APOS理论下基于GeoGebra的教学设计——以指数函数为例

Instructional Design Based on GeoGebra under the APOS Theory—Taking Exponential Functions as an Example

摘要: APOS理论是近年来美国数学家杜宾斯基(Dubinskt)等人提出的一种数学教学理论。他将数学概念的建立分为四个阶段：活动(Action)、过程(Process)、对象(Object)、图式(Scheme)，并用于指导教学实践。早期APOS理论只是被用在大学数学的教学中，现在该理论正逐步渗透于我们的中学数学教学中。GeoGebra是一款功能强大的动态数学软件，由奥地利数学家Markus Hohenwarter及其国际开发团队共同开发，旨在为全球校园提供免费使用的动态数学工具。它结合了几何、代数、微积分、概率统计、数据表、图形和计算等多种功能，为用户提供了一个综合性的数学学习、教学和科研平台。它是一款功能全面、易于使用的动态数学软件，适合学生、教师和任何对数学感兴趣的人使用。本文先介绍APOS理论和GeoGebra，然后运用APOS理论结合GeoGebra以指数函数为例进行教学设计。

Abstract: TAPOS theory is a mathematics teaching theory proposed in recent years by American mathematician Ed Dubinsky and others. It divides the formation of mathematical concepts into four stages: Action, Process, Object, and Scheme, and is applied to guide teaching practice. In the early days, the APOS theory was only used in college mathematics teaching, but now it has gradually penetrated into middle school mathematics teaching in China. GeoGebra is a powerful dynamic mathematics software co-developed by Austrian mathematician Markus Hohenwarter and his international development team, aiming to provide a free dynamic mathematics tool for campuses worldwide. It integrates multiple functions including geometry, algebra, calculus, probability and statistics, data tables, graphics and computation, offering users a comprehensive platform for mathematics learning, teaching and scientific research. As a full-featured and user-friendly dynamic mathematics software, it is suitable for students, teachers and anyone interested in mathematics. This paper first introduces the APOS theory and GeoGebra, then carries out an instructional design for exponential functions by applying the APOS theory combined with GeoGebra.