本文關(guān)鍵詞： 高中生 對數(shù)函數(shù) 學(xué)習(xí)困難　出處：《東北師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：對數(shù)函數(shù)是高中生新接觸的一類重要的基本初等函數(shù),但是由于對數(shù)符號的抽象性,函數(shù)學(xué)習(xí)的復(fù)雜性,對數(shù)函數(shù)的綜合性等諸多因素,導(dǎo)致學(xué)生關(guān)于對數(shù)函數(shù)的學(xué)習(xí)和理解明顯存在困難。盡管國內(nèi)數(shù)學(xué)教育工作者關(guān)于對數(shù)以及對數(shù)函數(shù)的研究成果頗豐,但是他們大多數(shù)都是在對數(shù)的發(fā)展史、對數(shù)函數(shù)的教學(xué)設(shè)計、對數(shù)函數(shù)的概念、性質(zhì)、解題及應(yīng)用等方面提出自己的觀點,而以對數(shù)函數(shù)為主實證研究卻很有限。筆者通過對部分高中教師和學(xué)生的訪談發(fā)現(xiàn),教師并不知道學(xué)生在對數(shù)函數(shù)學(xué)習(xí)過程中具體存在哪些學(xué)習(xí)困難,學(xué)生也無法通過教師的講解完全消除學(xué)習(xí)障礙。因此筆者以高中生對數(shù)函數(shù)的學(xué)習(xí)困難為研究內(nèi)容,選取吉林省長春市三所高中的不同年級學(xué)生為調(diào)查對象展開研究。在正式研究之前,筆者首先選取學(xué)校一高一的部分學(xué)生進(jìn)行預(yù)研究,根據(jù)預(yù)研究調(diào)查問卷反映出的問題,適當(dāng)修改問卷后才對三所學(xué)校的高中生展開正式調(diào)查。接下來筆者使用Excel和SPSS軟件對調(diào)查問卷的數(shù)據(jù)進(jìn)行了分析和處理,得到高中生關(guān)于對數(shù)函數(shù)知識的理解現(xiàn)狀,并總結(jié)了他們在這部分知識學(xué)習(xí)的過程中存在的四類學(xué)習(xí)困難：1.對數(shù)函數(shù)的概念辨析困難。在這類困難范圍內(nèi),學(xué)生分別有關(guān)于對數(shù)函數(shù)概念的陳述性知識記憶困難,對對數(shù)函數(shù)概念中變量的限定條件掌握不準(zhǔn)確,無法應(yīng)用對數(shù)函數(shù)的概念進(jìn)行辨析三類具體困難類型。2.數(shù)學(xué)思想的應(yīng)用困難。在高中階段要求學(xué)生掌握的七類基本數(shù)學(xué)思想中,有三類常常被應(yīng)用于解決對數(shù)函數(shù)的相關(guān)問題,分別是分類與討論思想、數(shù)形結(jié)合思想和轉(zhuǎn)化與化歸思想,而這三類數(shù)學(xué)思想的應(yīng)用也是學(xué)生的主要學(xué)習(xí)困難所在。3.對數(shù)型復(fù)合函數(shù)的理解困難。對數(shù)函數(shù)和復(fù)合函數(shù)都是高中數(shù)學(xué)學(xué)習(xí)的重點和難點,而將兩者結(jié)合成對數(shù)型復(fù)合函數(shù)對學(xué)生來說無疑是“雪上加霜”。學(xué)生在學(xué)習(xí)這部分知識主要存在三類困難：缺乏整體換元意識、忽略對函數(shù)定義域的考察和單調(diào)性的判斷困難。4.對數(shù)函數(shù)的相關(guān)知識基礎(chǔ)薄弱。有些學(xué)生之所以出現(xiàn)對數(shù)函數(shù)的學(xué)習(xí)困難,并不是對數(shù)函數(shù)知識掌握不足,而是對于對數(shù)函數(shù)相關(guān)的知識理解存在障礙。結(jié)合上述研究結(jié)果,筆者針對高中生關(guān)于對數(shù)函數(shù)的學(xué)習(xí)困難提出了五點教學(xué)建議：首先教師應(yīng)該盡量激發(fā)學(xué)生對對數(shù)函數(shù)的學(xué)習(xí)興趣,并且鼓勵學(xué)生勇于發(fā)現(xiàn)錯誤、提出疑難,然后設(shè)計適應(yīng)高中生認(rèn)知發(fā)展水平的教學(xué)活動,接下來引導(dǎo)學(xué)生建構(gòu)對數(shù)函數(shù)的知識框架,最后注重培養(yǎng)學(xué)生在數(shù)學(xué)學(xué)習(xí)過程中的反思習(xí)慣。
[Abstract]:Logarithmic function is an important basic elementary function in high school students' new contact. However, because of the abstraction of logarithmic symbol, the complexity of function learning, the comprehensiveness of logarithmic function and so on. As a result, there are obvious difficulties in learning and understanding logarithmic functions. Although there are many researches on logarithms and logarithmic functions by domestic mathematics educators, most of them are in the history of logarithmic development. The teaching design of logarithmic function, the concept, property, problem solving and application of logarithmic function are put forward. Through interviews with some senior high school teachers and students, the author finds that teachers do not know what learning difficulties students have in the process of learning logarithmic functions. Students can not completely eliminate the learning barriers through the teacher's explanation. Therefore, the author takes the learning difficulties of the logarithmic function of high school students as the research content. Three high schools in Changchun, Jilin Province, different grades of students as the research object. Before the formal study, the author first selected a part of the first high school students to carry out a pre-study. According to the pre-study questionnaire reflected the problem. After the proper revision of the questionnaire, three high school students were formally investigated. Then the author used Excel and SPSS software to analyze and process the data of the questionnaire. The present situation of high school students' understanding of logarithmic function knowledge is obtained, and the four kinds of learning difficulties existing in the process of learning this part of knowledge are summarized. 1. The concept of logarithmic function is difficult to distinguish. Within this kind of difficulty range. Students have difficulty in memorizing declarative knowledge about the concept of logarithmic function, and they are not accurate in grasping the qualification conditions of variables in the concept of logarithmic function. The concept of logarithmic function can not be applied to distinguish three kinds of concrete difficulty types. 2. The application of mathematical thought is difficult. In the senior middle school students are required to master the seven basic mathematical ideas. There are three kinds of problems which are often applied to solve the problem of logarithmic function, namely, classification and discussion, the combination of number and form, and the thought of transformation and transformation. The application of these three mathematical ideas is also the main learning difficulties of students .3.The understanding of logarithmic complex function is difficult. Logarithmic function and compound function are the key points and difficulties of senior high school mathematics learning. The combination of the two into a logarithmic complex function is undoubtedly "aggravated" for students. There are three main difficulties in learning this part of knowledge: the lack of overall awareness of changing elements. Ignoring the investigation of function definition and the difficulty of judging monotonicity. 4. The relative knowledge base of logarithmic function is weak. Some students have difficulty in learning logarithmic function, not because of lack of knowledge of logarithmic function. However, there are obstacles to understanding the knowledge related to logarithmic functions. The author puts forward five teaching suggestions for the difficulties of studying logarithmic function in senior high school students: first, teachers should try to arouse students' interest in logarithmic function, and encourage students to find mistakes and put forward difficulties. Then it designs the teaching activities to adapt to the cognitive development level of senior high school students, then guides the students to construct the knowledge frame of logarithmic function, and finally pays attention to the cultivation of students' reflective habits in the process of mathematics learning.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：G633.6

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