Research On Instructional Design Of Mathematical Concepts For Mathematical Understanding

The concept of mathematics is the cornerstone of high school mathematics and other related subjects,and concept learning is an important part of mathematics learning.In practical teaching,teachers can only observe students' grasp of concepts on the surface,such as memory or application,but it is difficult to find students' understanding of concepts.Mathematical understanding is an important way to ensure that students master concepts in high-tempo teaching,so it is very necessary to conduct teaching research on mathematical concepts pointing to mathematical understanding in both teaching theory and practice.In this study,literature review method,questionnaire method and comparative research method were used to deeply analyze the relevant literature,and investigate the status quo of mathematical concept learning and teaching,and finally put forward the teaching strategy of mathematical concept pointing to mathematical understanding.The problems of this paper are as follows:(1)analyzing and studying the status quo of mathematics concept learning and teachers' teaching of senior high school students;(2)Teaching strategies and principles of mathematical concepts for mathematical understanding.(3)The teaching process of mathematical concepts pointing to mathematical understanding.First of all,through reading a large number of relevant literature,surrounding the mathematical understanding,mathematics concepts and to mathematical understanding of mathematical concepts teaching from three aspects,the concept of a hierarchy of mathematical understanding,mathematics teaching and training methods,such as an in-depth research,found in mathematical understanding level and mathematics concept teaching process can be effective,Furthermore,six links are proposed in the teaching process of mathematical concepts,namely concept perception,experience understanding;Conceptual imagination,representation understanding;Conceptual generalization,formal understanding;Concept solidification,relationship understanding;Concept application,application understanding;Concept summary,thought understanding.Secondly,through the method of questionnaire survey,the status quo of students' mathematical concept learning and teachers' concept teaching are investigated,and the investigation conclusion is drawn.Based on the conclusion of literature analysis and current situation investigation,this paper puts forward the teaching principles and teaching strategies of mathematical concepts,which are effective transfer principle,development stage principle and spiral ascending principle respectively.The teaching strategy has the following seven points:(1)to design rich situations to achieve experiential understanding;(2)Design enlightening questions to achieve representation understanding;(3)Generalize from multiple angles to achieve formal understanding;(4)To build knowledge network to achieve connection and understanding;(5)Regression to practical problems to achieve application understanding;(6)Summarize and conclude to achieve ideological understanding;(7)Students' concept learning is evaluated according to their understanding level without a blanket approach.Finally,this study to several kind of important mathematical concept design to mathematical understanding of lesson plans,and the lesson plan was implemented,based on the in-class test results were analyzed,and found that point to mathematical understanding of mathematical concepts of instructional design have good class effect,can improve the level of students' conceptual understanding,provide operational concept teaching method of teaching.