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Measuring Up: How the Highest Performing State (Massachusetts) Compares to the Highest Performing Country (Hong Kong) in Grade 3 Mathematics

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Measuring Up: How the Highest Performing State (Massachusetts) Compares to the Highest Performing Country (Hong Kong) in Grade 3 Mathematics ® AMERICAN INSTITUTES FOR RESEARCH MEASURING UP: HOW THE HIGHEST PERFORMING STATE (MASSACHUSETTS) COMPARES TO THE HIGHEST PERFORMING COUNTRY (HONG KONG) IN GRADE 3 MATHEMATICS STEVEN LEINWAND American Institutes for Research® ALAN GINSBURG U.S. Department of Education APRIL 2009 This paper was supported by funds from the U.S. Department of Education and The Urban Institute. The paper does not necessarily represent the official positions of the U.S. Department of Education or The Urban Institute. The contents are the sole responsibility of the authors. 1000 THOMAS JEFFERSON STREET, NW | WASHINGTON, DC 20007-3835 CONTENTS Executive Summary ........................................................................................................................ 1 Measuring Up: How the Highest Performing State (Massachusetts) Compares to the Highest Performing Country (Hong Kong) in Grade 3 Mathematics ............................................. 5 I. Background and Methodology ................................................................................................ 6 Comparing Hong Kong and Massachusetts Performance ...................................................... 6 Hong Kong and Massachusetts Assessments ......................................................................... 7 Methodology for Comparing Assessments ............................................................................. 9 II. Numbers ............................................................................................................................... 12 Context .................................................................................................................................. 12 Findings................................................................................................................................. 13 Summary ............................................................................................................................... 18 III. Measurement ....................................................................................................................... 18 Context .................................................................................................................................. 18 Findings................................................................................................................................. 20 IV. Geometry ............................................................................................................................ 25 Context .................................................................................................................................. 25 Findings................................................................................................................................. 26 Summary ............................................................................................................................... 29 V. Data and Probability............................................................................................................. 29 Context .................................................................................................................................. 29 Findings................................................................................................................................. 30 Summary ............................................................................................................................... 34 VI. Algebra ............................................................................................................................... 34 Context .................................................................................................................................. 34 Findings................................................................................................................................. 34 Summary ............................................................................................................................... 36 VII. Summary Comparison and Implications ........................................................................... 36 Features That Make Items Challenging ................................................................................ 38 References ..................................................................................................................................... 40 Appendix 1: Massachusetts Mathematics Framework ............................................................... 1–1 Appendix 2: Item-by-Item Comparison of Massachusetts Grade 3 vs. Hong Kong Grade 3 .... 2–1 i American Institutes for Research® LIST OF TABLES Exhibit 1. Ranking of Hong Kong and Massachusetts on 2007 TIMSS-4 Mathematics: Grade 4 ........................................................................................................................................ 7 Exhibit 2. The Two Components of the Hong Kong Basic Competency Assessment ................... 8 Exhibit 3. Comparison of Key Features of Massachusetts and Hong Kong Grade 3 Mathematics Assessments ........................................................................................................ 10 Exhibit 4. Hong Kong and Massachusetts TIMSS Scores on the Number Domain: Average Score and Rank ........................................................................................................... 12 Exhibit 5. Hong Kong Basic Competency Assessment: Grade 3 Numbers ................................. 12 Exhibit 6. Summary of the Number Strand .................................................................................. 13 Exhibit 7. Number: Place Value ................................................................................................... 14 Exhibit 8. Number—Ordering Whole Numbers ........................................................................... 15 Exhibit 9. Number: Subtraction .................................................................................................... 16 Exhibit 10. Number: Fractions ...................................................................................................... 16 Exhibit 11. Number: Numerical Reasoning .................................................................................. 17 Exhibit 12. Number: Multiplication .............................................................................................. 18 Exhibit 13. Number: Estimation ................................................................................................... 18 Exhibit 14. Hong Kong and Massachusetts TIMSS Scores on the Measurement and Geometry Domains: Average Score and Rank ......................................................................... 19 Exhibit 15. Hong Kong Basic Competency Assessment: Grade 3 Measurement Domain .......... 19 Exhibit 16. Summary of the Measurement Strand ........................................................................ 20 Exhibit 17. Measurement—Units ................................................................................................. 21 Exhibit 18. Measurement—Instruments ....................................................................................... 21 Exhibit 19. Problems in Measurement—Conversion ................................................................... 22 Exhibit 20. Problems in measurement—Transitivity.................................................................... 23 Exhibit 21. Measurement—Elapsed Time .................................................................................... 23 Exhibit 22. Measurement—Calendar............................................................................................ 24 Exhibit 23. Measurement—Money ............................................................................................... 25 Exhibit 24. Hong Kong Basic Competency Assessment Framework: Grade 3 Geometry ........... 26 Exhibit 25. Summary of the Geometry Strand .............................................................................. 27 Exhibit 26. Geometry Problems—2-D Shapes ............................................................................. 28 Exhibit 27. Geometry Problems—3-D Shapes ............................................................................. 29 Exhibit 28. Hong Kong and Massachusetts TIMSS Scores on “Data Display”: Average Score ........................................................................................................................... 30 Exhibit 29. Hong Kong Basic Competency Assessment Framework: Grade 3 Data ................... 30 Exhibit 30. Summary of the Data and Probability Strand ............................................................ 31 Exhibit 31. Data and Combinations—Constructing Graphs ......................................................... 32 Exhibit 32. Data and Combinations—Interpreting Graphs........................................................... 33 Exhibit 33. Data and Combinations—Combinations.................................................................... 33 Exhibit 34. Patterns, Relations and Algebra—Patterns ................................................................ 35 Exhibit 35. Patterns, Relations and Algebra—Number Sentences ............................................... 36 Exhibit 36. Percentage of Items Requiring More Than Simple Recall of Concepts, by Mathematical Strand ...........................................................................................................
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