Research On The Status Quo Of Logarithmic Concept Teaching Based On APOS Theory

As an important mathematical concept in high school curriculum,logarithm is a necessary examination point for the college entrance examination every year.It is also the basic knowledge that the students must master.However,because of the abstract concept of logarithm,logarithmic symbols are not easy to understand intuitively,and logarithmic operations are more complex,which makes many students have difficulty in learning logarithm concept.In order to solve this problem,this paper tries to construct the teaching process of logarithmic concept based on the APOS theory proposed by American Mathematical educationist Ed Dubinsky.The APOS theory is based on constructivism theory concerned with mathematics learning process,is to further extend Piaget's "reflexive abstraction" learning theory,The theory has strong operability in practical teaching,and the four stage model also points out the ways and methods to construct mathematical concepts.Therefore,the logarithm concept teaching based on APOS theory should fully mobilize the enthusiasm of students,guide students to explore mathematics knowledge,analyze problem situations and construct reasonable cognitive structure.This paper is based on the logarithmic concept of 1 of the high school mathematics teaching material required by the Beijing Normal University,and combines the APOS theory to study the following three problems:(1)What is the understanding of current levels of the concept of logarithm among the students of senior high school?(2)What difficulties do for the understanding of the concept of logarithm by high school students?What are the causes of these difficulties?(3)How to discuss about the teaching design based on the APOS theory?Based on the three research methods of literature analysis,interview and questionnaire,108 students from two science classes of a senior high school in Xi'an were investigated to explore the current learning situation of logarithm concept for high school students.First,it introduces the status of logarithm concept in high school mathematics curriculum standard,the arrangement in textbooks and the proportion in the college entrance examination,highlighting the importance of logarithm concept.Secondly,we explore the necessity and feasibility of logarithm concept teaching under APOS theory.According to the four stage model of APOS theory,we divide the teaching target of logarithm concept under different knowledge dimensions.Thirdly,through the test,we can understand senior high school students' understanding level of logarithm concept,understand the high school students' interest in logarithm concept through questionnaires,and understand the following problems in logarithmic concept learning by interviews.Finally,aiming at the current learning situation of high school students' logarithmic concept,we designed a logarithmic concept teaching design guided by APOS theory,and pointed out some aspects should be paid attention to apply this theory to classroom teaching.The practice shows that APOS theory has the important significance to the teaching of logarithmic concept,which can improve the teaching method and stimulate student interest and improve the class effect.By encouraging students to participate in teaching activities designed by teachers,let students build a knowledge system of logarithmic concept in their hands and minds,help students understand the concept of logarithm deeply,and finally store it in cognitive structure by a comprehensive mental schema.Based on the teaching design of logarithm concept under the guidance of APOS the theory,which has activity,process,object and schema into four steps as design framework,set a series of interlinked problem strings at each stage to stimulate students interest,each steps infiltrate mathematical thinking to cultivate students'mathematical literacy.In order to make better use of APOS theory in educational practice,four suggestions are put forward:(1)continuously update education concept to inspire and guide classroom teaching;(2)the creative use of teaching materials to designed teaching content;(3)the proper use of multimedia technology and pay attention to the combination of the thought;(4)enhance the awareness of applied mathematics and adjust the pace of teaching properly.