Teaching Research On Sine And Cosine Theorems From The Perspective Of HPM

The triangle quantitative relation between edges and corners is the most basic connection since it is the fundamental figure of plane geometry.The solving triangle was born under the development of astronomy,navigation and geography throughout the trigonometry history,which reflects such essential knowledge in our daily life.Therefore,it is particularly important to study the solving triangle problem from the perspective of HPM.Integrating mathematics history into mathematics teaching is not only closer to students' cognition and logical thinking direction,but also helpful to stimulate their learning initiative.From the perspective of teachers,the relevant integration can help them improve teaching efficiency,promote teaching quality and enhance personal professional ability,which is of great help to carry out teaching work.This study has conducted two classes on Theorem of Sines and Theorem of Cosines respectively based on the HPM perspective,while the main processes included: literature review and sorting,class practice exploration,after-class questionnaire survey,student interview and after-class teaching reflection.The research questions are as follows: 1)What are the similarities between the logical order of their cognition with the development of mathematics history?2)Can the difficult problems in their learning process be solved by integrating the mathematics history into teaching? 3)Does the integration of the solving triangle in the mathematics history have any influence on students' knowledge,ability and mathematical literacy?The following conclusions are drawn through sorting and analyzing the questionnaire and interview records:The integration of the mathematics history is quite popular among students.Under this background,it makes the class more vivid and interesting,then retraces the way of exploring and developing the solving triangles,thus arousing students' learning enthusiasm and giving play to their creativity.In a word,the teaching of solving triangles with mathematics history can help students to solve the puzzles under the old teaching mode.However,HPM cannot completely replace the regular learning steps,while students' practice and exploration in the learning process are still necessary.At the same time,the puzzles that they have encountered in the learning process are exactly the problems that are difficult to solve in the history after various studies by predecessors.This shows the overlap between students' learning process and history,which highlights the necessity to understand the mathematics history.