The Study Of HPM Case

As the basic elementary function, exponential function and logarithmic function arethe important contents in high school mathematics. The definitions and properties ofthe exponential function and logarithmic function are given directly in themathematics textbooks in senior middle school, and the development of theknowledge is less concerned, to some extent, which impacts the learning ofexponential function and logarithmic function for the high school students.Mathematics education should get back to basics. Citing the historical material ofmathematics consciously, deriving the knowledge of the historical material ofmathematics and appling the researches of the historical material of mathematicscontribute to improve the understanding of mathematics nature for students.Rencently, there have been extensive investigations on combination of the history ofmathematics and mathematics education, and however, development andimplementation of cases for the specific history of mathematics and mathematicsclassroom teaching remains to be rich.In this thesis, by referring to Leonhard Eule (Introduction in Analysin Infinitorum),Nicolas Chuquet (Triparty en la science de nombres), John Napier (MirificiLogarithmorum Canonis Merchiston) and lots of historical material of mathematicsrelated to xponential function and logarithmic function, we show the evolution historyof the symbol of exponents and logarithms, development of exponents andlogarithms calculation. Furthermore, by combining the mathematics textbooks insenior middle school, HPM cases of exponential function and logarithmic functioncan be exploited.Finally, we implement HPM cases of exponential function and logarithmicfunction in classroom teaching of two classes in senior grade one. According toinvestigating the exercise of students and interviewing the students, we have:(1) Most students have a favourable view that the history of mathematics isincorporated into classroom teaching;(2) HPM cases have presented the evolutionary process of mathematical definition, mathematical proposition, mathematical thought and mathematical symbol,which enhance students to understand and master mathematical knowledge, and thenimprove the development of cognition for students.(3) By presenting the stories of mathematicians and the historical materialillustrations, HPM cases heighten the attraction of mathematics, animate classroomatmosphere and raise the study interest for students.(4) Through the implementation of HPM cases in classroom teaching, theconsciousness of handling mathematical materials flexibly and teaching reflectioncan be improved.The history of mathematics and mathematics classroom teaching integration of casedevelopment are as follows:(1) Teachers constantly improve their professional knowledge and professionalskills and extensive mining mathematical historical data, the development of teachingcase, improve math interesting, rich teaching contents and teaching mode;(2) The HPM case development should combine the student’cognitive level andknowledge structure, combing local examination system and mathematics textbooks,and teaching conditions of the school and the teaching ability;(3) To carry out the longer cycle more widely in the field of HPM case studlyeducation, not only to mathematics teaching as well as to education research hasimportant significance.