Different Paths in Mathematics in the United

and Similar Problems Education Reform States and China

Abstract This study combines a series of studies involving challenges that both China and the U.S. face in mathematics education reform. The findings from these studies indicate that both the teacher and the textbook play important roles in effective teaching. Results indicate that there are significant gaps in teachers’ pedagogical content knowledge and mathematics textbooks in these two countries. The study suggests that professional development programs need to be established to enable teachers to understand the content and pedagogical knowledge as well as how to use textbooks appropriately.

Introduction Both China and the U.S. face common problems in mathematics education. Both countries have been involved in mathematics reform during the past two decades.

Timeline Page 1

Timeline Page 2

Common Problems How to improve teachers’ knowledge and use of the standards How to improve pedagogical content knowledge and use of standards-based textbooks

Textbook Comparison Study “Math in My World” (McGraw-Hill, 1999) “Math” (PRC, 1995) Mathematics Content –China: definitions are conceptual, symbolic, and mathematically oriented –U.S.: definitions, activities, and concrete examples are real-life oriented Source: Sun, Y. (2001). Research and Comparison of Math Curriculum between China and USA. Masters thesis, Institute for Education Research, Beijing Normal University, China.

Textbook Comparison (Cont.) Content Organization –China: concentrate on the logic and consistency of the subject of mathematics –U.S.: emphasize the implication and meaning in real-life situations Mathematics Representation –China: symbolic representation, math reasoning –U.S.: graphic, table representation

Comparison of Math Content in 5 th Grade Textbooks 10% 20% 30% 40% 50% Number Equation & Function Geometry Probability & Statistics Math in My World (U.S.) Math (China) 60%

Area of polygon Cube Measurement Statistics Decimal multiplication and division Complicated operation Fraction Fractional addition/ subtraction Factor and multiplication Simple equation Math Topic Coverage in U.S. and China Textbooks 20% 40% 60% 80% 100% Math in My World U.S. Math China Division of integer/ decimal (2-digit-divisor) Addition/Subtraction of integer/decimal Division of integer/ decimal (1-digit-divisor) Measurement Ratio, percent and probability Fractional division/subtraction Multiplication of integer/decimal Data, statistics and table Perimeter, area and volume Geometry Integer and decimal Multiplication/division of integer with fraction Fraction

Pedagogical Content Knowledge Study Comparing U.S. and China middle school teachers’ knowledge and beliefs about teaching mathematics Surveys, observations, and interviews of teachers in Texas, Beijing, and Nanjing

Building on Students’ Math Ideas Source : An, S., Kulm, G., & Wu, Z. (In press). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education.

Addressing Students’ Misconceptions Source : An, S., Kulm, G., & Wu, Z. (In press). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education.

Engaging Students in Math Learning Source : An, S., Kulm, G., & Wu, Z. (In press). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education.

Promoting and Supporting Students’ Thinking about Mathematics Source : An, S., Kulm, G., & Wu, Z. (In press). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education.

Conclusion The textbooks are similar in major topics covered, but the U.S. attempts to teach a greater number of specific topics. Mathematics teachers’ pedagogical content knowledge is stronger in China. Professional development programs are needed to provide teachers with important knowledge and skills.

Authors’ Contact Information Ye Sun Xiaobao Li Zhonghe Wu Zhixia You Gerald Kulm Department of Teaching, Learning and Culture Texas A&M University