A Pedagogical Case Study Of Mathematical Problem Posing In High School From The HPM Perspective

The value of the history of mathematics in mathematics education has been universally recognized.The application of the history of mathematics to mathematics education is an important area of current research in mathematics teaching and learning.Many university scholars and front-line teachers are devoted to the development of HPM examples.Problem posing has also received much attention in the reform of the Chinese mathematics curriculum,and problem posing can foster students' sense of inquiry and increase their interest in learning mathematics.In the classroom,it is important for teachers to choose what kind of "problems" they should use to promote teaching and learning,and how they should guide students to ask questions.As a result,the development of HPM examples and problem-posing instruction are both hot issues in the current research.Based on the above understanding,We collected and reviewed literature from the perspective of historical occurrences.We found that the classical problems in the history of mathematics and the process of their formulation and solution can provide a lot of materials for teaching mathematical problem formulation.If the history of mathematics is integrated into the teaching of mathematical problem formulation,it should be able to play a complementary role.Therefore,a study of mathematical problem formulation based on the history of mathematics is necessary.In this paper,the following work is done.(1)We collated the relevant research results on HPM and problem posing.By reviewing a large amount of relevant literature,the author clarifies the meaning of problem-posing teaching from the perspective of HPM,and points out the relevant concepts of "HPM" and "problem-posing" under the guidance of the principle of historical occurrence,constructivism and the theory of the nearest developmental zone.(2)Questionnaire research was conducted.We selected senior students and teachers in two high schools in Shandong Province as the subjects of the study and conducted a study on the current situation of HPM and problem posing teaching through a questionnaire survey.(3)We summarizes the principles and strategies of teaching problem formulation from the HPM perspective by combining the existing theories and the analysis of the survey results from a practical mathematics classroom.A case of teaching basic inequality and a case of teaching the cosine formula of difference of two angles were designed.