数学问题表征对学生问题解决的影响及教学启示

The Influence of Mathematical Problem Representation on Students’Problem Solving and Its Teaching Enlightenment

问题表征是问题在学习者头脑中的呈现方式。数学问题解决的前提条件是学习者能够对数学问题进行准确的表征。准确表征的外在表现即学习者在对数学问题的本质进行深入挖掘的基础上,能正确把握信息、深度提炼信息、用不同的方式整合并提取信息,以确定解决问题可能用到的方法。在课堂教学中注重对学习者数学问题表征能力的培养是完善和发展学生认知结构、提高数学解题能力的重要途径。主要论述了两个方面的内容:一是问题表征对学生数学问题解决能力影响;二是提出了以培养和提高学生问题表征能力为核心的数学课堂教学策略,如因材施教、多元化表征和克服思维定式等。

The prerequisite of solving a problem is to excavate the essence of the problem,correctly grasp and refine the information,and accurately represent the problem.Problem representation refers to the way in which the problem is presented in the learner’s mind.The learner can extract and integrate key information in the problem space in different ways to determine the possible operators.This paper mainly discusses the influence of problem representation on students’ability to solve mathematical problems,and puts forward the strategies of mathematics classroom teaching based on the cultivation of problem representation.