Case-Based Reasoning And Mathematical Problem Solving

The research on Mathematical Problem Solving is one aspect in the field of mathematics education that attracts much attention. Since G. Polya put forth "plausible reasoning" in mathematical problem solving, the field of mathematics education has got much inspiration from it, and people come to realize that it is important to pay attention to such a question: how a specific solution is formed in a problem solver's mind? But for this question, those research by now still need much hard work to do. On the other side, Case-Based Reasoning (CBR) is a specific kind of Plausible Reasoning, and it is suitable for unfamiliar and complex situations. While under the mathematical problem solving situations, it is common for problem solvers to meet unfamiliar and complex cases. So CBR is important to some extent in mathematical problem solving.This thesis starts from two directions: 1) to review on CBR, and introduce two of its models as well as its features; 2) to review on the history of mathematical problem solving. Then to combine these two directions to form a knowledge foundation, so we can go on to compare CBR and Plausible Reasoning, and use CBR to analyze some obstacles that appear in the process of problem solving. At last, some useful advices on education will be suggested on the base of the former analyses.