The Research On Construction Of Senior High School Student's Derivative Cognitive Structure

In psychology,cognitive structure is the core factor affecting teaching activities.Mathematical cognitive structure affects students' ability to extract information and construct new knowledge,and their understanding and transfer of concepts.Based on this,this study relies on concept map as a tool to represent students' cognitive structure of derivative concept,tries to use the concept map drawn by students to discuss the characteristics of their cognitive structure of derivative concept,and provides suggestions for derivative teaching.According to previous scholars' research and students' answers,the author divides the organization of derivative cognitive structure into four types: sporadic type,tree type,diffusion type and network type.Most students can form a certain hierarchical structure,but there is a lack of horizontal connection between knowledge.The establishment of network cognitive structure depends on teachers' guidance and the establishment of effective branches.The characteristics of knowledge in students' cognitive structure mainly include:(1)less storage of derivative knowledge(2)more general concepts,mostly general language,and not good at multivariate representation.(3)Lack of procedural knowledge such as mathematical ideas and strategies.The test paper shows that students have a high level of understanding of the geometric meaning of derivative,the operation of derivative and the application of derivative in function,but a low level of understanding of the formal definition of change rate and derivative.The corresponding concepts with higher students' understanding level also appear more frequently in the concept map.The score of the concept map is significantly correlated with the score of the test paper,that is,students with good mathematical cognitive structure can have a higher academic level.In the interview,the author observed that students' problem-solving strategies are reflected in the concept map as follows: starting from the node activated by the topic,returning to the methodology near the original node through the superior concept derivative,and finally solving the problem back to the original node.Each problem-solving strategy forms a corresponding closed loop with the derivative concept,with a stable production formula.The operation of derivatives and mathematical thinking methods provide guidance and necessary operation means for problem-solving strategies outside the closed loop.According to the above investigation and analysis results,the author puts forward the corresponding teaching strategies:(1)multiple representation understanding and tamping the depth of internalization;(2)Strengthen hierarchical division and implement orderly memory;(3)Refine ideas and strategies to help migrate applications;(4)Moderate training to consolidate and improve the closed-loop production.(5)Comprehensive migration and application to build horizontal connection.