1. How Chinese Teach Mathematics Anna Larzelere - Wednesday, March 21, 2012 1

2. 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 2

3. Why? 3

4. According to a Chinese 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. 4

5. Good Teachers Have …  profound understandings of fundamental mathematics  deep and broad knowledge of teaching and curriculum  the 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. 5

6. 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. 6

7. 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 7 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.

8. But How do They Teach? Traditional Content Teaching Vs. Creative Activities 8 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.

9. 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 9 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.

10. 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. ?????????? 10 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.

11. Use of Questions  Discovery learning cannot happen 100% of the time  “Spoon-fed” teaching does not happen  Teachers can ask quality questions to get students thinking, and guide them to the learning objectives 11 Lianghuo, F., Ngai-Ying, W., Shiqi, L. (2004) How Chinese Learn Mathematics: Perspectives from Insiders. (pp 194-5) Singapore: World Scientific Publishing, Co.

12. 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? 12 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.

13. 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 13 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.

14. Use of Connections – Prior Knowledge  The 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? 14 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.

15. Use of Connections – Prior Knowledge  In reviewing prior knowledge, one can always find new knowledge - Confucius 15 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.

16. Use of Self-Reflection  think about problem solving  substitute answers into the original equation  check to see if it makes sense  reorganize knowledge and find errors  develops a deep understanding  fosters good learning habits 16 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.

17. What Does a Teacher’s Day 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 17 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

18. A Chinese Math Lesson Format Activity 1 Activity 2 Activity 3 Activity 4 Activity 5 Activity 6 Review 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. 18

19. Parts of A Chinese Math Lesson Lianghuo, F., Ngai-Ying, W., Shiqi, L. (2004) How Chinese Learn Mathematics: Perspectives from Insiders. (pp 112) Singapore: World Scientific Publishing, Co. 19  Review  Discussion  Transition  Connection  Practice

20. Other Factors o Curriculum o Language that lead Chinese students to deeper mathematics understanding and higher test scores 20

21. Content Repeated in Curriculum Chinese  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. 21 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.

22. 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 22 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.

23. 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" 23 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.

24. 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.  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.  Lianghuo, F., Ngai-Ying, W., Shiqi, L. (2004) How Chinese Learn Mathematics: Perspectives from Insiders. (pp 109) Singapore: World Scientific Publishing, Co.  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 24