The Concept Teaching Of Algebraic Expression In Junior High School Under The Guidance Of APOS Theory

Algebraic expression plays an important part in Mathematics to the students in Junior One.On the one hand,it is the link between the primary mathematics and the middle mathematics.On the other hand,it is the foundation of learning equation,function and other related knowledge.However,students have little interest in the algebraic learning and are lack of mastery of the algebraic expressions at present.The reason is that students do not really understand the concept of the algebraic expression and the teaching design don't show the process of the concept formation to the students.The APOS theory emphasizes the subjectivity of students in learning.The four-stage model which the APOS theory has proposed fits the students' cognitive structures and is good for students to complete the knowledge construction of mathematical concepts.There are many researches and applications which use the APOS theory to guide the teaching of mathematical concepts in senior high school these years,and they have achieved some success.Moreover,some attentions have been paid to junior high school mathematics.However,more researches and applications on the algebraic expressions in junior high schools are still being needed at present.This thesis is focused on the existing state of the algebraic expression teaching and learning,and then explores the concept teaching of the algebraic expression in junior high school under the guidance of the APOS theory.In this thesis,the subjective feelings of students in learning the algebraic expressions are investigated by the way of questionnaires,and the students'understanding of the algebraic expressions is analyzed by the APOS theory.It is found that most of the students are in the action stage,some are in the process stage,a few reach the object stage,and very few realize the schema stage.Aiming at the current situation of teaching,this thesis uses the APOS theory to analyze the content of the algebraic teaching and the process of students' knowledge construction,and proposes two class-hours of the teaching design.By the specific instructional design,the design ideas and methods guided by the theory are given,and teaching suggestions are offered based on the different stages.Finally,the teaching design concepts of this study are applied to the teaching practice,so that students can participate in the process of concept formation and independently complete the construction of concepts.The same questionnaire survey is conducted among the students in the experimental group,and the results are compared with those of the control group.The results show that the students in the experimental group are found of the algebraic knowledge more than those in the control group.Their application abilities in practice are higher and their understanding to the algebraic expressions' concepts is also greatly improved compared with the situation of the control group.By this research and the data analysis,it is believed that the teaching of the algebraic expressions' concepts in junior high school under the guidance of the APOS theory can help to increase the students' interest in learning mathematics,develop the students' mathematical ability and improve the teaching efficiency.It is hoped that this thesis will provide some references and enlightenments for the majority of front-line teachers in the teaching of the algebraic expressions' concepts in junior high school.