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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: Selected Mathematics Achievement Results for
the Philippines

Appendix D: Selected Mathematics Achievement Results for
Denmark, Sweden, and Switzerland (German Speaking) - Eighth Grade

Appendix E: Percentiles and Standard Deviations of Mathematics
Achievement

Appendix F: Acknowlegements

Table of Contents (PDF format, includes page numbers)

- Which Countries Participated?

Table 1: Countries Participating in TIMSS

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

(Eighth Grade)

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

Table 1.2: Distributions of Mathematics Achievement - Lower
Grade

(Seventh Grade)

Figure 1.2: Multiple Comparisons of Mathematics Achievement - Lower Grade (Seventh 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 (Seventh and Eighth 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 (Eighth Grade)

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

- What Are the Gender Differences in Mathematics Achievement?

Table 1.6: Gender Differences in Mathematics Achievement
- Upper Grade

(Eighth Grade)

Table 1.7: Gender Differences in Mathematics Achievement
- Lower Grade

(Seventh Grade)

- What Are the Differences in Median Performance at Age 13?

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

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 (Eighth Grade)

Table 2.2: Average Percent Correct by Mathematics Content
Areas -

Lower Grade (Seventh Grade)

Table 2.3: Profiles of Relative Performance in Mathematics
Content Areas -

Lower and Upper Grades (Seventh and Eighth 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 (Seventh and Eighth 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 (Eighth Grade)

Table 2.5: Average Percent Correct for Boys and Girls by
Mathematics

Content Areas - Lower Grade (Seventh Grade)

Chapter 3: Performance on Items Within Each Mathematics

Content Area

- What Have Students Learned About Fractions and Number Sense?

Table 3.1: Percent Correct for Fractions and Number Sense
Example Items -

Lower and Upper Grades (Seventh and Eighth Grades)

Figure 3.1: International Difficulty Map for Fractions and
Number Sense

Example Items - Lower and Upper Grades (Seventh and Eighth Grades)

Fractions and Number Sense Example Items

- What Have Students Learned About Geometry?

Table 3.2: Percent Correct for Geometry Example Items -
Lower and

Upper Grades (Seventh and Eighth Grades)

Figure 3.2: International Difficulty Map for Geometry Example Items - Lower and Upper Grades (Seventh and Eighth Grades)

Geometry Example Items

- What Have Students Learned About Algebra?

Table 3.3: Percent Correct for Algebra Example Items - Lower and Upper Grades (Seventh and Eighth Grades)

Figure 3.3: International Difficulty Map for Algebra Example Items - Lower and Upper Grades (Seventh and Eighth Grades)

Algebra Example Items

- What Have Students Learned About Data Representation, Analysis,

and Probability?

Table 3.4: Percent Correct for Data Representation, Analysis, and Probability Example Items - Lower and Upper Grades (Seventh and Eighth Grades)

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

Data Representation, Analysis, and Probability Example Items

- What Have Students Learned About Measurement?

Table 3.5: Percent Correct for Measurement Example Items - Lower and Upper Grades (Seventh and Eighth Grades)

Figure 3.5: International Difficulty Map for Measurement
Example Items -

Lower and Upper Grades (Seventh and Eighth Grades)

Measurement Example Items

- What Have Students Learned About Proportionality?

Table 3.6: Percent Correct for Proportionality Example Items - Lower and Upper Grades (Seventh and Eighth Grades)

Figure 3.6: International Difficulty Map for Proportionality
Example Items -

Lower and Upper Grades (Seventh and Eighth Grades)

Proportionality Example Items

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 - Upper Grade (Eighth Grade)

Table 4.2: Students' Reports on the Number of Books in the Home - Upper Grade (Eighth Grade)

Table 4.3: Students' Reports on the Highest Level of Education of Either Parent - Upper Grade (Eighth Grade)

Figure 4.1: Country Modifications to the Definitions of Educational Levels for Parents' Highest Level of Education

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

Table 4.4: Students' Reports on Whether They Agree or Strongly Agree That It is Important to Do Various Activities - Upper Grade (Eighth Grade)

Table 4.5: Students' Reports on Whether Their Mothers Agree or Strongly Agree That It is Important to Do Various Activities - Upper Grade (Eighth Grade)

Table 4.6: Students' Reports on Whether Their Friends Agree or Strongly Agree That It is Important to Do Various Activities - Upper Grade (Eighth Grade)

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

Table 4.7: Students' Reports on How They Spend Their Daily Out-of-School Study Time - Upper Grade (Eighth Grade)

Table 4.8: Students' Reports on How They Spend Their Daily
Leisure Time -

Upper Grade (Eighth Grade)

Table 4.9: Students' Reports on Total Amount of Daily Out-of-School Study Time - Upper Grade (Eighth Grade)

Table 4.10: Students' Reports on the Hours Spent Each Day
Watching

Television and Videos - Upper Grade (Eighth Grade) .

- How Do Students Perceive Success in Mathematics?

Table 4.11: Students' Self-Perceptions About Usually Doing Well in Mathematics - Upper Grade (Eighth Grade)

Figure 4.2: Gender Differences In Students' Self-Perceptions About Usually Doing Well in Mathematics - Upper Grade (Eighth Grade)

Table 4.12: Students' Reports on Things Necessary to Do Well in Mathematics - Upper Grade (Eighth Grade)

Table 4.13: Students' Reports on Why They Need to Do Well in Mathematics - Upper Grade (Eighth Grade)

What Are Students' Attitudes Towards Mathematics?

Table 4.14: Students' Reports on How Much They Like Mathematics - Upper Grade (Eighth Grade)

Figure 4.3: Gender Differences in Liking Mathematics - Upper Grade (Eighth Grade)

Table 4.15: Students' Overall Attitudes Towards Mathematics
- Upper Grade

(Eighth Grade)

Figure 4.4: Gender Differences in Students' Overall Attitudes Towards Mathematics - Upper Grade (Eighth Grade)

Chapter 5 : Teachers and Instruction

- Who Delivers Mathematics Instruction?

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

Table 5.2: Teachers' Reports on Their Age and Gender - Upper Grade (Eighth Grade)

Table 5.3: Teachers' Reports on Their Years of Teaching Experience - Upper Grade (Eighth Grade)

- 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 - Upper Grade (Eighth Grade)

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

Upper Grade (Eighth Grade)

- How Do Mathematics Teachers Spend Their School-Related Time?

Table 5.4: Teachers' Reports on the Proportion of Their Formally Scheduled School Time Spent Teaching Mathematics - Upper Grade (Eighth Grade)

Table 5.5: Teachers' Reports on Average Number of Hours Mathematics Is Taught Weekly to Their Mathematics Classes - Upper Grade (Eighth Grade)

Table 5.6: Average Number of Hours Students' Teachers Spend on Various School-Related Activities Outside the Formal School Day During the School Week - Upper Grade (Eighth Grade)

Table 5.7: Teachers' Reports on How Often They Meet with Other Teachers in Their Subject Area to Discuss and Plan Curriculum or Teaching Approaches - Upper Grade (Eighth Grade)

- How Are Mathematics Classes Organized?

Table 5.8: Teachers' Reports on Average Size of Mathematics Class - Upper Grade (Eighth Grade)

Figure 5.3: Teachers' Reports About Classroom Organization During Mathematics Lessons - Upper Grade (Eighth Grade)

- What Activities Do Students Do in Their Mathematics Lessons?

Table 5.9: Teachers' Reports on Their Main Sources of Written
Information When Deciding Which Topics to Teach and How to Present a Topic
- Upper Grade

(Eighth Grade)

Figure 5.4: Teachers' Reports About Using a Textbook in Teaching Mathematics - Upper Grade (Eighth Grade)

Table 5.10: Teachers' Reports on How Often They Ask Students to Practice Computational Skills - Upper Grade (Eighth Grade)

Table 5.11: Teachers' Reports on How Often They Ask Students to Do Reasoning Tasks - Upper Grade (Eighth Grade)

Table 5.12: Students' Reports on Frequency of Using Things from Everyday Life in Solving Mathematics Problems - Upper Grade (Eighth Grade)

- How Are Calculators and Computers Used?

Table 5.13: Students' Reports on Having a Calculator and Computer in the Home - Upper Grade (Eighth Grade)

Table 5.14: Teachers' Reports on Frequency of Students' Use of Calculators in Mathematics Class - Upper Grade (Eighth Grade)

Table 5.15: Teachers' Reports on Ways in Which Calculators Are Used at Least Once or Twice a Week - Upper Grade (Eighth Grade)

Table 5.16: Students' Reports on Frequency of Using Calculators in Mathematics Class - Upper Grade (Eighth Grade)

Table 5.17: Teachers' Reports on Frequency of Using Computers in Mathematics Class to Solve Exercises or Problems - Upper Grade (Eighth Grade)

Table 5.18: Students' Reports on Frequency of Using Computers in Mathematics Class - Upper Grade (Eighth Grade)

- How Much Homework Are Students Assigned?

Table 5.19: Teachers' Reports About the Amount of Mathematics Homework Assigned - Upper Grade (Eighth Grade)

Table 5.20: Teachers' Reports on Their Use of Students' Written Mathematics Homework - Upper Grade (Eighth Grade) .

- What Assessment and Evaluation Procedures Do Teachers Use?

Table 5.21: Teachers' Reports on the Types of Assessment
Given "Quite A Lot" or

"A Great Deal" of Weight in Assessing Students' Work in Mathematics
Class - Upper Grade (Eighth Grade)

Table 5.22: Teachers' Reports on Ways Assessment Information
Is Used

"Quite A Lot" or "A Great Deal" - Upper Grade (Eighth
Grade)

Table 5.23: Students' Reports on Frequency of Having a Quiz or Test in Their Mathematics Lessons - Upper Grade (Eighth Grade)

Appendix A: Overview of TIMSS Procedures: Mathematics

Achievement Results for Seventh- and Eighth-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 13-Year-Old Students

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

(Eighth Grade)

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

(Eighth Grade)

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

(Seventh Grade) .

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

(Seventh Grade)

Table A.8: Overall Participation Rates - Upper and Lower
Grades

(Eighth and Seventh 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

Table A.10: Percent Exact Agreement for Coding of Mathematics Items for International and Within-Country Reliability Studies

- Test Reliability

Table A.11: Cronbach's Alpha Reliability Coefficients -
TIMSS Mathematics

Test - Lower and Upper Grades (Seventh and Eighth Grades)

- Data Processing

- IRT Scaling and Data Analysis

- Estimating Sampling Error

Appendix B: The Test-Curriculum Matching Analysis

Table B.1: Test-Curriculum Matching Analysis Results - Mathematics -

Upper Grade (Eighth Grade)Table B.2: Test-Curriculum Matching Analysis Results - Mathematics -

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

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

Appendix C: Selected Mathematics Achievement Results for

The Philippines

Table C.1: Philippines - Selected Mathematics Achievement Results -

Unweighted Data

Appendix D: Selected Mathematics Achievement Results for Denmark, Sweden, and Switzerland (German-Speaking)–Eighth Grade

Table D.1: Denmark - Selected Mathematics Achievement Results

Table D.2: Sweden - Selected Mathematics Achievement Results

Table D.3: Switzerland (German-Speaking) - Selected Mathematics

Achievement Results

Appendix E: Percentiles and Standard Deviations of Mathematics Achievement

Table E.1: Percentiles of Achievement in Mathematics - Upper Grade

(Eighth Grade)Table E.2: Percentiles of Achievement in Mathematics - Lower Grade

(Seventh Grade)Table E.3: Standard Deviations of Achievement in Mathematics -

Upper Grade (Eighth Grade)Table E.4: Standard Deviations of Achievement in Mathematics -

Lower Grade (Seventh Grade)

© 1996 International Association for the Evaluation of Educational Achievement (IEA).

Mathematics Achievement in the Middle School Years: IEA's Third International Mathematics and Science Study / by Albert E. Beaton, Ina V.S. Mullis, Michael O. Martin, 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: 96-71251

ISBN 1-889938-02-5

For more information about TIMSS contact:

The International Study Center

Boston College

Manresa House

140 Commonwealth Ave.

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.