Research On The Application Of HPM In The Teaching Design Of Solid Geometry Under The Technology Integration

Since the 21st century,information technology has developed vigorously,providing more paths for mathematics classroom teaching.Especially in the recent years,affected by the global COVID-19 epidemic,information technology has played an important role in teaching.With the deepening of the new curriculum reform,many studies have shown that the history of mathematics can provide a variety of reference teaching materials for teaching,deepening students’ understanding of the nature of knowledge.As one of the important contents of middle school mathematics,solid geometry is not only a high-dimensional expansion of plane geometry in junior high schools,but also a solid foundation for spatial analytic geometry.It plays a pivotal role in developing students’ core literacy.However,due to reasons such as the layout of textbooks and the way teachers teach,the training of students’ logical thinking ability and spatial imagination ability is far from enough.At the same time,complex lines and planes can bring students a sense of boredom,and students’ enthusiasm for learning is weak.The historical background of solid geometry is profound,so it is very necessary to explore the application of multiple types and perspectives of mathematical history in classroom teaching under the integration of technology.This study selects two sections,"Axioms for depicting the positional relationship between spatial points,lines,and surfaces" and "Lines are perpendicular to planes",as the research objects.It combs relevant historical materials in history,examines the requirements of this section in the curriculum standard,and summarizes relevant knowledge points in the textbook.Based on the empirical investigation results,a teaching case of applying HPM to solid geometry under technology integration was developed.The main research conclusions are as follows:(1)The positive impact on students: understanding the connotation and extension of knowledge points,the origin and elimination of the pulse;Building a high-level and holistic knowledge structure;Accumulate activity experience and learn to learn and think;Broaden the thinking of problem solving and experience mathematical thinking methods;Develop core literacy and enhance comprehensive ability;Stimulate learning interest and cultivate positive emotions.(2)Material and usage of mathematical history: multiple definitions of planes,proof of the transitivity theorem of parallel lines in space,proof of the theorem for determining the perpendicularity of lines and surfaces,and special geometry in "Nine Chapters of Arithmetic".Adopt different fusion methods based on relevance and acceptance,and skillfully combine appropriate information technology means to dynamically display and visually present.(3)Teaching principles and suggestions: Five teaching principles;Four design methods;Establish a complete data resource library and hardware facilities,actively carry out lectures and seminars,master professional mathematics software,improve courseware production capabilities,and strengthen communication and sharing.This study provides new materials and paths for the application of HPM to the teaching of solid geometry from multiple types and perspectives from the perspective of technology integration,and enriches the relevant theoretical system.I hope that my superficial opinion can be used as a reference for front-line teachers.