Research And Practice On The Concept Of Function Based On The Vairant Exercise

As the kernel content and main thread of mathematics in high school, function not onlycovers the whole process of mathematics studying during senior middle school stage, but isthe basis of advanced mathematics as well as. It covers a very large portion of mathematicscontent in high school. There is a close contact between function and equation, inequality, andsequence, in which function studying influences greatly on that of the others. Function is thebasis as well as the useful instrument of advanced mathematics. So studying function is verysignificant. However, practice shows that students’ ability to grasp the function conception isquite poor; it is till one of the tough conceptions in students’ mathematics studying. In fact, itis difficult for students to learn function. Practice has proved that through the appropriatevariant exercise training can help students to understand and master the function knowledgebetter. So, how to design a variant exercises and how to achieve the purpose of promoting thefunction of teaching through variant practice? The paper aims to study the variant exercise ofhigh school and research nature of variant practice to solve these two problems.On the basis of integrating related materials, by combining teaching practice and my ownteaching experience，this paper classify, arrange, analyze the approaches of variation andrelated theories, aiming to put forward disciplines which includes destination principle,hierarchical principle, participatory, principles and the specific design methods ofvariant exercise which includes construct conditional variant, constructed conclusive variantexercise, tectonic setting variant exercise, constructed reverse variant exercise and constructintegrated variant exercise. According to the principle and construction method of variation, Iapplied to teaching practice by deciding the function concept and the nature of the variationMeanwhile, comparative tests is carried out by analyzing the errors which students madein learning function, using he experimental method in two parallel classes where students didvariant exercises. Through questionnaire and analysis of the test results, it is reasonable toconclude that the various practice will not only help to stimulate student interest in learning,but also help students form a good knowledge of the structure, and higher math skills, thusimproving students’ ability to solve problems. Moreover, the case study shows that variant exercise can improve student achievement, to some extent, to prove the validity of theexercise of the variant.Therefore, variant exercises will help students to grasp the essence of the functionknowledge and form good cognitive structure, and accumulate rich experience in mathematicsactivities, thus achieve the goal of promoting function teaching.