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APOS理论是美国数学教育家杜宾斯基等人提出的有关概念学习的一种理论。该理论认为数学概念的建构可以分成四个阶段:操作、过程、对象、图式。以指数函数为例,按照APOS理论四个阶段进行教学,首先,创设问题情境帮助学生进行操作;然后通过分析函数变量x与y之间的对应关系以及让学生自我举例,进行由外向内重复操作的过程;接着通过压缩重复操作的过程为一个整体得到对象;最后,对操作、过程、对象以及学生自己大脑中原有的相关问题进行整合,形成指数函数概念的心理图式。
APOS theory is a theory put forward by Dobinski et al., A mathematics educator in the United States, on concept learning. The theory holds that the construction of mathematical concepts can be divided into four stages: operation, process, object, schemata. Take the exponential function as an example, according to the four stages of APOS theory teaching, first of all, to create a problem situation to help students to operate; and then by analyzing the correspondence between the function variables x and y and let students self-examples, from outside to inside to repeat the operation The process of compressing repeated operations as a whole to get the object; Finally, the operation, process, objects and students related to the original problem in the brain to integrate the formation of the psychological function of the concept of exponential function.