58中英文雙語數(shù)學(xué)教育專業(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

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

33、for the Advancement of Science (2000). Middle grades mathematics textbooks: A benchmarks based evaluation. Washington, DC: Author.</p><p>　　An, S., Kulm, G., Wu, Z., Ma, F. & Wang, L. (October, 2002). A

34、comparative study of mathematics teachers’ beliefs and their impact on the teaching practice between the U.S. and China. Invited paper presented at the International Conference on Mathematics Instruction, Hong Kong.</

35、p><p>　　Cai, X.Q. & Lai, B. (1994). Analects of confucius. Beijing: Sinolingua.</p><p>　　Carpenter, T.P. & Lehrer, R. (1999). Teaching and learning with understanding. In E. Fennema & T

36、. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 19-32). Mahwah, NJ: Erlbaum.</p><p>　　Carroll, W.M. (1999). Using short questions to develop and assess reasoning. In L. Stiff (Ed.),

37、Developing mathematical reasoning in grades K-12: 1999 NCTM yearbook (pp. 247-253). Reston, VA: National Council of Teachers of Mathematics.</p><p>　　Education Department of Jiangsu Province (1998). Mathemat

38、ics: 11th textbook for elementary school. Nanjing, JS: Jiangsu Educational Publisher.</p><p>　　Elbaz, F. (1983). Teacher thinking: A study ofpractical knowledge. London: Croom Helm.</p><p>　　Ern

39、est, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249-254). New York: The Falmer Press.</p><p>　　Fennema, E. & Fran

40、ke, M.L. (1992). Teachers knowledge and its impact. In D.A. Grouws (Ed.), Handbook of mathematics teaching and learning (pp. 147-164). New York: Macmillan Publishing Company.</p><p>　　Fennema, E. & Rombe

41、rg, T.A. (1999). Mathematics classrooms that promote understanding. Mahwah, NJ: Lawrence Erlbaum Associates.</p><p>　　Glencoe. (2000). Mathematics: Applications and connections, Course 1. Glencoe: McGraw-Hi

42、ll.</p><p>　　Kaiser, G. (1999). International comparisons in mathematics education under the perspective of comparative education. In G. Kaiser, E. Luna & I. Huntley (Eds.), International comparisons in

43、 mathematics education (pp. 1-15). Philadelphia, PA: Falmer Press.</p><p>　　Kerslake, D. (1986). Fractions: Children's strategies and errors. Windsor, England: NFER-Nelson.</p><p>　　Kulm, G.

44、, Capraro, R.M., Capraro, M.M., Burghardt, R. & Ford, K. (April, 2001). Teaching and learning mathematics with understanding in an era of accountability and high- stakes testing. Paper presented at the research pre-s

45、ession of the 79th annual meeting of the National Council of Teachers of Mathematics. Orlando, FL.</p><p>　　Li, J. & Chen, C. (1995). Observations on China’s mathematics education as influenced by its tr

46、aditional culture. Paper presented at the meeting of the China-Japan-U.S. Seminar on Mathematical Education. Hongzhou, China.</p><p>　　Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ:

47、Lawrence Erlbaum Associates.</p><p>　　National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.</p><p>　　Nationa

48、l Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.</p><p>　　Pinar, W.F., Reynolds, W.M., Slattery, P. & Taubman, P.M. (1995). Unders

49、tanding curriculum. New York: Peter Lang.</p><p>　　Robitaille, D.F. & Travers, K.J. (1992). International studies of achievement in mathematics. In D.A. Grouws (Ed.), Handbook of mathematics teaching an

50、d learning (pp. 687-709). New York: Macmillan Publishing Company.</p><p>　　Shulman, L. (1985). On teaching problem solving and solving the problems of teaching. In E. Silver (Ed.), Teaching and learning math

51、ematical problem solving: Multiple research perspectives (pp. 439450). Hillsdale, NJ: Lawrence Erlbaum Associates.</p><p>　　Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard

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&

53、gt;　　Sowder, J. & Philipp, R. (1999). Promoting learning in middle-grades mathematics. In E. Fennema. & T.A Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 89-108). Mahwah, NJ: Lawrence Erl

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</p><p>　　Shushu An, Gerald Kulm , Zhonghe Wu</p><p><b>　　摘要：</b></p><p>　　本次研究就中國和美國在中學(xué)教授的數(shù)學(xué)教學(xué)內(nèi)容知識進行了比較。通過比較研究，結(jié)果表明，兩國數(shù)學(xué)教師的教學(xué)內(nèi)

57、容知識存在著顯著不同，這對教學(xué)實踐有著深遠(yuǎn)的影響。 中國教師通過依靠傳統(tǒng)的、更嚴(yán)格的實操來強調(diào)發(fā)展認(rèn)知過程和概念知識，這些實操證明了它們在教授數(shù)學(xué)內(nèi)容方面的價值。 美國教師強調(diào)了旨在促進創(chuàng)造力和探究的各種活動，試圖培養(yǎng)學(xué)生對數(shù)學(xué)概念的理解。 這兩種方法都有好處和局限性。 各國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，數(shù)學(xué)教學(xué)，學(xué)生認(rèn)知，教師知識，單位分?jǐn)?shù)</p><p>　　在過去的幾十年中，人們對數(shù)學(xué)教育的比較研究越來越重視，特別是在21世紀(jì)初數(shù)學(xué)教育改革運動方面。 根據(jù)Robitaille和Travers（1992）的研究，比較研究提供了在國際范圍內(nèi)分享、討論和辯論重要問題的機會。 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。 沒有比較，教師往往不會質(zhì)疑自己的傳統(tǒng)教學(xué)實踐，也不知道在構(gòu)建教學(xué)過程中有更好的選擇（第199頁）。</p><p><b>　　概念框架</b></p><p>　　舒爾曼的教學(xué)內(nèi)容知識模型</p><p>　　按照中國的說法，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體系”（p。47）。 Elbaz（1983）有同樣的觀點，“推動我們理解教師角色的最大力量的唯一因素是教師的知識現(xiàn)象”（第45頁）。</p><p>　　盡管教學(xué)內(nèi)容知識的三個部分對于有效教學(xué)都非常重要，但教學(xué)內(nèi)容知識的核心部分是教學(xué)知識。 圖1顯示了三個組成部分之間的互動關(guān)系，表明可以通過內(nèi)容和課程知識來增強教學(xué)知識。</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，如果一個概念或技能被教授的話。這種學(xué)習(xí)通常是在表層上實現(xiàn)的。教師常常滿意學(xué)生對事實和技能的認(rèn)識或記憶，但不了解學(xué)生對數(shù)學(xué)的想法或存在的誤解。這種不同的教學(xué)過程通常會導(dǎo)致分散和不連貫的知識。</p><p>　　一個把學(xué)習(xí)看作是理解的老師意識到，知識不夠充分，理解是通過將已有知識通過一個融合過程連接在內(nèi)化知識的層面上實現(xiàn)的。在這個過

62、程中，老師不僅注重概念理解和學(xué)習(xí)過程開發(fā)，確保學(xué)生理解并能夠運用這些概念和技能，而且始終如一地詢問學(xué)生的想法。使用這種融合過程的教師會發(fā)展出系統(tǒng)有效的方法來識別和開發(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，美國和中國的教師在數(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)美國教師建議參與并激勵學(xué)生通過各種活動（如操作和繪畫作品）。 如表三所示，在對問題3的回答中，64％的美國教師傾向于使用一個陳述 - 區(qū)域來說明分?jǐn)?shù)乘法 - 而67％的中國教師使用兩個陳述 - 區(qū)域和重復(fù)加法。</p><p>　　美國教師通過應(yīng)用操作手段，例如剪紙圈，唱小段歌曲，玩錢，使用地基十塊或繪畫和給區(qū)域涂色，引發(fā)學(xué)生對學(xué)習(xí)興趣的倍增，并讓學(xué)生參與到一個有意義的和具體的學(xué)習(xí)過程。 這種

64、“邊做邊學(xué)”的方式鼓勵學(xué)生通過探究和創(chuàng)造性過程獲得知識，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手操作的方式 （1998）。他報告了使用紙折疊來學(xué)習(xí)分?jǐn)?shù)乘法的有效性。 這項研究報告說，大多數(shù)美國教師使用區(qū)域表示來說明分?jǐn)?shù)倍增。</p><p>　　教學(xué)內(nèi)容知識的重要性</p><p>　　教師對數(shù)學(xué)的認(rèn)識離不開教師對課堂教學(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)合了知識內(nèi)容、課程知識以及聚焦學(xué)生思維的知識。它與內(nèi)容知識密切相關(guān)，與學(xué)習(xí)過程中內(nèi)容知識轉(zhuǎn)化的方式以及教師對學(xué)生思想認(rèn)識的方式有關(guān)。這項研究表明，深入廣泛的教學(xué)內(nèi)容知識對于有效教學(xué)是重要和必要的。理解教學(xué)包括一個融合的過程，在這個過程中，教師通過將先前的知識和具體模型連接到新知識上來建立學(xué)生的數(shù)學(xué)思想，重點放在概念理解和學(xué)習(xí)過程上。此外，教師應(yīng)該能夠識別學(xué)生的錯誤觀念，并能夠通過探究問題或使用各種

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

67、學(xué)習(xí)進程之間缺乏聯(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，也說明了對教師教學(xué)內(nèi)容知識的不同要求。</p><p>　　本次研究不一定適用于美國和中國的所有數(shù)學(xué)教師，因為樣本僅包括來自每個國家的一個城市，其中來自中國的23所學(xué)校和來自美國的12所學(xué)校。然而，這是一項內(nèi)部比較研究，中國的集中教育體系，一個城市可能代表中國的整個教育體系。不像美國一樣，一個地方控制著一個地方的教育體系，一個城市可能不會反映整個

68、美國情況。因此，其結(jié)果不一定適用于美國的教師。盡管如此，這些結(jié)果確實表明，從國際角度來看，教學(xué)內(nèi)容知識和促進對有效數(shù)學(xué)教學(xué)的進一步理解的重要性，它是基本組成部分。</p><p>　　REFERENCES</p><p>　　American Association for the Advancement of Science (2000). Middle grades mathemati

69、cs textbooks: A benchmarks based evaluation. Washington, DC: Author.</p><p>　　An, S., Kulm, G., Wu, Z., Ma, F. & Wang, L. (October, 2002). A comparative study of mathematics teachers’ beliefs and their i

70、mpact on the teaching practice between the U.S. and China. Invited paper presented at the International Conference on Mathematics Instruction, Hong Kong.</p><p>　　Cai, X.Q. & Lai, B. (1994). Analects of

71、confucius. Beijing: Sinolingua.</p><p>　　Carpenter, T.P. & Lehrer, R. (1999). Teaching and learning with understanding. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understa

72、nding (pp. 19-32). Mahwah, NJ: Erlbaum.</p><p>　　Carroll, W.M. (1999). Using short questions to develop and assess reasoning. In L. Stiff (Ed.), Developing mathematical reasoning in grades K-12: 1999 NCTM ye

73、arbook (pp. 247-253). Reston, VA: National Council of Teachers of Mathematics.</p><p>　　Education Department of Jiangsu Province (1998). Mathematics: 11th textbook for elementary school. Nanjing, JS: Jiangsu

74、 Educational Publisher.</p><p>　　Elbaz, F. (1983). Teacher thinking: A study ofpractical knowledge. London: Croom Helm.</p><p>　　Ernest, P. (1989). The impact of beliefs on the teaching of mathe

75、matics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249-254). New York: The Falmer Press.</p><p>　　Fennema, E. & Franke, M.L. (1992). Teachers knowledge and its impact. In D.A. Gr

76、ouws (Ed.), Handbook of mathematics teaching and learning (pp. 147-164). New York: Macmillan Publishing Company.</p><p>　　Fennema, E. & Romberg, T.A. (1999). Mathematics classrooms that promote understa

77、nding. Mahwah, NJ: Lawrence Erlbaum Associates.</p><p>　　Glencoe. (2000). Mathematics: Applications and connections, Course 1. Glencoe: McGraw-Hill.</p><p>　　Kaiser, G. (1999). International com

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