Different Paths 

in Mathematics  

in the United

and Similar Problems Education Reform  States and China

AbstractThis 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 5th Grade Textbooks

10%

20%

30%

40%

50%

Number

Equation

& Function

Geometr

y Probab

ility

& Statist

ics

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 WorldU.S.

MathChina

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, areaand 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.

0

10

20

30

40

50

60

Knowing Students'Prior Knowledge

ConstructingConcrete

Understanding

DevelopingAbstract Thinking

Perc

ent

U. S.

China

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.

0

10

20

30

40

50

60

70

80

90

100

Identifying Misconceptions Making Correction for Errors

Perc

ent

U. S.

China

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.

0

10

20

30

40

50

60

70

80

ConnectingConcrete Model to

Math Ideas

Using VariousRepresentations

Providing VariousActivities

Per

sent U. S.

China

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.

0

10

20

30

40

50

60

Using Activities toPromote Students'

Thinking

ProvidingSuggestions and

Questions toSupport Thinking

Using Strategies toEncourage

Reflective Thinking

Per

cent

U. S.

China

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 (yesun100@tamu.edu)Xiaobao Li (ramble007@tamu.edu)Zhonghe Wu (johnwu@tamu.edu)Zhixia You (zhixiayou@tamu.edu)Gerald Kulm (gkulm@coe.tamu.edu)

Department of Teaching, Learning and Culture

Texas A&M University