The Research On The Manifestation Of Mathematical Abstraction In The Function Master-Line Of Senior High School Textbooks

Mathematical abstraction,as a basic mathematical thought,is very important for high school mathematics learning and students' quality education.As the explicit representation of mathematical abstraction,mathematical abstraction has four representation: physical abstraction,Semi-symbolic abstraction,symbolic abstraction and formal abstraction.In the aspect of text research,the four representations of mathematical abstraction are mostly used in the analysis of junior high school mathematics textbooks or single knowledge point,and there are few studies on the whole master-line of high school mathematics textbooks.Because the content of function master-line is highly abstract and occupies a large proportion in senior high school mathematics curriculum,the content of function master-line can reflect mathematical abstraction more appropriately on the one hand,on the other hand,it also has enough material for its research.In order to study the mathematical abstraction in the master-line of function,this study firstly analyzed the content of function in the compulsory module of Senior High School of the People's Education Press,and counted the frequency of four representations of mathematical abstraction in the modules of situation introduction,inquiry activities,thinking,text,examples and after-school exercises,and revealed the division of mathematical abstract representations in the master-line of function.Publish information to help teachers understand the textbooks and provide help for the compilers of textbooks to review.Secondly,a questionnaire survey was conducted among teachers and students to find out their views on the content arrangement of the master-line.Finally,according to the results of the study,several strategies and some suggestions on the compilation of textbooks are put forward,which are helpful to cultivate students' abstract thoughts in mathematics teaching.It is found that:Among the manifestations of mathematical abstraction involved in the content of function master-line,the contents of various manifestations are not balanced.Among them,physical abstraction accounts for 7.74%,Semi-symbolic abstraction accounts for 40.02%,and symbolic abstraction accounts for 37.77%.The contents of different manifestations are also different in different types of content.73.7% of the teachers surveyed believed that the proportion of mathematical abstraction in textbooks was basically reasonable,and they often designed teaching according to textbooks.Students have different preferences for the representations involved in the contents of different modules in textbooks.Combining the feedback from teachers and students,this study puts forward some suggestions for the compilation of textbooks: adjusting the material abstraction in the preamble appropriately;retaining the Semi-symbolic Abstract content;interpreting the part of the symbolic abstract content appropriately;adding the formal abstract content to supplement the expansion of knowledge.