Comparative Study On The Teaching Design Of Pythagorean Theorem In Junior High School

Pythagorean theorem plays an important role in the study of plane geometry,and it is a big difficulty for teachers in the teaching of middle school mathematics.The article studies the problem of the Pythagorean theorem is a junior high school teaching design of comparative research,combing the theory of mathematics classroom teaching design,on the basis of the application of text analysis,comparison and case analysis,to 9 Pythagorean theorem teaching design of teaching goal,teaching process carry on comparative analysis to two dimensions.Three-dimensional target and the introduction,discovery and proof of the link to expand.This paper also reflects on the shortcomings of the Pythagorean theorem teaching and constructs the exploratory teaching of the Pythagorean theorem which reflects the new mathematics curriculum idea,in order to provide reference and inspiration for the middle school mathematics teachers to the Pythagorean theorem teachingThrough comparative analysis,it is found that the knowledge and skills of the three dimensional goals of instructional design of Pythagorean theorem are generally concerned with the mastery of the theorem and the understanding of the proof method,but the application of the theorem is ignored.The process and the method goal pay more attention to let the student experience the discovery of the theorem.By comparing the teaching process of theorems,the introduction methods can be summarized into three types: situation introduction,review introduction and jigsaw introduction.Teachers generally use the method of setting up situation as the beginning of a new lesson.There are three ways of discovery: first,square area is calculated in the grid drawing to obtain the area relationship between the three squares,and the relationship between the three sides is obtained from the area relationship;The second is to get the "zhao shuang string diagram" in the way of origami or jigsaw puzzle and discover the Pythagorean theorem.The third is to get the guess and discover the theorem by measuring the sides of right triangle.The first is to improve the teaching material mainly in the form of presentation,which is favored by teachers,but they do not advocate the way of review and jigsaw.The proof of Pythagorean theorem is mainly in the form of jigsaw puzzle and the teacher shows the picture directly,introduces it and guides the students to calculate and verify it.The common points are that the method of calculating area transforms the abstract geometric intuition into algebraic relations to strictly prove the conclusion,and the proving link does not show strong "inquiry".The connection between discovery link and proof link fully reflects the disconnect between discovery and proof link of Pythagorean theorem,and profoundly interprets the phenomenon that teachers pay more attention to exploration than to proof.