臺灣博碩士論文加值系統

本研究採內容分析法，分析臺灣、中國和新加坡三個國家之教科書內容，了解這三個國家國小高年級階段教科書設計的代數主題包含的心智習性類型和比例，並分析三個國家的代數主題之特色，以期能提供國小教學的實務應用。研究發現：一、三個國家之代數主題提供發展心智習性的內容，以數學思考與理解和抽象化兩大數學能力為主，兩心智習性合計比例約85％。二、臺灣教材較注重觀察問題中變數發展的趨勢及比較不同解題策略優缺點；中國教材則重點置於計算的一般化，透過類題的熟練和問題情境的擴展，以達到讓學生能有效地計算各式題目的目的；新加坡教材則明顯強調理解問題，加強培養學生理解問題中變數之間關係的能力。三、臺灣教科書特色為：1. 呈現不同解題策略的比較以增進學生對於解題規則的理解；2. 透過觀察、歸納問題中變數的關係培養邏輯推理能力。中國教科書特色為：1. 反覆練習基本問題以提升計算流暢度；2. 融入生活情境問題發現生活中的數學。新加坡教科書特色為：1. 算數題目與代數題目做連結以彌補學生代數學習之間隙；2. 反覆練習基本變數關係奠基代數解題的能力。

The purpose of this study is to use content analysis method to analyze the contents of textbooks in Taiwan, China and Singapore. The mainly focus is to explore the types and ratios of habits of mind of Algebra themes in the textbooks for the fifth and sixth grade students from these three countries. Further, after exploring the types and ratios, analyzing every different characteristic of Algebra themes is to provide application to pedagogics. The thesis discusses the findings: 1. Contents of algebra themes developing habits of mind is focus on two abilities of mathematic thinking and abstraction. The total ratio of the two habits of mind is 85%. 2. Taiwan’s course materials focus on observing development and trend of variables in questions and compare the pros and cons of different problem-solving strategies; China’s course materials focus on the general calculating, dexterity to questions and expansion of question situation so that students can solve different types questions efficiently; Singapore’s course materials focus obviously on realizing questions and cultivating students to enhance the ability of understanding the relation of variables. 3. The characteristics of Taiwan’s course materials: (1) Compare different problem-solving strategies for students to enhance realization to problem-solving rules; (2) Observe and summarize the relation of variables to cultivate inferential capacity. The characteristics of China’s course materials: (1) Practice constantly basic questions to improve calculation fluency. (2) Blend in life situation questions to discover mathematic in our life. The characteristics of Singapore’s course materials: (1) Associate calculating questions with algebra questions to supply any deficiency when students learn algebras. (2) Practice constantly basic variable relation to firm the ability of solving algebra questions.

中文摘要 ……………………………………………… Ⅰ
英文摘要 ……………………………………………… Ⅲ
目次 …………………………………………………… Ⅴ
表次 …………………………………………………… Ⅶ
圖次 …………………………………………………… Ⅸ
第一章 緒論
第一節 研究背景與動機 …………………………… 1
第二節 研究目的與問題 …………………………… 4
第三節 名詞釋義 …………………………………… 5
第四節 研究範圍與限制 …………………………… 7
第二章 文獻探討
第一節 三個國家數學教育目標及課程綱要之比較 …………………………………………… 9
第二節 代數之心智習性探索 ……………………… 21
第三節 國內外代數研究分析 ……………………… 28
第三章 研究方法與步驟
第一節 研究架構 …………………………………… 33
第二節 研究對象 …………………………………… 35
第三節 類目建構與資料處理 ……………………… 37
第四節 研究流程 …………………………………… 46
第四章 研究結果與發現
第一節 三個國家高年級代數教材在心智習性類型分析 …………………………………………… 49
第二節 三個國家高年級代數教材在心智習性子類型分析 …………………………………………… 58
第三節 三個國家高年級代數教材特色分析 ……… 68
第五章 結論與建議
第一節 結論 ………………………………………… 71
第二節 建議 ………………………………………… 83
參考文獻
中文部分 ……………………………………………… 85
外文部分 ……………………………………………… 87

中文部分
于红霞、何志波（2010）。素质教育改革：从量到质的转变－谈新加坡“少教多学”教育改革。遼寧師範大學學報（社會科學版），33(5)，73-76。
中國人民共和國（2011）。義務教育課程標準。北京：北京師範大學出版集團。
林碧珍、蔡文煥（2005）。TIMSS 2003臺灣國小四年級學生的數學成就及其相關因素之探討。科學教育月刊，（285），2-38。
周新富（2007）。教育研究法。臺北市:五南。
林施君、徐偉民、郭文金（2015）。線段圖教學對五年級學生代數文字題學習表現之影響。課程與教學，18(4)，161-192。
陳嘉皇（2007）。國小三年級學童代數推理教學與解題表現研究。高雄師大學報：自然科學與科技類，(23)，125-150。
陳嘉皇、梁淑坤（2014）。表徵與國小學生代數思考之初探性研究。教育研究集刊，(60:2)，1-40。
陳嘉皇（2017）。以心智習性為主之數學教科書內容比較研究。當代教育研究季刊，25（1），1-44。
陳維民、王國華（2010）。六年級學童在解未知數僅出現一次且在方程式同側不同位置時之解題類型研究。臺灣數學教師電子期刊，(22)，19-33。
徐偉民、徐于婷（2009）。國小數學教科書代數教材之內容分析：臺灣與香港之比較。教育實踐與研究，22（2），67-94。
徐偉民、曾于珏（2013）。臺灣、芬蘭、新加坡國小數學教科書代數教材之比較。教科書研究，6(2)，69-103。
教育部（2016）。十二年國民基本教育課程綱要數學領域。臺北市：教育部。
許伶靜（2012）。國小六年級學童代數問題解題歷程之研究。
黃資貴（2011）。國小中年級代數概念測驗編製與錯誤類型分析。
楊德清、陳仁輝（2011）。臺灣、美國和新加坡三個7年級代數教科書發展學生數學能力方式之研究。科學教育學刊，19（1），36-67。
趙曉燕、鍾靜（2010）。國小六年級學童對圖形樣式問題之解題探究。臺灣數學教師電子期刊，(24)，1-23。

外文部分
Arcavi, A. (1994). Symbol sense: informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24-35.
Bass, H. (2008, January). Helping Students Develop Mathematical Habits of Mind. Paper presented at a Project NExt Session on Joint Mathematics Meetings, San Diego, CA.
Costa, A. L., & Kallick, B. (2000). Discovering and Exploring Habits of Mind. Alexandria, VA: Association for Supervision and Curriculum Development.
Costa, A. L., & Kallick, B. (2009). Habits of Mind Across the Curriculum: Practical and Creative Strategies for Teachers. Virginis, Alexandria: Association for Supervision and Curriculum Development.
Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers grades 6-10. Portsmouth, NH: Heinemann.
Dilek Tanışlı. (2017). Integration of Algebraic Habits of Mind into the Classroom Practice. Elementary Education Online, 2017; 16(2): 566-583
Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170-218.
Goldenberg, P. (2009). Mathematical habits of mind and the language-learning brain: Algebra as a second language. Paper presented at an AMS-MAA-MER Special Session on Mathematics and Education Reform, Joint Mathematics Meetings, Washington, DC. Retrieved from http://www.
Graham, K., Cuoco, A., & Zimmermann, G. (2010). Focus in high school mathematics: Reasoning and sense making in algebra. Reston: National Council of Teachers of Mathematics.
Goldenberg, E. P., Mark, J., J. Kang, M. Fries, C. Carter, & T. Cordner.(2015). Making sense of algebra : developing students’ mathematical habits of mind. Portsmouth, NH: Heinemann.
Harel, G. (2007). The DNR system as a conceptual framework for curriculum development an instruction. In R. Lesh, J. Kaput & E. Hamilton (Eds.), Foundations for the future in mathematics education (pp. 263-280). Mahwah, NJ: Lawrence Erlbaum Associates.
Harel, G. (2008a). DNR perspective on mathematics curriculum and instruction: Focus on proving, part I. ZDM. Zentralblatt fu ¨r Didaktik der Mathematik, 40, 487–500.
Harel, G. (2008b). What is mathematics? A pedagogical answer to a philosophical question. In R. B. Gold & R. Simons (Eds.), Proof and other dilemmas: Mathematics and philosophy. Washington: Mathematical American Association.
Jarmila Novotná Maureen Hoch. (2008). How Structure Sense for Algebraic Expressions or Equations is Related to Structure Sense for Abstract Algebra. Mathematics Education Research Journal 2008, Vol. 20, No. 2, 93-104.
Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, & A. Pérez (Eds.), Eighth international congress on mathematical education: Selected lectures (pp. 271–290). Seville: S.A.E.M. Thales.
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707–762). Charlotte: Information Age.
Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. In Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2330-2339), Larnaca, Cyprus.
Mark, J., Cuoco, A., Goldenberg, E. P., & Sword, (2009). Developing mathematical habits of mind in the middle grades. Retrieved from http://www2.edc.org/cme/hom/ hom-middle-grades.pdf
Ministry of Education. (2012). Mathematics Syllabus. Singapore: Curriculum Planning and Development Division.
NCTM (National Council of Teachers of Mathematics). (2000). Principles and standards for school mathematics. Reston, VA: Author.
NCTM (National Council of Teachers of Mathematics). (2009). Executive summary: Focus in high school mathematics: Reasoning and sense-making. Reston: The Author.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
Schoenfeld, A. H. (2013). Reflections on problem solving theory and practice. The Mathematics Enthusiast, 10(1–2), 9–34.
Schüler-Meyer, A. (2017). Students development of structure sense for the distributive law . Educational Studies in Mathematics , 96 (1), 17-32.