58中英文雙語(yǔ)數(shù)學(xué)教育專(zhuān)業(yè)外文文獻(xiàn)翻譯成品中美數(shù)學(xué)教師在中學(xué)教授的教學(xué)內(nèi)容知識(shí)

1、<p>　　外文標(biāo)題：THE PEDAGOGICAL CONTENT KNOWLEDGE OF MIDDLE SCHOOL, MATHEMATICS TEACHERS IN CHINA AND THE U.S.</p><p>　　外文作者： Shushu An, Gerald Kulm , Zhonghe Wu </p><p>　　文獻(xiàn)出處: 《

2、Journal of Mathematics Teacher Education》?, 2004 , 7 (2) :145-172 </p><p>　　英文1869單詞， 10798字符，中文2701漢字。</p><p>　　此文檔是外文翻譯成品，無(wú)需調(diào)整復(fù)雜的格式哦！下載之后直接可用，方便快捷！只需二十多元。

3、</p><p>　　THE PEDAGOGICAL CONTENT KNOWLEDGE OF MIDDLE SCHOOL, MATHEMATICS TEACHERS IN CHINA AND THE U.S.</p><p>　　Shushu An, Gerald Kulm , Zhonghe Wu</p><p><b>　　ABSTRACT&l

4、t;/b></p><p>　　This study compared the pedagogical content knowledge of mathematics in U.S. and Chinese middle schools. The results of this comparative study indicated that mathematics teachers’ pedagogic

5、al content knowledge in the two countries differs markedly, which has a deep impact on teaching practice. The Chinese teachers emphasized developing procedural and conceptual knowledge through reliance on traditional, m

6、ore rigid practices, which have proven their value for teaching mathematics content. The Un</p><p>　　KEY WORDS: pedagogical content knowledge, mathematics teaching, student’s cognition, teacher’s knowledge,

7、unit fraction</p><p>　　During the past several decades, there has been increased attention to comparative studies in mathematics education, especially with respect to the movement of reforming mathematics ed

8、ucation in the beginning of the 21st Century. According to Robitaille and Travers (1992), comparative study provides opportunities for sharing, discussing, and debating important issues in an international context. Stig

9、ler and Perry (1988) observe:</p><p>　　Cross-cultural comparison also leads researchers and educators to a more explicit understanding of their own implicit theories about how children learn mathematics. Wi

10、thout comparison, teachers tend not to question their own traditional teaching practices and are not aware of the better choices in constructing the teaching process (p. 199).</p><p>　　CONCEPTUAL FRAMEWORK&l

11、t;/p><p>　　Shulman’s Model of Pedagogical Content Knowledge</p><p>　　According to a Chinese saying, if you want to give the students one cup of water, you (the teacher) should have one bucket of wa

12、ter of your own. Shulman (1985) believes that “to be ateacher requires extensive and highly organized bodies of knowledge”（p. 47). Elbaz (1983) has the same view, “the single factor which seems to have the greatest power

13、 to carry forward our understanding of the teacher’s role is the phenomenon of teachers’ knowledge” (p. 45).</p><p>　　Although all three parts of pedagogical content knowledge are very important to effective

14、 teaching, the core component of pedagogical content knowledge is knowledge of teaching. Figure 1 suggests the interactive relationship among the three components and shows that knowledge of teaching can be enhanced by c

15、ontent and curriculum knowledge.</p><p>　　There are two kinds of teaching beliefs regarding students’ learning: learning as knowing and learning as understanding. A teacher who holds the belief of learning a

16、s knowing often assumes that mathematics is learned and understood if a concept or skill is taught. This type of learning usually is achieved at a surface level. Teachers are often satisfied with students’ knowing or rem

17、embering facts and skills but are not aware of students’ thinking or misconceptions about mathematics. This diverge</p><p>　　A teacher who holds the belief of learning as understanding realizes that knowing

18、is not sufficient and that understanding is achieved at the level of internalizing knowledge by connecting prior knowledge through a convergent process. In this process, the teacher does not only focus on conceptual unde

19、rstanding and procedural development, making sure students that comprehend and are able to apply the concepts and skills, but also consistently inquires about students’ thinking. Teachers who use th</p><p>　

20、　Engaging Students in Mathematics Learning Use of Representations</p><p>　　The results show that there are differences in the way the U.S. and Chinese teachers engage students in mathematics learning. Most U

21、.S. teachers suggested engaging and motivating the students to learn the procedure of multiplication through various activities, such as manipulatives, and pictorial representations. In their responses to Problem 3, as s

22、hown in Table III, 64% of the U.S. teachers would prefer to use one representation -area to illustrate fraction multiplication - while 67% of Chines</p><p>　　By applying manipulatives, such as cutting a pape

23、r circle, singing a fraction song, playing with money, using base ten blocks, or drawing and coloring areas, the U.S. teachers sparked their students’ interest in fraction multiplication and engaged students in a meanin

24、gful and concrete learning process. This “l(fā)earning by doing” approach encourages students to acquire knowledge through inquiry and creative processes and fosters students’ creativity and critical thinking. The use of man

25、ipulatives </p><p>　　Importance of Pedagogical Content Knowledge</p><p>　　Teacher knowledge of mathematics is not isolated from its effects on teaching in the classroom and student learning (Fen

26、nema & Franke, 1992). Teachers’ pedagogical content knowledge combines knowledge of content, teaching, and curriculum, focusing the knowledge of students’ thinking. It is closely connected with the content knowledge,

27、 connected with the way of transformation of content knowledge in the learning process and in the way in which teachers know about the students’ thinking. This stud</p><p>　　Conclusion</p><p>　　

28、The results of this study indicated that mathematics teachers’ pedagogical content knowledge in the two countries differed markedly and this has a deep impact on teaching practice. The Chinese system emphasizes gaining c

29、orrect conceptual knowledge by reliance on traditional, more rigid development of procedures, which has been the practice of teaching and learning mathematics content for many years. The United States system emphasizes

30、a variety of activities designed to promote creativity and i</p><p>　　This study cannot necessarily be generalized to all mathematics teachers in the United States and China because the samples included only

31、 one city from each country, with 23 schools from China and 12 schools from the U.S. However, this is an internal comparative study and, with a centralized education system in China, one city may represent the whole syst

32、em of education in China. With a locally controlled education system as in the U.S., one city may not reflect the whole United States. Therefo</p><p>　　REFERENCES</p><p>　　American Association

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52、Educational Review, 57(1), 1-22.</p><p>　　Silver, E.A. (1998). Improving mathematics in middle school: Lessons from TIMSS and related research. Washington, DC: U.S. Department of Education.</p><p&

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54、baum Associates.</p><p>　　Sowder, J.T., Philipp, R.A., Armstrong, B.E. & Schappelle, B.P. (1998). Middle-grade teachers’ mathematical knowledge and its relationship to instruction. Albany, NY: State Univ

55、ersity of New York Press.</p><p>　　Stigler, J.W. & Perry, M. (1988). Cross-cultural studies of mathematics teaching and learning: Recent finding and new directions. In D. Grouws & T. Cooney (Eds.),&l

56、t;/p><p>　　中美數(shù)學(xué)教師在中學(xué)教授的教學(xué)內(nèi)容知識(shí)</p><p>　　Shushu An, Gerald Kulm , Zhonghe Wu</p><p><b>　　摘要：</b></p><p>　　本次研究就中國(guó)和美國(guó)在中學(xué)教授的數(shù)學(xué)教學(xué)內(nèi)容知識(shí)進(jìn)行了比較。通過(guò)比較研究，結(jié)果表明，兩國(guó)數(shù)學(xué)教師的教學(xué)內(nèi)

57、容知識(shí)存在著顯著不同，這對(duì)教學(xué)實(shí)踐有著深遠(yuǎn)的影響。 中國(guó)教師通過(guò)依靠傳統(tǒng)的、更嚴(yán)格的實(shí)操來(lái)強(qiáng)調(diào)發(fā)展認(rèn)知過(guò)程和概念知識(shí)，這些實(shí)操證明了它們?cè)诮淌跀?shù)學(xué)內(nèi)容方面的價(jià)值。 美國(guó)教師強(qiáng)調(diào)了旨在促進(jìn)創(chuàng)造力和探究的各種活動(dòng)，試圖培養(yǎng)學(xué)生對(duì)數(shù)學(xué)概念的理解。 這兩種方法都有好處和局限性。 各國(guó)教師的做法可能部分適用于幫助克服某一方面的不足。</p><p><b>　　關(guān)鍵詞：</b></p>

58、<p>　　教學(xué)內(nèi)容知識(shí)，數(shù)學(xué)教學(xué)，學(xué)生認(rèn)知，教師知識(shí)，單位分?jǐn)?shù)</p><p>　　在過(guò)去的幾十年中，人們對(duì)數(shù)學(xué)教育的比較研究越來(lái)越重視，特別是在21世紀(jì)初數(shù)學(xué)教育改革運(yùn)動(dòng)方面。 根據(jù)Robitaille和Travers（1992）的研究，比較研究提供了在國(guó)際范圍內(nèi)分享、討論和辯論重要問(wèn)題的機(jī)會(huì)。 Stigler和Perry（1988）觀察到：跨文化比較也使研究人員和教育工作者更加明確地理解他們自己關(guān)

59、于兒童如何學(xué)習(xí)數(shù)學(xué)的隱含理論。 沒(méi)有比較，教師往往不會(huì)質(zhì)疑自己的傳統(tǒng)教學(xué)實(shí)踐，也不知道在構(gòu)建教學(xué)過(guò)程中有更好的選擇（第199頁(yè)）。</p><p><b>　　概念框架</b></p><p>　　舒爾曼的教學(xué)內(nèi)容知識(shí)模型</p><p>　　按照中國(guó)的說(shuō)法，如果你想給學(xué)生一杯水，你（老師）應(yīng)該有一桶自己的水。 舒爾曼（1985）認(rèn)為，“作為教

60、師，需要有廣泛和高度組織的知識(shí)體系”（p。47）。 Elbaz（1983）有同樣的觀點(diǎn)，“推動(dòng)我們理解教師角色的最大力量的唯一因素是教師的知識(shí)現(xiàn)象”（第45頁(yè)）。</p><p>　　盡管教學(xué)內(nèi)容知識(shí)的三個(gè)部分對(duì)于有效教學(xué)都非常重要，但教學(xué)內(nèi)容知識(shí)的核心部分是教學(xué)知識(shí)。 圖1顯示了三個(gè)組成部分之間的互動(dòng)關(guān)系，表明可以通過(guò)內(nèi)容和課程知識(shí)來(lái)增強(qiáng)教學(xué)知識(shí)。</p><p>　　關(guān)于學(xué)生的學(xué)習(xí)有兩

61、種教學(xué)觀：學(xué)習(xí)就是認(rèn)知和學(xué)習(xí)。一個(gè)把學(xué)習(xí)看作是認(rèn)知的老師常常假定數(shù)學(xué)是學(xué)習(xí)和理解的，如果一個(gè)概念或技能被教授的話(huà)。這種學(xué)習(xí)通常是在表層上實(shí)現(xiàn)的。教師常常滿(mǎn)意學(xué)生對(duì)事實(shí)和技能的認(rèn)識(shí)或記憶，但不了解學(xué)生對(duì)數(shù)學(xué)的想法或存在的誤解。這種不同的教學(xué)過(guò)程通常會(huì)導(dǎo)致分散和不連貫的知識(shí)。</p><p>　　一個(gè)把學(xué)習(xí)看作是理解的老師意識(shí)到，知識(shí)不夠充分，理解是通過(guò)將已有知識(shí)通過(guò)一個(gè)融合過(guò)程連接在內(nèi)化知識(shí)的層面上實(shí)現(xiàn)的。在這個(gè)過(guò)

62、程中，老師不僅注重概念理解和學(xué)習(xí)過(guò)程開(kāi)發(fā)，確保學(xué)生理解并能夠運(yùn)用這些概念和技能，而且始終如一地詢(xún)問(wèn)學(xué)生的想法。使用這種融合過(guò)程的教師會(huì)發(fā)展出系統(tǒng)有效的方法來(lái)識(shí)別和開(kāi)發(fā)學(xué)生的思維。圖2總結(jié)了這些想法，表明在深入了解學(xué)生思維的情況下，教師可以大幅提升學(xué)生的學(xué)習(xí)能力，從而掌握內(nèi)容。</p><p>　　讓學(xué)生參與數(shù)學(xué)學(xué)習(xí)陳述</p><p>　　結(jié)果表明，美國(guó)和中國(guó)的教師在數(shù)學(xué)學(xué)習(xí)中吸引學(xué)生的方

63、式存在差異。 大多數(shù)美國(guó)教師建議參與并激勵(lì)學(xué)生通過(guò)各種活動(dòng)（如操作和繪畫(huà)作品）。 如表三所示，在對(duì)問(wèn)題3的回答中，64％的美國(guó)教師傾向于使用一個(gè)陳述 - 區(qū)域來(lái)說(shuō)明分?jǐn)?shù)乘法 - 而67％的中國(guó)教師使用兩個(gè)陳述 - 區(qū)域和重復(fù)加法。</p><p>　　美國(guó)教師通過(guò)應(yīng)用操作手段，例如剪紙圈，唱小段歌曲，玩錢(qián)，使用地基十塊或繪畫(huà)和給區(qū)域涂色，引發(fā)學(xué)生對(duì)學(xué)習(xí)興趣的倍增，并讓學(xué)生參與到一個(gè)有意義的和具體的學(xué)習(xí)過(guò)程。 這種

64、“邊做邊學(xué)”的方式鼓勵(lì)學(xué)生通過(guò)探究和創(chuàng)造性過(guò)程獲得知識(shí)，并培養(yǎng)學(xué)生的創(chuàng)造力和批判性思維。 Sowder等人在分形倍增中使用了動(dòng)手操作的方式 （1998）。他報(bào)告了使用紙折疊來(lái)學(xué)習(xí)分?jǐn)?shù)乘法的有效性。 這項(xiàng)研究報(bào)告說(shuō)，大多數(shù)美國(guó)教師使用區(qū)域表示來(lái)說(shuō)明分?jǐn)?shù)倍增。</p><p>　　教學(xué)內(nèi)容知識(shí)的重要性</p><p>　　教師對(duì)數(shù)學(xué)的認(rèn)識(shí)離不開(kāi)教師對(duì)課堂教學(xué)和學(xué)生學(xué)習(xí)的影響（Fennema＆F

65、ranke，1992）。教師的教學(xué)內(nèi)容結(jié)合了知識(shí)內(nèi)容、課程知識(shí)以及聚焦學(xué)生思維的知識(shí)。它與內(nèi)容知識(shí)密切相關(guān)，與學(xué)習(xí)過(guò)程中內(nèi)容知識(shí)轉(zhuǎn)化的方式以及教師對(duì)學(xué)生思想認(rèn)識(shí)的方式有關(guān)。這項(xiàng)研究表明，深入廣泛的教學(xué)內(nèi)容知識(shí)對(duì)于有效教學(xué)是重要和必要的。理解教學(xué)包括一個(gè)融合的過(guò)程，在這個(gè)過(guò)程中，教師通過(guò)將先前的知識(shí)和具體模型連接到新知識(shí)上來(lái)建立學(xué)生的數(shù)學(xué)思想，重點(diǎn)放在概念理解和學(xué)習(xí)過(guò)程上。此外，教師應(yīng)該能夠識(shí)別學(xué)生的錯(cuò)誤觀念，并能夠通過(guò)探究問(wèn)題或使用各種

66、任務(wù)來(lái)糾正錯(cuò)誤觀念。</p><p><b>　　結(jié)論</b></p><p>　　這項(xiàng)研究的結(jié)果表明，兩國(guó)數(shù)學(xué)教師的教學(xué)內(nèi)容知識(shí)存在明顯的不同，這對(duì)教學(xué)實(shí)踐有著深遠(yuǎn)的影響。中國(guó)的制度強(qiáng)調(diào)依靠傳統(tǒng)的、更嚴(yán)格的學(xué)習(xí)進(jìn)程來(lái)獲得正確的概念知識(shí)，這一直是數(shù)學(xué)教學(xué)和學(xué)習(xí)內(nèi)容多年的做法。美國(guó)制度強(qiáng)調(diào)旨在促進(jìn)創(chuàng)造力和探究以發(fā)展概念掌握的各種活動(dòng)，但通常在操作性和抽象思維之間，理解和

67、學(xué)習(xí)進(jìn)程之間缺乏聯(lián)系。這兩種方法在數(shù)學(xué)教學(xué)中都體現(xiàn)出了益處和局限性，也說(shuō)明了對(duì)教師教學(xué)內(nèi)容知識(shí)的不同要求。</p><p>　　本次研究不一定適用于美國(guó)和中國(guó)的所有數(shù)學(xué)教師，因?yàn)闃颖緝H包括來(lái)自每個(gè)國(guó)家的一個(gè)城市，其中來(lái)自中國(guó)的23所學(xué)校和來(lái)自美國(guó)的12所學(xué)校。然而，這是一項(xiàng)內(nèi)部比較研究，中國(guó)的集中教育體系，一個(gè)城市可能代表中國(guó)的整個(gè)教育體系。不像美國(guó)一樣，一個(gè)地方控制著一個(gè)地方的教育體系，一個(gè)城市可能不會(huì)反映整個(gè)

68、美國(guó)情況。因此，其結(jié)果不一定適用于美國(guó)的教師。盡管如此，這些結(jié)果確實(shí)表明，從國(guó)際角度來(lái)看，教學(xué)內(nèi)容知識(shí)和促進(jìn)對(duì)有效數(shù)學(xué)教學(xué)的進(jìn)一步理解的重要性，它是基本組成部分。</p><p>　　REFERENCES</p><p>　　American Association for the Advancement of Science (2000). Middle grades mathemati

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