Research On Teaching Design Of Logarithmic Function Based On APOS Theory

As one of the basic functions,logarithmic function is the key and difficult point of high school mathematics.It is difficult for teachers to "teach" and students to "learn".Dubinski's APOS theory not only points out that the learning process of students is structured,but also indicates the level of construction,and provides a specific teaching strategy for mathematics teachers to carry out mathematics teaching.Therefore,the teaching design of logarithm function based on APOS theory can enrich the teaching research of logarithm function.Beneficial to the teaching of logarithm function;Through the implementation of instructional design,the guiding role of APOS theory in logarithmic function learning can be tested.This research elaborates the research background,research status,research content and research method of instructional design of logarithmic function based on APOS theory,indicating the research significance of this paper.In addition,this study studied APOS theory and logarithm function in detail,which laid the theoretical foundation of this study.In this study,a scale of classroom observation--"log function" teaching method observation record form "was developed.In the practice school,a class of senior one was randomly selected for the classroom observation of log function teaching,so as to understand the current situation of" teaching "of log function.At the same time,the test volume of logarithm function was compiled to observe the current situation of students' "learning",and the following problems were found in the teaching of logarithm function :(1)the intuitive background was not deepened enough;(2)insufficient extraction of essential properties;(3)the essence of the concept is not refined enough;(4)insufficient network of related knowledge.Based on the above problems,the teaching design of logarithmic function based on APOS theory was carried out,and the teaching design was carried out from the four stages of APOS theory in stages.In the operation stage,students will experience the "operation" of taking logarithms to highlight the intuitive background and problem awareness.In the process stage,students regard logarithm function as a "process",highlighting essential attributes and corresponding ideas.In the object stage,students study the image,definition domain,range domain and monotonicity of logarithm function as a whole,highlighting the essence of concept and variant training.In the schematic stage,students form the knowledge network structure of logarithm function,and integrate logarithm function into the knowledge system to distinguish and connect with other knowledge,so as to highlight related knowledge and humanistic connotation.The practical research results show that there is a significant difference between the independent sample t test of the experimental class and the control class,and the performance of the experimental class is obviously better than that of the control class.Therefore,the teaching design of logarithmic function based on APOS theory is effective.Through the implementation of the teaching design of logarithm function based on APOS theory,students(1)find out the origin and development of logarithm function;(2)understood the spirit and method of logarithm function;(3)understood the humanistic connotation of logarithm function.