Knowledge Distribution And Teaching Research Of Mathematical Functions In Middle School

The reform of functions course and the teaching methods in middle school has always been the focus of the research of mathematics education.Although the new curriculum standard has reduced the difficulty of the function knowledge,it does not weaken the status and role of function knowledge in middle school curriculum.Meanwhile,the requirement for mathematical thinking ability and the ability to solve problem has been increased.To this end,teachers must provide students with effective learning guidance to enable students to effectively break through the barriers to thinking and enhance the ability to solve practical problems.This study takes the six basic functions listed in the textbook of the junior middle school mathematics(PEP)and the latest high school mathematics(Beijing Normal University Edition)used in the Yan'an area as the research object.Combining with the new mathematics curriculum standards,it makes a detailed analysis of the presentation and arrangement of the function knowledge in junior high school and senior high school.Guided by APOS theory,it measures the requirements of function knowledge for function thinking of students in middle school and puts forward four teaching strategies for teaching function knowledge.The main research methods of this study are content analysis method and the literature analysis.This thesis includes four parts: First,on the basis of combing the development and research of the curriculum of functions in middle school home and abroad,it puts forward the problems and methods of the research.Secondly,based on the detailed analysis of the distribution of the mathematical function knowledge in junior high school and senior high school and the characteristics of the function knowledge,and according to the new middle school math curriculum standards and knowledge of internal relations,it points out the juncture of the function knowledge between junior high school and senior high school.Thirdly,it introduces APOS theory,and considers the distribution of knowledge and the corresponding thinking ability requirements of function knowledge in middle school.It concludes that the function knowledge arrangement is consistent with the requirements of APOS theory.Finally,four teaching strategies are put forward for the existing problems:(1)putting emphasis on the generation and the formation process of the concept of function;(2)paying attention to students' initiative in participating teaching activities;(3)attaching importance to the permeation of mathematical thinking in the teaching of function course;(4)stressing the relationship between knowledge of function and the reality of life.Hopefully this study can help and inspire the teaching of function in middle school.