Research On Teaching Design Of Number And Algebra In Junior Middle School Under APOS Theory

Mathematical concept is a kind of thinking form which reflects the essential attributes of a kind of objective things in quantitative relation and spatial form,and the theorem rule formula in mathematics is also composed of mathematical concepts.It is precisely because of these characteristics of mathematical concepts that many mathematics teachers pay more attention to the role of concepts in the process of application,while ignoring the teaching of the essence of concepts,resulting in many students can solve problems,but do not understand its connotation.Number and Algebra in junior middle school mathematics has been occupied a large proportion of the relevant content.Its position is very important.And it is the basis of learning other mathematical knowledge.Only when teachers design teaching programs that fit students' development can students build a complete knowledge system.APOS theory,proposed by American educator Dubinsky,is a constructivist concept teaching theory,which provides teachers with a teaching strategy that is easy for students to grasp the essence of concepts.Based on this theory,this paper studies the teaching design of Integral form in the concepts of Number and algebra in junior middle school.First of all,we briefly introduce the background,significance,content and methods of the research in this paper.The main content is to use APOS theory to find a new method to guide the concept teaching for first-line teachers in middle schools in the Number and Algebra.Secondly,we briefly introduce the research and development of the Number and Algebra content about APOS theory at home and abroad,and briefly explain the concept which is similar to this theory--the theory of duality.Then,it discusses the two main modes of concept teaching at the present stage,and introduces the theoretical source of APOS and its four stages of "activity-process-object-diagram" in detail.Through the analysis of the content of Number and Algebra in middle school and the interpretation of the mathematics curriculum standard in compulsory education,this paper makes clear the basic and important position of Integral teaching in middle school.At the same time,we interviewed the first-line teachers to understand their concept teaching methods,their views on Integral form and their understanding of APOS theory.Then,through the discussion with the first-line teachers,the paper formulates the Integral part of the test paper,and uses the way of after class communication to understand the situation of students' mastery of the related concepts of Integral,and then analyzes the teaching materials and learning situation,and establishes the teaching objectives.Finally,this paper analyzes the teaching materials and learning situation and establishes the teaching objectives.Taking "Monomials" as an example,the instructional design is carried out to illustrate the instructional methods and ideas under the APOS theory,and on the basis of teaching practice,several advantages of using APOS theory to guide teaching are summarized.This paper argues that APOS theory allows students to construct knowledge actively,experience and feel the formation process of concepts,which is conducive to students' deep understanding of concepts,can better reflect students' dominant position in educational activities,and is more conducive to the overall realization of teaching objectives.It is hoped that this paper can provide a different approach for first-line teachers in concept teaching design and guide them to learn and research APOS theory to promote the improvement of teaching quality.