Teaching Research On Geometric Proof Of Junior High School Based On Van Hiele's Theory

As an important branch of mathematics,geometry has obvious educational value in cultivating students' observation ability,logical thinking ability and innovative spirit.The study of geometry is helpful to the cultivation of students' intuitive imagination literacy.Therefore,the study of geometry proof is particularly important for students.Students' learning of geometry is realized through teaching activities.Scientific and reasonable teaching activities can help students learn geometry well.Therefore,the teaching of geometry proof is an important problem faced by front-line teachers.At present,geometric problems have been widely concerned in the field of pedagogy and cognitive psychology,and a large number of research results have emerged.In pedagogy,van HIL's theory of geometric thinking level is a relatively mature teaching theory at home and abroad,and also a widely recognized teaching theory.In the field of cognitive psychology,the Cognitive Science Laboratory of Carnegie Mellon University conducted an in-depth analysis of the cognitive process of geometric proof in 2010.Using ACT-R cognitive simulation tool,this paper simulates the cognitive process of solving complex geometric proving problems,and on this basis,the cognitive decomposition of the problems is carried out.In this paper,the methods of literature research,investigation and experimental research are used to analyze the theory of Van Hiele's theory,and then the application of Van Hiele's theory is discussed.The theory is mainly used in the evaluation of the level of geometric thinking,the design of geometric teaching and so on.This paper focuses on the design of geometric teaching.Under the guidance of Van Hiele's theory,ACT-R theory is integrated to seek the convergence point of the two,and the integration of the two in the process of geometry teaching is completed.The geometry teaching flow chart based on the two is designed,the geometry teaching design scheme is constructed,and the geometry teaching case is designed.And the teaching cases of "the shortest path problem" and "the judgment of triangle congruence" are studied,and the two groups of students are compared.SPSS software is used to objectively analyze the test results of the learners,and to explore the influence of the geometry teaching design based on Van Hiele's theory on the students' geometry thinking level.Research shows that Van Hiele's theory and ACT-R theory have similar points.Teaching research based on Van Hiele's theory can effectively promote students' geometric prooflearning and provide a certain reference for teachers' teaching design,but In this paper,the geometric proof teaching model is still in its infancy.For more complicated geometric proof teaching strategies,it needs to be gradually improved in practice.