how chinese teach mathematics anna larzelere - wednesday, march 21, 2012 1

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How ChineseTeach

MathematicsAnna Larzelere - Wednesday, March 21, 2012

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ABC World News Video

Chinese students beat US student test scores in Reading, Science and

Mathematics

Source: YouTube.com retrieved March 7,2012 http://www.youtube.com/watch?v=Lfr2rTW3UMk

http://www.youtube.com/watch?v=Lfr2rTW3UMk

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Why?

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According to aChinese saying …

if you want to give the students one cup of water,

you (the teacher)should have one bucket of

water of your own. An, S., Kulm, G., & Wu, Z. (2004). The Pedagogical Content Knowledge of Middle School, Mathematics Teachers in China and the U.S. Journal of Mathematics Teacher Education. 7(2) 145-172.

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Good Teachers Have …profound understandings of

fundamental mathematicsdeep and broad knowledge of

teaching and curriculumthe ability to connect their

knowledge of content, curriculum, and teaching

An, S., Kulm, G., & Wu, Z. (2004). The Pedagogical Content Knowledge of Middle School, Mathematics Teachers in China and the U.S. Journal of Mathematics Teacher Education. 7(2) 145-172.

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Focus is Key

American Teachers great attention to

procedural knowledge emphasize how to

calculate without understanding the underlying rationale in depth

Chinese Teachers emphasize the

understanding of concepts from multiple perspectives

require students to master computation fluently but also pay attention to the ability to select a proper and effective method to operate

Lianghuo, F., Ngai-Ying, W., Shiqi, L. (2004) How Chinese Learn Mathematics: Perspectives from Insiders. Singapore: World Scientific Publishing, Co.

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o Development and application of learned skills

o Examinations are important, but not “taught to”

o Teachers aim to help students transfer skills to other problems they encounter

o Confident students perform well


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But How do They Teach?

Traditional Content Teaching

Vs.Creative Activities


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Use of Models

93% of US teachers use concrete or pictorial models Pizzas, Hershey bars, fraction pieces

Only 42% of Chinese teachers use models Definitions, unit fractions,

connections to prior knowledge


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Use of Questions

100% of Chinese teachers were able to use questions or tasks to correct the misconceptions of students, compared with 61% of the U.S. teachers.

??????????An, S., Kulm, G., & Wu, Z. (2004). The Pedagogical Content Knowledge of Middle School, Mathematics Teachers in China and the U.S. Journal of Mathematics Teacher Education. 7(2) 145-172.

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Use of Questions

Discovery learning cannot happen 100% of the time

“Spoon-fed” teaching does not happenTeachers can ask quality questions to

get students thinking, and guide them to the learning objectives

Lianghuo, F., Ngai-Ying, W., Shiqi, L. (2004) How Chinese Learn Mathematics: Perspectives from Insiders. (pp 194-5) Singapore: World Scientific Publishing, Co.

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Typical Questions Teachers Ask

U.S. Teachers Do you have the problem

set up correctly? How did you order these? Explain why you put the

fraction in that order.

Chinese Teachers What measurements are

being compared in the ratio of 3:8?

How can we make changes in order to get two equivalent ratios?

Can you directly order fractions by comparing numerators only while the numerators and denominators are all different?


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Use of Connections – Real Life

Relating to students’ lives engages and motivates them

These connections help students link using manipulatives and solving problems through procedures


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Use of Connections –

Prior KnowledgeThe monkey’s mother bought a

watermelon and cut it into 9 pieces; every monkey ate 2/9 of the pieces. How many pieces did four monkeys eat? How do you express this problem in addition? How do you express this problem in multiplication? Which method is easier?


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Use of Connections –

Prior KnowledgeIn reviewing prior

knowledge, one can always find new knowledge

- Confucius


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Use of Self-Reflectionthink about problem solvingsubstitute answers into the original

equationcheck to see if it makes sensereorganize knowledge and find errors develops a deep understandingfosters good learning habits


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What Does a Teacher’sDay Look Like?

Primary grade teachers are very skilled Plenty of time for collaboration Students and teachers have time for breaks Teachers instruct large groups of students Communication lines are open between teachers and

parents Teachers are invested in each student’s overall

development and wellbeing

Source: National Council for Teachers of Mathematics website – Article by Annie Han retrieved March 11, 2012.

http://www.nctm.org/resources/content.aspx?id=1618

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A Chinese Math Lesson FormatActivity

1Activity

2Activity

3Activity

4Activity

5Activity

6Review formula

of a triangle

Practice to

calculate areas of triangles

with given

base and height

Observe 3

triangles and

discuss the

relation-ship of their areas

Order triangles based on area and discuss

Finding out

specific triangles among a group of triangles

Drawing specific triangles

in different shapes

Lianghuo, F., Ngai-Ying, W., Shiqi, L. (2004) How Chinese Learn Mathematics: Perspectives from Insiders. (pp 109) Singapore: World Scientific Publishing, Co.

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Parts of A Chinese Math Lesson


ReviewDiscussionTransitionConnectionPractice

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Other Factors oCurriculum

oLanguagethat lead Chinese

students to deeper

mathematics understanding

and higher test scores

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Content Repeated in CurriculumChinese

38% of the concepts in Japanese secondary school textbooks were repeated once and only 6% were repeated more than once.

US 70% of the concepts in

American secondary school textbooks were repeated at least once, nearly 25% were repeated twice, and 10% were even repeated three times.

Cai, J. (1995). A Cognitive Analysis of U. S. and Chinese Students' Mathematical Performance on Tasks Involving Computation, Simple Problem Solving, and Complex Problem Solving. Journal for Research in Mathematics Education. 7. 1-151.

The fact that U.S. curriculum contains so much old content may contribute to students' boredom if they sense that they do the same thing in mathematics year after year.

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Language of Mathematics

Chinese 11, 12, and 20 are

spoken as "ten-one," "ten-two," and "two-ten"

spoken name of a written number reveals the place value of that number

English the spoken names do not

always conform to their written form

Spoken names for the numerals 11, 12, and 20 lack the elements of tens and ones contained in them


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Language – Units and Dates

Units "36 buses" will be written

or spoken as "36 LIANG buses.“

25 desks, the unit is ZHANG, "25 ZHANG desks."

Almost everything has a unit.

Similar to “12 ounces of Coke”

Dates Spoken names of days

and months correspond exactly to their numerical sequence

Monday in spoken Chinese is "week one" and January is "one month"


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References An, S., Kulm, G., & Wu, Z. (2004). The Pedagogical Content

Knowledge of Middle School, Mathematics Teachers in China and the U.S. Journal of Mathematics Teacher Education. 7(2) 145-172.



Source: National Council for Teachers of Mathematics website – Article by Annie Han retrieved March 11, 2012. http://www.nctm.org/resources/content.aspx?id=1618

YouTube.com. Video retrieved March 7,2012 http://www.youtube.com/watch?v=Lfr2rTW3UMk

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