Research On The Present Situation Of Junior Mathematics Teaching On Proofs By Contradiction Based On Core Literacy

Mathematics teaching is an important way to achieve the goal of mathematics curriculum and the educational values.The new compulsory education curriculum standard(2011)pointed out that "effective mathematics teaching activities are the unity of both teaching and learning,embodying the concept of" people-oriented "and promoting the all-round development of students".Through a school survey,the researcher's tutor found that vocational school students' answers to math questions like "a 2m long board is folded into two sections,proving that at least one section is not less than 1m" are not promising.From the results of extreme statistics,seven students of the 147 students who responded effectively could solve the problem of using mathematical classified discussion correctly,and only one student solve the problem of using proofs by contradiction correctly.The researcher believes that there are problems in the current mathematics teaching of proofs by contradiction.Students lack the effective training of reverse thinking ability and the consciousness of reverse thinking,which even affect their ability to identify life phenomena,causing negative social effects.The paper first analyzes the literature about proofs by contradiction,then it defines proofs by contradiction,reverse thinking and the core literacy as well as the relations between them.Moreover,the research surveys junior middle school math teachers,which is carried out through qualitative research methods,such as structured questionnaire survey,online communication and optimized teaching plan.Based on results of the study research,this it offers the corresponding proposals and countermeasures:(1)the teachers pay less attention currently to the teaching of proofs by contradiction;(2)the application consciousness of reverse thinking needs to be improved;(3)teaching of proofs by contradiction should practice daily life closely.How to improve the teaching of proofs by contradiction,it proposes appropriate pedagogical advice and measures.(1)cultivate students' learning interest,train divergent thinking and strengthen;(2)enrich teaching and produce cognitive conflict;(3)carry out daily teaching and cultivate reverse thinking.