A Study On The Teaching Design Of "The Meaning Of Equations" Based On APOS Theory

The learning of mathematical concepts is the root of mathematics learning and has an important guiding role for students to solve complex practical problems.The APOS theory emphasizes that students’ learning process of mathematical concepts is a process of constructing their minds,and the investigation of teaching mathematical concepts based on APOS theory can reflect students’ thinking process of constructing mathematical concepts and reveal the essence of learning mathematical concepts in elementary school.This study adopts a theoretical and practical approach to use the APOS theory to design the teaching of "the meaning of equations" in elementary school mathematics as an example.Then,a class of fifth grade students in Primary School A in Nantong City was used as the research object.The new teaching design is based on the four-stage model of APOS theory.Finally,the APOS theory-based teaching design was implemented and analyzed,and it was found that the APOS theory-based classroom teaching of "the meaning of equations" enabled students to grasp the essential concept of equations and gradually formed the awareness and ability of extracting equivalence.At the same time,combining the characteristics of elementary school mathematics teaching and the teaching practice of this class,we made some reflections on the teaching of elementary school mathematics concepts based on APOS theory:teachers should be good at mining teaching resources in the activity stage;focus on the organization of students’ investigation activities in the process stage;focus on guiding students to deepen their conceptual understanding in the object stage;focus on improving students’ knowledge system in the schema stage.