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一、中文部分
王文科(2001)。教育研究法。台北市:五南。 李源順(2017)。南一數學一上。南一書局企業股份有限公司。 李源順(2017)。南一數學一下。南一書局企業股份有限公司。 李源順(2017)。南一數學二上。南一書局企業股份有限公司。 李源順(2017)。南一數學二下。南一書局企業股份有限公司。 李源順(2017)。南一數學三上。南一書局企業股份有限公司。 李源順(2017)。南一數學三下。南一書局企業股份有限公司。 李源順(2017)。南一數學四上。南一書局企業股份有限公司。 李源順(2017)。南一數學四下。南一書局企業股份有限公司。 李源順(2017)。南一數學五上。南一書局企業股份有限公司。 李源順(2017)。南一數學五下。南一書局企業股份有限公司。 李源順(2017)。南一數學六上。南一書局企業股份有限公司。 李源順(2017)。南一數學六下。南一書局企業股份有限公司。 林長壽(2017)。翰林數學一上。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學一下。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學二上。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學二下。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學三上。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學三下。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學四上。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學四下。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學五上。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學五下。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學六上。翰林出版事業股份有限公司。 林長壽(2017)。翰林數學六下。翰林出版事業股份有限公司。 林碧珍(主編)(2007b)。數學教學案例-低年級。台北:師大書苑。 林碧珍、蔡文煥(2005)。TIMSS 2003台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頁。 施舜玉、林碧珍(2011)。如何運用分配律於相關教材之行動研究。2011資訊科技融入教學與教師專業發展國際學術研討會。新竹市:國立新竹教育大學數 理教育研究所。 柯富渝(2013)。台灣、芬蘭、新加坡國小數學教科書幾何教材之分析比較(未出版碩士論文)。國立屏東教育大學應用數學系,屏東。 徐偉民(2013)。國小教師數學教科書使用之初探。科學教育學刊,21(1),25-48頁。 張欽斐(2003)。從經驗知識延伸到形式知識內在關連以分配律為例。科學教育學刊,14,85-104。 教育部(2008)。97年國民中小學九年一貫課程綱要。台北市:教育部。 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。 郭良彥(2006)。國小六年級學童速算能力之研究。國立新竹教育大學,新竹。 甯平獻主編(2010)。數學教材教法。台北市:五南書局。 黃光雄、簡茂發(1993)。教育研究法(二版)。台北市:師大書苑。 楊瑞智(2017)。康軒數學一上。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學一下。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學二上。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學二下。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學三上。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學三下。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學四上。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學四下。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學五上。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學五下。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學六上。康軒文教事業股份有限公司。 楊瑞智(2017)。康軒數學六下。康軒文教事業股份有限公司。 歐用生(1991)。內容分析法(1991)。台北市:師大書苑,229-254頁。 歐用生(1994a)。教育研究法。台北市:師大書苑。 謝如山(2000)。國民小學基本學力測驗--數學能力指標的另向省思。桃園縣國民 小學基本學力評量與指標發展研討會。 謝宜玲(2002)。在課堂討論情境下國一學生文字符號概念級運算相關法則的認知。未出版碩士論文,國立高雄師範大學,高雄。 謝堅(1998)。實驗課程對四則運算教材的處理。載於台灣省國民學校教師研習 會(主編),國民小學數學科新課程概說(高年級)(頁 78-97)。台北:台灣省國民學校教師研習會。 謝堅、蔣治邦、吳淑娟(2002)。國小數學教材分析-整數的數量關係。台北:國立教育研究院籌備處。 藍順德(2003)。教科書開放政策的演變與未來發展趨勢。國立編譯館館刊,31,2-25頁。 藍順德(2003)。教科書開放政策的演變與未來發展趨勢。國立編譯館館刊,31,3-11頁。 鐘宜興(2002)。俄羅斯教育研究。高雄:復文。
二、英文部分
Baek, J. M. (2008). Developing algebraic thinking through explorations in multiplication. In C. E. Greens & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (pp. 141–154). Reston, VA: National Council of Teachers of Mathematics. Baroody, A. J. (1998). Fostering children’s mathematics power: An investigative approach to K-8 mathematics instruction. Mahwah, NJ: Lawrence Erlbaum Associates. Blume, G.W., & Mitchell, C.E. (1983). Distributivity : A useful model or an abstract Entity.Science and Mathematics﹐83, 216-221. Bruner, J. S. (1960/1977). The process of education. Cambridge, MA: Harvard University Press. Cai J, Ni Y. (2011). Investigating Curricular Effect on the Teaching and Learning of Mathematicsina Cultural Context: Theoretical and Methodological Considerations [J]. International of Educational Research, 50(2): 65-70. Cai, J. (2004). Why do U.S. and Chinese students think differently in mathematical problem solving? Impact of early algebra learning and teachers’ beliefs. Journal of Mathematical Behavior, 23, 135–167. Cai, J., & Moyer, M. (2008). Developing algebraic thinking in earlier grades: Some insights from international comparative studies. In C. E. Greens & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (pp. 169–180). Reston, VA: National Council of Teachers of Mathematics. Cai, J., Lew, H. C., Morris, A., Moyer, J. C., Ng, S. F., & Schmittau, J. (2005). The development of students’ algebraic thinking in earlier grades: A cross-cultural comparative perspective. ZDM: The International Journal on Mathematics Education, 37(1), 5–15. Carpenter, T. P., Franke, L. P., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic & algebra in elementary school. Portsmouth, NH: Heinemann. Colhoun, J., Gentner, D., & Loewenstein, J. (2005). Learning abstract principles through principle-case comparison. In B. C. Love, K. McRae, & V. M. Sloutsky (Eds.). Proceedings of the 30th Annual Conference of the Cognitive Science Society (pp. 1659–1664). Austin, TX: Cognitive Science Society. Flournoy, F. (1964). Applying basic mathematical ideas in arithmetic. The Arithmeic Teacher, 11: 104-108. Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology, 95, 393–408. Gentner, D., Loewenstein, J., & Thompson, L. (2004). Analogical encoding: Facilitating knowledge transfer and inte- gration. In K. Forbus, D. Gentner, & T. Regier (Eds.), Proceedings of the 26th Annual Conference of the Cognitive Science Society (pp. 452–457). Chicago, IL: Cognitive Science Society. Gray, R. F. (1965). An experiment in the teaching of introductory multiplication. The Arithmetic Teacher, 12: 199-203. Grouws. D. A., Smith,M. S., & Sztajn. P. (2004). The preparation and teaching practice of U.S. Mathematics teachers: Grades 4 and 8. In P.K loosterman & F. Lester(Eds). The 1990 through 2000 mathematics assessments of the National Assessment of Educational Progress: Results and interpretations (pp.221-269). Reston. VA: NCTM. Hsieh, J. S. (1999). Children’s understanding of the uses of parentheses. Unpublished doctoral dissertation, University of Illinois, Urbana-Champaign. Li, X., Ding M., Capraro, M. M., & Capraro, R. M. (2008). Sources of differences in children’s understandings of mathematical equality: Comparative analysis of teacher guides and student texts in China and in the United States. Cognition and Instruction, 26, 195–217. Lloyd, G. M. (2008). Curriculum use while learning to teach: One student teacher's appropriation of mathematics curriculum materials. Journal for Research in Mathematics Education, 63-94. Mayer, R. E. (1987). Eudcational psychology: A cognitive approach. Boston: Little, Brown. Mayer, R. E. (2001). Multimedia learning. New York: Cambridge University Press. Meixia Ding & Xiao bao Li (2010). A Comparative Analysis of the Distributive Property in U.S. and Chinese Elementary Mathematics Textbooks, Cognition and Instruction, 28(2): 146-180. Moreno, R., & Mayer, R. C. (1999). Multimedia-supported metaphors for meaning making in mathematics. Cognition and Instruction, 17, 215–248. Murata, A. (2008). Mathematics teaching and learning as a mediating process: The case of tape diagrams. Mathematical Thinking and Learning, 10, 374–406. National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Nicol, C. C., & Crespo, S. M. (2006). Learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational studies in mathematics, 62(3), 331-355. Pashler, H., Bain, P. M., Bottge, B. A., Graesser, A., Koedinger, K., McGaniel, M. (2007). Organizing instruction and study to improve student learning (NCER 2007–2004). Washington, DC: National Center for Education Research. Piroli, P. L., & Anderson, J. R. (1985). The role of learning from examples in the acquisition of recursive programming. Canadian Journal of Psychology, 39, 240–272. Renkl, A. (2002). Worked-out examples: Instructional explanations support learning by self-explanations. Learning and Instruction, 12, 529–556. Renkl, A., Atkinson, R. K., & Große, C. S. (2004). How fading worked solution steps works—A cognitive load perspective. Instructional Science, 32, 59–82. Renkl, A., Atkinson, R. K., Maier, U., & Staley, R. (2002). From example study to problem solving: Smooth transitions help learning. Journal of Experimental Education, 70, 293–315. Rittle-Johnson, B., & Star, J. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99, 561–574. Schifter, D. (1999). Reasoning about operations: Early algebraic thinking in grades K–6. In L. V. Stiff & F. R. Curcio (Eds.). Developing mathematical reasoning in grades K–12 (pp. 62–81). Reston, VA: National Council of Teachers of Mathematics. Schmidt, W. H., Wang, H. C., & McKnight, C. C. (2005). Curriculum coherence: An examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37, 525–559. Stein, M. K., Remillard, J., Smith, M. S. (2007). How curriculum influences student learning. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 319-370). Charlotte, NC: Information Age Publishing. Stevenson, H. W., & Stigler, J. W. (1992). The learning gap: Why our schools are failing and what we can learn form Japanese and Chinese education. New York: Simon & Schuster. Stigler, J., Fuson, K., Ham, M., & Kim, M (1986). An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction, 3, 153–171. Sweller, J. (1999). Instructional design in technical areas. Victoria, Australia: Australian Council of Education. Tsai, Y.L. & Chang, C.K. (2008). Using combinatorial approach to improve students' learning of the distributive law and multiplicative identities. International Journal of Science and Mathematics Education﹐7 (3), 501-531. Watson, J.M. (1993). The distributive property undersold. School Science and Mathematics﹐93(6): 316-320. Weaver, J.F. (1973). 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