Instructional Design Of Mathematical Concepts Based On APOS Theory In Geogebra Environment

Mathematical concept is the basic of taking part in mathematical reasoning and proof.Mathematics concept teaching is the important part of mathematical education. With thecoming of information age, the practice and the research on using the modern informationtechnology to optimize the teaching of mathematical conception is gradually going deeper. Inrecent years, GeoGebra is warmly welcomed and recognized for the advantage of its own.How to design teaching with the help of GeoGebra, is becoming a topic, which is debated byteaching professors from different fields.Through the study of related literature, I founded that lots of professors and researchersare devoted into the research on mathematical conception teaching under the theory of APOS,and the concept teaching based on the theory of APOS fits more into students’ cognitiveprocess. Besides, it contributes to students getting the essence of mathematical concept.However, the research on combining the APOS theory with modern information technologyand applying it into the mathematics concept teaching is very rare.First of all, through the analysis on the connotation of four stages of APOS, and thefunction and feature of GeoGebra, it is founded that the APOS theory is related to GeoGebra.For this reason, I try to put them and the mathematics concept teaching together, and thendesign the mode pattern of mathematics concept teaching process’ four stages under theGeoGebra circumstances. Secondly, this article try to design the mathematics conceptteaching through7aspects, then taking derivative concepts as example, under the GeoGebracircumstances, design the derivative concept teaching based on the APOS theory. Finally, Idesign the derivative concept of electronic textbooks based on the GeoGebra platform.Under the GeoGebra’s dynamic teaching environment, teachers’ mathematical conceptteaching guided by the APOS theory. This method is not only in line with the developmentrequirement of National Education Reform and Development of Long-term PlanningPrograms, it can break through the cognitive impairment of middle school students and makethem grasp the essence of mathematical concepts, but also it can achieve the new ways ofteaching and learning characterized by independent, inquiry and cooperation. By this means,it could reflect student’s main body status and then achieve good teaching effect.