A Study On The Relationship Between Functional Concept Image And Teaching Of Senior One Students ——A Case Study Of J High School In Shanghai

Chinese mathematician Hua Luogeng once said,"The learning process of mathematics is the process of constantly establishing various concepts." Mathematical concept is the logical starting point of mathematics,the basis of students' cognition,and plays an important role in mathematics teaching.In the 1980 s,the theory of concept image and concept definition proposed by Vinner and others received much attention in the modern study of mathematical concept learning.Without the help of concept image,students can not really construct an accurate and complete understanding of the concept.The German mathematician F.Klein believed that the concept of function was the "cornerstone" of middle school mathematics.Under the background that the new textbook of Shanghai Education Edition was put into use shortly,the researchers paid attention to the changes of functional concept image of senior one students before and after using the new compulsory textbooks of Shanghai Education Edition,and explored the relationship between functional concept image and teaching.Taking function as the carrier,this study focuses on the transformation of concept image of senior one students before and after teaching.Before and after the function teaching of senior one,the researcher tested the concept image of senior one students in J high school in Shanghai.During this period,the researcher observed and recorded the function-related classroom teaching in senior one,and interviewed the students with outstanding performance in two test papers,and explored the relationship between functional concept image and teaching of senior one students.Specifically,this study includes the following three research questions:(1)What kind of functional concept image and concept definition do students have before learning the concept of function in senior one?(2)After learning the concept of function in senior one,what kind of functional concept image and concept definition do students have,and what are the similarities and differences compared with before learning?(3)In the teaching process of function in senior one,what are the reasons for the changes in students' functional concept image and concept definition?Through the analysis of the data,the following three conclusions are drawn:(1)Before teaching,students have generated five types of functional concept images: structure,symbol,image,mathematical convention and process.The five types of functional concept definitions are defined as corresponding relation,dependency relation,rule,formula and representation.The relationship between concept image and concept definition is not deep when students solve cognitive tasks.Students' cognitive model can be described by "dependent concept image".(2)After teaching,the types of functional concept images of students were the same as before,but the frequency of using structural function concept images increased significantly.Different from before teaching,there is no functional concept definition of rule class after teaching,and there is interaction between concept image and concept definition when students solve cognitive tasks.Students' cognitive model can be described by "concept image dominant relationship".(3)In the teaching process of function of senior one,teachers' application of teaching representation in classroom teaching,students' own daily experience and learning methods are the reasons for the change of students' concept image and cognitive model.On this basis,this study finally puts forward some teaching suggestions.