Research On The Status Of Mathematical Cognitive Structure Of Junior Middle School Students With The Examples Of Linear Function And Quadratic Function

As powerful tools for solving mathematical problems,functions play a significant role in the learning process of junior middle school mathematics.Many students do not have a good grasp of their learning and have not formed a sound network of knowledge system.At the beginning of the research of this paper,the exam paper was compiled based on the theory of CPFS structure,and 146 junior high school students in R Middle School were tested on the status of cognitive structure.The survey data was analysed and presented with results of the overall distribution of scores and the testing of differences.Combined with the test results and records of case interview,existing problems and their causes were examined with the data analysed.Teaching strategies,which aim at improving the cognitive structure of functions of junior middle school students,were then put forward,and two typical topics of functions in junior high school were designed for teaching.Research findings are as follows: The overall proportion of junior high school students' mathematical cognitive structure is relatively balanced,while the one of high-cognition group needs to be improved;There is no significant difference on CPFS structure regarding gender;The testing group is ideal in the structures of conception and proposition.The cognitive structure of the students with excellent learning is hierarchical and organised,while those with learning difficulties have not been able to form a fairly stable conception(or proposition)system structure;Some students lack the awareness of actively organising what they have learnt during their learning process,and do not think deeply when solving mathematical problems.Teaching strategies that can be applied are as follows: we can use motivational stimulus strategies to overcome difficulties and stimulate learning motivation;elaborative strategies to deepen students' memorisation in the application of function conception and proposition;organisational strategies to help students form related conception and proposition systems;flexible thinking training strategies and lay focus on the analogy and transfer of knowledge,so as to expand the knowledge bank;metacognition strategies to have students focused on reflection and communication and help them form the habit of actively structuring their knowledge networks.