研究生: |
林育萱 |
---|---|
論文名稱: |
國中階段符號感意涵與評量方式之探究 An investigation on the components of symbol sense and their assessment at the junior high school level |
指導教授: | 譚克平 |
學位類別: |
碩士 Master |
系所名稱: |
科學教育研究所 Graduate Institute of Science Education |
論文出版年: | 2013 |
畢業學年度: | 101 |
語文別: | 中文 |
論文頁數: | 162 |
中文關鍵詞: | 符號感 |
英文關鍵詞: | symbol sense |
論文種類: | 學術論文 |
相關次數: | 點閱:143 下載:4 |
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數字是算術的重要元素,符號則是代數的重要元素。代數是國中數學課程與教學不可或缺的重要主題,然而從研究者教學經驗發現,相較於數字計算等一般化算術,國中學生較不容易掌握代數符號。九年一貫課程綱要在數與量主題中提及應培養學生的數感,且數感在國內外已累積相當多研究。那麼代數主題裡是否也應培養學生具備「某種感」呢? 答案是肯定的。Arcavi(1994)指出,符號感為代數教學的重要一環(Arcavi, 1994)。雖然符號感漸漸開始受到重視,但符號感的相關研究仍十分稀少,國內更是尚未出現符號感的相關研究。因此本研究主要目的為分析符號感意涵,整理與開發出符號感構成要素,進一步設計適合國中階段的符號感評量方式。
故本研究共有兩大部份:研究一透過文獻分析、小組討論、專家審查等內容流程,探索符號感意涵,進一步整理、開發符號感的可能構成要素。研究二則依據研究一所整理的符號感構成要素,設計適合國中階段的符號感試題,經過多次試寫、小範圍施測與訪談,最後請專家審查,逐步修正試題,最後於正式施測階段找117位學生進行測驗,分析學生的作答表現。
從研究一結果將符號感分為三大向度,每個向度下有數個子成分,共七個子成分。從研究二的結果發現開放式問答題型較適用於符號感測驗,且學生作答表現可對比出明顯具備符號感與欠缺符號感的情形。並由此作答表現進一步呼應研究一所整理之符號感構成要素。
Number is the important element of arithmetic, while symbol is of algebra. Algebra is a major project in junior-high-school math curriculum and instruction. However, from my own teaching experience, I found that it is more difficult for the junior high school students to master algebraic symbol than to master general arithmetic. Grade 1-9 Curriculum Guidelines tells that we should develop students’ number sense; also, there are a lot of studies concerning number sense whether foreign or native. Then, when it comes to algebra, should students be developed some sense? The answer is absolutely yes. Arcavi (1994) announced symbol sense is the principal key to algebraic instruction. Although we become to take focus on symbol sense, we still do much rare relative study, not to mention the internal study. Therefore, my major study propose is to analyze the meaning of symbol sense as well as sort and build the construction of symbol sense and moreover, to design a suitable symbol-sense assessment for junior high school students.
There are two parts in my study. My first part is to inquiry the meaning of symbol sense by analyzing document, panel discussion, and experts’ investigation. My second part, depending on my first part, is to design a suitable symbol-sense assessment for junior high school students; through trying tests many times, testing within narrow range; and after experts’ investigation, I revised my tests step by step so that on the formal stage, I found 117 students to do my tests and analyzed their answering performance.
From my first part, there are three major dimensions dividing symbol sense; each has several minor elements, and total seven minor elements. From my second part, I found that the open essay questions are proper to symbol-sense assessment, and they contrasted students who have symbol sense with those who do not. The students’
answering performance may also respond to the construction of symbol sense in my first part.
中文部分
中國大陸教育部(2001)。全日義務教育數學課程標準(實驗稿)。中國:教育部。
王兄(2007)。數學教學中的符號感:表像圖式意義下的理解。中國教育學刊,1, 019。
王寬明、何郁群(2010)。初中數學教學中的符號感培養,教育科學論壇(4),42-44。
史炳星、馬雲鵬、唐復蘇(2002)。在解決問題的過程中發展學生的符號感。數學教育學報,11(2) ,57-60。
李星雲(2007)。小學數學教學培養策略之二:數學符號感的認識及其培養策略。廣西教育(11A),9-10。
林福來、黃敏晃(1993)。分數啟蒙課程的分析,批判與辯證,科學教育學刊,1(1),1-27。
胡惠茹(2009)。不同二次函數表徵問題對國三學生解題影響之探究。國立台南大學碩士論文,未出版。
洪萬生(1996)。數學史與代數學習,科學月刊,319期。
洪萬生(1991)。清初西方代數之輸入,收入《孔子與數學》,臺北明文書局。
范建芬(2008) 。如何培養學生的符號感。江西教育,9,38。
黃毅英(1992)。九十年代的學校數學教育,數學傳播,64期,79-87。
陳霈頡、楊德清(2005)。數學表徵應用在教學上的探究。科學教育研究與發展季刊,40,48-61。
劉稀鳳(2009)。初中生符號意識的調查研究。東北師範大學碩士論文,未出版。
劉雲章(2006)。講活符號,發展學生的符號感。湖南教育(教育綜合),3,004。
蔡聰明(1995)。代數是什麼?(下)。科學月刊,302期。
鄭毓信(2002)。 「數感」、「符號感」 與其它-《課程標準》大家談。數學教育學報,11(3),30-32。
謝孟珊(2000)。以不同符號表徵未知數對國二學生解方程式表現之探討。國立臺北師範學院數理教育研究所碩士論文,未出版。
顧繼玲、張新華(2010)。再談「符號感」。中國數學教育,7,5-7。
戴文寶、邱守榕(1999)。國一學生由算術領域轉入代數領域呈現的學習現象與特徵。科學教育(10),148-175。
教育部(2008)。國民中小學九年一貫課程綱要-數學學習領域。台北:教育部。
郭生玉(1988)。心理與教育測驗,第三版。台北:精華書局。
英文部分
Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24-35.
Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the Learning of Mathematics, 25(2), 42-47.
Bergsten, C. (1999). From sense to symbol sense. European Research in Mathematics Education, II, 126-137.
Bergsten, C. (2003). A classification of algebraic tasks. A paper presented at the seminar New trends in mathematics education research: An international perspective. Bologna, February 27, 2003.
Booth, L.R. (1984). Algebra: Children’s strategies and errors. Windsor, UK: NFER-Nelson.
Booth, L.R. (1988). Children’s difficulties in beginning algebra. The Ideas of Algebra, K-12, 20-32.
Christou, K. P., Vosniadou, S., & Vamvakoussi, X. (2007). Students' interpretations of literal symbols in algebra. In S. Vosniadou, X. Vamvakoussi, & A. Baltas (Eds.), Reframing the conceptual change approach in learning and instruction (pp. 283-297). Amsterdam: Elsevier Science.
DeLoache, J. S. (2004). Becoming symbol-minded. Trends in Cognitive Sciences, 8(2), 66-70.
Driscoll, M. (1999). Fostering Algebraic Thinking. Westport, CT: Heinemann.
Foster, D. (2007). Making meaning in algebra: Examining students’ understandings and misconceptions. In A. H. Schoenfeld (Ed.), Assessing mathematical proficiency (pp.163-175). New York, NY: Cambridge University Press.
Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59–78.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326.
Kinzel, M.T. (2001). Linking task characteristics to the development of symbol sense. Mathematics Teacher, 94(6), 494-499.
Küchemann, D.E. (1981). Algebra. In: Hart, K.M. (Ed.), Children’s understanding of mathematics: 11 - 16 , 102 -119. London: John Murray.
McNeil, N. M., & Alibali, M. W. (2004). You'll see what you mean: Students encode equations based on their knowledge of arithmetic. Cognitive Science, 28, 451-466.
Naidoo, K. S. K. (2009). An Investigation of Learners' Symbol Sense and Interpretation of Letters in Early Algebraic Learning. Unpublished Masters dissertation. University of Witwatersrand, Edenvale.
National Council of Teachers of Mathematics. Commission on Standards for School Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics.
National Research Council (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.
Novotná, J., y Hoch, M. (2008). How Structure Sense for algebraic Expression or
Equations is related to Structure Sense for Abstract Algebra. Mathematics Education Research Journal, 20(2), 93-104.
Pierce, R., & Stacey, K. (2001). A framework for algebraic insight. In: J. Bobis, B. Perry & M. Mitchelmore (Eds.), Numeracy and Beyond. Proceedings of the 24th annual conference of the Mathematics Education Research Group of Australasia, Sydney, Vol 2 ( pp 418-425). Sydney, Australia: MERGA.
Pierce, R., & Stacey, K. (2004). Monitoring progress in algebra in a CAS active context: Symbol sense, algebraic insight and algebraic expectation. International Journal for Technology in Mathematics Education, 11(1), 3-11.
Pierce, R., & Stacey, K. (2007). Developing algebraic insight. Mathematics Teaching Incorporating Micromath, 203, 12-16.
Pope, S., & Sharma, R. (2001). Symbol sense: Teacher’s and student’s understanding. Proceedings of the British Society for Research into Learning Mathematics, 21(3), 64-69.
Rovinelli, F. J., & Hambleton, R. K. (1977). On the use of content specialists in the assessment of criterion-referenced test item validity. Dutch Journal for Educational Research, 2, 49–60.
Sutherland, R. (1999). Algebra and symbol sense in the formation of engineers. Teaching Mathematics and its Applications, 18(4), 179-184.
Samo, M.A. (2009). Students' Perceptions about the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Government Girls Secondary School Karachi. International Journal for Mathematics Teaching and Learning.
Seo, K. -H., & Ginsburg, H. P. (2003). “You’ve got to carefully read the math sentence. . . ”: Classroom context and children’s interpretations of the equal sign. In A. J. Baroody & A. Dowwker (Eds.), The development of arithmetic concepts and skills. Hillsdale, NJ: Lawrence Erlbaum.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational studies in mathematics, 22(1), 1-36.
Sfard, A & Linchevski, L. (1994). The gains and pitfalls of reification- the case of algebra, Educational Studies in Mathematics, 27 (4), 235-457.
Sharma, R. (2000). Researching Students’ Symbol Sense, Proceedings of the British Society for Research into Learning Mathematics, 20(3)
Skemp, R. R. (1987). The psychology of learning mathematics. Hillsdale, NJ:
Lawrence Erlbaum.
Tall, D., & Thomas, M. (1991). Encouraging versatile thinking in algebra using the computer. Educational Studies in Mathematics, 22(2), 125-147.
Zehavi, N. (2004). Symbol sense with a symbolic-graphical system: A story in three rounds. Journal of Mathematical Behavior, 23(2), 183-203.