A Study On Senior High School Students' Cognitive Development Of Mathematical Proof

It was found by the investigation of this research that students usually performed poorly at the beginning of learning mathematics in colleges,especially mathematical proving and proof.This study took the divisions of the understanding in mathematical cognition,according to three worlds of mathematics,as a rationale to explore the nature of senior high school students' understanding in mathematical proving and proof from the angle of cognition.First all of,the definition of mathematical proving and proof has been defined based on the literature review.The rationale of this research essay was formed by taking following analysis into considerations: the analysis of the three worlds of mathematics and its content,features,order of development and how it was related to mathematical proving and proof.Additionally,the writer(I)made full use of tests and interviews,these two effective research methods,to explore the senior high school students' cognitive process of the understanding in Mathematical proving and proof.Mind maps were adopted to demonstrate the students' cognitive process of understanding and some obstacles causing problems to understand mathematical proving and proof.To obtain reliable data,128 senior high school students were selected as the participants taking Paper A and B tests.In terms of data analysis,Chi-square and nonparametric test were used.Combining with the interviews' data on the students' cognitive development levels and features of mathematical proving,the research findings were: senior high school students' cognitive development of mathematical proving and proof has so far reached to a relative high level in the conceptual world.The situation of their cognitive development also goes well in the conceptual world.Finally,to study the senior high school students' cognitive development of mathematical proving and proof in the formal world,the writer(I)adopted case-study,interviews and took the definition of “new collection” as an example;The students' abilities of dealing with abstract algebraic questions were studied through tests and comparative approaches.Main results are presented as following: 1.Students have great difficulties solving mathematical questions related to abstract collections and algebraic,because senior high school students' cognitive development has not yet perfectly integrated into the formal world.2.The senior high school students who have accepted the trainings of mathematical proving usually performed better than those who have not,and their constructions were diverse.But for those untrained students,they were likely to think concretely and lack of the capabilities of constructing abstract proving.After referring to two above studies,the writer(I)was able to conclude that the senior high school students' cognitive development of mathematical proving could be improved through systematic and scientific trainings,although it has not yet integrated into the formal world perfectly.A couple of teaching advice is proposed at the end of this essay according to the conclusions of this study.