The Study Of "Explanatory Proofs" In Secondary Mathematics

At present,the teaching of secondary mathematics overemphasizes the importance of formalization.However,it overlooks students' understandings and the fact that non-formalization can foster students' abilities to guess reasonably.This paper mainly uses literature research,questionnaire survey,case study and interview to study explanatory proofs in secondary mathematics.On this basis,suggestions are put forward to the teaching of mathematics and the compilation of mathematic textbooks.This article uses the literature research to study the researches of explanatory proofs at home and abroad.The study finds that domestic researches are not as much as those in foreign countries,and there are few researches on the forms and levels of explanatory proofs both here and abroad.On the basis of literature review,the three-dimensional framework of this study is established: the contents,forms and levels of explanatory proofs.To ensure the reliability of the framework of the levels of explanatory proofs,32 mathematics teachers in middle schools were investigated on it.Based on the research framework,a questionnaire survey and interviews are conducted on the present situation of the use of explanatory proofs in secondary mathematics.And three case studies are used to discuss the application of explanatory proofs in secondary mathematics: the application of explanatory proofs of level 1 in the teaching of "Number and Algebra",the application of explanatory proofs of level 2 in the teaching of "Graphics and Geometry",and the application of explanatory proofs of level 3 in solving problems.Moreover,in the first two teaching cases,3 students were selected respectively to conduct interviews in order to understand the attitudes of the students.Through the study,the preliminary conclusions of this paper are as follows: from the cognitive perspective,most middle school teachers are aware of the importance and the usefulness of explanatory proofs.However,compared with the cognitive level,there is still a weak lack of teachers' performance on the level of behavior.From the perspective of the levels of explanatory proofs,most of the teachers think explanatory proofs of level 1 are more suitable for the teaching of mathematical concepts,explanatory proofs of level 2 are more suitable for the teaching of mathematical concepts and theorems,and explanatory proofs of level 3 are more suitable for the teaching of mathematical theorems and problem solving.From the perspective of the forms of explanatory proofs,teachers tend to use multiple-representations and technologies,while other forms of explanatory proofs are relatively less used.From the results of case studies,the interviewed students consider that this method of teaching which uses explanatory proofs can promote the understanding and grasp of knowledge.In the meantime,when we use explanatory proofs to solve word problems,it must be ensured that we adopt explanatory proofs of level 3.Finally,several suggestions are put forward on this basis.