Transcript WERA Symposium November 23,2010

WERA Symposium
November 23, 2010
Wu-Teh Hsiang
Syracuse University
Email: [email protected]
A Comparison
of
Mathematics Education/Teaching
in
China and the United States
Wu-Teh Hsiang
Email: [email protected]
Education
Learning
Teaching
Education
Learning
Learning Conferences!
Teaching
Education Conferences
Education
Learning
Teaching
Learning Conferences!
Education Conferences
Learning and Teaching
Education
Learning
Teaching
Learning Conferences!
Education Conferences
Learning and Teaching
The ultimate goal is students to learn, to retain, to apply
and to teach their knowledge!
Education
Learning
Teaching
Learning Conferences!
Education Conferences
Learning and Teaching
The ultimate goal is students to learn, to retain, to apply
and to teach their knowledge!
Learning
Teaching
Leaning
Teaching
Systems, Curricula, Methods of Teaching
in
Mathematics 1-12
China
United States
Department of Education: National level, Department of Education: National level,
State level. (Yes)
Province level, County level. (Yes)
Systems, Curricula, Methods of Teaching
in
Mathematics 1-12
China
United States
Department of Education: National level, Department of Education: National level,
State level. (Yes)
Province level, County level. (Yes)
National Curriculum Standards (Yes)
National Curriculum Standards (No)
Systems, Curricula, Methods of Teaching
in
Mathematics 1-12
China
United States
Department of Education: National level, Department of Education: National level,
State level. (Yes)
Province level, County level. (Yes)
National Curriculum Standards (Yes)
National Curriculum Standards (No)
State Curriculum Standards (Yes).
Each District has some autonomy.
Systems, Curricula, Methods of Teaching
in
Mathematics 1-12
China
United States
Department of Education: National level, Department of Education: National level,
State level. (Yes)
Province level, County level. (Yes)
National Curriculum Standards (Yes)
National Curriculum Standards (No)
State Curriculum Standards (Yes).
Each District has some autonomy.
3 versions of text books nationwide.
More than 20 versions of text books
nationwide.
Systems, Curricula, Methods of Teaching
in
Mathematics 1-12
China
United States
Department of Education: National level, Department of Education: National level,
State level. (Yes)
Province level, County level. (Yes)
National Curriculum Standards (Yes)
National Curriculum Standards (No)
State Curriculum Standards (Yes).
Each District has some autonomy.
3 versions of text books nationwide.
More than 20 versions of text books
nationwide.
Recommended Teaching Method
changes less often.
Recommended Teaching Method
changes more often.
Method of Evaluation
Method of Examination is used almost in every country as a
Method of Evaluation. Each country puts different weight on the
method of examination verses other method of evaluation.
China
United States
Method of Evaluation
Method of Examination is used almost in every country as a
Method of Evaluation. Each country puts different weight on the
method of examination verses other method of evaluation.
China
China puts more weight
on the Method of
Examination.
United States
United States puts less
weight on the Method of
Examination. US uses other
additional methods of
evaluation.
China
科舉制度 [ke ju zhi du]
[ke ju zhi du] was an examination system
existed for two thousand years, before the
Republic. It was a method used by the
Chinese emperors to select talented civil
servants.
China
科舉制度 [ke ju zhi du]
[ke ju zhi du] was an examination system
existed for two thousand years, before the
Republic. It was a method used by the
Chinese emperors to select talented civil
servants.
United States
United States does not such a tradition yet.
Other method of evaluation has its importance.
Memorization and Reasoning
Memorization and reasoning are both fundamentally important for a
person to learn complex new ideas. When it comes to developing an
educational system or a teaching method, each culture, each society
develops its own recipe, balancing these components in their own way.
No education system or teaching method can rely only on one without
the other. There is the constant debate in educating a youngster how
much emphasis should be place on memorization verses reasoning.
Memorization and Reasoning
Memorization and reasoning are both fundamentally important for a person to
learn complex new ideas. When it comes to developing an educational system
or a teaching method, each culture, each society develops its own recipe,
balancing these components in their own way. No education system or
teaching method can rely only on one without the other. There is the constant
debate in educating a youngster how much emphasis should be place on
memorization verses reasoning.
China
Require 2nd graders to
memorize the multiplication
facts.
United States
Encouraged 3nd graders to
know the multiplication facts.
Memorization and Reasoning
Memorization and reasoning are both fundamentally important for a person to
learn complex new ideas. When it comes to developing an educational system
or a teaching method, each culture, each society develops its own recipe,
balancing these components in their own way. No education system or
teaching method can rely only on one without the other. There is the constant
debate in educating a youngster how much emphasis should be place on
memorization verses reasoning.
China
Require 2nd graders to
memorize the multiplication
facts.
More on memorization.
United States
Encouraged 3nd graders to
know the multiplication facts.
More on reasoning.
Memorization and Reasoning
Memorization and reasoning are both fundamentally important for a person to
learn complex new ideas. When it comes to developing an educational system
or a teaching method, each culture, each society develops its own recipe,
balancing these components in their own way. No education system or
teaching method can rely only on one without the other. There is the constant
debate in educating a youngster how much emphasis should be place on
memorization verses reasoning.
China
Require 2nd graders to
memorize the multiplication
facts.
More on memorization.
United States
Encouraged 3nd graders to
know the multiplication facts.
More on reasoning.
How does each culture (not just China or US) develop or evolve into its
own recipe of balancing memorization and reasoning?
How Chinese system might have evolved into more weight on memorization?
shi
How Chinese system might have evolved into more weight on memorization?
shi
• 周髀算經“矩出于九九八十一”
How Chinese system might have evolved into more weight on memorization?
shi
• 周髀算經“矩出于九九八十一”
• 漢趙君卿注“推圓方之率，通廣長之數，當須乘除以計之。
九九者，乘除之原也。”
How the US system might have evolved into more weight on reasoning?
How the US system might have evolved into more weight on reasoning?
It might be:
• The successes in Sciences and Technology - scientific method.
• The Mathematical Logic Reasoning.
• Lead to scientific method of studying on almost every subject.
• From Chinese 6th grade mathematics book.
• From Chinese 6th grade mathematics book.
Reasoning
There are chickens and rabbits in a cage. Counting the heads,
there are 11 heads. Counting the legs, there are 32 legs.
How many chickens and rabbits are in the cage?
China
Introduced in 6th grade.
• If there were 11 rabbits in the cage,
there would be 44 legs.
• If we replace a rabbit by a chicken,
there would be 42 legs.
• If we replace another rabbit by another
chicken, there would be 40 legs.
• Therefore, (44 - 32)/2 = 6 chickens,
and (11 - 6) = 5 rabbits in the cage.
United States
Supplemented in 7th grade or later.
Let x = # of chickens, and y = # of rabbits. Then
x + y = 11
2x + 4y = 32
2x = 12
2x + 4y = 32
4x + 4y = 44
2x + 4y = 32
x=6
y=5
• Therefore, there are 6 chickens,
and 5 rabbits in the cage.
Reasoning
There are chickens and rabbits in a cage. Counting the heads,
there are 11 heads. Counting the legs, there are 32 legs.
How many chickens and rabbits are in the cage?
China
Introduced in 6th grade.
• If there were 11 chickens in the cage,
there would be 22 legs.
• If we replace a chicken by a rabbit,
there would be 24 legs.
• If we replace another chicken by
another rabbit, there would be 26 legs.
• Therefore, (32 - 22)/2 = 5 rabbits,
and (11 - 5) = 6 chickens in the cage.
United States
Supplemented in 7th grade or later.
Let x = # of rabbits, and y = # of chickens. Then
x + y = 11
4x + 2y = 32
2x + 2y = 22
2x = 10
2x + 2y = 22
4x + 2y = 32
x=5
y=6
• Therefore, there are 5 rabbits,
and 6 chickens in the cage.
Reasoning
There are chickens and rabbits in a cage. Counting the heads,
there are 11 heads. Counting the legs, there are 32 legs.
How many chickens and rabbits are in the cage?
United States
China
Introduced in 6th grade.
• If each chicken raise 1 leg, and each
rabbit raise 2 front legs, there would
be 16 legs.
Supplemented in 7th grade or later.
Let x = # of rabbits, and y = # of chickens. Then
x + y = 11
4x + 2y = 32
x + y = 11
2x + y = 16
• Each rabbit has 1 more leg touch the
ground then each chicken.
• Therefore, (16 - 11) = 5 rabbits,
and (11 - 5) = 6 chickens in the cage.
x + y = 11
x=5
x=5
y=6
• Therefore, there are 5 rabbits,
and 6 chickens in the cage.
What does China and United States Mathematics
Education in common?
Mathematics Education in China and United
States have a lot in common, 1 - 12 in both
countries cover essentially the same topics in their
curricula, the topics often are within one year in
the two countries.