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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 5th
Grade Textbooks
60%
50%
40%
30%
20%
10%
Math in My World (U.S.)
Math (China)
Math Topic Coverage in U.S. and China
Textbooks
Data, statistics
and table
Geometry
Simple equation
100%
Factor and multiplication
Fractional addition/
subtraction
Fraction
Multiplication/division
of integer with fraction
Fractional
division/subtraction
Division of integer/
decimal (2-digit-divisor)
Division of integer/
decimal (1-digit-divisor)
Multiplication of
integer/decimal
Addition/Subtraction
of integer/decimal
Integer and decimal
Ratio, percent
and probability
Perimeter, area
and volume
Measurement
80%
Fraction
Decimal multiplication
and division
40%
Complicated operation
Statistics
60%
Measurement
Cube
20%
Area of polygon
Math in My World
U.S.
Math
China
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
60
50
Percent
40
U. S.
30
China
20
10
0
Knowing Students'
Prior Knowledge
Constructing
Concrete
Understanding
Developing
Abstract Thinking
Source: An, S., Kulm, G., & Wu, Z. (In press). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S.
Mathematics Teacher Education.
Journal of
Addressing Students’ Misconceptions
100
90
80
Percent
70
60
U. S.
50
China
40
30
20
10
0
Identifying Misconceptions
Making Correction for Errors
Source: An, S., Kulm, G., & Wu, Z. (In press). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S.
Mathematics Teacher Education.
Journal of
Engaging Students in Math Learning
80
70
Persent
60
50
U. S.
40
China
30
20
10
0
Connecting
Concrete Model to
Math Ideas
Using Various
Representations
Providing Various
Activities
Source: An, S., Kulm, G., & Wu, Z. (In press). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S.
Mathematics Teacher Education.
Journal of
Promoting and Supporting Students’
Thinking about Mathematics
60
Percent
50
40
U. S.
30
China
20
10
0
Using Activities to
Promote Students'
Thinking
Providing
Suggestions and
Questions to
Support Thinking
Using Strategies to
Encourage
Reflective Thinking
Source: An, S., Kulm, G., & Wu, Z. (In press). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S.
Mathematics Teacher Education.
Journal of
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 ([email protected])
Xiaobao Li ([email protected])
Zhonghe Wu ([email protected])
Zhixia You ([email protected])
Gerald Kulm ([email protected])
Department of Teaching, Learning
and Culture
Texas A&M University