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提高学生的数学解题能力,有诸多条件和因素,而解题后反思是提高数学解题能力的一个重要方面。在长期的教学过程中我发现:不少同学在完成作业或进行大量解题训练之后,普遍缺少这个环节。何谓“解题反思”?一道数学题经过认真思考解出答案之后,必须认真地进行如下探索:命题的意图是什么?考核我们哪些方面的知识和能力?解题结论是否正确合理?求解论证过程是否判断有据,严密完善?本题有无其他解法?众多解法中哪一种最简捷?把本题的解法和结论进一步推广,能否得到更普遍性的结论?……如此种种,就是“解题反思”。
There are many conditions and factors in improving students’ ability to solve problems in mathematics. Rethinking after solving problems is an important aspect of improving the ability of solving problems in mathematics. In the long-term teaching process, I discovered that many students generally lack this link after completing their homework or doing a lot of problem solving training. What is “solving problem reflection”? After a math problem has been carefully thought out to solve the answer, it must be carefully explored as follows: What is the intention of the proposition? What aspects of our knowledge and ability are we assessing? Is the problem conclusion correct and reasonable? Whether the process of argumentation is well-founded, tightly improved, and whether there is any other solution to this question? Which of the most concise solutions is the most simple one? To further generalize the solution and conclusion of this question, can we get a more general conclusion? “Solving problem reflection.”