Research On The Instructional Design Of Function In Senior High School Based On Variation Theory

Function is the core knowledge of high school mathematics,and its thoughts and methods throughout the mathematics course.Because function is highly abstract,and the function problems are complex and changeable,it has always been a difficult problem in teaching as well as learning.The variation theory emphasizes variation as a necessary condition for learners to be able to discern new aspects of an object of learning.Creating effective space of variation can help students to understand the object of learning from different perspectives.Therefore,the author has carried out research on the instructional design of function in senior high school based on variation theory.The research adopts several scientific methods,including literature research,questionnaires,interviews,action research and case studies.First of all,this research combs the relevant knowledge of variation theory and the present situation of function teaching with literature research method,and summarizes the steps of instructional design of functional content in senior high school based on variation theory.Secondly,this research investigates the students’ understanding of function in senior high school with questionnaires and interviews methods,and analyzes the teaching content of function in senior high school,takes “the concept of function”,“the monotonicity of function” and“the root of equation and the zero of function” as example to give detailed illustration.Thirdly,combined with the viewpoint of the variation theory and the characteristics of the function content,the research puts forward the effective teaching strategies and finishes the instructional design.Finally,the research carries out the instructional design of “the concept of function" and gets feedback through analyzing students’ performance to evaluate the teaching effectiveness based on variation theory.There are four main parts in the conclusion of this research.First,the steps of instructional design of functional content in senior high school based on Variation Theory are as follows:(1)analyze teaching objectives and determine learning content;(2)diagnose learning difficulties and determine key features;(3)design the space of variation according to key features;(4)combine teaching strategies to finish the instructional design;(5)implement teaching and adjust the teaching content according to the classroom situation;(6)through post-test and after-class homework to test the teaching effectiveness.Second,the students’ understanding of function in senior high school: they have a deep impression on several kinds of concrete functions that they have learned in junior high school,but they only memorize the concept of function mechanically.There are misunderstandings in the variables and forms,corresponding relations,representations,abstract representations,and "non-standard forms" and so on.Third,the teaching strategies of high school function based on Variation Theory are as follows:(1)set up doubts through variation to stimulate learning motivation;(2)review the old knowledge to activate existing experience;(3)give different examples to discern critical aspects;(4)discuss with each other in class to expand the space of learning;(5)practice with variation to strengthen the understanding of the essence of concepts;(6)reflect on and improve learning ability.Fourth,the instructional design of function in senior high school based on variation theory is useful to stimulate students’ enthusiasm for mathematics learning,help students understand function content further and optimize teaching effectiveness.