The Teaching Research Of Pythagorean Theorem Based On Textbook Comparison

The Pythagorean theorem is included in every country’s textbooks.What are the similarities and differences of theorem arrangement in different textbooks?What kind of link design can effectively help students break through key points? Around this,using the literature method,We studied and selected 78 pieces of core journal literatures of Pythagorean theorem,and analyzed them from six aspects: chronological distribution,journal distribution,institution distribution,author situation,research method and research content.Based on the above analysis,questionnaire and interview were used.Taking grade 8 students of a middle school in hangzhou as the object,the author conducted a pre-school basic investigation and post-school homework error attribution,and found that:(1)most students have already had some contact with the theorem before the formal study of the theorem.(2)the conclusion of the theorem requires students to have certain analytical and inductive thinking methods and the ideological consciousness of applying mathematics.The predictability and frustration tolerance of the students in grade 8 are not mature,thus forming difficulties.(3)Students know little about the history of Pythagorean theorem.In view of the above learning situation,we collected six editions of Chinese and foreign textbooks,and compared them from five dimensions,namely,theorem discovery,theorem description,theorem demonstration,theorem application and theorem history.We got the following enlightenment:(1)theorem discovery: most textbooks adopt the design idea from special to general.(2)theorem description: the slide courseware adopts symbols and graphics to reduce the text presentation and transform the text representation of the theorem into verbal explanation.(3)theorem argumentation: most textbooks contain theorem proofs,and there are more than three kinds of proofs,among which zhao shuang’s string graph proofs,presidential proofs and Pythagoras proofs are frequently used.(4)application of the theorem: the design of example exercises should focus on making students reach level three and level four after learning,properly enrich the life background of example exercises,reasonably classify exercises after class,such as consolidation homework,inquiry homework,expansion homework.(5)theorem history: it is natural to introduce the history of mathematics appropriately in theorem discovery and theorem demonstration.On this basis,the Pythagorean theorem teaching redesign is formed and the design is compared with the teaching contrast experiment.The results show that: In the link of theorem discovery,students have a stronger sense of discovery and a better memory of the discovery process.In the proof of theorem,to a certain extent,it is helpful to deepen students’ mastery of the proof method.