A Study On The Relationship Between The Cognitive Structure Of Analytic Geometry And The Ability To Ask Questions Of Senior Two Students

Mathematical problem posing can not only develop students' ability of inquiry and creative thinking,but also reflect their level of mathematical understanding,which has gradually attracted the attention of the educational circle.Scholars have made substantial achievements in the status survey,influencing factors and training research of problem posing,but there is still a lack of empirical research in the cognitive process.This paper studies the relationship between the cognitive structure and the problem posing ability of senior two students in analytic geometry.On the basis of theoretical research and referring to the existing test papers,the analytical geometry cognitive structure test paper and the problem posing ability test paper are designed.Through the analysis of the preliminary test,the reliability and validity are good,which indicates that the test paper is reliable and effective.Through the quantitative and qualitative analysis of the formal test,the following conclusions can be summarised with some educational suggestions:(1)The cognitive structure of analytic geometry of Grade 2 students is general and there are individual differences.The cognitive structure score of male students was slightly lower than that of female students,and there was no significant difference.Also there are no significant difference between male and female students in different cognitive structure groups.(2)The analytical geometry problem posing ability of Grade 2 students is weak,and the average score of each dimension from high to low is: fluency,complexity,novelty and flexibility.The non-directional problem raising ability is higher than the directional problem raising ability in the total score and all dimensions.There are slight differences in the ability of directional and non-directional problem posing between male and female students in each dimension,but there are no significant difference.(3)There is a significant positive correlation between cognitive structure and problem posing ability in analytic geometry and Pearson's coefficient is 0.26.Thereinto,the correlation between cognitive structure and directed problem prosing ability is higher than that of non-directed problem posing ability.There is a significant positive correlation between cognitive structure and novelty of question posing.(4)The cognitive structure of analytic geometry has an effect on the ability of problems posing.The problem posing ability of the high cognitive structure group is higher than that of the middle and low cognitive structure group,and there are significant differences.The problem posing ability of the middle cognitive structure group is slightly higher than that of the low cognitive structure group,and there is no significant difference.Thereinto,different cognitive structure groups have significant differences in the ability to pose directional problems,while the difference in the ability to posenon-directional prolems does not reach the level of significance.According to the research results,the following suggestions are put forward: to improve students' ability of problem posing by improving their cognitive structure;Develop students' cognitive structure through problem posing activities;Increase non-directional questions to raise students' awareness of problems.