An Experimental Study On Students Higher Level Mathematics Cognition
An experimental study on students' higher-level mathematics cognition Bao, Jansheng (ECNU) [email_address]
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.
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.
A framework for assessments of mathematical cognition L4 ： Analysis L2 ： Concept L3 ： Comprehension L1 : Calculation Higher levels Lower levels
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 .
A comparative study between China and UK (Bao, 2002)
Another comparative study between China and UK (Bao, 2006)
The curriculum is not the only reason, the Chinese traditional teaching style also does matter.
Advantages and disadvantages of traditional Chinese teaching styles <ul><li>Teaching step by step: Are the steps too small? </li></ul><ul><li>High efficiency: Do students need more free space? </li></ul><ul><li>Sample-based practice: Where to find the original ideas? </li></ul><ul><li>Pursuing high scoring: What is beyond the skills? </li></ul><ul><li>Teacher-centered: Do students need more opportunities to do by themselves? </li></ul>
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).
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
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
What we should always keep in mind is: <ul><li>The two basics are still necessary for students to develop higher levels of mathematical cognition </li></ul>