On The Teaching Of Fraction Concept In Primary School Based On APOS Theory

Fraction is the core content of “Number and Algebra”in mathematics curriculum standard for compulsory education,it is the key and difficult point in elementary mathematics teaching,at the same time,it is the link between Integers,Decimals and Percentages,furthermore it is the basis for extending the concept of Rational Numbers.But,in practical teaching,because of the abstraction and complicated connotation of fraction,it is not well understood by pupils and there are some problems in the learning of fraction,so teachers are forced to explore effective methods to help pupils solve these problems.APOS theory reveals the psychological development process of mastering mathematical concepts and provides methods for mathematical concept teaching.So,this paper explores the concept teaching of fraction in primary schools with the APOS theory.There are five main parts in this dissertation:Part one,introduction.It introduces the research background,the purpose and significance of this research as well as the contents and methods of this research;meanwhile,making a review literature to obtain the information of current research about related issues at home and abroad.Part two,APOS theory and the teaching of mathematics concepts.The connotation of APOS theory is interpreted at the first.APOS theory describes the psychological construction process of students in learning mathematics.Only Action,Process and Object,the three stages have been experienced integrally by students,can a comprehensive mental Schema constructed in the learning of math concepts,based on continuous reflection and construction.,the comprehensive mental Schema would help students knows recognize the nature of concepts.Then it analyzes the feasibility of APOS theory for the teaching of fraction concept,that is,the APOS theory that attaches importance to the subjective position of students accords with the concept of curriculum standard;the APOS theory reveals the process from Process to Object is in line with the arrangement of the content of fraction in textbook;the APOS theory that pays attention to the psychological construction of students which conforms to the cognitive rules of students;the APOS theory focusing on the learning process is conducive to the cultivation of students' key competencies.Part three,the survey on the understanding level of fraction concept for pupils and the teaching status of fraction concept.This part mainly introduce the purpose and objects of this investigation,as well as the design of test paper and questionnaire.On the purpose of knowing about the pupil's understanding level of fraction concept and the teaching status of fraction concept,“ the test paper of the understanding level of pupil's fraction concept” and“the questionnaire of the teaching status of fraction concept” were used as the research tools to investigate 450 students from three primary schools in Haikou named A,B and C there and33 math teachers in primary school from Haikou.Part four,the results and analysis of this investigation.1.After the analysis of the pupil's understanding level of fraction concept,some conclusions are drawn there: The first,the understanding of fraction concept is at a medium level for pupils,their understanding level is decreasing with the increasing of the difficulty of fraction concept;The second,students performed very well in Aliquot,most of them have reached the Schema stage;for the simple fraction and the unitage concept,most students have reached the Object stage;the understanding of the equivalent fraction is is relatively poor,most students have reached the Process stage.Thirdly,For the understanding ability of fraction concept,there is no significant differences between boys and girls in primary school from the perspective of gender differences.Fourth,from the perspective of school differences,there is a certain impact that the quality of school teaching would make on the learning of fraction concept for pupils.Fifthly,According to the analysis of the test paper that pupils did.the problems existing in each stage of pupils can be summarized as: the single understanding of the definition of the fraction concept in the Action stage,the pupils cannot accurately summarize the nature of the fraction concept in the Process stage,the pupils couldn't form a clear fraction concept in the Object stage,the pupils couldn't build a good relationship among the concepts in the Schema stage.2.After the analysis of the teaching status of fraction,some conclusions are drawn there:First of all,although most teachers are aware of the importance of student's self-construction of fraction concept,but they have not implemented this idea into practice.Secondly,in the teaching of fraction concept,the teacher did not select the corresponding methods based on the student's ability.Finally,although teachers are aware of the importance of the theory of conceptual teaching,but they rarely use the theory of conceptual teaching to guide theirteaching.Part five,the teaching exploration of fraction concept based on APOS theory.This part constructs a teaching structure based on APOS theory about the fraction teaching,then designs a teaching cases under the teaching structure.In order to make the teaching steps of the fraction concept correspond to the process of psychological construction about students,a framework about the teaching of fraction concept based on APOS theory is constructed there,that is: Action,creating activity — sensing the concept initially,acquiring image;Process,reflecting the action—understanding the nature,generating image;Object,the consolidation and application of concept—formalizing and refining the concept;Schema,connecting the concept system — organizing the structure of the concept,achieve the self-generation.According to the framework,the teaching case of the fraction concept was preliminarily designed there.In order to make teachers apply the APOS theory in the teaching of fraction successfully,several suggestions are put forward: paying attention to the essence of teaching and avoiding the formalization of teaching;playing the guiding roles of teachers in teaching to avoid the "inaction" of teachers;the teaching contents must be worth exploring;the teaching activities should be adapted to the characteristics of students' psychological development.