本文關(guān)鍵詞：高中生數(shù)學(xué)符號(hào)語言掌握現(xiàn)狀的調(diào)查研究　出處：《華中師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

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【摘要】：《全日制義務(wù)教育數(shù)學(xué)課程標(biāo)準(zhǔn)》明確提出要培養(yǎng)學(xué)生的“符號(hào)意識(shí)”。整個(gè)中學(xué)階段是學(xué)生學(xué)習(xí)、掌握數(shù)學(xué)符號(hào)語言的關(guān)鍵時(shí)期。初中階段是形成對(duì)數(shù)學(xué)符號(hào)語言的感性認(rèn)識(shí),初步到達(dá)簡化和加速學(xué)生思維過程的訓(xùn)練；而高中階段是形成對(duì)數(shù)學(xué)符號(hào)語言的理性認(rèn)識(shí),數(shù)學(xué)符號(hào)的寬度、廣度、深度各方面都有加深,達(dá)到培養(yǎng)鍛煉學(xué)生的抽象思維的目的。數(shù)學(xué)符號(hào)語言的學(xué)習(xí),是學(xué)好數(shù)學(xué)的關(guān)鍵。為此,本研究對(duì)高中三個(gè)學(xué)段的學(xué)生進(jìn)行調(diào)查研究,了解他們對(duì)數(shù)學(xué)符號(hào)語言的掌握現(xiàn)狀。首先,分析數(shù)學(xué)符號(hào)語言研究的背景、研究的意義,并假設(shè)學(xué)生數(shù)學(xué)符號(hào)語言掌握程度的高低與其數(shù)學(xué)成績的好壞呈正相關(guān)。認(rèn)為了解學(xué)生數(shù)學(xué)符號(hào)語言的掌握現(xiàn)狀,可以為研究“學(xué)困生”的問題開辟一條新的研究途徑。接著,概述了數(shù)學(xué)符號(hào)語言的相關(guān)研究現(xiàn)狀,包括數(shù)學(xué)語言、數(shù)學(xué)符號(hào)感以及數(shù)學(xué)符號(hào)語言的研究現(xiàn)狀。其次,對(duì)數(shù)學(xué)符號(hào)語言的內(nèi)涵進(jìn)行界定,并基于中學(xué)數(shù)學(xué)對(duì)數(shù)學(xué)符號(hào)語言的不同形式進(jìn)行劃分。從數(shù)學(xué)符號(hào)的直觀形式和傳遞數(shù)學(xué)意義的本質(zhì)內(nèi)涵兩個(gè)方面來介紹數(shù)學(xué)符號(hào)語言的特點(diǎn),在直觀形式上,數(shù)學(xué)符號(hào)具有間接性、直觀性。在數(shù)學(xué)符號(hào)傳遞數(shù)學(xué)意義的本質(zhì)內(nèi)涵上,數(shù)學(xué)符號(hào)具有的特點(diǎn)是：傳遞數(shù)學(xué)意義的抽象性,復(fù)雜性,精確性,規(guī)范性。緊接著,介紹數(shù)學(xué)符號(hào)語言的價(jià)值,除了介紹其對(duì)數(shù)學(xué)發(fā)展的價(jià)值外,并聯(lián)系數(shù)學(xué)符號(hào)與數(shù)學(xué)思維和中學(xué)數(shù)學(xué)學(xué)習(xí)的關(guān)系來介紹其價(jià)值,認(rèn)為數(shù)學(xué)符號(hào)承載數(shù)學(xué)知識(shí),是數(shù)學(xué)知識(shí)的載體,是數(shù)學(xué)思維的依賴工具,其本身具有的美感可以激發(fā)學(xué)生學(xué)習(xí)數(shù)學(xué)的興趣。之后,概括了數(shù)學(xué)符號(hào)傳遞數(shù)學(xué)意義的多樣性,即同一個(gè)數(shù)學(xué)符號(hào)可以承載不同的數(shù)學(xué)意義,同一個(gè)數(shù)學(xué)意義也可以由不同的數(shù)學(xué)符號(hào)來表達(dá)。再次,指出本研究的調(diào)查對(duì)象以及具體實(shí)施調(diào)查的過程。并根據(jù)調(diào)查收集的數(shù)據(jù),運(yùn)用軟件對(duì)高中階段學(xué)生掌握數(shù)學(xué)符號(hào)語言的現(xiàn)狀進(jìn)行了分析。本研究獲得的結(jié)論是：(1)對(duì)于同一個(gè)數(shù)學(xué)符號(hào)語言,不同的學(xué)生有不同的理解,對(duì)于同一個(gè)數(shù)學(xué)意義,不同的學(xué)生用數(shù)學(xué)符號(hào)語言表達(dá)的結(jié)果是不同的。(2)普遍學(xué)生都認(rèn)為對(duì)數(shù)學(xué)符號(hào)的分析與講解很重要；(3)數(shù)學(xué)符號(hào)語言掌握的越好的學(xué)生,他們的數(shù)學(xué)成績就越好,數(shù)學(xué)符號(hào)語言掌握得越不好的學(xué)生,他們的數(shù)學(xué)成績就越不好;另一方面,得出高中生在學(xué)習(xí)數(shù)學(xué)符號(hào)語言方面主要存在的困難是：(1)多個(gè)數(shù)學(xué)符號(hào)組合在一起時(shí),學(xué)生難以理解與表述,即是不能準(zhǔn)確理解復(fù)合數(shù)學(xué)符號(hào)。(2)學(xué)生不能準(zhǔn)確、清晰地掌握同一數(shù)學(xué)符號(hào)可以具有不同的數(shù)學(xué)意義,也不能掌握同一數(shù)學(xué)意義可以利用多種數(shù)學(xué)符號(hào)來表示,也就是說學(xué)生理解的數(shù)學(xué)符號(hào)語言是單一的。(3)在數(shù)學(xué)符號(hào)的表示上存在不準(zhǔn)確性、不完整性以及書寫的不規(guī)范性。(4)不能很好的將數(shù)學(xué)符號(hào)語言與文字語言進(jìn)行轉(zhuǎn)化。(5)學(xué)生在書寫或是使用數(shù)學(xué)符號(hào)時(shí),很容易出現(xiàn)負(fù)遷移的現(xiàn)象。最后,根據(jù)研究的結(jié)果,對(duì)數(shù)學(xué)符號(hào)語言的教學(xué)進(jìn)行反思。分析概括目前的數(shù)學(xué)符號(hào)語言教學(xué)現(xiàn)狀,認(rèn)為老師對(duì)數(shù)學(xué)符號(hào)語言的教學(xué)對(duì)學(xué)生掌握數(shù)學(xué)符號(hào)語言程度的影響很大,并針對(duì)數(shù)學(xué)符號(hào)語言教學(xué)提出了相應(yīng)的教學(xué)建議。
[Abstract]:"The full-time compulsory education mathematics curriculum standard" clearly put forward to cultivate the students "consciousness of symbols". The middle school stage is the key period of learning, to master the language of mathematical symbols. The junior middle school stage is the formation of perceptual knowledge of the language of mathematical symbols, preliminary to simplify and accelerate the process of training students' thinking; and the high school stage is the formation of knowledge the language of mathematical symbols of the rational, mathematical symbol width, breadth, the depth has deepened, to train students abstract thinking. The symbolic language of mathematics learning, the key is to learn mathematics. Therefore, this study investigated three high school schools students, understand their current situation of master mathematics sign language. First, analysis of the language of mathematical symbols in the background, the significance of the research, and assuming that the students master the language of mathematical symbols and their mathematics achievement level That is a positive correlation. To understand the status quo of students to master the language of mathematical symbols, can open up a new way to study the "underachievers". Then, summarizes the related research status of mathematical symbol language, including the language of mathematics, mathematics symbol sense and the research status of mathematical symbol language. Secondly, defines the the connotation of the language of mathematical symbols, and different forms of middle school mathematics mathematical symbol language based on division. From the two aspects of the visual form of mathematical symbols and transfer mathematical meaning essence to introduce the characteristics of mathematical symbol language, in the form of intuition, mathematical symbols is indirect, intuitive. The mathematic essence in mathematical symbols, mathematical symbols with the characteristics are: transfer the meaning of mathematics abstraction, complexity, accuracy and standardization. Then, introduce the language of mathematical symbols The value, in addition to the introduction of the development of mathematics value, and the relationship of mathematical thinking and mathematics learning to introduce its value, bearing the symbol that mathematics knowledge of mathematics, mathematics is the carrier of knowledge, mathematical thinking depends on the tool, its beauty can arouse students' interest in learning mathematics. And summarizes the diversity of mathematical symbols transfer mathematical meaning, namely the same mathematical symbols can carry different mathematical meanings, the same mathematical meaning can be expressed by different mathematical symbols. Thirdly, points out the research object of this paper and the concrete implementation process. According to the survey data collected in the survey, application status the software to master the language of mathematical symbols of the high school students are analyzed. The conclusions are: (1) for the same symbolic language of mathematics, different students have different The understanding for the same mathematical meaning, different students with the mathematical symbol language expression is different. (2) general students that analysis of mathematical symbols and explanation is very important; (3) the better the students master the language of mathematical symbols, their math scores can master the language of mathematical symbols it is not good for students, their mathematics achievement is not good; on the other hand, the main problems in learning mathematical symbol language difficulties of senior high school students are: (1) a number of mathematical symbols when combined together with the students to understand, that is not an accurate understanding of complex mathematical symbols (. 2) students can not accurately and clearly grasp the same mathematical symbols can have different mathematical meanings, they can not grasp the same mathematical meaning can use a variety of mathematical symbols, that is to say the students understand the language of mathematical symbols is single. (3 In the representation of mathematical symbols) are uncertain, incomplete and writing is not normative. (4) not very good will be the language of mathematical symbols and language conversion. (5) students in writing or using mathematical symbols, it is prone to the phenomenon of negative transfer. Finally, according to the study the reflection on the teaching of mathematics symbols. The analysis summarized the mathematical symbol language teaching at present, teachers think of the symbolic language of mathematics teaching for students to master the language of mathematical symbols of large, and according to the mathematical symbol language teaching and puts forward the corresponding teaching suggestions.

【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：G633.6

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