Research On The Major Concepts Of Mathematics And Its Teaching

The research of the Big Ideas of discipline has been paid much attention by many countries,and many countries have written the Big Ideas of discipline into the curriculum standard.China's 2017 version of the curriculum standards for ordinary senior high schools also put forward the Big Ideas of discipline for the first time.The curriculum standards point out: "Further select the subject content,attach importance to the Big Ideas of discipline as the core,make the curriculum content structured,themed,contextualized,and promote the implementation of the core quality of the discipline".In fact,the philosophy of teaching based on Big Ideas is also suitable for college mathematics teaching.At present,the domestic about academic research of the Big Ideas is still in its infancy,therefore,the study of mathematics Big Ideas and its teaching is of great significance,The research of teaching based on mathematics Big Ideas in the normal universities has important guiding and demonstrative significance.On the basis of the existing research on the Big Ideas,this paper tries to give the theoretical construction of the Big Ideas of mathematics,including the definition of concepts,types and levels,characteristics and values,and extraction paths.It refines15 Big Ideas of "thought and method types".A number of extraction cases of Big Ideas of "viewpoint types" are given.This paper expounds the key points of the teaching of the Big Ideas in mathematics: to determine the teaching objective and the Big Ideas,to choose the appropriate unit as the carrier,to carry out the teaching design of pursuing understanding;Some practical cases are given.Although experts in the field of pedagogy have summarized the extraction path of some Big Ideas,it is not easy to extract Big Ideas for specific disciplines,especially mathematics disciplines with a high degree of abstraction,especially the extraction of Big Ideas at the levels of chapters,sections and knowledge points.In view of this,a case study in the major concept extraction part,we give some practical cases and analysis of these cases from probability and statistics,mathematical logic and other courses,these cases based on our recent ten years of observation and inquiry,and based on a large number of literature analysis,especially in recent years in the research on probability and statistics course teaching reform.The path analysis of Big Ideas extraction is not limited to high school or university,but is studied as a whole,which not only conforms to the teaching concept of Big Ideas,but also establishes a research on the connection between university and high school.Therefore,this study has enlightening significance for both college and middle school mathematics teaching,and has profound guiding value for the basic education stage,especially for the "statistics and probability" teaching.As for the implementation of Big Ideas teaching,we believe that teaching objectives and Big Ideas should be determined first,and then appropriate units should be selected as carriers,and the goals should be achieved through core problems.In the part of teaching practice cases,we choose the contents of probability statistics and linear algebra courses to carry out research,which has demonstration and reference significance for the teaching of Big Ideas of mathematics.Of course,as an earlier attempt to carry out this kind of research,there is basically no similar literature for reference.The key points of implementation are mainly from practical reflection,so there must be some imperfections,and we accept criticism.