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杜宾斯基提出的APOS理论是基于对皮亚杰的数学学习的“自反抽象”理论的一个拓展.APOS理论下的数学认知包含活动、过程、对象和图式四个阶段.这四个阶段体现了一个概念的二重性认知:不仅有动态的概念建构过程和概念图式的整合过程,还有静态的概念图式的最终结果.在教学中根据概念的二重性进行教学设计,将有利于学生对数学概念的理解和掌握.一、APOS理论下的定积分学习根据APOS理论,数学概念学习需要经历
Dubinsky’s APOS theory is based on an extension of Piaget’s mathematical learning theory of “reflexive abstraction.” Mathematical cognition under the theory of APOS includes four stages of activity, process, object and schema. These four stages reflect the duality of a concept: not only the process of dynamic conceptual construction and the integration of conceptual schema, but also the final result of static conceptual schema.In the teaching, the teaching design is based on the duality of concepts, Will help students understand and master the concept of mathematics.A, APOS theory of definite integral learning According to APOS theory, mathematical concepts need to learn experience