本文選題：函數(shù) + 易錯(cuò)問(wèn)題�。� 參考：《西華師范大學(xué)》2017年碩士論文

【摘要】：函數(shù)作為貫穿整個(gè)數(shù)學(xué)學(xué)習(xí)的一條主線,其在每個(gè)人的學(xué)習(xí)和生活中均具有十分重要的作用。而作為剛剛正式接觸函數(shù)的初中生來(lái)說(shuō),函數(shù)更是抽象并且難以理解的,對(duì)于函數(shù)內(nèi)容出現(xiàn)的錯(cuò)誤更加不是偶然的,而是每屆學(xué)生重復(fù)走著的彎路。在平時(shí)的教學(xué)過(guò)程中,由于教師的精力有限,不可能照顧周全每一個(gè)學(xué)生,因而本文期望通過(guò)研究少數(shù)中等水平的學(xué)生學(xué)習(xí)函數(shù)過(guò)程中易錯(cuò)的問(wèn)題來(lái)概括整體學(xué)生學(xué)習(xí)函數(shù)易錯(cuò)問(wèn)題,首先通過(guò)測(cè)試研究部分中等學(xué)生學(xué)習(xí)函數(shù)過(guò)程中易錯(cuò)的問(wèn)題,訪談得出他們錯(cuò)誤的原因。主要分為函數(shù)概念認(rèn)知水平不夠,習(xí)慣性聯(lián)想導(dǎo)致錯(cuò)誤,函數(shù)分類(lèi)討論不全以及解決綜合性問(wèn)題策略性錯(cuò)誤等四個(gè)方面錯(cuò)誤類(lèi)型,再根據(jù)部分學(xué)生的測(cè)試結(jié)果中挑選出易錯(cuò)問(wèn)題對(duì)整體學(xué)生進(jìn)行測(cè)試,最后再分析整體學(xué)生的測(cè)試卷得出以下結(jié)論。八年級(jí)局部學(xué)生的錯(cuò)誤率呈“N”型,思維定勢(shì)錯(cuò)誤率最高,其次是綜合類(lèi)策略問(wèn)題,對(duì)于函數(shù)的概念問(wèn)題錯(cuò)誤率最低。然而八年級(jí)的整體錯(cuò)誤呈“V”型,函數(shù)概念錯(cuò)誤率高于思維定勢(shì)錯(cuò)誤率,而思維定勢(shì)錯(cuò)誤率高于分類(lèi)討論不全導(dǎo)致的錯(cuò)誤率,綜合性策略性問(wèn)題錯(cuò)誤率高于分類(lèi)討論錯(cuò)誤率。八年級(jí)的局部錯(cuò)誤率和整體錯(cuò)誤率相比類(lèi)似,然而八年級(jí)局部學(xué)生中的思維定勢(shì)錯(cuò)誤率不能代表整體學(xué)生,局部學(xué)生其他三種錯(cuò)誤率還是可以代表整體學(xué)生的錯(cuò)誤情況。九年級(jí)局部學(xué)生的錯(cuò)誤率呈“N”型,即思維定勢(shì)錯(cuò)誤率最高,綜合類(lèi)解決問(wèn)題策略問(wèn)題導(dǎo)致的錯(cuò)誤率其次。由于分類(lèi)討論不全導(dǎo)致的錯(cuò)誤率最低,而九年級(jí)整體錯(cuò)誤率仍然呈“N”,可見(jiàn)九年級(jí)局部學(xué)生錯(cuò)誤率可以代表整體學(xué)生在函數(shù)學(xué)習(xí)過(guò)程中所犯的錯(cuò)誤�？傮w來(lái)看,由于九年級(jí)函數(shù)類(lèi)型的增多,學(xué)生的思維定勢(shì)導(dǎo)致的錯(cuò)誤增多,對(duì)于分類(lèi)討論錯(cuò)誤的比較,八九年級(jí)的水平相差不大。八年級(jí)學(xué)生對(duì)于函數(shù)的概念理解更加深刻,故對(duì)于函數(shù)概念的錯(cuò)誤率遠(yuǎn)低于九年級(jí)學(xué)生的錯(cuò)誤率。由于九年級(jí)引進(jìn)了二次函數(shù),綜合類(lèi)題型較多的與幾何思想,最值問(wèn)題,換元法等聯(lián)系起來(lái),綜合能力要求更高,故九年級(jí)學(xué)生的綜合類(lèi)函數(shù)的求解能力低于八年級(jí)學(xué)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.
【學(xué)位授予單位】：西華師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：G633.6

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本文編號(hào)：2023706