Instructional Design Of Concepts Of Differentiation Based On APOS Theory In Desmos Environment

Mathematical concept is the essential of mathematical proof and derivation,and the teaching of Mathematical concept is a significant part of Mathematical teaching.In the post-epidemic era,the informationization teaching appears particularly important.Teachers are using the information technology to unify the mathematics concept teaching the design and the practice to deepen day by day.In recent years,Desmos,as an online interactive dynamic instructional interaction application,has been sought after by many mathematics educators abroad for its unique advantages and characteristics.Although there are many domestic studies on dynamic instructional application of Geogebra for instructional design,there are still few studies on Desmos applications that can achieve online interaction.Based on APOS theory and Desmos dynamic interactive environment,this paper studies the process of concept teaching,and takes derivative concept teaching as an example to design interactive electronic textbooks for derivative concept teaching,which can provide teaching reference for both offline and online information teaching in the future.This paper adopts case analysis method,questionnaire method and interview method.First of all,this paper studies the research on the application of Geometer's Sketchpad,Geo Gebra and Desmos dynamic teaching research at home and abroad by leterature research method,and then through a survey of domestic mathematics teachers in the derivative concept teaching part of APOS theory part of the implementation of teaching,analysis of the meaning of the four stages of APOS and Desmos application characteristics,and then investigates the present circumstance of the teaching of APOS theory in the part of derivative concept teaching by teachers at home and abroad by questionnaire method.After the educational experiment,the students were investigated by questionnaires and interviews in order to objectively investigate the learning effect of APOS derivative concept teaching in Desmos environment and the students' subjective feelings.Finally,three conclusions were drawn:(1)The design of teaching process shall take the APOS theory as the guiding direction,focus on the background and application of derivatives,enable students to contact relevant concepts and meet the requirements of the new curriculum standards,and the APOS theory emphasizes students' active participation in classroom activities,advocates exchanges among students,and fully reflects students' subjectivity.(2)In the teaching of mathematical concepts,Desmos is used to realize the transformation from static state to dynamic state,from finite state to infinite state,to synchronize the changes of images and data,and to highlight the essential attributes of mathematical concepts.In combination with the derivative teaching of Desmos,students' understanding of the essence of derivative concepts can be promoted.(3)The online interactivity of Desmos can be fed back to teachers in real time,and teachers can judge classroom teaching effect and adjust teaching direction and strategy in real time.It is a rare booster to realize wisdom education in the information age.