Design Research On Teaching Of Arithmetic Progression Which Based On HPM

With the deepening of curriculum reform in China,the study of HPM has developed to a new stage of "History of Mathematics for Education's sake".Mathematics education in the new era pays more attention to the context of mathematical knowledge,every mathematical concept has its origin,and the background and reasons can be found in the historical development of mathematics.Arithmetic series is not only one of the important contents of senior high school textbooks,but also one of the important knowledge points in the college entrance examination.The in-depth study of arithmetic series is conducive to the gradual establishment of a complete mathematical system of senior high school students,but also helps to develop the core literacy of mathematical abstraction,mathematical reasoning,mathematical modeling,mathematical operations and other mathematical disciplines of senior high school students.Based on the above background,the research on the teaching design of arithmetic series from the perspective of HPM has important theoretical significance and practical value.Through the analysis of the relevant literature,this paper sums up the current situation and existing problems of arithmetic series teaching from the perspective of HPM.On the basis of the research on the history of mathematics and the teaching literature of arithmetic series,according to the relevant documents of the Ministry of Education and the teaching hints and academic requirements of the middle difference series in the Mathematics Curriculum Standard of General Senior High School(2017Edition),and using the method of system science,this paper puts forward the design principles and methods of arithmetic series teaching from the perspective of HPM.The study selected the non-randomly assigned control group post-test design method to observe and test six parallel classes in a senior middle school in C city,andinterviewed the participating teachers.The implementation of arithmetic series teaching from the perspective of HPM is analyzed by using SPSS23.0 and EXCEL2010 software.the post-test data show that the correct rate of concept test is 57.48% in the experimental group,46.49% in the control group,75.50% in the experimental group and 67.97% in the control group.The correct rate of the problem-solving test in the teaching class of the experimental group was 58.22%,while that of the control group was 55.46%.The above research shows that instructional design based on the equivalent difference series from the perspective of HPM is better than traditional teaching,which not only helps to improve the quality of classroom teaching and help students to master knowledge,but also helps to cultivate the creative application ability of senior high school students.According to the investigation and analysis results of classroom observation,knowledge mastery feedback and teachers' teaching reflection from the perspective of HPM,from the two dimensions of teachers' teaching and students' learning,it is concluded that teaching design based on HPM perspective can not only stimulate senior high school students' interest in learning and promote their knowledge mastery,but also improve teachers' teaching enthusiasm and optimize teachers' knowledge structure.It is also pointed out that the teaching of equivalent difference series according to the HPM perspective may have negative effects such as increasing the difficulty of understanding,aggravating the pressure of learning,upgrading the difficulty of lesson preparation and increasing teaching tasks.Finally,the paper puts forward some suggestions,such as reducing students' learning difficulty and improving teachers' teaching efficiency,in order to provide reference and help for high school teachers' research and teaching.