數學解題策略教學之研究

A Study of Mathematics Problem Solving in Teaching Effects

本文基於數學解題對數學教學及學習的重要性，採用文獻調查的研究方法，目的在於探討數學解題的意義、數學解題的歷程模式、數學解題的教學原則，以及回顧國內、外有關數學解題策略之教學研究的成果，並提出在教學上的建議。各節內容摘要如下：1.數學解題是一個人面臨有關數學上的問題時，一時無法立即獲知答案，必須運用以往的知識和經驗，求出解答的過程。2.數學解題歷程的探討，從一般數學解題的認知歷程，隨著與認知心理學的相結合，其內涵更形豐富。3.數學解題的教學原則，從教學內容和教學方法兩方面提示。4.相關研究結果的檢討：有效的策略教學研究通常奠基於述說清楚的訓練；策略教學的效果，需視受試學生的能力而定；部分研究顯示接受解題訓練的學生會具較積極正面的學習態度。5.以數學解題為重心的教學模式，應為今後數學教育所應努力的方向。

The purposes of this study were (1)to define the concept of mathematics problem solving， (2)to introduce the models of mathematics problem solving， (3)to offer some suggestions to mathematics problem solving in teaching (4)to review studies of mathematics problem solving in teaching effects， (5)to draw a conclusion. The main content are summarized as the followings.1. Mathematics problem solving is the process that someone try to to solve a problem of Mathematics.2. Because of cognitive psychology， the model of mathematics problem solving became more rich.3. Some suggestions of content and method were offered to mathematics problem solving in teaching.4. In the studies reviewed， effective strategy instruction often seems to depend upon explicit training. There are no overall positive effects for strategy. Rather， the results of instruction seem to depend on the abilities of the student being taught.5. Mathematics problem solving would be the center of mathematics teaching.