The Application Study Of Plausible Reasoning In High School Mathematical Function

Function is one of the main line in the teaching materials of high school mathematics, and it is the keycontent of high school mathematics. Although plausible reasoning has been rated as a part of the content inthe teaching materials of high school mathematics by the Curriculum Standard of High SchoolMathematics (the experimental edition), deductive reasoning is still the focus of the math teachers in thepractical function of teaching content. In order to grasp and understand the part of the content of function,and improve the problem solving skills, it is too easy for students to fall into a pure and blind "inscribessea" tactics. The thinking model of plausible reasoning is in accord with the general process which peopleget knowledge. And it tallies with human cognitive perception and the discoverable disciplines ofmathematical knowledge. For the characteristics of simple, plausible reasoning is very easy to be acceptedand mastered by students. Plausible reasoning is an important method of mathematical discovery andinnovation, its importance in mathematical teaching and learning can’t be ignored. Therefore, making anapplication study of plausible reasoning in high school mathematical function is necessary and importantfor the method of math teachers’ teaching and the way of students’ learning.By the view of four basic models of plausible reasoning (induction, analogy, specialization andgeneralization), this article has made an analyses of the concept of function and the four kinds of basicelementary functions (exponential function, logarithmic function, power function, trigonometric functions)in three dimensions of teaching materials, teaching and problem solving of function. And we can come toconclusions as follows.Firstly, the content of function is arranged and studied by the method of “summing up concreteexamples in the general form of the function, then make a particular study on the specific function, andmake the conclusion generalized into common characteristics for every function”.Secondly, the teaching of the function concept should obey the rule “on the basis of being familiarwith the teaching material, introduce specific instances, guide the student to observe, conclude andsummarize the concept of function, study the nature of function with the help of images of functions”. Thenthe teaching of the basic elementary functions can analogize the method. It can help the students master the study method of function, understand the nature of function.Thirdly, using the methods of analogy, induction, specialization and generalization in the problemsolving of function, can guide the students to contact their prior knowledge, and reduce the difficulty ofthinking.