HPM视角下中学数学可视化教学设计与实践——以“球的体积公式”为例

Teaching Design and Practice of Mathematics Visualization in Middle School from the Perspective of Mathematics History and Mathematics Education—Taking the “Volume Formula of a Ball” as an Example

摘要: HPM视角下的数学教学的基本方法就是借鉴历史、重构历史、追求自然的发生教学法。“可视化”是指通过可以觉察的视觉方式将思维进行外化呈现的方式。在教学中，通过可视化的载体建构模型，结合学生的认知结构，促进学生形成清晰明确的知识结构。本文从HPM的视角下重新对球的体积内容进行整合，以可视化的方式呈现，探索符合学生认知规律且顺应球的体积历史发展规律的教学设计并付诸于教学实践，采用借鉴、重构历史的方式，让数学史自然而然地融入到球的体积的教学过程中去。

Abstract: The basic method of mathematics teaching from the perspective of HPM is to draw on history, re-construct history, and pursue the occurrence of nature. “Visualization” refers to the way in which thoughts are externalized through perceptible visual means. In teaching, through the visual carrier construction model, combined with students’ cognitive structure, promote students to form a clear and definite knowledge structure. This paper re-integrates the volume content of the ball from the perspective of HPM, presents it in a visual way, explores the teaching design that conforms to the laws of students’ cognition and conforms to the historical development law of the volume of the ball, and puts it into teaching practice, and adopts the method of borrowing and reconstructing history, so that the history of mathematics can be naturally integrated into the teaching process of the volume of the ball.