Action Research On Plane Vector Teaching From HPM Perspective

In middle school mathematics,vector is not only an important method to prove plane analytic geometry,but also a powerful tool to solve solid geometry problems.This is because the vector has the dual characteristics of number and shape,and can exist in the coordinate system in multi-dimensional form.Its importance is self-evident.The research shows that the integration of mathematics history into mathematics teaching will produce many benefits to students.Therefore,based on the research of HPM teaching theory and the development history of vector,this paper carries out the action research of vector teaching from the perspective of HPM.In order to make the students in the same class feel the vector teaching from various HPM perspectives and experience the impact of different teaching methods on the learning effect,in the first round of teaching,the concept of vector and the coordinates and operations of plane vector adopt the teaching methods of teaching and inquiry respectively to convey the story of mathematicians to students and show the process of mathematicians creating mathematical knowledge.After the teaching,through the comments of excellent teachers and the feedback information of students,combined with the problems found in the questionnaire survey,improve the first round of HPM teaching cases and present the second round of teaching.In the second round of teaching,the concept of vector adopts inquiry teaching,and the coordinates and operation of plane vector adopt lecture teaching to explain the research methods of mathematicians to students.Through the interview,we can understand the students' recognition of different teaching methods from the perspective of HPM.Combined with the students' completion of after-school homework,we draw the following conclusions:(1)Vector teaching from the perspective of HPM can use different ways of integrating mathematical history into teaching and different teaching methods to carry out teaching,which can show the educational value of mathematical history from different angles.(2)The integration of mathematical history into vector teaching not only improves students' learning enthusiasm,promotes students' understanding of concepts,broadens students' mathematical thinking,improves learning effect,but also increases students' knowledge of mathematical history.(3)With the help of mathematical history materials,it can cultivate students' ability to think independently,explore and solve problems,make students not afraid of setbacks and failures,and enhance their confidence in facing difficult situations.