数学问题解决思维策略及其教学

【作者】 吕宝珠；

【导师】 李延林； 周春荔；

【作者基本信息】 首都师范大学 ， 数学教育， 2002， 硕士

【摘要】 问题是数学的心脏。数学的真正组成部分是问题和问题解决。数学教学的核心就是培养学生解决数学问题的能力。问题解决具有明显的策略性。它影响问题解决的进程和质量。本文从四个方面阐述数学问题解决思维策略及其教学。(1)基于数学教育的观点，其一阐述了具有教育价值的数学问题的涵义及其基本特征：数学问题具有主体相对性、障碍性以及待解性，指出数学问题必须具有对于学生的适合性，要能够促进学生积极主动思维，有利于提高学生数学能力。其二结合现代认知心理学的理论，对数学问题解决的涵义、基本特征及其思维模式作出了概括分析；(2)依据数学问题解决的思维模式，探讨了解决中学数学问题过程中在问题表征、寻求解答、实施解答、反思评价各个阶段的若干思维策略；并针对每种思维策略对其应用条件或关键要求及操作原则等作出具体分析，增强了可操作性，以利于指导教学；(3)采用出声思维的实验方法研究了高中学生在数学问题解决过程中寻求解答阶段选择思维策略的特点，表明模式识别、化归、顺向推理是学生较倾向于使用的策略；特殊化、一般化策略学生在认识和操作上都存在较严重的缺陷。同时对学生应用上述思维策略的具体运用情况作了分析讨论，提出了教学建议，以期给数学问题解决思维策略的教学提供有益的帮助；(4)简要论述了数学问题解决思维策略训练的教育意义；结合教育理论与教学实践，具体提出了实施思维策略训练的教学策略、教学途径及教学技术。更多还原

【Abstract】 Problem is the heart of mathematics. The real mathematics component is problems and problems-solving.The key purpose of mathematics education is to develop the students’ ability to solve the mathematics problems. This thesis analyses thinking strategy in solving mathematical problems and its instruction. It includes four parts. (1) First, the author discusses the conception and basic properties of mathematical problems with educational values in accordance with the situation in the middle school education, pointing out that mathematical problems must be suit for the students. Second, combining the theory of modern cognition psychology, the author gives a very general account of the conception , basic properties and thinking model of the solution of mathematical problems. (2) Following thinking model and the phase of the solution of mathematical problems, the author probes into a certain number of thinking strategies ,and analyses their apply conditions, operate principles, the aim of which is to guide instruction. (3) Adopting the method of thinking aloud, the author researches the distinguishing characteristics of the thinking strategies in the process of the solution of mathematical problems. It shows which thinking strategies are often used by senior middle school students , and shows which one existes defect. Basing on the research, the author puts forward some instruction suggestion indicates the purpose of which is to help the problem-solving instruction. (4) The author elaborates educational significance, instructive ways and means on thinking strategy training.更多还原