Research On The Influence Of Definition Teaching On Mathematics Classroom Efficiency In Senior High School ——Taking Trigonometric Function As An Example

Mathematical concept is a very important part of mathematic.It is the basis for mathematical reasoning and judgment,the basis for establishing mathematical theorems,rules and formulas,and the starting point for forming mathematical thinking methods.Concept reflects the thought of objective things.And it is the abstract generalization of objective things in people's mind.It is invisible and untouchable.It should be expressed in words,which is to define the concept.To clarify the concept is to clarify the connotation and extension of the concept.Therefore,concept definition is a logical method to reveal the connotation or extension of a concept.The definition of revealing concept connotation is called connotation definition,and the definition of revealing concept extension is called extension definition.In the process of teaching,teachers often explain the definition directly and then use it,and pay little attention to how the definition comes from.As a result,students can't understand the center of the definition.They can only imitate the teacher in the process of using the definition.In the later stage,students will forget this knowledge point quickly.Mathematics curriculum standards for senior high schools(2017 Edition)pointed out that high school mathematics has four main lines,one of which is function.Among the basic elementary functions learned in high school,trigonometric function has always been the focus of the college entrance examination.In the process of learning trigonometric function,students find that it has many properties and formulas,which are easy to confuse and forget.If students learn enough about trigonometric function,they will find that its periodicity,symmetry,induction formula and so on are derivatives of the definition.In order to find a better teaching method to improve the learning efficiency of trigonometric function definition,The author carry out teaching experiments about this class(Class 1,section 4,Chapter 1,compulsory 4 of Beijing Normal University Edition).Students in one class are randomly divided into two parts.One part of the teaching mode is to obtain the definitions of sine function and cosine function through experiencing the occurrence and development of knowledge;the other part of the teaching method is to give the function directly.After the definition of sine function and cosine function,we can find the relationship between them and the previous knowledge.Complete the same test after class.The test questions mainly investigate students' understanding and application of the definitions of sine function and cosine function.Through comparing the average of the test results,the conclusion is that there is no significant difference between the average of the two groups.However,the experimental data are only different from the critical value a little,which shows that the average of the two groups is still different.By consulting materials,the author arranges four typical teaching design of "trigonometric function of arbitrary angle".They are: teaching design integrated into the history of mathematics;teaching design integrating mathematics culture;problem scaffolding teaching design;eight step teaching design of arbitrary angle trigonometric function concept based on APOS theory.The author tries to integrate these instructional designs with her own ideas and make a new design.It is hoped that when this new design is implemented,it can help other teachers improve the teaching efficiency.