The Application Of Dynamic Mathematics Technology To Solve Open-ended Problem Of Plane Geometry In Junior High School

The education informatization 2.0 action plan of China's ministry of education points out that information technology should be deeply integrated into subject teaching,and the teaching mode should be innovated to improve the effectiveness of subject teaching.China's compulsory education mathematics curriculum standards(2011 edition)particularly emphasizes that teachers and students are encouraged to use modern technological means to deal with complex calculations and solve practical problems,so as to obtain more time and energy to explore and discover mathematical laws and cultivate innovative spirit and practical ability.The teaching of the open-ended problem is conducive to the implementation of the "four abilities" and the cultivation of innovative spirit advocated by the mathematics curriculum standards for compulsory education(2011 edition).The open-ended problem of plane geometry is an important carrier to train students' core qualities such as intuitive perception,intuitive imagination,abstract thinking and logical reasoning.But these open-ended problems have the diversity conditions of openness,methods and conclusions variability,so they are not easy to answer even if the students participant observation,experiment,mathematical,conjecture analogy and induction activity.How to improve the teaching of plane geometrical open-ended problem is still a topic of mathematics education.Hawgent dynamic mathematics technology has such functions as operation object mathematicization,mathematical object dynamic,mathematical thinking visualization,etc.By integrating this technology into the teaching of plane geometrical open-ended problem,it may improve the effectiveness of the teaching of plane geometrical open-ended problem.This study tries to explore the application of dynamic mathematics technology to solve open problems of plane geometry under the guidance of Polya's theory of mathematical problem solving and mathematical multi-representation learning theory,including theoretical research and practical research.In terms of theory,through the combination of literature review and summary,this paper first summarizes the basic research situation of plane geometry,mathematical open-ended problems,dynamic mathematical technology,and puts forward the basic problems of the research.Then,it summarizes the basic viewpoints of Polya's theory of mathematical problem solving and mathematical multi-representation learning theory.Finally,this paper proposes the instructional strategies of applying dynamic mathematics technology to solve the open-ended problems of plane geometry: representing multiple information,highlighting key information,exploring multiple approaches,and solving dynamic variable problems.Each strategy is explained in detail and the corresponding application case is provided.In the aspect of practical research,through the method of teaching experiment,case study and investigation interview,the author conducts teaching practice with the example of triangle line segment and difference multiplier relation,and discusses the influence of the above strategies on students' learning process and results.The research results show that: the instructional strategy of applying dynamic mathematics to solve plane geometrical open-ended problem can promote students' learning of plane geometry.The concrete performance is: the experimental class student's mathematics study result and study efficiency is significantly higher than the control class;The cognitive load of experimental class is lower than that of control class;Compared with the control class,the students in the experimental class have improved their classroom participation,mathematical comprehension ability,problem solving ability and positive emotion involvement.