Teaching Design Of Solving Binary First-order Equations Based On Historical-genetic-principle

The binary first-order equations is one of the core contents of algebra teaching in junior middle school.The elimination thought in solving binary first-order equations is widely used in students' subsequent study.However,students have some problems when they study the binary first-order equations,such as low interest in learning and incorrect understanding of the elimination thought.The value of mathematical history to mathematics education has been recognized by many mathematics educators.The Historical-genetic-principle is increasingly used to guide teaching.This research has combed the historical development process of solving binary first-order equations.Then,under the guidance of L.Radford's teaching design framework,the teaching process of solving binary first-order equations is designed according to historical sequence,which attempts to enhance students' interest in learning and promote students' understanding of elimination.Firstly,through interview of teachers,revise the preliminary scheme according to the teacher's suggestion.Secondly,through individual interviews with students after actual teaching,we can know the students' interest in learning and their understanding of elimination thought,and the degree of acceptance of this kind of teaching.Finally,the teaching scheme is revised again.This research draws the following conclusions:(1)The historical development of solving binary first-order equations is as follows: The Zhichu method of < Nine Chapter arithmetic >?Liu Hui's method of Mutual multiplication and New equation method?Qin Jiushao's method of using the maximum common divisor in mutual multiplication.(2)Under the teaching of Historical-genetic-principle,students have higher interest in learning and can understand the thought of elimination.And they are more interested in thehistory of mathematics for solving binary first-order equations and can accept teaching in historical order.(3)The teaching design of solving binary first-order equations is successful which based on Historical-genetic-principle.This teaching design enlightens mathematics teachers that to arouse students' interest in learning and promote students' understanding of mathematical thoughts,we could follow the historical development process of knowledge in teaching,combine the actual situation of students,reconstruct history,and show the historical development process of knowledge.