A Probe Into The Ancient Historical Materials Of Elementary School Fractions Teaching From The Perspective Of HPM

HPM theory is a theory about the history of mathematics and mathematics education,and has formed a relatively mature framework and research system.In recent years,the research results of HPM have been increasing day by day,and the effectiveness of its theories in mathematics education practice has been verified.The content of fractions is the focus of elementary school mathematics teaching and the difficulty of learning mathematics for elementary school students.Although there have been related studies on the application of HPM to elementary school mathematics teaching,there is no research literature that combines HPM with elementary school fraction teaching.Based on the analysis of the requirements of the curriculum standards for fraction teaching and sorting out the existing fraction historical data in elementary school mathematics textbooks,this article further excavates and sorts out historical materials related to elementary fraction teaching,and puts forward the principles and principles of applying relevant historical materials to elementary fraction teaching.Suggest.This article mainly uses literature analysis method,text analysis method,case design method,etc.for discussion and research.Lay the foundation for the research by searching the related literatures about the integration of the history of mathematics into the teaching of mathematics,the teaching value of the history of mathematics,and the teaching of fractions.Use the "text analysis method" to analyze the related score teaching content in the textbook and the related score historical data in detail,use the relevant classics as the source of historical data,and organize and analyze the historical data,select the elementary school score-related topics for case design,Exploring the principles of integration of historical fractional materials and fractional teaching.Through research,it is found that fractional teaching from the perspective of HPM conforms to the recommendations of the "Mathematics Curriculum Standards" that the requirements of mathematics culture and the historical materials of mathematics advocated can be penetrated into the whole set of teaching materials,and at the same time it is in line with the three-dimensional goals of mathematics teaching.Primary school mathematics textbooks have included historical data related to fractions,but the number of historical data in the textbooks is generally small.And "Nine Chapters of Arithmetic","Exploring the Origin of Ancient Arithmetic Poems","Arithmetic Books","Sun Tzu Suan Jing","Abacus Books","A Brief History of Mathematics","A Concise History of Mathematics","This is the easy-to-read history of mathematics","Celebrities· "Interesting Questions" and other classics and writings contain a wealth of historical data on fractions,which can be matched with the content of elementary school fractions.Through sorting out the historical data related to fractions in the above classics,42 pieces of historical data related to fractions were sorted out.Based on the HPM teaching theory,five principles suitable for the integration of historical data of elementary school fractions are put forward,to find the connection point between historical data and the topic of fractions,and to combine the knowledge points of score teaching and the expression of historical data to classify and integrate the collected historical data of fractions,and to integrate them.Divided into 13 categories.A specific analysis and elaboration on the integration of 13 categories of historical mathematics materials into fraction teaching is made.Taking the "about points" teaching design as a case study,it aims to better integrate historical materials and fraction teaching,and serve as an integrated demonstration of fraction historical materials and fraction teaching.Combining the research experience of historical materials for fractional teaching from the perspective of HPM,the following suggestions are made on "the excavation and collection of historical materials of mathematics,the selection of historical materials of mathematics,and the application of historical materials of mathematics".First of all,the search for historical materials of mathematics can be based on related historical ancient books.,Archaeological documents,cultural history materials,etc.;historical materials can be collected from multiple angles,types,and scopes.Secondly,in the selection of historical materials,historical materials that contain relevant mathematical thinking and methods and have positive educational significance should be selected;at the same time,non-scientific historical content that is difficult,knowledge biased,and old in concept should be avoided.Finally,in the application of historical materials of mathematics,according to the needs of the subject,under the guidance of three-dimensional goals,combined with the principle of HPM,historical materials of mathematics should be applied as links such as introduction,new teaching,consolidation,practice or extracurricular extension;in addition,historical materials and topics The content should be closely related,and the content of historical materials and the topics of the professor should match each other.