Research On The Instructional Design Of Primary School Mathematics Concept Based On APOS Theory

In many elementary school mathematics concepts,double concept learning is a very critical point of knowledge.Because it is not only an important turning point in the cognitive structure of students’ mathematics,but also a thinking jump in which students differ from one another in relation to the ratio relationship.Through the research and investigation,the author discovered that not only students have puzzles about the understanding of times;even mathematics teachers have blind areas for double of teaching.In the background of constructivism,Dubinsky,an American educationist,put forward the APOS theory for learning mathematical concepts,revealing the formation and construction process of students’ mathematical concepts from four stages: activity,process,object and schema.At present,APOS theory has achieved good results in the study of mathematics concept teaching in China.On the basis of APOS theory,this research takes "double cognition" as the teaching content,carries on the instructional design research,and probes into the general thought and method of the elementary school mathematics concept instructional design under the guidance of the APOS theory.First of all,by analyzing the teaching contents and teaching activities,the study proves that APOS theory can be used to guide the concept instructional design of integer and fractional times.Then the excellent instructional design cases are compared and analyzed,and the general principles of APOS theory used in primary school mathematics concept are summarized.Finally,based on the APOS theory and teaching design principles,the teaching framework is constructed,and the teaching design of integer and decimal times under APOS theory is finally completed.Based on this,the author puts forward several suggestions on APOS theory used in the design of mathematics concept teaching in primary school: properly choosing teaching content,considering students’ psychological development,reasonably constructing teaching framework,orderly arranging teaching activities and well-documented t instructional design,following the connotation of APOS theory.