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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 TIMSS 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)

- Which Countries Participated?

Table 1: TIMSS 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 TIMSS Countries

Table 4: Public Expenditure on Education at Primary and Secondary Levels in TIMSS 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 TIMSS Procedures: Mathematics

Achievement Results for Third- and Fourth-Grade Students

- History

- The Components of TIMSS

Figure A.1: Countries Participating in Additional Components
of

TIMSS Testing

- Developing the TIMSS 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

- TIMSS Test Design

- Sample Implementation and Participation Rates

Table A.2: Coverage of TIMSS 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: TIMSS Within-Country Free-Response Coding Reliability
Data

for Population 2 Mathematics Items

- Test Reliability

- Data Processing

Table A.10: Cronbach's Alpha Reliability Coefficients - TIMSS 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)

© 1997 International Association for the Evaluation of Educational Achievement (IEA).

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 TIMSS contact:

The International Study Center

Boston College

Manresa House

140 Commonwealth Avenue

Chestnut Hill, MA 02467

United States

Funding for the international coordination of TIMSS 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 TIMSS.

The Mathematics Achievement in the Primary School Years was released in June 1998 and written by Ina V.S. Mullis, Michael O. Martin, Albert E. Beaton, Eugenio J. Gonzalez, Dana L. Kelly, and Teresa A. Smith.