First of all,"General High School Mathematics Curriculum Standards(2017 Edition2020 Revised)" emphasizes the integration of mathematics culture into the curriculum content;Secondly,in recent years,the relationship between the history of mathematics and mathematics education,namely the value of HPM,has been increasingly paid attention to by the mathematics education circle and front-line teachers,but in the actual teaching activities,it faces the dilemma of "high evaluation,low application";Finally,function is through the main line of high school mathematics curriculum,the concept of function is the foundation of function.Based on the above facts,the author determines the research questions of this paper:(1)What cognitive difficulties do high school students encounter in learning the concept of function?(2)What influence does the concept teaching of mathematical history integrating function have on students’ grasp of conceptual knowledge?(3)What is the influence of the concept teaching of mathematical history integrating function on students’ emotional attitude towards learning mathematics?This research is divided into 6 chapters.Chapter 1: Introduction--introducing the research background,research problems and research significance;Chapter 2: Literature review and theoretical basis--introducing the birth of HPM,research review of HPM at home and abroad,development history of function concept,practice research review of function concept,historical similarity theory and re-creation theory.Chapter 3: Research design--introducing research ideas,research methods,research objects and research tools;Chapter 4: Research process;Chapter 5: Analysis of questionnaire results;Chapter 6:Summary.Through the above research process,the conclusions of the research question are as follows:1.Students are familiar with the analytic expressions and images of functions they have learned,and many students cannot correctly distinguish the unfamiliar analytic expressions of functions and images of scattered shape functions.The students memorized the concept definition,but did not use it flexibly.They could only achieve cognitive assimilation,but could not achieve cognitive adaptation.Many students’ understanding of functions stayed at the stage of "variable dependence",but failed to reach the stage of "set correspondence".To some extent,it shows that students’ cognition of function concept has historical similarity.2.The concept teaching of mathematical history integrating function has a positive influence on students’ grasp of conceptual knowledge,but the effect is different.For the students with lower mathematical level,this teaching method has the most obvious effect in promoting the students’ understanding of knowledge.For the middle level students,the positive effect is the second;For students with higher mathematical proficiency,the effect was the weakest.This teaching method not only deepens the students’ understanding of knowledge,but also expands their horizons,enriches the knowledge of mathematics history and improves the literacy of mathematics culture.3.The teaching of mathematical history with the concept of function has a positive influence on students’ attitude towards learning mathematics.In addition to increasing students’ interest in learning and confidence in learning mathematics,it also cultivates students’ rigorous and realistic qualities,insisting on the truth,constantly exploring and not afraid of setbacks.Meanwhile,it also shows that mathematics is a part of human culture. |