| Mathematical concepts are the logical starting point of mathematics,the core of mathematical thinking,the typical content of teacher teaching,and the important foundation for students’ mathematical learning With the implementation of the "General High School Mathematics Curriculum Standards(2017 Edition)",the new high school mathematics textbooks compiled on this basis have also undergone changes.Classifying mathematical concepts in new textbooks and studying their teaching status can help teachers understand the content arrangement of mathematical concepts in textbooks more deeply,so as to creatively use the textbooks for concept teaching,and develop students’ mathematical core qualities such as mathematical abstraction and logical reasoning.Guided by the theory of concept acquisition method,mathematization theory,CPFS theory and meaningful learning theory,this study employs the way of research,such as literature research,content analysis,questionnaire survey,case analysis and the others to analyze the content of the mathematical concepts in the first and second volumes of the“compulsory textbooks for senior high school mathematics”(PEP A edition)complied according to the "senior high school mathematics curriculum standard(2017 edition)".On this foundation,the author conducts a research for investigating on the present situation of high school mathematics teachers’ teaching of mathematical concepts using the PEP A edition mathematics textbooks.The specific research contents were as follows:First of all,combing and analyzing the content research,type research,and application status quo of mathematical concepts in textbooks at home and abroad,it was found that due to the short use time of the new mathematical textbooks for senior high school by PEP A edition,there is a little research on the analysis and the teaching status quo of mathematical concepts in the textbooks,and then the direction and content of the research are clarified.Secondly,the classification and quantitative analysis of the mathematical concepts in the new and compulsory textbook for senior high school by PEP A edition are carried out.According to the way of defining mathematical concepts in the textbook,they are divided into six types: "generic concept","operational concept","agreed concept","extensional concept","descriptive concept" and "relational concept".Then make quantitative statistics on various types of mathematical concepts under different chapters and themes,analyze the distribution characteristics of different types of concepts,and grasp the compilation characteristics and design intentions of mathematical concepts in the new and compulsory textbook for senior high school by PEP A edition,so as to lay a foundation for subsequent research.Thirdly,based on the six types of mathematical concepts,the questionnaire Survey on the Status Quo of Mathematical Concept Teaching in the new and compulsory textbook for senior high school by PEP A edition was compiled from the cognitive and use dimensions,and the new teaching of mathematical concepts by senior high school mathematics teachers was observed and recorded,aiming to grasp how teachers use the new textbooks for mathematical concept teaching.The questionnaire surveyed 208 senior high school math teachers from different schools in Shanxi and Guangdong provinces.After analyzing the data,it was found that: Most teachers can realize the importance of introducing mathematical concepts,and they can’t guide students to realize the necessity of generating new concepts;There are significant differences between teachers’ professional titles and teachers’ understanding of the way in which mathematical concepts are defined;There is a significant correlation between teachers’ professional title and their understanding of mathematical concept acquisition;The number of "agreed concepts" in the new high school mathematics textbooks is the largest,but they have not received the attention of most teachers;Most teachers choose to use examples and exercises to help students consolidate concepts,but only a few teachers and students construct a systematic network of mathematical conceptual structures.Finally,based on the analysis and investigation of the mathematical concepts and their teaching status in the new textbooks,this paper proposes countermeasures for the rational teaching of mathematical concepts in the new textbooks,including: Highlight the necessity and superiority of the generation of mathematical concepts;Grasp the different types of mathematical concepts in the new textbooks and implement teaching;Draw on the experience of expert teachers in using mathematical concept teaching methods;Improve teachers’ attention to "agreed concept" in the textbooks;Pay attention to the refinement and systematization of mathematical concepts. |
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