Teaching Research On The Incorporation Of Mathematics Culture Into Mathematics Class Learning Dynamic System

The newly promulgated Mathematics Curriculum Standard of General Senior High School(2017)attaches great importance to mathematical culture.It not only emphasizes the integration of mathematics culture into course content in the part of curriculum structure,but also proposes the integration of mathematics into mathematics teaching activities in the part of teaching suggestion.However,integration of mathematics culture into mathematics teaching in senior middle school has been puzzling math teachers of senior high schools.Mathematics classroom learning dynamical system is a three-level three-dimensional generation system composed of “start”,“maintenance” and “intention generation” which describes the progress of mathematics classroom learning.The mathematics classroom learning dynamical system regards the teaching problem as the source of the operation of the start system,the maintenance system and the intention generation system.The quality of questions in teaching direct affects the operation of the systems.As the core of mathematics,mathematics culture can be used as the materials and situations of questions used in teaching to improve the quality.Therefore,this research attempts to design mathematics situation and questions used in teaching based on mathematics culture to realize the operation of mathematics learning dynamical system and integrate mathematics culture into mathematics teaching curriculum concept.Mathematics classroom learning dynamical system is a three-level three-dimensional generation system composed of “start”,“maintenance” and “intention generation” which describes the progress of mathematics classroom learning.The mathematics classroom learning dynamical system regards the teaching problem as the source of the operation of the start system,the maintenance system and the intention generation system.The quality of questions in teaching direct affects the operation of the systems.As the core of mathematics,mathematics culture can be used as the materials and situations of questions used in teaching to improve the quality.Therefore,this research attempts to design mathematics situation and questions used in teaching based on mathematics culture to realize the operation of mathematics learning dynamical system and integrate mathematics culture into mathematics teaching curriculum concept.By reviewing the literature and research about the concept of mathematics culture,the integration of mathematical culture into teaching,and the dynamical system of mathematics classroom learning,the study first establishes the theory of integrating mathematics culture into the dynamical system of mathematics classroom learning through experience summarization method and analytical synthesis method.Secondly,based on the relevant theory,the teaching design of three subjects—Radian System,Trigonometric Function at Any Angles and Cosine Formula of Angle Difference,is implemented combined with the content of mathematics teaching in senior high school.Thirdly,by interviewing with 5 senior high school mathematics teachers about their opinions and viewpoints on teaching design,the effect of teaching design of integrating mathematics culture into classroom learning dynamical system is initially tested.The main conclusions of the study are as follows:Firstly,for the theoretical research of integrating mathematics culture into mathematics classroom learning dynamical system,this paper looks for the combination of mathematics culture and mathematics classroom learning dynamical system:(1)Teachers create situation based on mathematics culture and initiate students' thinking;(2)Teachers design question chain based on mathematics culture and maintain students' thinking;(3)Teachers summarize mathematical knowledge and mathematical thinking methods,and generate intention.Moreover,the feasibility of integrating mathematics culture into mathematics classroom learning dynamical system is analyzed:(1)at the teacher level,the implementation and promotion of curriculum reform increase the approaches of accessing to mathematics culture and integrating mathematics culture into teaching;(2)at the level of students,based on the theory of constructivism,students expect to experience the recreation process of mathematical knowledge;(3)at the level of teaching material,the content of mathematics culture in teaching material is increased.These conditions make it feasible to integrate mathematics culture to mathematics classroom learning dynamical system.The principles of integrating mathematics culture into mathematics classroom learning dynamical system are proposed,including relevance,development,usefulness,process and interestingness.Finally,the ways of integrating mathematics culture into mathematics classroom learning dynamic system are explored on the basis of the combination points.Secondly,based on theoretical exploration,the teaching scheme of integrating mathematics culture into mathematics classroom learning dynamical system is studied and designed,including A edition published by the People's Education Publishing House,compulsory course 4.Radian System,Trigonometric Function at Any Angles and Cosine Formula of Angle Difference.Thirdly,the five interviewed teachers speak highly of the teaching design of integrating mathematics culture into mathematics classroom learning dynamical system,and pointed out that it is the same as the traditional teaching mode,which is beneficial to the students' profound understanding of mathematics knowledge,correct understanding of the mathematics essence,and cultivating students' mathematics literacy.The innovation of the research:(1)A new research perspective: the integration of mathematics culture into mathematics classroom teaching is discussed from the perspective of learning;a new research content from the perspective of learning(what students learn and what teachers teach);(2)New research contents: The research attempts to combine mathematics culture and mathematics classroom learning dynamical system,which enriches the research on the integration of mathematics culture in mathematics classroom teaching.The limitation of the research:(1)The way of integrating mathematics culture into mathematics classroom learning dynamical system is less abundant,and only the creation situation,design of teaching questions and summary based on mathematics culture are considered;(2)The teaching design effect of integrating mathematics culture in mathematics classroom learning dynamical system is examined superficially.The interview with senior high school mathematics teachers is not persuasive.