Research On Teaching,Learning And Examination Of Abstract Functions In High School Mathematics

Function is the core content of senior high school mathematics.Abstract function as a "dark line" in function knowledge.It is an important undefined module of mathematical knowledge in senior high school.However,due to its abstract,symbolic and concealed characteristics,there are some learning disabilities for students to learn and master it.At present,most of the existing studies focus on the problem-solving strategies of abstract functions.Therefore,The innovation of this paper lies in the integrated study of abstract function teaching,learning and examination in senior high school,and puts forward more detailed teaching strategies,learning strategies and propositional suggestions.Hope to play a role in attracting jade.This study uses questionnaire method,test investigation method and interview method.To investigate the current situation of teaching and learning of abstract functions in high school mathematics.First of all,This paper makes a difference analysis of students' test scores from four aspects:arts and science,gender,usual academic performance and interest in mathematics learning in the SPSS statistical software.And analyzes the correlations between learning habits,learning attitudes,intelligence factors and test paper scores.we find that the correlation is from strong to weak:learning habits,intelligence factors and learning attitude.Through the above analysis results combined with the specific answers of the test paper and the questionnaire,get the influencing factors and obstacles in the process of abstract function learning,which can be divided into the following four aspects:non-intellectual factors,intellectual factors,relevant knowledge factors and teaching factors.On this basis,the attribution of learning disabilities of abstract functions is analyzed,and draws a conclusion:(1)Most students do not form a correct cognitive view,and some students exist the fear.Few students have the habit of summarizing their knowledge and summarizing the types of questions after class,thus forming non-intellectual obstacles.(2)Liberal arts students rely more on rigid and mechanical memory when they memorize mathematical knowledge.The students' ability to apply the number-form combination method of thinking to the related questions of function is at the middle level and the ability of abstract functions to be concretized is weak,whichresults in intellectual barriers.(3)Most students have no overall understanding of function-related knowledge and knowledge is confused.The inadequate understanding of mathematical concept representation results in the weak ability of mathematical language transformation.Thus the obstacles of knowledge factors are formed.According to the obstacles of students,teaching strategies are put forward from the perspective of teachers.Construct a slow class of function-related concepts of "wonderful slow introduction,clear slow reasoning,careful slow analysis";Infiltrating mathematics thought into daily teaching and improve the students mathematical thinking.Emphasis should be placed on the teaching of different forms of external representation of concepts to cultivate students' ability of mathematical language transformation.From the student's point of view,this paper puts forward learning strategies.Correct learning attitude and improve mathematics metacognitive level.Summarizing knowledge points related to abstract functions by mind mapping and forming systematic knowledge network.According to the current situation of teaching,Collate and analyze the relevant contents of curriculum standards,textbooks and college entrance examination questions.From the proposer's point of view,this paper puts forward three suggestions on the proposition system based on the core literacy examination,the principle of knowledge convergence and the perspective of high viewpoint.