Research On "Problem Chain" Design Of Mathematical Concept Teaching From HPM Perspective

The essence of education lies in educating people,and the essence of educating people lies in morality.The new round of high school mathematics curriculum standards clearly proposes that the value of moral education in mathematics should be fully tapped.The history of mathematics,as an important part of mathematical culture,is the implementation of "cultivating people with morality",an effective carrier of moral education.However,there is an awkward situation of "high evaluation and low application" in the history of mathematics when it is integrated into mathematics teaching.Based on this background,this research incorporates the "question chain" design concept into the HPM instructional design.The following three tasks have been done using the literature research method and the questionnaire survey method:First,the HPM design theory and the "question chain" design concept are combined to build a development framework for HPM instructional design under the "question chain" design concept.The framework revolves around one center: With student development as the center and the cultivation of students' core accomplishment in mathematics as the basic goal;based on two basic points: mathematics and history;following four principles: goal,science,hierarchy,and inspiration;Implement five strategies: set migration issues in the preparation of the organization,set up heuristic questions in the concept formation,set inductive questions in key historical places,set up error correction questions in student obstacles,and set malleable questions in the deepening of knowledge;Through three types of problem chains: progressive problem chains,bifurcated problem chains,and summary problem chains,the history of mathematics is incorporated into the design of mathematical teaching.We call it the "One Two Three Four Five" operating framework.Second,the survey analyzes the main obstacles and reasons for students' understanding of trigonometric functions.The survey found that students have a relatively shallow grasp of the essential attributes of the concept of arbitrary angles,and have not established the relationship between angles and rotations;they have not realized the necessity of introducing the radian system,and they understand the connection and difference between the two measurement systems of radians and angles inadequate;do not recognize the necessity of learning the arbitrary angle trigonometric function,and replace the coordinate definition of the arbitrary angle trigonometric function with the definition of the acute angle trigonometric function.Third,taking trigonometric function generation teaching as an example,according to the "one two three four five" operating framework,a trigonometric function prologue,radian system(two hours),and arbitrary angle trigonometric functions are provided for four HPM lessons.The course examples are aimed at students' obstacles in understanding the concept of trigonometric functions,and purposefully introducing historical materials in mathematics,which not only broadens students' horizons but also improves students' cognition of trigonometric functions.They have a more accurate grasp of concepts,a more comprehensive and deeper understanding.The "One Two Three Four Five" operating framework proposed in this article is based on pedagogy and psychology theory,combined with the characteristics of mathematics education and the value of the history of mathematics.It is operable and can provide a reference for front-line teachers.