural State 73 ( 4.2) 21 ( 42) 8 ( 0.4) 252 ( 2.4) 231 ( 3.5)! Nation 50 (10.8) 268 ( 4.0)i 40 (10.0) 247 ( 7.8)! 10 ( 7.3) .44) Otivar State 87 ( 1.2) 26 ( 13) 5 ( 0.4) 258 ( 1.1) 250 ( 1.5) 247 ( 2$) Nation 83 ( 3.9) 31 ( 3.5) ( 1.9) 207 ( 2.3) 255 ( 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 New Mexico TABLE Altai Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ MO NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week Abotd Once a Weak or Less TOTAL P4M1111.1 and Proficiency Porcesitale and Proficiency Permatage and Proficiency State 06 ( 1.2) 25 ( 1.2) 8 ( 0.3) 256 ( 0.9) 253 ( 1.4) 247 ( 3.0) Nation 62 ( 3.4) 31 ( 3.1) ( 1.8) 267 ( 1.8) 254 ( 2.9) 200 ( 5.1)1 PARENTS' EDUCATION NS non-greduate State 62 ( 3.5) 31 ( 3.1) 7 ( 1.5) 243 ( 2.1) 240 ( 3.1) ( "") Nation 67 ( 245 ( 5.5) 3.2) 27 ( ( 5.2) .41 6 ( .44 ( 2.1) NS graduate State 67 ( 1.8) 27 ( 1.7) 6 ( 0.6) 248 ( 1.4) 248 ( 2.4) ( "") Nation 81 ( 4.4) 34 ( 3.7) 6 ( 1.5) 257 ( 2.5) 250 ( 2.9) *** ( Some conage State 70 ( 264 ( 2.5) 1.6) 22 ( 259 ( 2.3) 32) 8 ( *el ( 1.3) 4.41 Nation 68 ( 4.2) 28 ( 3.7) 6 ( 1.9) 272 ( 2.7) 258 ( 5.2) ( ***) College graduate State 71 ( 1.6) 24 ( 1.6) 275 ( 1.6) 267 ( 2.8) ( Nation ( 4.0) 31 ( 3.9) ( 3.1) 281 ( 2.2) 265 ( 3.1) GENDER Male State 68 ( 1.5) 25 ( 1.5) 7 ( 0.6) 262 ( 1.4) 255 ( 2.1) 253 ( 4.9) Nation 80 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2,1) 256 ( 3.6) 261 ( 6.7)1 Female State 69 ( 1.5) 26 ( 1.5) 5 ( 0.6) 255 ( 1.3) 251 ( 2.0) 114,11^ 4,111 Nation 65 ( 296 ( 3.6) 1.8) 28 ( 3.3) 253 f 2.5) 7 ( 2.2) #.) .,. The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT 115 New Mexico TABLE Al lb I Teachers' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PPOFIC1ENCY 1000 NAEP TRIAL At Least Several Tknes STATE ASSESSMENT a Week About Once a Waak Less than Wee My - TOTAL 01411ellallia and Proficiency Percentage and Prefidency Pereeniage and Preliciency State 33 ( 1.0) 29 ( 1.2) 81(14 248 ( 1.1) 259 ( 14) 201 (1.3 Nation 34 ( 3.8) 33 ( 3.4) 32 33 256 ( 2.3) 200 ( 23) 274 t 2.7) RACEIETNNIOITY White State 27 ( 1.4) 29 ( 2.1) 44 ( 2.0) 206 ( 2.0) 277 ( 1.4) 274 ( 2.1) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.6) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Hispank State 36 ( 1.6) 30 ( 1.9) 34 ( 13) Nation 243 ( 1.5) 41 ( 7.7) 249 ( 1.6) 26 ( $.3) 250 ( 1.5) 33 ( 7$) 242 ( 3.2)1 244 ( 5.1)1 257 ( 2.3)1 Ant/Pecan Indian State 49 ( 3.7) 23 ( 2.3) 29 ( 3.6) 229 ( 2.5) 241 ( 2.7) 24$ ( 36) Nation 10 (18.6) ell* ( ) 76 (36.2) 0**) 13 (18.5) timt) TYPE OF COMMUNITY Advantaged urban State 16 ( 3.0) ( 30 (12,4) ( *41 53 (116) Nation 59 (13.9) 273 ( 3.4)1 20 ( 6.0) 441 21 ( 82) Disadvantaged urban State 50 ( 4.3) 30 ( 4.1) es- 20 ( 22) Nation 50 (13.9) 22 (112) 28 (10.7) 237 ( 2.4)1 25$ C 8.3)1 263 ( 4.1)1 Extreme rural State 32 ( 3.1) 19 ( 2.6) 49 ( 4.4) 245 ( 3.1) 254 ( 3.2) 256 ( 22) Nation 27 (14.3) ( .44) 49 (12.7) 258 ( 6.7)1 24 (10.1) ( *41 Other State 34 ( 1.2) 32 ( 1.3) 35 ( 14) 247 ( 1.1) 257 ( 12) 260 ( 2.1) Nation 30 ( 44) 3$ ( 4.3) 36 ( 42) 256 ( 3.3) 259 ( 2.8) 272 ( 2.9) 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. ! 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 New Mexico TABLE Al lb I Teachers' Reports on the Frequency of (cmtinued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Least Soveral Times STATE ASSESSMENT a Week About Once a Week LOSS than Weekly TOTAL Ponentege and Proficiency Percentage and Psoffickney Percentage and Proficiency State 33 ( tO) 248 ( 1.1) 20.( 259 ( 1.2) 14) 3$ ( 2.1 ( 1.4) 1.3) Nation 34 ( 18) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 2$0 ( 2.3) 274 ( 2.7) PARENTS' MCAT KS noniraduate State 4$ ( 3.5) 28 ( 2.9) 25 ( 32) 238 ( 2.0) 243 ( 2.9) 243 ( 43) Nation 35 ( 6.0) 29 ( 6.3) 36 ( 8.9) 239 ( 3.5) 250 ( 4$)I HS graduate State 37 ( 2.1) 30 ( 2.0) 33 ( 1.9) 244 ( 2.1) 248 ( 2.6) 251 ( 1.8) Nation ( 5,3) 36 ( 4.5) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 263 ( 3.4) Some college State 31 ( 23) 29 ( 2.6) 40 ( 2.7) 255 ( 2.3) 207 ( 2$) 265 ( 2.3) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 280 ( 2.8) 266 ( 42) 278 ( 2.6) College graduate State 27 ( 1.7) 29 ( 1.8) 45 ( 2.0) 284 ( 1.9) 277 ( 2.6) 275 ( 2.1) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3$) 284 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Make State 34 ( 1.8) 27 ( 1.6) 38 ( 1.9) 251 ( 1.6) 262 ( 2,5) 265 ( 2.1) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.6) 257 ( 3.2) 261 ( 2.8) 275 ( 3,2) Female State 32 ( 1.4) 31 ( 1.9) 37 ( 2.1) 246 ( 1.5) 257 ( 1.9) 257 ( 2.0) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 27? ' 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. '1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 117 New Mexico TABLE Al2 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT , - At West Onc a Week Lass Than Once a Week Never TOTAL Pareentage and Pre Mow PIVINIANO Sad Pralidengi Spereentage and Prelkioncy State 24 ( 0.9) 24 ( 0.9) 52 1.0) 256 ( 145) 263 ( 1.6) 253 1,0) Nation 29 ( 2.5) 20 ( 1.4) 44 2.9) 258 ( 2.7) 247 ( 2.0) 261 ( 1.6) RACE/ETHNICITY White State 23 ( 1.4) 2$ ( 1.8) 49 ( 1.8) 272 ( 2.7) 276 ( 2.2) 269 ( 1.3) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 268 ( 3.1) 272 ( 1.9) 270 ( 1.7) Hispanic State 22 ( 1.4) 22 ( 12) 55 ( 1.6) 248 ( 1.9) 251 ( 1.7) 245 ( 1.2) Nation 37 ( 52) 22 ( 3.8) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) American Indian State 32 ( 2.9) 16 ( 1.9) 52 ( 2.8) 236 ( 3.5) 248 ( 3.0) 235 ( 2.4) Nation 31 ( ( 5.1) 35 ( *114 5.5) 33 ( 4.44 5.0) .4,4) TYPE Of COMMUNITX Advantaged urban State 4444 4.44) ,4444 ( .41 Nation 27 (13.9) ( 4.) 33 ( 286 ( 44) 5.4)1 40 (13.4) 272 ( 3.5)1 Disadvantaged urban State 29 ( ( 5.4) 4.) 22 ( 33) 49 ( 4444 ( 5.6) 4441 Nation 31 ( 5.7) 20 ( 2.8) 49 ( 6.3) 245 ( 4.0)I 267 ( 6.4)1 245 ( 3.7)1 Extreme rural State 26 ( 2.5) 26 ( 22) 48 ( 2.8) 255 ( 3.1) 258 ( 2.0) 249 ( 2.5) Nation 34 (10.8) 27 ( 3.8) 39 (1113) 249 ( 5.2)1 264 ( 3$)1 258 ( 6.2)1 Other State 22 ( 1.1) 24 ( 1.0) 53 ( 1.3) 255 ( 2.1) 2152 ( 1.81 252 ( 1.1) Nation 27 ( 2.8) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 284 ( 2.1) 262 ( 2.2) The standard errors of the esumated statistics appear in parenli 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 pe;mit a reliable estimate (fewer than 62 students). 113 1 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A 12 I Students' Reports on the Frequency of Small ("mitinued) i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 NAEP TRIAL STATE ASSESSMENT At Lust Once a We* Less Than Once a Weak Never TOTAL Prolaktiey 24( Percolate Percentage mid Prellakemy PiveMency 52 ( tO) State 258 ( 1.8 2:341 1.61 253 ( 1.0) Nation 28 ( 2.5 26 1.4 44 ( 2.9) 258 ( 2.7) 267 2.0 261 ( 14) PARENTS' EDUCATION RS nm-graduato State 24 ( 2.8) 24 ( 2.4) 53 ( 3.5) 238 ( 3.2) 244 ( 2.7) 239 ( 2.2) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4.5) 242 ( 3.4) 244 ( 3.0) 242 ( 2.7) NS weasel* State 24 ( 1.8) 23 ( 1.6) 53 ( 2.3) 2411 ( 2.2) 252 ( 2.3) 246 ( 14) Nation 28 ( 3.0) 28 ( 1.8) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some coNege State 23 ( 2.2) 25 ( 2.3) 51 ( 2.6) 262 ( 3.0) 264 ( 24) 261 ( 1.4) Nation 27 ( 3.9) 27 ( 2.4) 46 ( 3.8). 266 ( 3.8) 268 ( 3.3) 266 ( 2.1) Collage graduate State 25 ( 1.8) 28 ( 1.8) 48 ( 2.0) 270 ( 2.9) 279 ( 2.7) 269 ( 1.8) Nation 28 ( 3.0) 28 ( 1.9) 44 ( 3.6) 270 ( 2.7) 278 ( 2.8) 275 ( 2.2) GENDER Male State 24 ( 1.2) 25 ( 1.4) 51 ( 1.7) 254 ( 1.9) 268 ( 2.4) 257 ( 1.4) Nation 31 ( 2.9) 28 ( 1.7) 41 ( 29) 259 ( 3.3) 288 ( 2.8) 262 ( 1.8) Female State 24 ( 1.3) 23 ( 1.4) 53 ( 1.5) 258 ( 2.3) 258 ( 2.1) 250 ( 12) Nation 26 ( 2.4) 27 ( 1.8) 47 ( 3.2) 257 ( 2.8) 266 ( 1.7) 260 ( 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. r *0 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 New Mexico TABLE A13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Ai Least Once a Week Less Than Once a Weak NOW TOTAL Percentage and Proadency Percentage and Proficiency Percentage and Proficiency State n ( 1.1) 31 ( 1.2) 47 ( 1.2) 251 ( 1.4) 261 ( 1.4) 250 ( 10 ) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.6) 289 ( 1.5) 250 ( 14) RACE/ETHNICITY White State 20 ( 1.8) 32 ( 1.7) 4$ ( 2.0) 269 ( 2.4) 273 ( 2.5) 272 ( 1.3) Nation 271 1$) 33 ( 1.6) 40 ( 25) 260 ( 2$) 275 ( 14) 26$ ( 1.8) Hispanic State 21 ( 1.4) 31 ( 2.0) 48 ( 1.9) 241 ( 2.0) 251 ( 1.3) 247 ( 12) Nation 38 ( 42) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4,3) 240 ( 1.9) American Indian State 30 ( 32) 22 ( 2.7) 42 ( 3.7) 234 ( 2.4) 249 ( 42) 234 ( 2.5) Nation ***) 37 ( 82) 2$ ( $.8) .4") TYPE OF COMMUNITY Advantaged urban State 18 ( 7.8) 22 ( 2.8) 1.) 80 ( 8.8) Nation 36 (10.3) 33 ( 4.8) 32 (11.1) 278 ( 8.1) 284 ( 3.2)1 281 ( 5.9)1 Disadvantaged urban State 29 ( 3.4) 23 ( 4.9) 48 ( 5.4) ,ft Nation 35 ( 6.6) 19 ( 2.1) 48 ( 0.4) 249 ( 5.3)f 256 ( 5.7)1 248 ( 4.8)1 Extreme rural State 23 ( 2.7) 29 ( 24) 47 ( 3.2) 243 ( 3.0) 260 ( 1.9) 253 ( 2.4) Nation 21 ( 3.1) *. 37 ( 4.7) 262 ( 42)1 43 ( 5.0) 251 ( 5.2)I Other State 21 ( 1.1) 251 ( 1.5) 32 ( 1,5) asta ( 1.9) 47 ( 1.3) 254 ( 1.1) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 256 ( 2.9) 270 ( 1.8) 260 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A 13 I Students' Reports on the Use of Mathematics (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 NAEP TRIAL STATE ASSESSMENT , At Least Once a Week Less Than Once a Week Neve r TOTAL mid Pradency and Maoism Prelkioncy State 22 ( 1.1) 31 ( 12) 47 12) 251 ( 1.4) 281 (1.4) 258 1.0) Nation 28 ( 1.8) St ( 42) 41 2.2) 2.8) 208 ( 1.5) 258 1.8) PARENTS' goucKnoN HS nen-graduati State 20 ( 2.8) 28 ( 3.0) 48 ( 3.8) 235 ( 2.8) 245 ( 2.7) 240 ( 2.8) Nation 27 ( 42) 26 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) HS graduat State 20 ( 1.7) 29 1.1) 51 ( 2.0) 243 ( 2.9) 251 2.1) 247 ( 1.7 Nation 27 ( 2.7) 31 2.4) 43 ( 3.3 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Sam collage State 1$ ( 2.4) 31 ( 2.1) 45 ( 2.7) 260 ( 2.9) 261 ( 2.0) 283 ( 1.7) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.6) 261 ( 3.5) 274 ( 22) 263 ( 2.1) College graduate State 23 ( 1.7) 31 ( 1.8) 46 ( 1.7) 264 ( 2.7) 277 ( 2.8) 272 ( 1.7) Nation 30 ( 24) 32 ( 2.0) 38 ( 2.4) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Maio State 23 ( 1.6) 32 ( 1.6) 45 ( 1.9) 254 ( 2.1) 264 ( 1.8) 258 ( 1.4) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 256 ( 2.9) 271 ( 2.1) 200 ( 1.8) Femal. State 21 ( 1.3) 29 ( 1.5) 50 ( 1.8) 247 ( 1.9) 251 ( 1.7) 254 ( 1.4; Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 268 ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said wish 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 r-2 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 New Mexico TABLE A14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1990 /MEP TRIAL Almost Every Day Simla About Om* a Wsok or STATE ASSESSMENT Times a Week Less , - TOTAL Percentage and Pre Odom Penuntege and Prollelsoey Petventege end Predetency State 78 ( 0.9) 13 ( 0,9) 9 ( 0.0) 259 ( 249 ( 2.4) 245 ( 1.4) Nation 74 ( 1.9) 14 ( 0.6) 12 ( 1.8) 207 ( 12) 252 ( 1.7) 242 ( 4.5) RACE/ETHNICITY White State $O ( 12) 13 ( 1.4) 7 ( 0.6) 274 ( 1.5) 262 ( 3.8) 265 ( 3.0) Nation 78 ( 274 ( 2.5) 1.3) 13 ( 258 ( 0.8) 2.2) 11 ( 252 ( 22) 5.1y Hispanic State 78 ( 1.3) 12 ( 104) 10 0.8) 249 ( 1.0) 243 ( 3.1) 239 ( 1.9) Nation 81 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) American Indian State 71 ( 242 ( 2.3) 2.0) 18 ( 22$ ( 1.9) 44) 12 ( 1.9) .441 Nation ram Of COMMUNITY 61 ( 01.4 44) 22 ( 3.6) 17 ( 4.0) Advantaged urban State 72 ( 2.1) ***) ( 19) 22 ( 3.3) Nation 73(11.1) 288 ( 4.6)1 13 ( ( 1.7) +94) 14 (10.4) Dtsadvantaged urban State 68 ( 8.8) 18 ( 7.0) 16 ( 5.2) 258 ( 3.2) ( Nation 09 ( 2,$) 15 ( 2.5) 15 ( 22) 253 ( 3.7)1 243 ( 44)1 235 ( 8.5)1 Extreme neat State 82 ( 1.6) 13 ( 1.7) 6 ( 1.1) 256 ( 2.0) 243 ( 5.0) ( Nation SS (11.3) 15 ( 3.6) 17 ( 112) 283 ( 4.2)1 Other State 7$ ( 1.0) 13 ( 0.9) 8 ( 0.5) 257 ( 1.1) 248 ( 2.8) 242 ( 1,8) Nation 75 ( 2.2) 14 ( 1.0) 10 ( 1.9) 287 ( 1.8) 252 ( 2.6) 239 ( 42)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 a this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 I' r-r A THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A 14 I Students' Reports on the Frequency of (continued) I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1111/0 !IAEA TRIAL STATE ASSESSMENT , Almost Every Day . Several Times a We* About Ones a Wm* or Lass TOTAL State Nation PARENTS' EDUCATION NS non-graMmts State Nation HS graduat State Nation Some college State Nation Collage gradual* State Nation GENDER M. State Nation Female State Nation floventago and Pnliskany 259"/ LI 74 I 1.9) ( 1.2) 72 ( 2.8) 243( 1.8) 84( 3.4) 245( 2.3) 7111( 1.7) 249 ( 1.4) 71 ( 3.8) 258 ( 1.8) 77 ( 2.0) 205 ( 1.3) 80 ( 2.0) 270 ( 1.9) 81 ( 1.5) 274 ( 1.7) 77 ( 2.7) 279 ( 1.8) 77 ( 1.2) 281 ( 1.2) 72 ( 2.4) 268 ( 1.8) 79 ( 1.1) 257 ( 1.2) 78 ( 1.8) 285 ( 1.3) paramiaga Parcantaga and and Pralkinny Prallaisacy 13 ( ( 0.6) 249 ( 2.4 245 ( 1.4) 14 ( 0.8 12 ( 1.8) 252 ( 1.7 242 ( 4.5) .) 14 1.8) 18 ( 2.0) 1$ ( 3.1) 13 ( 1.7) 9 ( 1.2) 248( 3.3) 241 ( 3.9) 18 ( 1.8) 13 ( 2.8) 249 ( 32) 239 ( 3.4)1 15 ( 1.7) 8 ( 12) 251 ( 3.0) Mt* ( *01 11 ( 12) .1.0) 9 ( *411 ( 1.7) ***) 12 ( 12) 7 ( .0) 284 ( 3.3) ( 041 13 ( 0.5) 10 < 2.3) 280 ( 2.8) 257 ( 8.4)1 13 ( 12) 10 ( 0.9' 253 ( 2.8) 252 ( 10 ( 1.2) 12 ( 2.1) 252 ( 2.5) 242 ( 8.1) 13 ( 1.1) 9 ( 0.7) 245 ( 2.8) 237 ( 2.9) 13 ( 1.0) 11 ( 1.6) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent txrtainty 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). THE 1990 NAEP TRIAL STATE ASSESSMENT 123 New Mexico TABLE Al5 I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1190 NAEP TRIAL At Least Several Times STATE ASIMISMENT a week Abeut Once a Weak Less Than Weekly _ TOTAL Panaantaga and Praia Sew State 34 ( 1.2) 250 ( 14) Nation 38 ( 2.4) 2S3 ( 2.2) MCVIIHIM[ White State 30 ( 1.9) 270 ( 2.2) Nation 35 ( 2.9) 262 ( 2.5) Hispanic State 33 ( 1.8) 243 ( 1.8) Nation 44 ( 4.1) 238 ( 3.9) American Indian State Si ( 3.9) 228 ( 2.2) Nation 41 ( 4.2) ( 4") TYPE OF COMMUNITY Advantaged titan State 45 ( 8.1) Nation 50 ( 9.0) 271 ( 3.3)1 Disadvantaged 'aim State 55 ( 5.9) 259 ( 4.8) Nation 37 ( 5.8) 240 ( 4.8)1 Eldreme nral State 30 ( 3.1) 240 ( 32) Nation 42 (10.1) 249 ( 4.0)i Other State ( 1.2) 248 ( 1.4) Nation 38 ( 2.9) 252 ( 3.0) Partenbne and Prallaiancy 25 (0.9) 254 ( 1.3) 2$ ( 1.2) 281 ( 1.4) 24 ( 1.7) 285 ( 2.2) 24 ( 1.3) 289 ( 1.5) 26 ( 1.2) 248 ( 1.8) 25 ( 3.4) 247 ( 3.3) 23 ( 2.5) 247 ( 4.2) 30 (11.3) 25 ( 5.3) ( 1111 25 ( 4.2) 23 ( 3.8) 253 ( 4.1)1 23 ( 1.9) 253 ( 3.2) 30 ( 4.4) 258 ( 3.4)1 25 ( 1.0) 253 ( 1.3) 26 ( 1.2) 281 ( 2.1) illensantaga and Pealleiancy 41 1.1) 263 1.2) 37 2.5) 272 ( 1.9) 48 ( 1.9) 278 ( 1.7) 41 ( 3.0) 277 ( 2.0) 41 ( 1.9) 251 ( 1.4) 32 ( 4.3) 248 ( 3.3) 26 ( 2.6) 247 ( 2.3) 28 (12.5) ...) 31 ( 5.4) ( 31 ( 9.3) 299 ( 5.3)1 19 ( 3.2) e.. 41 ( 6.7) 25$ ( 4.2)1 48 ( 3.4) 281 ( 2.1) 28 ( 7.5) 267 ( 7.3)1 42 ( 13) 261 ( 1.5) 38 ( 2.9) 272 ( The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE AIS I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1NO NAEP TRIAL STATE ASSESSMENT LAI Least Sow* Times a Week About Once a week . Less Than weekly TOTAL Percentage and Proficiency Pervenlage end Proficiency Percentage and Proficiency State 34 ( 12) 25 (0.9) 41 ( 1.1) 250 ( 1.4) 254 1.3) 263 ( 1.2) Nation 36 ( 2.4) 25 ( 1.2) 37 ( 2.5) 0'3 ( 2.2) 261 ( 1.4) 272 ( 1.9) PARENTS' EIXICAIION HS non-greduate State 39 ( 3.0) 28 ( 2.9) 33 ( 32) 236 ( 2.6) 239 ( 13) 248 ( 3.7) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) NS gracktate State 30 ( 1.7) 26 ( 22) 38 ( 2.0) 244 ( 2.4) 246 ( 2.3) 252 ( 1.7) Nation t O ( 32) 29 ( 2 2) 32 ( 3.6) 247 ( 2.7) 256 ( 2.5) 262 ( 22) Some cotiege State 29 ( 22) 25 ( 2.3) 48 ( 2.7) 253 ( 2.4) 280 ( 2.5) 209 ( 1.9) Nation 34 ( 3.4) 26 ( 2.2) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) College graduate State 31 ( 22) 23 ( 1.7) 46 ( 2.0) 268 ( 2.3) 269 ( 2.7) 276 ( 2.1) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 273 ( 2.5) 285 ( 2.3) GENDER Male State 35 ( 1.4) 25( 1.1) 40 ( 1.6) 255 ( 1.9) 257 ( 2.2) 265 ( 19) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 263 ( 2.3) 274 ( 2.4) Female State 33 ( 1.6) 24 ( 1.4) 42 ( 1.6) 245 ( 1.8) 251 ( 1.8) 281 ( 1.4) Nation 37 ( 2.5) 25 ( 1$) 38 ( 2.6) 253 ( 2.1) 259 ( 1.8) 269 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 New Mexico TABLE A18 Students' Reports on Whether They Own a Calculator and Winther Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT ._ Own a Calculator . Teacher &plains Calculator Use Yes No Yes No I BI/K Percentage and Proficiency Percentile, and PrelicketCy Percentage and Proficiency Percintage and Proliciency State 07 ( 0.3) 3 ( 03) 4? ( 53 ( 257 ( 0.8) 231 ( 3.6) 252 1.1 200 1.1 Nation 97 ( OA) 3 ( 0.4) 49 23 51 2.3 263 ( 1.3) 224 ( 3.8) 258 1.7 205 1.5 RACE/ETHNICITY White State 99 ( 0.3) 1 ( 0.3) 44 ( 22) 50 ( 272 ( 1.2) 289 1.5) 274 ( 1.0 Nation 96 ( 0.3) 48 2.6) 54 ( 270 ( 1.5) ( 203 1.8) 273 ( 1.1 Mspanic State 95 ( 24$ ( 0.8) 0.9) 5 ( 44* ( 0.6) 47 244 ( 1.5) ( 1.3) 53 ( 1.0) 250 ( 12) Nation 62 ( 12) 8 ( 1.2) 63 ( 43) 37 ( 4.3) 245 ( 2.7) *et ) 243 ( 3.4) 245 ( 2.9) American Indian State 96 ( 1.2) 4 ( 12) 59 ( 22) 41 ( 2.2) .235 ( 1.7) 232 ( 2.3) 245 ( 2.5) Nation St ( 114* ( 3.1) *41 vv. ( 3.1) ..**) 71 .4* (16.7) ( 29 (18.1) ( win TYPE Of COM wimv Advantaged urban State 100 ( 0.0) 0 ( 0.0) 40 ( 54) 00 5.5) 284 ( 4.1) IMP* OM) Nation 99 ( 1.0) ( 1.0) 45 (122) 55 (121) 281 ( 34)1 f 278 ( 2.5)! 255 ( 6.4)1 Disadvantaged urban State 96 ( 258 ( 0.8) 2.7) 4 ( 0.8) 47 255 ( 4.3) ( 4.a) 53 4.3) ein Nation 94 ( 1.2) 6 ( 1.2) 53 ( 7,5) 47 ( 7.5) 250 ( 34)1 247 ( 4.1)1 251 ( 3.6)1 Extreme rival State 97 ( 02) 3 ( 0.9) 49 ( 3.1) 51 $.1) 253 ( 1.8) ( "4) 248 ( 1.9) 280 ( 2.0) Nation 96 ( 1.3) 4 ( 1.3) 42 ( 8.7) 56 8.7) 257 ( 3.9)1 0iir es) 251 ( 43)1 261 ( 4A)1 Other State 97 ( 0.4) 3 ( 0.4) 48 ( 1.4) 52 ( 1.4) 256 ( 0.9) 251 ( 1.3) 259 ( 1.5) Nation 97 ( 0.5) 3 ( 0.5) 50 ( 2.7) 50 ( 2.7) 263 ( 1.7) 233 ( 5.4) 258 ( 2.1) 208 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. **' Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 126 13i THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A 18 Students' Reports on Whether They Own , (c43ntinued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT a Calculator Teacher Bcpla Ins Calculator Use Yes No Yes No TOTAL Parcerdaga and Pivelancy ParoiNtsee and Prallaioncy Parvanlapi and Plisidancy Parosniap and State 97 ( 0.3) 3 ( 0.3) 4? ( 1.2) 53 ( 1.2) 257 ( 231 ( 3.8) 252 ( 1.1) 280 ( 1.1) Nation 97 ( 0.4 3 ( OA) 49 ( 2.3) 51 ( 2.3) paRENTr EDUCATION 283 ( 1.3 234 ( 3.8) 251 ( 1.7) 288 ( 1.5) liS non-groduate state 92 ( 242 ( 1.3) 1.6) 8 ( 1.3) «se ( ikon 49 ( 237 ( 3.3) .2.0) 51 ( 244 ( 3.3) 22) Nation 92 ( 243 ( 1.6) 2.0) 8 (1.8) ,044. 4..6) 53 ( 242 ( 4.15) 2.9) 47 ( 243 ( 4.8) 2.5) 145 graduate State 97 ( 24$ ( 0.9) 1.4) 3 ( 0.9).) 49 ( 242 ( 2.5) 1.4) 51 ( 253 ( 2.5) 1.7) Nation 97 ( 0.6) 3 ( 0.6) 54 ( 3.0) 46 ( 3.0) 255 ( 1.5) 252 ( 1.9) 258 ( 2.0) Some college State 99 ( 0.4) ( 0.4) 47 ( 2.4) 53 ( 2.4) 252 ( 1.2) ( 259 ( 2.1) 285 ( 16) Nation 98 ( 288 ( 0.9) 1.8) 4 ( .44 ( 0.9) 48 ( 265 ( 32) 2.4) 52 ( 20$ ( 32) 2.2) CoNage graduate State 99 ( 0.4) 1 ( 0.4) 46 ( 16) 54 ( 1.9) 272 ( 1.6) 270 ( 1.9) 275 ( 1.8) Nation 99 ( 0.2) I ( 0.2) 48 ( 2.8) 54 ( 2.0) 275 ( 1.6) ( *41 268 ( 22) 280 ( 1.9) DEADER M. State 98 ( 259 ( 0.4) 1.1) 2 (( 0.4) .41 47 ( 254 ( 1.7) 1.5) 53 ( 284 ( 1.7) 1.4) Nation 97 ( 0.5) 3 ( 0.5) 51 ( 2.6) 49 ( 2.6) 254 ( 1.7) *** ( ".) 258 ( 2.1) 260 ( 2.1) Female State 96 ( 0.6) 4 ( 0.6) 4$ ( 1.9) 52 ( 1.9) 255 ( 0.9) ( 250 ( 1.5) 258 ( 1.4) Nation 97 ( 202 ( 0.5) 13) 3 ( ( 0.5) ***) 47 ( 25$ ( 2.5) 1.7) 53 ( as3 ( 2.5) 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 127 New Mexico TABLE A19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1040 NAEP TRIAL STATE ASSESSMENT Working Problems kt Class Doing Problems at Homo Taking Quizzos or Torts Almost {----- Almost Never Always Always NOM I Almost Always Never 41.=11111.111111110 ,IMINMON110e, TOTAL Pountage mad iliVaoloncy State 44 1.2 24S 1.0 Nation 44 1.5 254 1.3 RACE/ETHNICITY Whits State 40 1.7) 282 1.8) Nation 48 1.7) 282 1.7) Hispanic State 47 ( 2.0) 241 ( 1.1) Nation 51 ( 2.9) 239 ( 2.8) American Indian State 46 ( 2.8) 232 ( 1.9) Nation 33 ( 4.,... ( 91) ....) TYPE OF COMMUNITY Advartagad urban State 34 ( 8.7) le** ( Mrs) Nation 51 ( 5.4) 270 ( 4.7)1 Dludvantagod urban State MO. * Nation 52 ( 3.1) 241 ( 3.8)1 Extrema rural State 43 ( 2.1) 245 ( 2.8) Nation 46 ( 7.4) 240 ( 4,3)1 Other State 44 ( 1.0) 246 ( 1.2) Nation 48 ( 1.9) 254 ( 2.4) Porcentas4 Points. Peasniage Pawls. Pareseday ind end and and and Prelloioncy Praidsacy Prallokomy Praliciany "WMvay 27 1.1 24 ( 0.9 17 0.3 289 14 255 ( IA 262 2.0 23 1.9 10 ( 1.3 10 0.9 272 1.4 281 ( 1.8 283 1.8 31 ( 1.2) 27 ( 1.7) 18 ( 1.0) 281 ( 2.1) 270 ( 2.1) 278 ( 2.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 278 ( 13) 270 ( 1.7) 260 ( 23) 28 ( 1.7) 24 ( 1.4) 18 ( 1.2) 258 ( 1.7) 245 ( 1,7) 252 ( 2.0) 18 ( 3.3) 28 ( 3.2) 21 ( 2.1) 252 ( 3.3)I 238 ( 4.8) 244 ( 3.1) 22 ( 2.4) 18 ( 2.0) 18 ( 3.2) 255 ( 3.8) 236 ( 25) 238 ( 3.4) 23 ( 4.9) 15 ( 4.9) 32 (10.1) 1.4. ( see) *** ( ***) *,, ( *41 *et ( *Gel 23 (10.7) t 24 ( 3.3) GO* 4**) 22 ( 4$) 259 ( 5.0 28 ( 1.9) 268 ( 1.6) 29 ( 0.5) 268 ( 0.1)1 28 ( 1.3) 207 ( 1.9) 22 ( 2.0) 272 ( 1.8) 26 ( 4.8) ( 0.1 32 ( 8.1) 274 ( 4.9)1 26 ( 2.4) *** 30 ( 3.3) 240 ( 5.2)1 21 ( 2.2) 245 ( 2.9) 20 ( 2.5) ( *64 ) 25 ( 1.1) 253 ( 1.7) 32 ( 1.7) 203 ( 2.3) **It 4s44) 15 ( 2.7) s- 24 ( 2.3) 254 ( 4.8)1 19 ( 2.1) 256 ( 3.9) 23 ( 3.9) 203 ( 4.4)1 17 ( 0.8) 263 ( 2.2) 18 ( 1.1) 263 ( 2.8) 19 ( 0.11 38 ( 1.0) 245 ( 1.5 270 ( 1.3 27 ( 1.4 30 ( 2.0 263 ( 2A 274 ( 1.3 17 ( 1.3) 48 ( 1.3) 280 ( 2.5) 281 ( 1.8) 25 ( 1.8) 32 ( 2.3) 263 ( 2.15) 279 ( 1.2) 21 ( 1.4) 93 ( 1.0) 239 ( 2.1) 259 ( 1.5) 28 ( 2.7) 22 ( 3.1) 237 ( 3.2) 256 ( 4.2) 18 ( 2.3) 27 ( 2.3) 22$ ( 3.4) 253 ( 3.2) 20 ( 8.2) isiv. ( ...) 21 ( .,...* ( 7.8) 441 14 ( 3.4) 51 ( 5.3) «Hi) 31 ( 3.8) 2$ ( 9.8) 281 ( 7.8)1 285 ( 4.2)1 17 ( 3.0) *In 33 ( 4.3) ***) 27 ( 2.9) 27 ( 4.8) 240 ( 4.9)1 203 ( 5.0)1 10 ( 1.9) 36 ( 1.9) 244 ( 3.8) 268 ( 1.0) 24 ( 0.6) ***) 37 ( 270 ( 8.3) 4,0)I 20 ( 1.0) 37 ( 1.2) 244 ( 1.8) 209 ( 1.7) 27 ( 1.8) 29 ( 2.1) 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 i within ± 2 standard errors of the estimate for the sample. The per,xntPos may not total 100 percent because the "Sometimes" category is not included. 1 Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students), 128 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico 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 MO NAEP TRIAL STATE ASSESSMENT T WorkiClng Problems in ass Doing Problems at Nome .. Taking Quizaes or Tests Almost Always Never Almost Always . . Never Almost Always , Never . VIA State Nation PARENTS' EDUCATION N3 noogradisate State Nation HI graduate State Nation Some college State Nation Deft"' graduato State Nation GENDER M. State Nation Female State Nation Percentage astri Proliciony 44 1.2) 24$ 1.0) 48 1.5) 254 1.5) 49 ( 10) 234 ( 2.1) 54 ( 3.3) 240 ( 2.3) 47 ( 2.4) 242 ( 1.7) 52 ( 2.5) 249 ( 1.4) 38 2.5) 253 ( 1.8) 46 ( 2.8) 258 ( VI) 41 ( 2.0) 2e1 ( 1.9) 45 ( 1.9) 265 ( 1.7) 48 ( 1.6) 251 ( 1.5) 50 ( 1.7) 256 ( 1.9) 41 ( 13) 244 ( 1.5) 48 ( 2.0) 252 ( 1.7) Percsenage and Proliciency Percentage and Proficiency Percentage end Proficiency Percentage end Proficiency Peotentage end Prolicioncif 27 ( 1.1) 24 0.9) 17 ( as) 19 ( 0.8) 38 ( 1.0) 268 ( 1.5) 255 262 ( 2.0) 245 ( 1.5) 270 ( 23 ( 1.9) 30 1.3 19 ( 04) 27 ( 1.4) 30( 2.0 272 ( 14) 261 ( 1.8 263 ( 1.8) 253 ( 2.4) 274 ( 1.3 28 ( 253 ( 2.8) 3-5) 18 ( 2.7) *.«.) 20 ( ipeo, 2/) 18 ( 235 ( 24) 4.1) 33 ( 253 ( 3.0) 2.9) *el 26 ( 244 ( 3.1) 3.8) 22 ( 244 ( 2.6) 4.2) 32 ( 237 ( 3.6) 2.3) 24 ( 251 ( 3.2) 4.6) 25 ( 2.0) 25 ( 1.8) 17 ( 1.3) 23 ( 1.5) 35 ( 2.0) 258 ( 2.3) 247 ( 2.3) 253 ( 2.9) 239 ( 2.8) 259 ( 1.9) 20 ( 2.4) 29 ( 1.9) 16 ( 1.5) 26 ( 1.8) 27 ( 2.2) 265 ( 2.7) 250 ( 2.4) 258 ( 2.4) 248 ( 2.8) 285 ( 2.0) 33 ( 2.8) 23 ( 2.1) 18 ( 1.7) 18 ( 1.9) 4t ( 2.4) 272 ( 2.7) 257 ( 2.5) 267 ( 4.0) 249 ( 2.7) 273 ( 1.8) 26 ( 2.8) 2$ ( 2.0) 20 ( 1.0) 26 ( 2.4) 35 ( 2.5) 272 ( 2.5) 267 ( 3.0) 268 ( 3.2) 255 ( 3.8) 275 ( 2.0) 28 ( 1.8) 28 ( 1.9) 18 ( 1.5) 18 ( 1.5) 42 ( 1.8) 283 ( 2.5) 268 ( 2.3) 280 ( 3.1) 280 ( 2.5) 285 ( 2.1) 25 ( 2.4) 33 ( 2.0) 18 ( 1.4) 28 ( 1.8) 33 ( 2.7) 284 ( 1.8) 274 ( 2.2) 276 ( 2.8) 268 ( 2.8) 285 ( 2.0) 25 ( 1.4) 25 ( 1.5) 17 ( 1.1) 18 ( 1.4) 36 ( 1.5) 272 ( 1.7) 258 ( 2.2) 268 ( 2.3) 248 ( 2.4) 275 ( 1.6) 20 ( 2.0) 23 ( 1.8) 19 ( 1.3) 27 ( 1.5) 26 ( 2.1) 275 ( 2.2) 264 ( 2.8) 263 ( 2.5) 256 ( 3.0) 277 ( 1.9) 30 ( 1.7) 24 ( 1.4) 17 ( 1.3) 20 ( 1.2) 40 ( 1.7) 265 ( 2.1) 252 ( 11) 258 ( 2.7) 243 ( 2.1) 288 ( 1.8) 26 ( 2.1) 32 ( 1.6) 18 ( 12) 27 ( 1.8) 33 ( 2.1) 269 ( 1.8) 259 ( 1.7) 263 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. 61** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 3 THE 1490 NAEP TRIAL STATE ASSESSMENT 129 New Mexico TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT High "Calculator-We" Group Other "Ca kulatorAlse" Droup TOTAL Percentage and Pridiciency Parasites& and Proficiency State 45 ( 1.3) 55 ( 1.3) 283 ( 1.2) 250 ( 1.0) Nation 42 ( 1.3) 56 ( 1.3) 272 ( 1.8) 255 ( 1.5) RACE/ETHIIICITY White State 51 ( 12) 49 ( 1.9) 278 ( 1.8) 200 ( 1.6) Nation 44 ( 1.4) 56 IA) 277 ( 1.7) 263 ( 1.7) Hispanic State 42 ( 2.0) 58 ( 2.0) 251 ( 1.7) 243 ( 1.4) Nation 38 ( 4.2) 64 ( 42) 254 ( 4.6) 238 ( 3.0) American Indian State 30 ( 2.9) 04 ( 2.9) 247 ( 3.8) 231 ( 2.3) Nation 29 (12.0) 44, 71 (12.0) - ipon TYPE OF COMMUNITY Advantaged urban State 80 ( 9.5) 40 ( 9.5) ( Nation 50 ( 3.8) 50 ( 3.8) 288 ( 4.9)1 275 ( 4.4)1 Disadvantaged ',Wm State 44 ( 8.8) 58 ( 8.8) ( Nation 38 ( 4.2) 82 ( 4.2) 282 ( 5.8)! 244 ( 3.9)1 Extreme rural State 41 ( 2.7) 59 ( 2.7) 281 ( 2.4) 249 ( 2.3) Nation 39 ( 5.8) 81 ( 5.8) 289 ( 4.4)1 248 ( 4.3)1 Other State 45 ( 1.4) 55 ( 1.4) 282 ( 1.5) 249 ( 1.3) Nation 42 ( 1.4) 58 ( 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 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). 13 3 130 THE 1990 NAEP TRIAL STATh ASSESSMENT New Mexico TABLE A20 I Students' Knowledge of Using Calculators (confirmed) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRLAI. STATE ASSESSMENT MO "Ca It:Water-Use" Oraie Other "Calculator-Use" Group TOTAL parawday and 'radio lacy Parconasea and ProGaisney State 45 ( 1.3) 55 ( 13) 263 ( 1.2) 250 ( 1.0) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.5) 255 1.5) PAREAffS EDUCATION NS non-graduate State 41 ( 3.6) 59 ( 3.6) 245 ( 237 ( 2.1) Nation 34 ( 3.3 248 ( 4.4 242 ( 2.4) NS graduate State 39 ( 2.4) 61 ( 2.4) Nation 252 ( 40 ( 2.6) 2.2) 244 ( 1.6) 00 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some collage State 44 ( 2.9) 56 ( 2.9) 266 ( 2.1) 258 ( 1.7) Nation 48 ( 2.2) 52 ( 2.2) 277 ( 2.6) 2S8 ( 2.5) College graduate State 55 ( 2.1) 45 ( 2.1) 278 ( 1.6) 285 ( 2.4) Nation 4$ ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER Male State 43 ( 2.0) 57 ( 2.0) 287 ( 1.8) 254 ( 1.7) Nation 30 ( 2.0) 01 ( 2.0) 274 ( 255 ( 23) Female state ate ( 1.9) 54 ( 1.9) 200 ( 1.8) 246 ( 1.6) Nation 45 ( 1.8) S5 ( 1.8) 209 ( 1.7) 264 ( 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. 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 New Mexico TABLE A24 I Students' Reports 'ypes of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MOO MEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Fair 1.111ms - TOTAL and Pr aftaknay PeraMillie and Prollatancy Pantants. and Prellaianay State 26 ( 1.4) 31 ( 0.9) 40 ( 1.1) 243 ( 1.4) 256 ( 1.1) 206 ( 1.3) Nation 21 ( 1.0) 30 ( 1.0) 46 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) RAU/ETHNICITY White State 16 ( 1.2) 30 ( 2.0) 55 ( 1.8) 262 ( 2.8) 269 ( 1.7) 276 ( 1.5) Nation 16 ( 1.1) 29 ( 1.3) 56 ( 1.5) 251 ( 22) 268 ( 1.5) 276 ( 1.7) Hispanic State 38 ( 1.8) 33 ( 1.3) 29 ( 1.5) 239 ( 13) 248 ( 1.4) 256 ( 2.0) Nation 44 ( 3.0) 30 ( 2.4) 2e ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) American Indian State 34 ( 2.5) 31 ( 2.1) 35 ( 2.4) 231 ( 3.1) 23$ ( 3.3) 243 ( 3.0) Nation 29 (11.1) 40 ( 4.9) 31 ( 92) 11,94 .41 TYPE OF COMMUNITY Mvantaged urban State 13 ( 8.5) 34 ( 7.8) 52 (12.3) ***) Nation 13 ( 3.8) 26 ( 2.1) 61 ( 4.9) 287 ( 3.6)1 Disadvantaged urban State 31 ( 51) 38 ( 4.0) 34 ( 0.1) edr* 41.114 IN* ( ) Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.6) 243 ( 2.9)! 247 ( 3.7)1 257 ( 4.9)1 Extreme wral State 26 ( 1.4) 34 ( 2.4) 40 ( 2.5) 244 ( 3.0) 252 ( 2.8) 259 ( 2.4) Nation 17 ( 4.9) .h.$) 33 ( 253 ( 3.2) 4.3)1 50 263 ( 5.1) ( 5.6)1 Other State 30 ( 1.4) 30 ( 1.0) 40 ( 4.2) 242 ( 1.5) 254 ( 1.4) 265 ( 1.6) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 13) 244 ( 2.6) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sa7.)ple. 'nterpret with caution -- the nature of the sample does not allow accurate determination of the vari0 dity estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 137 132 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A24 I Students' Reports on Types of Reading (c°ntinued) I Materials in the Home PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1380 MEP TRIAL. STATE ASSESSMENT Zara to Two Types Throw Types Rar Types TOTAL. and Prallciasay Parasalap Oralielsomar 1114woodiga and lionealeacy State 211 ( 1.1) 31 (0.9) 40( 243 ( 1.4) 258 1.1 286(1.3 Nation 21 ( 1.0) 30 (1.01 48 ( 1.3 244 ( 2.0) 2S8 272 ( 1.5) Melar.13MAIM le non-graduate State 55 ( 3.2) 28 ( 2.7) 16 ( 23) 239 ( 2.1) 242 ( 2.8) Mr* ( ***) Nation 47 ( 4.0) 2$ ( 3.0) 25 ( 2.6) 240 ( 3.4) 243 ( 3.3) 246 ( 3.3) RS graduals State 31 ( 2.0) 37 ( 1.9) 32 ( 2.3) 242 ( 2.3) 248 ( 1.7) 252 ( 24) Nation 26 ( 22) 33 ( 1.9) 40 ( 1.7) 248 ( 2.2) 253 ( 2.7) 200 ( 2.1) Sam collage State 23 ( 22) 33 ( 2.4) 44 ( 2.2) 238 ( 2.9) 25$ ( 2.3) 268 ( 2.2) Nation IT ( 15) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) Collage graduate State 14 ( 1.2) 28 ( 2.0) 58 ( 2.0) 253 ( 3.3) 272 ( 1.7) 276 ( 1.9) Nation 10 ( 0.8) 2$ ( 1.8) $2 ( 2.0) 254 ( 2.8) 260 f 2.5) 260 ( 1,6) GENDER Maio State 2$ ( 1.5) e ( 1.3) 41 ( 1.6) 246 ( 2.0) ( 1.5) 266 ( 1.6) Nation 21 ( 1.5) ( 1.5) 48 ( 1.4) 244 ( 2,3) 259 ( 2.1) 273 ( 2.0) Female State 29 ( 1.7) 31 ( 1.4) 40 ( 1.4) 240 ( 1.6) 252 ( 1.6) 264 ( 1.8) Nation 22 ( 1.2) 29 ( 1.4) 49 ( 1.9) 244 ( 2.2) 266 ( 1.9) 270 ( 1.7) AIL The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 138 THE 1990 NAEP TRIAL STATE ASSESSMENT 133 New Mexico TABLE A25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One Hour or Loss Two Hours Three HO= FOX to Five Hours SIX Hours or Afore TOTAL Pereenter and Preiciency 14 ( 0.6) 261 ( 2,0) 12 ( 0.8) 209 ( 2.2) 15 ( 1.1) 278 ( 2.3) 13 ( 1.0) 278 ( 2.5) 12 ( 0.9) 248 ( 2.9) 14 ( 2.4) 1144. ( Mal 15 ( 22) 13 ( 5.0) Olt ( ) 18 ( 1.5) 11.11 18 ( 1.4) ( 1.4) 9 ( 12) 44. ( 12 ( 1.3) 25$ ( 4.4) 14 ( 3.3) ,.) 15 ( 0.8) 260 ( 2.1) 12( 1.0) 268 ( 2.6) Peroentage end Proficiency 24 ( 1.0) 263 ( 1.7) 21 ( 0.9) 266 ( 1.8) 29 ( 2.1) 279 ( 2.3) 23 ( 12) 275 ( 2.2) 21 ( 1.1) 251 ( 2.3) 20 ( 2.5) 245 ( 3.2) 21 ( 2.2) 236 ( 2.7) 17 ( $.4) ***) 39 ( 8.8) 44. ( 4.1 25 ( 4.3) 22 ( 4.8) *** 17 ( 3.1) 250 ( 4.0)1 2$ ( 2.3) 257 ( 2.1) 19 ( 2.6) 23 ( 1.2) 262 ( 2.3) 21 ( 1.0) 209 ( 2.3) Perceitene and Proadency 24 ( 0.9) 257 ( 1.3) 22 ( 0.8) 265 ( 1.7) 24 ( 1.3) 271 ( 2.0) 24 ( 1.1) 272 ( 1.9) 24 ( 1.4) 249 ( 1.4) 19 ( 2.1) 242 ( 5.6) 26 ( 2.7) 239 ( 2.9) 21 (104) ***) 20 ( 2.7)) 21 ( 1.8) 4.4.) 27 ( 4.9) 19 ( 2.1) 25$ ( 5.0)1 26 ( 1.5) 252 ( 2.6) 23 ( 2.0) ( 24 ( 1.1) 257 ( 1.7) 23 ( 1.2) 265 ( 2.1) Percenisp end Preldency 2? ( 1.2) 252 ( 1.2) 26 ( 1.1) 200 ( 1.7) 23 ( 1.9) 264 ( 2.1) 27 ( 1.4) 207 ( 1.7) 32 ( 1.8) 248 ( 1.4) 31 ( 3.1) 247 ( 3.5) 24 ( 3.6) 245 ( 4.1) 28 ( 5.7) *4,1 14 ( 5.5) **- 30 ( 4.3) *** ( "e) 34 ( 64) ( 34 ( 2.4) 251 ( 4.7)1 28 ( 2.3) 251 ( 2.7) 20 ( 2.7) 256 ( 3.6)1 2? ( 1.4) 250 ( 1.4) 27 ( 1,2) 250 ( 2.2) Percentege and Prolidency 11 ( 0.7) 243 ( 2.0) 16 ( 1.0) 245 ( 1.7) ( 0.9) 257 ( 3.4) 12 ( 1.2) 253 ( 2,8) 12 ( 0.9) 239 ( 3.1) 17 ( 12) 236 ( 3.8) 14 ( 1.8) 22 ( 8.4) ***) 11 ( 5.4) it** 6 ( 2.0) 4,441 11 ( 2.7) 20 ( 3.2) 236 ( 44)! 9 ( 1.1) 244 ( 4.1) 19 ( 3.8) 12 ( 0.9) 240 ( 2.4) 17 ( 1.4) 240 ( 2.5) State Nation RACE/ETHNICITY White State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extrnme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 1 rl 11 4/ THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A25 I Students' Reports on the Amount of Time Spent (continued) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY .. 1900 NAEP TRIAL One How or TWo Fow to Five 3fx Hours or STATE ASSESSMENT Less Hours Three Hours Hours More _ TOTAL Peroenbige and Proficiency Peramtage and Ploilciency Patents IP and Proficiency Pintentags and itialidency PettaresiN and Predawn State 44 ( 0.0) 24 ( 1.0) 24 ( 0.9) 27 ( 1.2) 11 ( 0.7) 281 ( 2.0) 203 ( 1.7) 2571 12) 252 ( 1.2) 243 ( 2.0) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 ( 1.1) 16 ( 1.0) 209 ( 22) 2.8 ( 1.8) 265 ( 13) 260 ( 1.7) 245 ( 1.7) PARENTS EDUCATION HS non-graduate State 13 ( .44 ( 2.1) 21 ( 244 ( 2.9) 3.2) 21 ( 244 ( 3.3) 3.2) 29 ( 242 ( 3.4) 2.8) 10 ( 2.1) Nation 12 ( 22) 21 ( 2.8) set ( wen 28 ( 244 ( 2.9) 3.2) 20 ( 2.4) i Irtor) HS graduate State 10 ( 1.1) 23 ( 2.0) 25 ( 2.0) 30 ( 22) 11 ( 12) 247 ( 3.8) 250 ( 1.8) 249 ( 2.6) 247 ( 1.8) 241 ( 4.2) Nation 8 ( 1.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 19 ( 1.6) 249 ( 4.7) 257 ( 2.8) 259 ( 3.2) 253 ( 2.5) 243 ( 3.0) Sane college State 14 ( 1.7) ( 2.4) 20 ( 2.4) 28 ( 2.4) 8 ( 1.5) 260 ( 2.8) ( 3.1) 264 ( 2.6) 259 ( 2.3) Irft ***) Nation 10 ( 1.4) 25 ( 2.4) 23 ( 2.6) 28 ( 22) 14 ( 1.5) 275 ( 2.7) 289 ( 3.5) 267 ( 24) 242 ( 3.4) Coitege graduate State 18 ( 1.4) 27 ( 2.0) 23 ( 1.8) 22 ( 1.7) 10 ( 12) 279 ( 2.3) 281 ( 3.0) 271 ( 2.7) 26$ ( 2.5) 254 ( 3.1) Nation 17 ( 1.3) 22 ( 1.6) 23 ( 1.1) 25( 1.5) 12 ( 1.1) 282 ( 2.0) 280 ( 24) 277 ( 2.2) 270 ( 2.4) 255 ( 3.2) GENDER M. state 13 ( 1.0) 24 ( 1.4) 25 ( 1.3) 27 ( 15) 11 ( 1.0) 268 ( 2.9) 206 ( 1.8) 280 ( 2.0) 253 ( IA) 247 ( 2.1) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 28 ( 1.3) 17 ( 1.5) 269 ( 3.3) 207 ( 2.8) 287 ( 2.2) 262 ( 2.1) 248 ( 2.5) Femal state 15 ( 0.8) 24 ( 1.3) 23 ( 1.3) 27 ( 1.6) 11 ( 0.9) 255 ( 3.0) 201 ( 2.5) 254 ( 1.6) 251 ( 1.7) 238 ( 3.0) Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 1.6) 16 ( 1.2) 269 ( 2.8) 209 ( 2.2) 264 ( 1.8) 258 ( 1.9) 241 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 140 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 New Mexico TABLE A26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL STATE ASSESSMENT None _ One or Pim Days Uwe' Days or Mors TOTAL Parosntage Pre Adam lasrantage and Prolidecky Parcoalaga and Praildwicy State 35 ( 1.0) 3? ( 1.1) 27' ( 1.0) 262 ( 1.0) 250( 1.3) 245 ( 1.2) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 205 ( 1.8) age ( 1.5) 250 ( 1.0) RACE/ETHNICITY Mit* State 38 ( 2.1) 38 ( 22) 24 ( 1.5) 275 ( 1.6) 270 ( 2.0) 290 ( 1A) Nation 43 ( 1.2) 34 ( 1.2) 23 ( 12) 273 ( 1.8) 272 ( 1.7) 24$ ( 2.1) Hispanic State 34 ( 12) 36 ( 1.7) 30 ( 1.7) 253 ( 1.3) 248 ( 1.5) 240 ( 1.7) Nation 41 ( 3.3) 32 ( 22) 27 ( 2.0) 245 ( 4.0) 250 ( 3.3) 235 ( 3.1) American Indian State 32 ( 2.3) 36 ( 2.8) 32 ( 2.5) 244 ( 2.9) 241 ( 2.4) 22$ ( 2.6) Nation 23 ( *44 ( 6.6) .44) *1* 4141 38 ( «hi ( 52) TYPE Of COMMUNITY Advantaged urban State 47 ( 8.2) 36 ( .44 ( 8.1) 18 ( *** 3.5) Nation 47 ( 284 ( 2.3) 4.4)1 38 ( 279 ( 2.6) 4.5)1 15 ( ( 3.7) .44) Disadvantaged urban State 34 ( 4.8) 35 ( 3.9) 30 ( 3.1) 44. 444) Nation 42 ( 3.3) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 256 ( 4.2)1 238 ( 0.3)1 Eutrernit neat State 35 ( 2.1) 36 ( 2.4) 28 ( 1.5) 259 ( 1.4) 253 ( 2.4) 245 ( 2.0) Nation 43 ( 257 ( 4.4) 4.1)1 32 ( 264 ( 4.2) 5.8)1 25 ( .44 ( 3.9) Other State 36 ( 1.2) 37 ( 1.4) 27 ( 1.4) 201 ( 12) 258 ( 1.4) 243 ( 1.4) Nation 45 ( 1.3) 22 ( 1.1) 23 ( 1.1) 265 ( 2.2) 266 ( 1.9) 251 ( 2.4) 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. 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 1 I THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A26 I Students' Reports on the Number of Days of (continued) I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Nona Om or Two Days Throe Da Ys or Moro 1 TOTAL Pamela", and 14'4So:bogy Poroonlage and PreAdancy Parowdaga and Proildonoy State 30 ( 1.0) 37 ( 1.1) 27 ( 1.0) 262 ( 1.0) 250 ( 1.3) 245 ( 1.2) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 206( 1.5) 250 (1.9) PARENTS' EDUCATION NS noniraduato State 30 ( 3.3) 35 ( 2.6) 35 ( 2.9) 244 ( 2.7) 242 ( 32) 237 ( 2.6) Nation 36 ( 32) 20 ( 3.1) 38 ( 3.5) le graduate 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) State 36 ( 1.8) 35 ( 2.0) 29 ( 2.0) 254 ( 1.8) 248 ( 1.9) 240 ( 2.5) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.6) 249 ( 2.4) Some college State 36 ( 2.2) 39 ( 2.5) 2$ ( 2.0) 268 ( 2.3) 2es ( 1.7) 249 ( 2.7) Nation 40 ( 1.8) 37 ( 1.6) 23 ( 1.6) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) College graduate State 38 ( 1.5) 40 ( 2.3) 22 ( 1.9) 276 ( 2.0) 274 ( 2.7) 281 ( 2.4) Nation 51 ( 1.6) 33 ( 12) 18 ( 1-3) 275 ( 2.1) 277 ( 1.7) 285 ( 3.1) GENDER Male State 38 ( 1.4) 36 ( 1.4) 26 ( 1.3) 255 ( 1.3) 263 ( 2.1) 248 ( 1.7) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 1.4) 266 ( 2.0) 267 ( 2.1) 250 ( 2.8) Female State 35 ( 1.5) 37 ( 1.4) 28 ( 1.8) 259 ( 1.6) 256 ( 1.3) 244 ( 1.5) Nation 43 ( 1.4) 32 ( 1.1) 25 ( 1.3) 264 ( 2.3) 266 ( 1.7) 250 ( 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. 1 4 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 New Mexico TABLE Ari I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111110 NAV TRIAL STATE ASSESSMENT StronfilY AS mil *am Undedded, Disagree, Strongly Disagree TOTAL Panasniags and Pawl latency Parepatain and Praddaacy Parcentage and Pradalarny State 20 ( 13) Si ( 13) 23 ( 0.9) 268 ( 1.6) 256 ( 1.1) Nation 27 ( 13) 49 ( 1.0) 24 1.2 271 ( 1.9) 262 ( 1.7) 251 1.8 RegaNI_IICITY %MN* State 32 ( 2.4) 44 ( 2.0) 20 ( 1.4) 281 ( 2.4) 272 ( 1.5) 258 ( 1.8) Nation 26 ( 1.6) 411 ( 1.3) 211 ( 1.5) libpanle 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) State 23 ( 1.6) 53 ( 2.0) 24 ( 1.4) 256 ( 1.7) 244 ( 1.2) 237 ( 2.0) Nation 24 ( 2.5) 44 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 236 ( 3.8) American Indian State 19 ( 3.5) 51 ( 3.6) 29 ( 2.2) 247 ( 3.4) 240 ( LS) 226 ( 3.3) Nation 23 ( 7.4) 48 (14.9) 29 ( 44 9.5).) TYPE OF COMMUNITY Advantaged urtan State 42 ( 1.4) 40 ( 4.8) 18 ( 3.2) ( Nation 17 ( 32) 55 ( 2.4) 24 ( 4.2) 280 ( 4.1)1 Disadvantaged urban State 45 ( 5.1) 21 ( 4.8) ( ***I Nation 28 ( 2.9) 44 ( 2.9) 26 ( 3.2) 200 ( 5.6)1 249 ( 4.8)1 240 ( 4.5)1 Extreme rural State 22 ( 1.5) 51 ( 2.6) 27 ( 2.5) 262 ( 2.7) 254 ( 2.3) 244 ( 2.8) Nation 34 270 ( 2.8) 3.9)1 49 ( 252 ( 22) 4.1)1 17 ( ( 1.4) **A) Other State 25 ( 1.5) 52 ( 1.7) 23 ( 1.0) 267 ( 2.1) 255 ( 1.2) 241 ( 1.5) 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 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 If the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 135 THE 1990 NAEP TRIAL STATE ASSESSMENT New Mexico TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE 14311ESSMENT StrontOY Agivs Are* ecidad. Disagras, Strongly Disagree .. TOTAL Peroontaga and lirolidancy Porcantage and Proliciaim Percantage and Proadancv State 24 ( 1.3) 51 ( 1.3) 23 ( 0.9) 236 ( 1.6) 2$6 ( 1.1) 243 ( 1.2) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 202 ( 1.7) 251 ( 1.9) PARENTS EDUCATION 1111 non-gracluato State 20 ( 2.1) 47 ( 3.8) 33 ( 3.4) 246 ( 3.5) 243 ( 2.7) 232 ( 3.1) Nation SO ( 3.3) 30 ( 3.6) 243 ( 2.6) 238 ( 4.3) NS graduate State 22 ( 2.3) 54 ( 2.3) 24 ( 1.9) 256 ( 2.6) 247 ( 1.8) 241 ( 2.4) Nation 27 ( 2.1) 47 ( 2.3) 26 ( 2.0) 262 ( 2.7) 255 ( 2.3) 245 ( 2.4) Soma collage State 27 ( 2.7) 51 ( 2.5) 22 ( 1.8) 273 ( 2.9) 261 ( 2.0) 251 ( 2.7) Nation 28 ( 2.5) 47 ( 2.4) 25 ( 1.6) 274 ( 3.1) 267 1.9) 258 ( 32) College graduate State ( 1.9) 49 ( 13) 17 ( 1.3) 279 ( 2.5) 273 ( 1.7) 256 ( 2.0) Nation 30 ( 2.3) 51 ( 1.6) 19 ( 1.8) 280 ( 2.4) 274 ( 2.2) 266 ( 2.5) GENDER Mal. State 27 ( 1.8) 52 ( 1.6) 20 ( 1.3) 272 ( 2.4) 25$ ( 1.2) 240 ( 13) Nation 2$ ( 1.5) 4$ ( 1.2) 24 ( 1.4) 273 ( 2.3) 283 ( 2.0) 251 ( 2.4) Female State 25 ( 1.3) 49 ( 1.6) 26 ( 1.5) 285 ( 1.8) 255 ( 1.7) 240 ( 1.7) Nation 26 ( 1.7) 50( 1.7) 25 ( 1.9) 289 ( 2.1) 262 ( 13) 252 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 'Po* Sample size is insuflicient to permit a reliable estimate (fewer than 62 students). 1 4 1 THE 1993 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, developinent 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), Educatkinal 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 Govereors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Finally, and most importantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment Special recognition is due the Council of Chief State School Officers (CCSSO) for its considerable contributions to the program, especially its management of the National Assessment Planning Project. That project resulted in the mathematics framework and objectives for the assessment and recotnmendations about reporting the results of the program. In particular, we note the significant contra:mikes of Ramsay Selden, Director of the State Education Assessment Cosner for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGS) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Devolopment and Mathematim Scale Anchoring Panels. These people from school districts, colleges and universities, and State Education Agencies worked tirelessly to help ETS staff develop the a.ceccment and a framework for interpreting the results. Under the NAEP contract to ETS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mazzeo, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffler, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distaution, and processing of the materials were the responslility 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 conputer-generated data with high resolution text &Ad graphics normally found only in typeselting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Mane° oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koffler wrote the teat for the report. Kent Ashworth was responsUe 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. ti cr.; UR GOVERNMENT PRINTING OFFICE 1991 0 - 293-275 QL 3 (BK. 35) 14C