The Research On Optimizing Teaching Of Fundamental Inequality

In decades,the application of modern educational technology based on the learning concept of multi-representations of mathematics,has been an important topic in the research on mathematics education at home and abroad.And it has an important impact on the learning process for students.In practical teaching,most teachers integrate the learning concept of multi-representations of mathematics into instructional design with feeling and experience.However,it has been found that the value and significs of it has not been fully played out.The fundamental inequality is placed in the basal and core position in the theory of inequality.It contains abundance of mathematical multi-representations.It is a powerful tool to solve other mathematical problems and application problems,and is a good material to cultivate students' mathematical abstraction thinking,intuitive imagination,logical reasoning and other core competencies.In the existing study,many researchers have conducted a teaching research on the fundamental inequality.However,the fundamental inequality teaching based on the learning concept of multi-representations of mathematics should to be further explored.Based on the above thinking,in order to find the problems and put forward some proposals,the paper takes the study of fundamental inequality as a carrier to explore the value and significance of the learning concept of multi-representations in the instructional design of a specific lesson.Then,the paper will hoping to provide the theory and practice reference to develop teaching based on the learning concept of multi-representations of mathematics for front-lines teachers on the teaching and education.The paper consists of two pieces:theory research and practice research.In theory research,based on the learning concept of multi-representations of mathematics,the paper puts forward the strategies to optimize the teaching of fundamental inequality combined with theoretical and experience.Firstly,the paper puts forward the strategy of embedded support based on information packaging principle.Secondly,the paper puts forward the strategy of multi-sensory interactive based on active behavior principle.Thirdly,the paper puts forward the strategy of stimulate an appetite based on positive affection principle.Finally,the paper puts forward the strategy of dynamic visual presentation based on double channel principle.The paper optimized the instructional design of fundamental inequality based on building the teaching strategy.In practical research,the research methods are the trials,interviews and observations.The paper shows how to apply the teaching strategies and instructional designs based on the learning concept of multi-representations of mathematics.At the same time,the paper investigates the impact on the cognitive load,learning achievement and efficiency of students.The study results show that the teaching strategies and instructional designs are great helpful to improve learning achievement of students,and can decrease students' the cognitive load in the process of learning significantly.But due to some reasons,it has no effect on efficiency.