A High Level Of Abstraction In Mathematics And Senior Mathematics Teaching

Content:A high level of abstraction is one of the prominentcharacteristics of mathematics differing from other sciences.Highlight should be thrown on abstraction in senior mathematicsteaching. This thesis analyses its effect on pratical teaching from theangle that mathematics is of high-level-abstraction——not only doesit attribute to the phenomenon that high-middle-school mathematicsis "hard to teach and learn", but also it plays an important role in theformation and development of students' abstraction thinking.According to these effects, the article discusses both in aprropriatelydescending the level of abstraction in mathematical knowledge andfostering students' abstraction thinking, pointing out the problem inthese two aspects as well as the reason of abstraction thinking'sformation. Questionnaire survey method and interview are used toabtain the opinions and viewpoints of teachers and students throughwhat the author proposes that in order to decrease the level ofabstraction, actions such as visualizing the abstract concepts,concretizing the abstract symbols, textualizing the abstract problems,intuiting the abstract methods, popularizing the abstract expressionshould be taken. On the other hand, the article argues effective waysto cultivate students' abstraction thingking attaching to improvingstudents' level of thinking, elaborating that three factors——textbook, teachers and students could be take into account to solvethe issues arising in students' abstraction thingking cultivation.In regard to descending knowledges' abstraction and fosteringstudents' abstraction thinking are not opposite in practical teaching,the author tries to seek a way to combine abstraction and concretetogether in order to complete the goal of lowering the level ofabstraction of mathematics knowledge in the meantime thefosteration of students' abstraction thinking isn't cut down. Teachersought to adopt different methods to make the combination in differentteaching stages and insist on choosing fitting abstract and concretemethods, and they should make an effort to do adequate preparation before class, supervising the control on the class and reflection intime after class. In the thesis two examples are used to indicate thatboth abstraction and concrete need the rule of appropiation, and acase study of the usage of function property is also provided at last todiscribe the teaching process contained teaching strategy discussedabove.