数学教学设计的新视角——透过鼓励学生思维活动从感觉效应过渡到运动效应的视点

A New Perspectivein Mathematics Teaching Design:Through the Perspective of Encouraging Students’Transition From Sensory Effects to Motor Effects in Their Thinking Activities

发生数学认识的途径主要分为递进的两方面:感性认识与理性认识.感性认识的基础是数学思维主体的感觉效应,通过关于某种现象性的类比形成数学知识;理性认识的基础是数学思维主体的运动效应,利用数学知识的结构性,通过关于探究空间形式与数量关系的本质发生数学认识.后者可以把握数学知识的本质与规律,数学教师在教学设计及其课堂实施中,要想方设法帮助数学思维主体发生数学认识时,从感觉效应过渡到运动效应,从而提高数学教学的有效性.

The path to mathematical cognition consists of two progressive aspects:perceptual cognition and rational cognition.The basis of perceptual cognition is the sensory effect of the subject of mathematical thinking,which forms mathematical knowledge through some phenomenal analogy;where as the basis of rational cognition is the movement effect of the subject of mathematical thinking,which,by using the structure of mathematical knowledge and through exploring the nature of the relationship between spatial form and quantity,generates mathematical understanding.The latter helps grasp the essence and laws of mathematics knowledge.In instructional design and classroom implementation,mathematics teachers should strive to find ways to help the subject of mathematics thinking achieve the transition from the sensory effect to the motion effect,thus to improve the effectiveness of mathematics teaching.