初中生函数内容解题易错问题研究

发布时间：2018-06-15 21:25

本文选题：函数 + 易错问题　；参考：《西华师范大学》2017年硕士论文

【摘要】：函数作为贯穿整个数学学习的一条主线,其在每个人的学习和生活中均具有十分重要的作用。而作为刚刚正式接触函数的初中生来说,函数更是抽象并且难以理解的,对于函数内容出现的错误更加不是偶然的,而是每届学生重复走着的弯路。在平时的教学过程中,由于教师的精力有限,不可能照顾周全每一个学生,因而本文期望通过研究少数中等水平的学生学习函数过程中易错的问题来概括整体学生学习函数易错问题,首先通过测试研究部分中等学生学习函数过程中易错的问题,访谈得出他们错误的原因。主要分为函数概念认知水平不够,习惯性联想导致错误,函数分类讨论不全以及解决综合性问题策略性错误等四个方面错误类型,再根据部分学生的测试结果中挑选出易错问题对整体学生进行测试,最后再分析整体学生的测试卷得出以下结论。八年级局部学生的错误率呈“N”型,思维定势错误率最高,其次是综合类策略问题,对于函数的概念问题错误率最低。然而八年级的整体错误呈“V”型,函数概念错误率高于思维定势错误率,而思维定势错误率高于分类讨论不全导致的错误率,综合性策略性问题错误率高于分类讨论错误率。八年级的局部错误率和整体错误率相比类似,然而八年级局部学生中的思维定势错误率不能代表整体学生,局部学生其他三种错误率还是可以代表整体学生的错误情况。九年级局部学生的错误率呈“N”型,即思维定势错误率最高,综合类解决问题策略问题导致的错误率其次。由于分类讨论不全导致的错误率最低,而九年级整体错误率仍然呈“N”,可见九年级局部学生错误率可以代表整体学生在函数学习过程中所犯的错误。总体来看,由于九年级函数类型的增多,学生的思维定势导致的错误增多,对于分类讨论错误的比较,八九年级的水平相差不大。八年级学生对于函数的概念理解更加深刻,故对于函数概念的错误率远低于九年级学生的错误率。由于九年级引进了二次函数,综合类题型较多的与几何思想,最值问题,换元法等联系起来,综合能力要求更高,故九年级学生的综合类函数的求解能力低于八年级学生。
[Abstract]:Function, as a main line running through the whole mathematics learning, plays an important role in the study and life of everyone. As a formal contact function of junior high school students, the function is abstract and difficult to understand, for the content of the function error is not accidental, but every class of students repeated detours. In the normal teaching process, due to the limited energy of the teacher, it is impossible to take good care of every student. Therefore, this paper hopes to generalize the error-prone problem of the whole student learning function by studying the error-prone problems in the process of learning function of a few middle level students. First, the error-prone problem in the course of learning function of some middle school students is studied by testing. The interview found out why they were wrong. There are four types of errors, such as insufficient cognitive level of function concept, error caused by habitual association, incomplete discussion of function classification and strategic error in solving comprehensive problems. According to the test results of some students, the error-prone problems are selected to test the whole students. Finally, the following conclusions are drawn by analyzing the test papers of the whole students. The error rate of local students in grade 8 is "N" type, the error rate of thinking stereotype is the highest, the next is the comprehensive strategy problem, and the error rate of the concept problem of function is the lowest. However, the overall error rate of grade 8 is "V". The error rate of function concept is higher than that of thinking set, while the error rate of thinking stereotype is higher than that caused by incomplete classification discussion, and the error rate of comprehensive strategic problem is higher than that of classification discussion. The local error rate of the eighth grade is similar to the overall error rate, but the thinking stereotype error rate of the local students in the eighth grade can not represent the whole students, and the other three error rates of the local students can still represent the error situation of the whole students. The error rate of local students in Grade 9 is "N", that is, the rate of thinking fixed error is the highest, and the error rate caused by comprehensive problem-solving strategy problem is the second. Because the error rate caused by incomplete classification discussion is the lowest, and the overall error rate of ninth grade is still "N", it can be seen that the error rate of local students in ninth grade can represent the mistakes made by the whole students in the process of functional learning. In general, due to the increase of the function types of ninth grade, the errors caused by students' thinking stereotype increased, and the level of the eighth and ninth grade was similar to the comparison of classification and discussion errors. The eighth grade students have a deeper understanding of the concept of function, so the error rate of the concept of function is much lower than that of the ninth grade students. Because of the introduction of quadratic function in grade 9, the more comprehensive class questions are connected with geometric thought, the most value problem, the method of exchanging elements, and so on, the comprehensive ability is higher, so the ability of solving the comprehensive class function of ninth grade students is lower than that of the eighth grade students.
【学位授予单位】：西华师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

【参考文献】