【摘要】：數(shù)學(xué)語言是數(shù)學(xué)知識(shí)和思維的載體,是進(jìn)行數(shù)學(xué)交流的有效工具,甚至可以說“數(shù)學(xué)教學(xué)就是數(shù)學(xué)語言的教學(xué)”。數(shù)學(xué)語言按其表現(xiàn)形式可分為文字語言、符號(hào)語言和圖式語言三種類型。在解決問題的過程中,往往需要進(jìn)行不同形式語言的轉(zhuǎn)換,而數(shù)學(xué)語言轉(zhuǎn)換能力也是數(shù)學(xué)能力的重要標(biāo)志。21世紀(jì),人們已經(jīng)進(jìn)入了一個(gè)“讀圖”時(shí)代,學(xué)生應(yīng)該具備一定的讀圖、作圖和用圖的能力,具備一定的圖式語言轉(zhuǎn)換能力是現(xiàn)代社會(huì)對(duì)所有學(xué)生的要求。為了了解高一新生圖式語言轉(zhuǎn)換能力的現(xiàn)狀,筆者通過對(duì)文獻(xiàn)的分析研究制定出相應(yīng)的測(cè)試題,并走訪邯鄲市不同層次的多所學(xué)校進(jìn)行了預(yù)測(cè)試,最終選定四所學(xué)校的209名高一學(xué)生作為樣本進(jìn)行了正式測(cè)試。問卷主要從將圖式語言轉(zhuǎn)換為文字語言、將圖式語言轉(zhuǎn)換為符號(hào)語言以及圖式語言自身的轉(zhuǎn)換三個(gè)方面來測(cè)試,并在問卷調(diào)查后對(duì)個(gè)別學(xué)生、教師進(jìn)行了訪談來彌補(bǔ)問卷調(diào)查的不足。經(jīng)整理分析最終得出高一學(xué)生圖式語言轉(zhuǎn)換能力在以下幾方面相對(duì)較差:將圖形語言轉(zhuǎn)換成文字語言、將圖像語言轉(zhuǎn)換成符號(hào)語言、圖表語言內(nèi)部的轉(zhuǎn)換。具體結(jié)論如下:(1)絕大多數(shù)學(xué)生數(shù)學(xué)語言表達(dá)能力較弱,出現(xiàn)表述不清、用詞不準(zhǔn)確、表述冗長等現(xiàn)象;(2)大多數(shù)學(xué)生讀圖能力較差,不能理清圖中各元素的相互位置關(guān)系以及所包含的數(shù)量關(guān)系,不能將圖形的形狀和數(shù)量關(guān)系結(jié)合起來進(jìn)行描述;(3)大多數(shù)同學(xué)對(duì)特殊函數(shù)的圖像在形的方面有一定的掌握,但是對(duì)它們隱含的一些數(shù)量關(guān)系不是很明確;(4)絕大多數(shù)的學(xué)生符號(hào)應(yīng)用意識(shí)差,不了解符號(hào)語言的幾何意義;(5)一半學(xué)生用圖的意識(shí)薄弱,忽視圖中文字和符號(hào)語言的描述,導(dǎo)致理解出現(xiàn)偏差;(6)學(xué)生的作圖能力較差,僅有極少數(shù)學(xué)生能夠正確規(guī)范的做出圖形;(7)學(xué)生將圖形語言轉(zhuǎn)換為圖像語言的能力相對(duì)稍強(qiáng)。針對(duì)高一新生圖式語言轉(zhuǎn)換能力的現(xiàn)狀,提出高中階段提高學(xué)生圖式語言轉(zhuǎn)換能力的教學(xué)建議,有關(guān)加強(qiáng)學(xué)生讀圖訓(xùn)練的具體策略:(1)培養(yǎng)學(xué)生的讀圖興趣,提高學(xué)生的讀圖能力;(2)豐富學(xué)生讀圖的素材,提高學(xué)生讀圖能力。有關(guān)加強(qiáng)學(xué)生作圖訓(xùn)練的具體策略:(1)教師應(yīng)重視基礎(chǔ)圖形的教學(xué),;(2)課堂上,教師應(yīng)該給學(xué)生展示作圖的機(jī)會(huì);(3)教師應(yīng)該培養(yǎng)學(xué)生良好的作圖習(xí)慣。有關(guān)加強(qiáng)學(xué)生用圖訓(xùn)練的具體策略:(1)在圖式語言的基礎(chǔ)上發(fā)展其它形式的數(shù)學(xué)語言;(2)教師在平時(shí)教學(xué)中重視圖式語言;(3)注重概念教學(xué),精講概念的含義。
[Abstract]:Mathematical language is the carrier of mathematics knowledge and thinking, it is an effective tool for mathematical communication, and it can even be said that "mathematics teaching is the teaching of mathematical language". Mathematical language can be divided into three types according to its manifestation: literal language, symbolic language and schematic language. In the process of solving problems, it is often necessary to change different forms of language, and the ability of mathematical language conversion is also an important symbol of mathematical ability. In the 21st century, people have entered an era of "reading pictures". Students should have the ability to read, draw and use drawings, and the ability of schema language conversion is the requirement of all students in modern society. In order to understand the current situation of schema language conversion ability of freshmen in Senior one, the author made the corresponding test questions through the analysis and study of the literature, and visited many different schools in Handan City to carry out prediction tests. A sample of 209 freshmen from four schools was selected for formal testing. The questionnaire is mainly tested from three aspects: transforming schema language into literal language, transforming schema language into symbolic language and transforming schema language into schema language itself. Teachers conducted interviews to make up for the deficiencies of the questionnaire survey. After finishing and analyzing, it is concluded that the ability of schema language conversion is relatively poor in the following aspects: converting graphics language into text language, image language into symbolic language, and internal transformation of chart language. The specific conclusions are as follows: (1) the majority of students' mathematical language expression ability is weak, the expression is not clear, the words are not accurate, the expression is long and so on; (2) most students have poor ability to read pictures and can not clearly understand the relationship between the position and quantity of each element in the graph, and can not combine the shape and quantity of the graph to describe it; (3) most of the students have a certain grasp of the image of the special function in shape, but some of the implicit quantitative relationships are not very clear; (4) most of the students have poor awareness of the application of symbols and do not understand the geometric meaning of symbolic language. (5) half of the students have weak consciousness of using pictures and ignore the description of characters and symbolic languages in pictures, which leads to the deviation of understanding. (6) students' ability of drawing is poor, only a few students can make graphics correctly and normatively; (7) students' ability of converting graphics language to image language is relatively strong. In view of the present situation of schema language conversion ability of freshmen in senior high school, the author puts forward some teaching suggestions on how to improve students' schema language conversion ability in senior middle school. The specific strategies for strengthening students' reading ability are as follows: (1) cultivating students' interest in map reading; Improve students' reading ability; (2) enrich students' reading materials and improve students'reading ability. The specific strategies for strengthening students' drawing training are as follows: (1) teachers should attach importance to the teaching of basic graphics (,; (2), teachers should show students the opportunity of drawing, and (3) teachers should cultivate students' good drawing habits. The specific strategies to strengthen the training of students' drawing: (1) to develop other forms of mathematical language on the basis of schematic language; (2) to attach importance to schema language in normal teaching; (3) to pay attention to the teaching of concepts and to elaborate on the meaning of concepts.
【學(xué)位授予單位】：河北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：G633.6

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