Research On Instruction Of Logarithm Review Lesson From The Perspective Of HPM:A Case Study

The concept of “logarithm” has become a difficult concept in high school mathematics due to its abstractness and difficulty.After learning the new course,students still generally have some cognitive obstacles to logarithm.In today’s textbook,the concept of logarithm is derived from inverse operation,and teachers often use exponent to teach logarithm.But in history,logarithm was not come from exponent.Although there is a historical teaching material named “the invention of logarithm” to supplement,however,the effect of this material is not satisfactory because the limitation of class hours,and the material’s readability needs to be improved.In view of above considerations,this study aims to further clarify the cognitive obstacles in logarithm learning.From the perspective of HPM,the teaching design of logarithm review lesson reconstructs the history of mathematics,rewriting the teaching material and make it complement the lesson,so that students can learn logarithm spirally and experience the process from generation to development of logarithm,which can solve students’ cognitive obstacles and provide teachers with new teaching ideas.This paper aims to study the following research questions:(1)What cognitive obstacles do students have in logarithm learning?(2)What are the effects of integrating history of mathematics into logarithm review lesson on overcoming students’ cognitive obstacles?(3)What influence does integrating history of mathematics into logarithm review lesson have on students’ emotion and attitude?The research methods are questionnaire and interview.The research conclusions are as follows.Based on the historical study of logarithm,relevant literature analysis and the questionnaire survey of 33 teachers,we find that the common cognitive obstacles are:(1)the necessity of learning logarithm;(2)the effect of logarithm;(3)the nature of logarithm;(4)the reciprocal operation relationship between logarithm and exponent.This study selects the first two cognitive obstacles,implement teaching cases to observe the influence of integrating the history of mathematics into logarithm review lesson on students.Based on the students’ questionnaire,interview results and classroom videos,the influences of integrating the history of mathematics into logarithm review lesson on students include:(1)In the aspect of overcoming cognitive obstacles,the history of mathematics can help to explore the development process of mathematics in history,promote students’ understanding of the essence of mathematics to a certain extent,improve students’ cognition,and help students overcome some cognitive obstacles;(2)In the aspect of emotion and attitude,the history of mathematics can restore the humanistic outlook of mathematics,help students understand the diverse cultures of mathematics,enhance their interest and confidence in learning and help them develop good conduct and ethics.At the same time,the history of mathematics is also helpful to improve students’ core literacy of mathematics,and abilities of reading and understanding,communication and representation in mathematics.The historical teaching materials and micro videos are new ways to improve mathematics review lesson.Thus it can be seen that integrating the history of mathematics into logarithm review lesson has great value and deserves further study.