魅影直播 1995 Mathematics in the Primary School Years: Table of Contents

TABLE OF CONTENTS for Mathematics Achievement in the Primary School Years: IEA's Third International Mathematics and Science Report

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Executive Summary

Introduction

Chapter 1: International Student Achievement in Mathematics

Chapter 2: Average Achievement in the Mathematics Content Areas

Chapter 3: Performance on Items Within Each Mathematics Content Area

Chapter 4: Students' Backgrounds and Attitudes Towards Mathematics

Chapter 5: Teachers and Instruction

Appendix A: Overview of 魅影直播 Procedures

Appendix B: The Test-Curriculum Matching Analysis

Appendix C: Percentiles and Standard Deviations of Science Achievement

Appendix D: Acknowlegements

Table of Contents (PDF format, includes page numbers)

Executive Summary

Introduction

Which Countries Participated?

Table 1: 魅影直播 Countries Testing in the Primary Grades

Table 2: Information About the Grades Tested

What Was the Nature of the Mathematics Test?

How Do Country Characteristics Differ?

Table 3: Selected Demographic Characteristics of 魅影直播 Countries

Table 4: Public Expenditure on Education at Primary and Secondary Levels in 魅影直播 Countries

Figure 1: Centralization of Decision-Making Regarding Curriculum Syllabi

Figure 2: Centralization of Decision-Making Regarding Textbooks

Figure 3: Centralization of Decision-Making Regarding Examinations

Chapter 1 : International Student Achievement in Mathematics

What Are the Overall Differences in Mathematics Achievement?

Table 1.1: Distributions of Mathematics Achievement - Upper Grade
(Fourth Grade)

Figure 1.1: Multiple Comparisons of Mathematics Achievement - Upper Grade
(Fourth Grade)

Table 1.2: Distributions of Mathematics Achievement - Lower Grade
(Third Grade)

Figure 1.2: Multiple Comparisons of Mathematics Achievement - Lower Grade
(Third Grade)

What Are the Increases in Achievement Between the Lower and
Upper Grades?

Table 1.3: Achievement Differences in Mathematics Between Lower and Upper Grades
(Third and Fourth Grades)
What Are the Differences in Performance Compared to Three Marker Levels of International Mathematics Achievement?

Table 1.4: Percentages of Students Achieving International Marker Levels in Mathematics - Upper Grade (Fourth Grade)

Table 1.5: Percentages of Students Achieving International Marker Levels in Mathematics - Lower Grade (Third Grade)

What Are the Gender Differences in Mathematics Achievement?

Table 1.6: Gender Differences in Mathematics Achievement - Upper Grade
(Fourth Grade)

Table 1.7: Gender Differences in Mathematics Achievement - Lower Grade
(Third Grade)

What Are the Differences in Median Performance at Age 9?

Table 1.8: Median Mathematics Achievement: 13-Year-Old Students

How Does Fourth-Grade Performance Compare with Eighth-Grade Performance?

Figure 1.3: Mathematics Performance at Fourth and Eighth Grades Compared with the International Averages

Table 1.9: Increases in Mathematics Performance Between the Fourth and Eighth Grades

Chapter 2 : Average Achievement in the Mathematics Content Areas

How Does Achievement Differ Across Mathematics Content Areas?

Table 2.1: Average Percent Correct by Mathematics Content Areas -
Upper Grade (Fourth Grade)

Table 2.2: Average Percent Correct by Mathematics Content Areas -
Lower Grade (Third Grade)

Table 2.3: Profiles of Relative Performance in Mathematics Content Areas -
Lower and Upper Grades (Third and Fourth Grades)

What Are the Increases in Achievement Between the Lower and
Upper Grades?

Figure 2.1: Difference in Average Percent Correct Between Lower and
Upper Grades (Third and Fourth Grades) Overall and in Mathematics
Content Areas

What Are the Gender Differences in Achievement for the
Content Areas?

Table 2.4: Average Percent Correct for Boys and Girls by Mathematics
Content Areas - Upper Grade (Fourth Grade)

Table 2.5: Average Percent Correct for Boys and Girls by Mathematics
Content Areas - Lower Grade (Third Grade)

Chapter 3: Performance on Items Within Each Mathematics
Content Area

What Have Students Learned About Whole Numbers?

Table 3.1: Percent Correct for Example Item 1 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.2: Percent Correct for Example Item 2 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.3: Percent Correct for Example Item 3 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.4: Percent Correct for Example Item 4 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.5: Percent Correct for Example Item 5 -
Lower and Upper Grades (Third and Fourth Grades)

Figure 3.1: International Difficulty Map for Whole Numbers Example Items- Lower and Upper Grades (Third and Fourth Grades)

What Have Students Learned About Fractions and Proportionality?

Table 3.6: Percent Correct for Example Item 6 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.7: Percent Correct for Example Item 7 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.8: Percent Correct for Example Item 8 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.9: Percent Correct for Example Item 9 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.10: Percent Correct for Example Item 10 -
Lower and Upper Grades (Third and Fourth Grades)

Figure 3.2: International Difficulty Map for Fractions and Proportionality Example Items - Lower and Upper Grades (Third and Fourth Grades)

What Have Students Learned About Measurement, Estimation,
and Number Sense?

Table 3.11: Percent Correct for Example Item 11 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.12: Percent Correct for Example Item 12 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.13: Percent Correct for Example Item 13 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.14: Percent Correct for Example Item 14 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.15: Percent Correct for Example Item 15 -
Lower and Upper Grades (Third and Fourth Grades)

Figure 3.3: International Difficulty Map for Measurement, Estimation, and Number Sense Example Items - Lower and Upper Grades (Third and Fourth Grades)

What Have Students Learned About Data Representation, Analysis,
and Probability?

Table 3.16: Percent Correct for Example Item 16 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.17: Percent Correct for Example Item 17 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.18: Percent Correct for Example Item 18 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.19: Percent Correct for Example Item 19 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.20: Percent Correct for Example Item 20 -
Lower and Upper Grades (Third and Fourth Grades)

Figure 3.4: International Difficulty Map for Data Representation, Analysis, and Probability Example Items - Lower and Upper Grades (Third and Fourth Grades)

What Have Students Learned About Geometry?

Table 3.21: Percent Correct for Example Item 21 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.22: Percent Correct for Example Item 22 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.23: Percent Correct for Example Item 23 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.24: Percent Correct for Example Item 24 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.25: Percent Correct for Example Item 25 -
Lower and Upper Grades (Third and Fourth Grades)

Figure 3.5: International Difficulty Map for Geometry Example Items -
Lower and Upper Grades (Third and Fourth Grades)

What Have Students Learned About Patterns, Relations, and Functions?

Table 3.26: Percent Correct for Example Item 26 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.27: Percent Correct for Example Item 27 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.28: Percent Correct for Example Item 28 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.29: Percent Correct for Example Item 29 -
Lower and Upper Grades (Third and Fourth Grades)

Table 3.30: Percent Correct for Example Item 30 -
Lower and Upper Grades (Third and Fourth Grades)

Figure 3.6: International Difficulty Map for Patterns, Relations, and Functions Example Items - Lower and Upper Grades (Third and Fourth Grades)

Chapter 4 : Students' Backgrounds and Attitudes Towards Mathematics

What Educational Resources Do Students Have in Their Homes?

Table 4.1: Students' Reports on Educational Aids in the Home: Dictionary, Study Desk/Table, and Computer

Table 4.2: Students' Reports on the Number of Books in the Home

Table 4.3: Students' Reports on Frequency with Which They Speak the Language of the Test at Home

Table 4.4: Students' Reports on Whether or Not Their Parents Were Born in the Country

Table 4.5: Students' Reports on Whether or not They were Born in the Country

What Are the Academic Expectations of Students, Their Families, and Their Friends?

Table 4.6: Students' Reports on Whether They Think That It Is Important to Do Various Activities

Table 4.7: Students' Reports on Whether Their Mothers Agree or Strongly Agree That It is Important to Do Various Activities

Table 4.8: Students' Reports on Whether Their Friends Think That It Is Important to Do Various Activities

How Do Students Spend Their Out-of-School Time During the School Week?

Table 4.9: Students' Reports on th Amount of Out-of-School Time Spent Studying Mathematics or Doing Mathematics Homework on a Normal School Day

Table 4.10: Students' Reports on How They Spend Their Leisure Time on a Normal

Table 4.11: Students' Reports on the Hours Spent Each Day Watching
Television and Videos on a Normal School Day

How Do Students Perceive Success in Mathematics?

Table 4.12: Students' Self-Perceptions About Usually Doing Well in Mathematics

Figure 4.1: Gender Differences In Students' Self-Perceptions About Usually Doing Well in Mathematics

Table 4.13: Students' Reports on Things Necessary to Do Well in Mathematics

What Are Students' Attitudes Towards Mathematics?

Table 4.14: Students' Reports on How Much They Like Mathematics

Figure 4.2: Gender Differences in Liking Mathematics

Table 4.15: Students' Overall Attitudes Towards Mathematics

Figure 4.3: Gender Differences in Students' Overall Attitudes Towards Mathematics

Chapter 5 : Teachers and Instruction

Who Delivers Mathematics Instruction?

Table 5.1: Requirements for Certification Held by the Majority of Lower- and Upper-Grade Teachers

Table 5.2: Teachers' Reports on Their Age and Gender

Table 5.3: Teachers' Reports on Their Years of Teaching Experience

What Are Teachers' Perceptions About Mathematics?

Figure 5.1: Percentage of Students Whose Mathematics Teachers Agree or Strongly Agree with Statements About the Nature of Mathematics and Mathematics Teaching

Figure 5.2: Percent of Students Whose Mathematics Teachers Think Particular Abilities Are Very Important for Students' Success in Mathematics in School

How Do Mathematics Teachers Spend Their School-Related Time?

Table 5.4: Teachers' Reports on Average Number of Hours Mathematics Is Taught Weekly to Their Mathematics Classes

Figure 5.3: Percent of Students Who Are Taught Both Mathematics and Science by a Single Classroom Teacher

Table 5.5: Average Number of Hours Students' Teachers Spend on Various School-Related Activities Outside the Formal School Day During the School Week

Table 5.6: Teachers' Reports on How Often They Meet with Other Teachers in Their Subject Area to Discuss and Plan Curriculum or Teaching Approaches - Upper Grade (Fourth Grade)

How Are Mathematics Classes Organized?

Figure 5.4: Teachers' Reports on What Factors Limit How They Teach Class

Table 5.7: Teachers' Reports on Average Size of Mathematics Class

Figure 5.4: Teachers' Reports About Classroom Organization During Mathematics Lessons

What Activities Do Students Do in Their Mathematics Lessons?

Table 5.8: Teachers' Reports on Their Familiarity with National and Regional Mathematics Curriclum Guides

Table 5.9: Teachers' Reports on Their Main Sources of Writt nforation When Deciding Which Topics to Teach and How to Present a Topic

Figure 5.6: Teachers' Reports About Using a Textbook in Teaching Mathematics

Table 5.10: Teachers' Reports on How Often They Ask Students to Practice Computational Skills

Table 5.11: Teachers' Reports on How Often They Ask Students to Do Reasoning Tasks

Table 5.12: Students' Reports on Using Things from Everyday Life in Solving Mathematics Problems

How Are Calculators and Computers Used?

Table 5.13: Students' Reports on Having a Calculator and Computer in the Home

Table 5.14: Teachers' Reports on Frequency of Students' Use of Calculators in Mathematics Class

Table 5.15: Teachers' Reports on Ways in Which Calculators Are Used at Least Once or Twice a Week

Table 5.16: Students' Reports on Frequency of Using Calculators in Mathematics Class

Table 5.17: Teachers' Reports on Frequency of Using Computers in Mathematics Class to Solve Exercises or Problems

Table 5.18: Students' Reports on Frequency of Using Computers in Mathematics Class

How Much Homework Are Students Assigned?

Table 5.19: Teachers' Reports About the Amount of Mathematics Homework Assigned

Table 5.20: Teachers' Reports on Their Use of Students' Written Mathematics Homework

Appendix A: Overview of 魅影直播 Procedures: Mathematics
Achievement Results for Third- and Fourth-Grade Students

History
The Components of 魅影直播

Figure A.1: Countries Participating in Additional Components of
魅影直播 Testing

Developing the 魅影直播 Mathematics Test

Figure A.2: The Three Aspects and Major Categories of the Mathematics Framework

Table A.1: Distribution of Mathematics Items by Content Reporting Category
and Performance Category

魅影直播 Test Design
Sample Implementation and Participation Rates

Table A.2: Coverage of 魅影直播 Target Population

Table A.3: Coverage of 9-Year-Old Students

Table A.4: School Participation Rates and Sample Sizes - Upper Grade
(Fourth Grade)

Table A.5: Student Participation Rates and Samples Sizes - Upper Grade
(Fourth Grade)

Table A.6: School Participation Rates and Sample Sizes - Lower Grade
(Third Grade) .

Table A.7: Student Participation Rates and Samples Sizes - Lower Grade
(Third Grade)

Table A.8: Overall Participation Rates - Upper and Lower Grades
(Fourth and Third Grades)

Indicating Compliance with Sampling Guidelines in the Report

Figure A.3: Countries Grouped for Reporting of Achievement According to Their Compliance with Guidelines for Sample Implementation and Participation Rates

Data Collection
Scoring the Free-Response Items

Table A.9: 魅影直播 Within-Country Free-Response Coding Reliability Data
for Population 2 Mathematics Items

Test Reliability
Data Processing

Table A.10: Cronbach's Alpha Reliability Coefficients - 魅影直播 Mathematics Test - Lower and Upper Grades (Third and Fourth Grades)

IRT Scaling and Data Analysis
Estimating the Link Between Fourth- and Eighth Grade Performance

Table A.11: Mathematics Performance at the Third, Fourth, Seventh, and Eighth Grades based on the Population 2 (Seventh- and Eighth-Grade) Scale

Estimating Sampling Error

Appendix B: The Test-Curriculum Matching Analysis

Table B.1: Test-Curriculum Matching Analysis Results - Mathematics -
Upper Grade (Fourth Grade)

Table B.2: Test-Curriculum Matching Analysis Results - Mathematics -
Lower Grade (Third Grade)

Table B.3: Standard Errors for the Test-Curriculum Matching Analysis Results - Mathematics - Upper Grade (Fourth Grade)

Table B.4: Standard Errors for the Test-Curriculum Matching Analysis Results - Mathematics - Lower Grade (Third Grade)

Appendix C: Percentiles and Standard Deviations of Mathematics Achievement

Table C.1: Percentiles of Achievement in Mathematics - Upper Grade (Fourth Grade)

Table C.1: Percentiles of Achievement in Mathematics - Lower Grade (Third Grade)

Table C.1: Standard Deviations of Achievement in Mathematics - Upper Grade
(Fourth Grade)

Table C.1: Standard Deviations of Achievement in Mathematics - Lower Grade
(Third Grade)

Appendix D: Acknowledgments

Mathematics Achievement in the Primary School Years: IEA's Third International Mathematics and Science Study / by Ina V.S. Mullis, Michael O. Martin, Albert E. Beaton, Eugenio J. Gonzalez, Dana L. Kelly, and Teresa A. Smith

Publisher: Center for the Study of Testing, Evaluation, and Educational Policy,
Boston College.

Library of Congress Catalog Card Number: 97-67235

ISBN 1-889938-04-1

For more information about 魅影直播 contact:

The International Study Center
Boston College
Manresa House
140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

Funding for the international coordination of 魅影直播 is provided by the U.S. National Center for Education Statistics, the U.S. National Science Foundation, the IEA, and the Canadian government. Each participating country provides funding for the national implementation of 魅影直播.

魅影直播 1995 is a project of the International Study Center
Boston College, Lynch School of Education