Research On Teaching Design Of Integrating Mathematical Culture Into Trigonometric Function In Senior High School

Since the new curriculum reform,we can find that many contents related to mathematics culture and mathematics history have gradually appeared in the Mathematics Curriculum Standards for Ordinary Senior High Schools(2017 Edition),which also have basic teaching requirements.At home and abroad,there have been mature studies on the way and value of integrating the history of mathematics into mathematics teaching,but how to integrate the history of mathematics into mathematics teaching is still in the stage of continuous exploration.This paper discusses the application of the history of mathematics in the teaching of mathematics in senior high school based on the curriculum standard of Mathematics in Senior High School(Experiment)and some concrete examples.Mathematical concept is the basis of mathematical rules,formulas and theorems,the cornerstone of calculation,reasoning,judgment and demonstration,and the premise and important guarantee of cultivating students' thinking ability.In this context,this paper investigates the current situation of the integration of mathematical history in the teaching of mathematical concepts in senior high schools,finds problems and summarizes rules,and constructs the teaching mode of the integration of mathematical history,which provides a specific way for the integration of mathematical history into the teaching of mathematical concepts in senior high schools.The core problem of this paper is: how to construct the teaching mode of the integration of mathematics history and mathematics concept teaching in senior high school? In order to form a scientific understanding of this study,this paper adopts the literature analysis method to analyze the literature related to the integration of mathematical history into high school mathematics teaching,mathematics concept teaching and mathematics history into high school mathematics concept teaching,and analyzes the HPM theory,constructivism theory,APOS theory and recreation theory.At the same time,it analyzes the textbooks and interprets the "curriculum standards" of the relevant courses of senior high school mathematics concept,and demonstrates the necessity and feasibility of integrating the history of mathematics into the teaching of senior high school mathematics concept.Next,based on the part of high school students and teachers in heilongjiang province as the investigation object,using the method of questionnaire and interview method to survey the high school mathematics concept teaching into the overall situation of the history of mathematics,the investigation results show that the history of high school students' mathematical literacy level is not high,teachers of history of mathematics in the classroom teaching situation is not very ideal,However,most students hold a positive attitude towards learning the history of mathematics.In high school mathematics classroom teaching,teachers can use mathematical historical materials to help students understand and master mathematical knowledge,so as to effectively improve their understanding and grasp of mathematical thinking and methods.Accordingly,this paper constructs a highly operable "Modern teaching APOS mode from the perspective of mathematical history",and gives relevant suggestions based on the above proposed teaching mode from three perspectives.Teaching material Angle: with pictures and pictures,rich mathematical historical materials;Add "probability and statistics" part of mathematical historical materials;Add "reconstruction" mathematical historical materials into the way.Teachers' point of view:excavate relevant historical facts and create teaching situation;Pursue the historical track,highlight the essence of concept;Set the sequence of questions skillfully to generate mathematical concepts.Students: Enrich teaching resources by using school-based courses;Carry out research study,expand the scope of knowledge.Finally,based on this teaching model,specific teaching cases are given for middle school teachers' reference.