2009年4月21日下午，厦门大学嘉庚三215会议室，数学教育沙龙。

1. An experimental study on students' higher-level mathematics cognition Bao, Jansheng (ECNU) [email_address]

2. An ongoing research project This presentation will briefly introduce an ongoing 3-year research project, which aims at the improvements of students’ higher levels mathematical cognition.

3. Results from Qingpu Experimental Research Group Qingpu Experimental Research Group had conducted two large scale Mathematical Cognition Tests on grade eight students in 1990 and 2007. The results shows that, on the first three mathematical cognitive levels ( Calculation Level, Concept Level and Comprehension Level ), students’ performance in 2007 were mach better than that of the students 17 years’ ago. But on the topmost level ( analysis level ), students’ performance has no any improvements 17 years’ later.

4. Two large scale surveys in 1990 and 2007

5. A framework for assessments of mathematical cognition L4 ： Analysis L2 ： Concept L3 ： Comprehension L1 : Calculation Higher levels Lower levels

6. The above results were witnessed by some international comparative studies. Some researches ( e.g., Cai, 1995, 1998, 2000a, 2000b; Cai & Hwang, 2002 ; Ma, 1999 ) used a variety of assessment tasks and analyzed cognitive aspects of problem solving to examine U.S. and Chinese students’ mathematical thinking beyond computation, correctness, and problem solving. These researches show that the U.S. sample had higher mean score than did the Chinese sample on the process-open, non-routine tasks .

7. Why???

8. A comparative study between China and UK (Bao, 2002)

9. Another comparative study between China and UK (Bao, 2006)

10. The curriculum is not the only reason, the Chinese traditional teaching style also does matter.

12. What do we want to do?

13. Research questions How to improve Chinese students’ performance on higher levels of mathematical cognition? It is well-documented that having routine problem solving skills does not necessarily mean having non-routine problem solving skills (Hatano, 1988; Steen, 1999; Sternberg, 1999).

14. Quasi-experiment design Mathematics tasks that need higher levels mathematical cognition Effective teaching for the developments of higher levels mathematics cognition Improvements of students’ performance on topmost level of mathematical cognition

15. Pre-tests and post tests Tests on topmost level of math cognition Grade 6 Grade 7 Grade 8 Grade 9 2009.9 2010.9 2011.9 2012.9 (year) A 68 A 79 A 67 A 78 A 89 A 66 A 77 A 88 A 99 A 69

17. Thanks ！