Teaching Research Of Function Concept In Senior High School Based On Historical-genetic-principle

Mathematical concept is the basis of mathematics,it makes the teaching of mathematics concepts become the most important part of mathematics teaching.In particular,the teaching of functional concepts is extremely important.As a teaching difficulty,there are still some problems in the teaching of function concepts.Most of the existing teaching have not linked the teaching of functions with the historical cognitive processes of the concept of functions.In order to solve this problem,we need to find a suitable entry point.Educational researchers have concluded through studies that if learners want to learn effectively,they must experience important parts of the history of their knowledge.To a large extent,the occurrence of individual knowledge and the process of human knowledge have similarities-the principle of historical occurrence.First of all,the study adopts the literature research method and sorts out the relevant literatures on the principle of historical occurrence.After these works,it puts forward a new idea: to re-understand the theory from two dimensions: horizontal and vertical.On the one hand,for a single point of knowledge,the cognitive barriers presented by students are largely similar to those experienced by mathematicians in history;on the other hand,for a certain student,thinking There is a great degree of similarity between the process of cognition and the process of historical evolution.Then according to the actual mathematics teaching background,a more in-depth understanding of the history of the principle of occurrence,in order to better use the theory of mathematics teaching.Then,the research method of questionnaire survey was used to understand the cognitive barriers and cognitive process of students' knowledge of function concept under current teaching status.Firstly,the historical development process of the concept of function was combed,and then the results of the investigation were compared with the historical development process,and the conclusion that the knowledge of the function concept of the student had historical similarity was obtained.It is proved that knowledge of functional concept knowledge,cognitive barriers in the students' understanding,and the entire cognitive process are similar to the historical obstacles and historical development processes of mathematicians.Application basis that meets the principle of historical occurrence.Finally,the study used the theoretical basis of the principle of historical occurrence,the concept teaching of high school function is related to teaching design.Firstly,a concept teaching strategy based on the principle of historical occurrence is proposed,that is,to reconstruct the history problem and reconstruct the historical sequence,corresponding to two dimensions: horizontal and vertical.Then,the teaching design related to the concept of function,the first lesson of the concept of the function as a representative case,the design of the teaching process is divided into four parts: concept introduction,concept generation,concept understanding and application,and the classroom summary.The main part of the "concept generation" contains three links: analytical-variable dependencies,variable dependencies-variable correspondence,variable theory-correspondence.It also summarized on the basis of the history in principle,the advantages of teaching design related to the concept of function analysis,respectively from the process of teaching target experience knowledge of teaching situation,three aspects to refactor and order of teaching process.