| In 2002,Professor Yu Ping of Nanjing Normal University proposed the CPFS structure theory,which is a cognitive structure unique to the psychology of mathematics learning,compounded by four units: concept domain,concept system,proposition domain,and proposition system.A well-constructed CPFS structure is conducive to students’ understanding and transfer of knowledge as well as the development of mathematical ability,so it is necessary to seek measures to improve the CPFS structure in students’ minds based on the CPFS structure theory.In this paper,we used tests,unstructured interviews,and participant observation to select cases with typical problems,analyze and summarize the problems in the CPFS structure of trigonometric functions of typical cases,and propose a targeted plan to improve the CPFS structure of the cases,and carry out a two-month intervention.It was found that the CPFS structure of trigonometric functions in typical cases had the following problems: the cases did not have a perfect trigonometric function concept domain and concept system,mainly in the following ways:(1)they were not clear about the origin of the definition of trigonometric functions,they could not grasp the concept of trigonometric functions accurately,and their cognition was stuck at the level of trigonometric functions in junior high school;(2)they were vague about the origin of trigonometric function properties,and they remembered trigonometric function images and properties in isolation.The case also does not have a perfect trigonometric function proposition domain,proposition system,mainly in:(1)the trigonometric function proposition knowledge is unclear,not clear about the process of obtaining the proposition;(2)the trigonometric function proposition between the launch of the relationship is not clear,isolated,fragmented memory formula.The following measures were taken to address the problems of the CPFS structure of trigonometric functions: the main measures taken for the domain of trigonometric function concepts and concept systems are:(1)let students experience the process of acquiring trigonometric function concepts,using different definition methods to deepen students’ knowledge;(2)let students experience the two-way process of discovering trigonometric function properties from trigonometric function images and deriving trigonometric function images from trigonometric function properties.The main measures taken for the trigonometric function proposition domain and proposition system are:(1)make good use of the scaffolding role of the unit circle to feel the process of obtaining propositions from the geometric properties of the circle using algebraic methods;(2)focus on allowing students to experience the process of deriving propositions from each other.The results of the pre-test compared with the post-test showed that both study participants after the intervention instruction showed significant improvement and enhancement in the level of trigonometric CPFS structure and academic performance in mathematics.This study not only provides an understanding of the current situation and typical problems of trigonometric CPFS structure of high school students nowadays,but also provides front-line teachers with referenceable teaching measures to optimize students’ trigonometric CPFS structure,improve teaching efficiency and at the same time,improve students’ academic performance in mathematics. |
