中文部分
王志銘（2008）。從資優兒童自發性解法鷹架學生分數除法學習表現之探究---以當量除為例。國立嘉義大學數學教育研究所碩士論文，未出版：嘉義。
王志銘、劉祥通（2007）。一位資優生自發性解題表現之探究~以分數除法之當量除為例。資優教育季刊，104，8-19。
朱中梧（2003）。國小一般能力資優生之數學解題探究。國立台北師範學院數理教育研究所碩士論文，未出版，台北市。
朱建正（1997）。國小數學課程的數學理論基礎。行政院國家科學委員會專題研究成果報告（NSC-85-2513-S-002-001）。台北市：行政院國家科學委員會。
朱敬先（1995）。教學心理學（三版）。台北市：五南。
江奇婉（2010）。國中個案資優生解速率問題之研究。國立嘉義大學數理教育研究所碩士論文，未出版，嘉義。
江奇婉、劉祥通（2010）。以追趕問題為例探討資優個案的解題表現。資優教育季刊，116，18-24。
吳武典(1997)。教育改革與資優教育。資優教育季刊，63，1-7。
吳慧珠、李長燦（2003）。Vygotsky 社會認知發展理論與教學應用。載於張新仁主編，學習與教學新趨勢（頁105-158）。台北市：心理。
呂佳蓉（2011）。國小五年級空間能力優異學生對空間關係問題的解題表現。國立臺北教育大學數學暨資訊教育學系研究所碩士論文，未出版，台北市。
李玉惠（2000）。資優生真的有較好的後設認知嗎。資優教育季刊，76，12-17。
李佩樺（2008）。鷹架學生的數學學習－以資優生解連比問題為資產。國立嘉義大學數理教育研究所碩士論文，未出版，嘉義。
李佩樺、劉祥通（2008）。分析國小資優生解連比問題之自發性策略。資優教育季刊，106，8-17。
周筱亭、黃敏晃（2002）。國小數學教材分析─比（含線段圖）。臺北縣：國立教育研究院籌備處。
林香（2003）。國小數學資優生的解題策略探究－以圖畫表徵策略為例。國立台北師範學院數理教育研究所碩士論文，未出版，台北市。
林香、張英傑（2004）。國小數學資優生運用畫圖策略解題之探究。國立臺北師範學院學報，17（2），1-22。
林碧珍（2010）。比與比值初始概念的教學初探。新竹教育大學教育學報，27（1），127-160。
翁宜青、劉祥通（2003）。一位國小三年級學生解簡單式比例問題之研究。科學教育研究與發展季刊，31，32-53。
翁嘉聲（2001）。國小數學教學形成群體討論文化之個案研究。國立台北師範學院數理教育研究所碩士論文，未出版，台北市。
高珮珊（2005）。一位小三資優生在分數「部分-整體」問題之解題表現。 國立嘉義大學特殊教育研究所碩士論文，未出版，嘉義。
國立編譯館（2000）。國民小學數學教學指引第10冊（五下）。臺北市：作者。
張春興（1996）。教育心理學-三化取向的理論與實踐（修訂版）。台北市：東華。
張英傑、林香、朱中梧、洪慧津、施惠珍（2003，11月）。國小數學資優兒童的解題策略探究－以小學數學奧林匹亞競賽選手為例。載於國立台北師範學院主編，九十一年度教育論文學術發表手冊，台北市。
張祥瑞（2009）。分析資優生解速率問題之研究。國立嘉義大學數學教育研究所碩士論文，未出版，嘉義。
教育部（1975）。國民小學課程標準。臺北市：作者。
教育部（1993）。國民小學課程標準。臺北市：作者。
教育部（2000）。九年一貫課程數學領域暫行綱要。臺北市：作者。
教育部（2003）。國民中小學九年一貫課程綱要。臺北市：作者。
教育部（2008）。97年國民中小學課程綱要。臺北市：作者。
郭生玉（2005）。心理與教育研究法。臺北：精華書局。
郭美如（1998）。後設認知的教學成效及其相關變數之分析--以小六及國一數學資優生為對象。國立臺灣師範大學科學教育研究所碩士論文，未出版，台北市。
陳志瑲（2007）。國小數學資優生代數解題與與非代數解題之探究－以參賽亞太地區奧林匹亞選手為例。國立臺北教育大學數學教育研究所碩士論文，未出版，台北市。
陳英豪（2007）。影響資優生數學解題能力之重要因素。網路社會學通訊，61。檢索於2011年4月17日，網址http://mail.nhu.edu.tw/ ~society/e-j/61/61_59.htm
黃茂在、陳文典（2004）。「問題解決」的能力。科學教育月刊，273，21-42。
黃家杰（2003）。國小一般智能資優資源班新生數學解題歷程之分析。國立中山大學教育研究所碩士論文，未出版，高雄市。
黃家杰、梁淑坤（2007）。小學一般智能資優資源班新生數學解題歷程之分析。台灣數學教師（電子）期刊，12，1-16。
黃繼仁、周立勳、甄曉蘭（2001）。國小教師國語教學信念及相關因素之調查研究。教育研究集刊，47，107-132。
楊代誠（2002）。國中數學課室教師進行師生對談歷程及影響因素之研究。彰化師範大學科學教育研究所碩士論文，未出版，彰化縣。
楊瑞智（1994）。國小五、六年級不同能力學童數學解題的思考過程。國立台灣師範大學科學教育研究所博士論文，未出版，台北市。
楊錦連（1999）。國小高年級兒童解決比例問題之研究。國立嘉義師範學院國民教育研究所碩士論文，未出版，嘉義。
楊麗華（2001）。「合作—省思」數學教學活動方案對國小資優兒童解題能力與數學態度影響之研究。台北市立師範學院國民教育研究所碩士論文，未出版，台北市。
葉建德（2004）。一位七年級學生解速率問題的研究。國立嘉義大學數學教育研究所碩士論文，未出版，嘉義。
葉晉佳（2009）。二位七年級資優生在數規形規的解題表現之研究。國立嘉義大學數學教育研究所碩士論文，未出版，嘉義。
劉松柏（2010）。探討小六一般智能資優生在因數與倍數應用題解題策略與歷程之研究。國立屏東教育大學數理教育研究所碩士論文，未出版，屏東。
劉貞宜（2000）。數學資優生的解題歷程分析-以建中三位不同能力的數學資優生為例。國立臺灣師範大學特殊教育研究所碩士論文，未出版，台北市。
劉哲源、劉祥通（2008）。國一資優生在對因倍數問題的解題分析。資優教育研究，8（1），47-66。
劉哲源（2009）。國一資優生解因倍數問題之個案研究。國立嘉義大學數學教育研究所碩士論文，未出版，嘉義。
劉晉瑋（2010）。一位國小五年級資優生解時分針問題之解題表現。國立嘉義大學數學教育研究所碩士論文，未出版，嘉義。
劉晉瑋、劉祥通、康淑娟（2010）。國小資優生在時分針問題之解題表現分析。資優教育季刊，117，33-40。
劉祥通（2004）。國小學生高年級分數構念、運算能力、及基準化能力之研究成果報告(1/3)。行政院國家科學委員會專題研究成果報告（NSC-92-2521-S-425-001）。台北市：國科會。
劉祥通（2007）。分數與比例問題解題分析：從數學提問教學的觀點（增訂一版）。臺北市：師大書苑。
劉錫麒(1994)。從國小新數學課程標準的基本理念談討論活動的重要。國教園地，50，4-7。.
劉祥通、周立勳 （1999）。國小比例問題教學實踐課程之開發研究。國立臺中師範學院數理學報，3（1），1-25。
蔡子雲（2008）。探討國小六年級資優生對速率問題之解題表現。國立嘉義大學數學教育研究所碩士論文，未出版，嘉義。
蔡子雲、劉祥通（2007）。資優生在想什麼-速率篇？資優教育，7（1），29-47。
蔡典謨、陳長益、李永昌（1998）。「資賦優異學生降低入學年齡、縮短修業年限及保送甄試辦法」之制訂研究。國立高雄師範大學特殊教育系印行。
蔡啟禎（2004）。國小中年級資優生數學解題歷程分析。國立中山大學教育研究所碩士論文，未出版，高雄市。
蔡清田（2010）。論文寫作的通關密碼：想畢業？讀這本。臺北：高等教育。
謝淡宜（1998）。小學五年級數學資優生與普通生數學解題時思考歷程之比較。臺南師院學報，31，225-268。
謝淡宜（1999）。國小數學資優生及普通生「數學解題」歷程之比較（四年級），台南師院學報，32，297-367
顏榮義（2001）。國一一般資優生的解題歷程分析。國立高雄師範大學數學系碩士論文，未出版，高雄市。
魏宗明、劉祥通（2003）。兒童對數學比例問題的建構。科學教育研究與發展季刊，32，87-108。

外文部分
American Association for the Advancement of Science (1993). Benchmarks for science literacy. New York, NY: Oxford University Press.
Assouline, S., & Lupkowski-Shoplik, A. (2005). Developing math talent: A guide for educating gifted and advanced learners in math. Waco, TX: Prufrock Press.
Baker, A., K. Schirner, & J. Hoffman. (2006). Mutliage mathematics: Scaffolding young children’s mathematical learning. Teaching Children Mathematics 13(1), 19-21.
Barba, R. H. (1990). Problem solving pointers. Science Teacher, 57(7), 32-35.
Behr, M. J., & Post, T. R. (1988). Teaching rational number and decimal concepts. In T. R. Post (Ed.), Teaching mathematics in grades K-8 (pp.190-229). Boston, MA: Allyn and Bacon.
Berk, L. E., & Winsler, A. (1999). 鷹架兒童的學習：維高斯基與幼兒教育（古瑞勉譯）。臺北：心理。（原著出版於1995）。
Bodrova, E., & Leong, D. J. (1996). Tools of the mind: The Vygotskian approach to early children education. New Jersey, NJ: Englewood Cliffs.
Bogdan, R. C., & Biklen, S. K. (2003). Qualitative research for education: An introduction to theories and methods (4th ed.). Boston, MA: Allyn & Bacon.
Borkowski, J. G., & Kurtz, B. E. (1984). Children’s metacognition: Exploring relations among knowledge, process, and motivational variables. Journal of Experimental Child Psychology, 37(2), 335-354.
Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
Carr, M., & Jessup, D. L. (1997). Gender Differences in First-Grade Mathematics Strategy Use: Social and Metacognitive Influences. Journal of Educational Psychology, 89(2), 318-328.
Carr, M., Alexancler, J., & Schanenflugel, P. (1996). Metacognition and giftedness: Where gifted children do and do not excel on metacognitive tasks. Raper Review, 18(3), 212-217.
Chamberlin, M. T., & Chamberlin, S. A. (2010). Enhancing preservice teacher development: Field experiences with gifted students. Journal for the Education of the Gifted, 33(3), 381-416.
Chamberlin, S. A. (2002). Analysis of interest during and after model-eliciting activities: A comparison of gifted and general population students. Unpublished doctoral dissertation, Purdue University.
Christou, C., & Philippou, G. (2002). Mapping and development of intuitive proportional thinking. Journal of Mathematical Behavior, 20, 321-336.
Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 159-178). New York, NY: Macmillan.
Cyert, R. M. (1980). Problem solving and educational Policy. In D.T. Tuma & F. Reif (Eds.), Problem solving and education: Issues in teaching and research. Hillsdale, NJ：Erlbaum.
Davis, G. A., & Rimm, S. B. (2004). Education of the gifted and talented (5 th ed.). Boston, MA: Pearson/ A and B.
Debra, J. P. (1992). The negotiation of meaning and the transfer of responsibility for learning through teacher scaffolding and student self-scaffolding of instruction. University of Texas at Austin, Dissertation.
Denzin, N. K. (1978). The logic of naturalistic inquiry. In N. K. Denzin (Eds.), Sociological methods: A sourcebook. New York, NY: McGraw-Hill.
Desoete, A., & Veenman, M. (2006). Metacognition in mathematics: Critical issues on nature, theory, assessment and treatment. In A. Desoete & M. Veenman (Eds.), Metacognition in mathematics education (pp.1-10). New York, NY: Nova Science Publishers.
Diezmann, C. M., & Watters, J. J. (2001). The collaboration of mathematically gifted students on challenging tasks. Journal for the Education of Gifted, 25(1), 7-31.
Doolittle, P. E. (1998). Vygotsky’s zone of proximal development as a theory foundation for cooperative learning. Virginia Polytechnic Institute and State University.
Efklides, A., Kourkoulou, A., Mitsiou, F., & Ziliaskopoulou, D. (2006). Metacognitive knowledge of effort, personality factors, and mood state: Their relationship with effort-related experiences. Metacognition and Learning, 1, 33-49.
Erickson, F. (1986). Qualitative methods in research on teaching. In Wittrock （Ed.）, Handbook of Research on Teaching, 119-161. NY: Macmillan.
Farnham-Diggory, S. (1992). Cognitive processes in education (2nd ed.). New York, NY: HarperCollins Publishers, Inc.
Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B.Resnick (Ed.), The nature of intelligence (pp.231-235). Hillsadle, NJ: Erlbaum.
Flavell, J. H. (1979). Metacognition and cognition monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34, 906-911.
Gallagher, J., Harradine, C. C., & Coleman, M. R. (1997). Challenge or boredom? Gifted students' views on their schooling. Roeper Review, 19(3), 132-136.
Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16, 163-176.
Gentry, M., Gable, R. K., & Springer, P. (2000). Gifted and nongifted middle school students: Are their attitudes toward school different as measured by the new affective instrument, My Class Activities…? Journal of the Education of the Gifted, 24, 74-96.
Ginsburg, H. P. (1989). Children’s arithmetic: How they learn it and how you teach it. Austing, TX: Pro-Ed.1
Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews, in mathematics education research. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517-545). Mahwah, NJ: Lawrence Erlbaum.
Good, T., & Brophy, J. (2000). Looking In Classrooms (8th ed.). New York, NY: Longman.
Groen, G. J., & Resnick, L. B. (1977). Can preschool children invent addition algorithms? Journal of Educational Psychology, 69(6), 645-652.
Hart, K. (1981). Ratio and proportion. In K. Hart (Ed.), Children's understanding of mathematics: 11-16 (pp. 88-101). London, UK: John Murray.
Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of successful and unsuccessful problem solvers. Journal of Education Psychology. 87, 18-32.
Hembree, R., & Marsh, H. (1993). Problem solving in early childhood: Building foundations. In Jensen R. J. (Ed.), Research ideas for the classroom: Early childhood mathematics (pp. 151-170). New York, NY: Macmillan.
Higgins, K. M. (1997). The effect of year-long instruction in mathematical problem solving on middle-school students’ attitudes, beliefs, and abilities. The Journal of Experimental Education, 66(1), 5-28.
Hoffer, A. (1992). Ratios and proportional thinking. In T. Post (Ed.), Teaching mathematics in grades K-8 research-based methods (2nd ed, pp. 303-330). Needham Heights, MA: Allyn and Bacon.
Holton, D., & Clarke, D. (2006). Scaffolding and metacognition. International Journal of Mathematical Education in Science and Technology, 37(2), 127-143.
Hoover, S. M. (1994). Scientific problem finding in gifted fifth-grade students. Roeper Review, 16(3), 156-159.
Howley, A., Pendarvis, E., & Gholson, M. (2005). How talented students in a rural school district experience school mathematics. Journal for the Education of the Gifted, 29(2), 123-160.
Ishida, J. (2002). Students' evaluation of their strategies when they find several solution methods. The Journal of Mathematical Behavior, 21(1), 49-56.
Jacobs, V. R., Lamb, L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169-202.
Johnson, S. D. (1994). Research on problem solving instruction: What works, what doesn’t? The Technology Teacher, 53(8), 27-29.
Kanevsky, L., & Keighley, T. (2003). To produce or not to produce? Understanding boredom and the honor in underachievement. Roeper Review, 26, 20-28.
Kaput, J. J., & West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235-287). New York, NY: State University of New York Press.
Karplus, R. Pulos, S., & Stage, E. (1983). Proportional reasoning of early adolescents. In R. Lesh & M. Landau (Eds.), Acquisition of mathematical concepts and processes (pp. 45-89). New York, NY: Academic Press.
Kenny, P., Lindquist, M., & Heffernan, C. (2002). Butterflies and caterpillars: Multiplicative and proportion reasoning in the early grades. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp. 87-99). NCTM Yearbook. Reton, VA: NCTM.
Kieren, T. E. (1980). Knowing rational numbers: Ideas and symbols. In M. Lindquist (Eds.), Selected issues in mathematics education, Chicago, IL: National Society for the Study of Education. Reston, VA: NCTM.
Kilpatrick, J. (1985). A retrospective account of the past 25 years of research on teaching mathematical problem solving. Paper presented in Silver, E. A. (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 1-15). Hilsdale, N.J.: Erlbaum Associates.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren (pp. 224-236). Chicago, IL: University of Chicago Press.
Lachance, A., & Confrey, J. (1995). Introducing fifth graders to decimal notation through ratio and proportion. Owens, D., Reed, M. & Millsaps, G. (Eds.), Proceedings of the Seventeenth Annual Meeting 16 of PME-NA, Vol. 1, Columbus, OH: Eric clearinghouse for science, mathematics, and environmental education (pp. 395-400). Ohio State University.
Lamon, S. J. (1993). Ratio and proportion: Connecting content and children’s thinking. Journal for Research in Mathematics Education, 24(1). 41-61.
Lamon, S. J. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 89-120). Albany, NY.: State University of New York Press.
Lamon, S. J. (1995). Ratio and proportion: Elementary didactical phenomenology. In J. T. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 167-198). New York, NY: State University of New York Press.
Lamon, S. J. (1999). Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers. London, England: Lawrence Erlbaum Associates.
Larson, L. C. ( 1983 ). Problem-solving through problems. New York, NY: Springer.
Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). Reston, VA: Lawrence Erlbaum Associates & National Council of Teachers of Mathematics.
Lester, F. K. (1980). Research on mathematical problem solving. In R. J. Shumway (Ed.). Research in mathematics education (pp. 286-323). Reston, VA: NCTM.
Lester, F. K., Jr. (Ed.). (2007). Second handbook of research on mathematics teaching and learning. Charlotte, NC: Information Age.
Levin, S. (2002). Proportional reasoning: One problem, many solutions! In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions: 2002 Yearbook. Reston, VA: NCTM.
Levin, S. W. (1999). Fractions and division: Research conceptualizations, textbook presentations, and student performances (doctoral dissertation). University of Chicago, 1998. Dissertation Abstracts International 59: 1089A.
Light, P., & Butterworth, G. (Eds.). (1993). Context and cognition: Ways of learning and knowing. Hillsdale, NJ: Lawrence Erlbaum.
Liljedahl P. (2009). In the words of the creators. In R. Leikin, A. Berman & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (Ch. 4, pp. 51-69). Rotterdam, the Netherlands: Sense Publishers.
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Beverly Hill, CA: Sage.
Lo, J., & Watanabe, T. (1995). A fifth grader's attempt to expand her ratio and proportion concepts. Paper presented at the annual meeting of the North America chapter of the international group for the psychology of mathematics education (17th).
Lo, J. J., & Watanabe, T. (1997). Developing ratio and proportion schemes: A story of a fifth grader. Journal for Research in Mathematics Education, 28(2), 216-236.
Lo, J. J., Watanabe, T., & Cai, J. (2004). Developing ratio concepts: An Asian perspective. Mathematics Teaching in the Middle School, 9, 362-367.
Lucangeli, D., & Cabrele, S. (2006). The relationship of metacognitive knowledge, skills and beliefs in children with and without mathematical learning disabilities. In A. Desoete & M. V. Veenman (Eds.), Metacognition in Mathematics Education (pp. 103-133). New York, NY: Nova Science Publishers, Inc.
Manouchehri, A., & Lapp D. A.(2003). Unveiling Student understanding: The role of Question in instruction. Mathematics Teacher, 96(8), 562-566.
Mason, J. (2000). Asking mathematical questions mathematically. International Journal of Mathematical Educational in Science and Technology, 31(1),97-111.
Mayer, R. E., & Hegarty, M. (1996). The process of understanding mathematical problems. New Jersey, NJ: Lawrence Erlbaum Associates.
Mayer, R. E. (1987). Educational Psychology: A cognitive approach, Boston, MA: Brown and Company.
Mayer, R. E. (1991). Thinking, problem solving, cognition (2nd ed.). New York, NY: Freeman.
Mayer, R. E. (1992). Thinking, problem solving, cognition, 387-414. New York, NY: W. H. Freeman and Company.
Mayer, R. E.（2003). Learning and instruction. New Jersey, NJ: Pearson Education.
McMaken-Marsh, A. (2007). Reflections on teaching an unanswered question: Finding factors of large numbers. Teaching Children Mathematics, 384-386.
Meyer, D. K., & Turner, J. C. (2002). Discovering emotion in classroom motivation research. Educational Psychologist, 37(2), 107-114.
Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. Journal of Mathematical Behavior, 22, 335-368.
Montague, M. (1991). Gifted and learning-disabled gifted students’ knowledge and use of mathematical problem-solving strategies. Journal for the Education of the Gifted, 14(14), 393-411.
Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. Journal of Learning Disabilities, 25(4), 230-248. .
Montague, M., Bos, C., & Doucette, M. (1991). Affective, cognitive, and metacognitive attributes of eighth-grade mathematical problem solvers. Learning Disabilities Research & Practice, 6, 145-151.
Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. Journal of Learning Disability Quarterly, 31, 37-44..
National Council of Teachers of Mathematics. (1991）. Curriculum and evaluation standards for school mathematics. Reston, VA: The Author.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics, Reston, VA: The Author.
National Council of Teachers of Mathematics. (1993). Asseessment in the mathematics classroom. Reston, VA: The Author.
National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: The Author
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: The Author.
Ng, S. F., & Lee, K. (2009). The model method: Singapore children’s tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282-313.
Noelting, G. (1980a). The development of proportional reasoning and the ratio concept: Part 1-Differentiation of stages. Educational Studies in Mathematics, 11, 217-253.
Noelting, G. (1980b). The development of proportional reasoning and the ratio concept: Part2-Problem-structure at successive stages; problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11, 331-363.
Pape, S. J., Bell, C. V., & Yetkin, I. E.(2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics, 3(53), 179-202.
Patrick, W. T. (1994). The development of the concept of speed and its relationship to concepts of rate. In G. Hare, & J. Confrey (Ed.), The development of multiplicative reasoning in the learning of mathematics (pp. 179-233).
Piaget, J. (1964). Cognitive development in children: development and learning. Science teaching and the development of reasoning. Karplus, R. et al. (Eds.) U. of California, Berkeley.
Piaget, J. (1971). Genetic Epistemology. New York, NY: W. W. Norton & Company.
Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children. New York, NY: W. W. Norton.
Piaget, J., & B. Inhelder. (1969). Psychology of the child. London: Routledge & Kegan Paul.
Polya, G. (1945). How to solve it? Princeton University Press.
Polya, G. (1957). How to solve it? Garden City, New York, NY: Doubleday and Co., Inc.
Posner, G. Strike, K., Hewson, P., & Gertzog, W. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 6(2), 211-227.
Pugalee, D. K. (2001). Writing, mathematics, and metacognition: Looking for connections through students’ work in mathematical problem solving. School Sscience and Mathematics, 5, 236-245.
Renzulli, J. S. (1977). The enrichment triad model: A guide for developing defensible programs for the gifted and talented. Mansfield Center, CT: Creative Learning Press.
Renzulli, J. S., Reis, S. M., & Smith, L. H. (1981). The revolving door identification model. Mansfield Center. Connecticut, CT: Creative Learning Press.
Rotigel, J. V. (2000). Exceptional mathematical talent: Comparing achievement in concepts and computation. Unpublished doctoral dissertation, Indiana University of Pennsylvania, Indiana, PA.
Ruiz, E. F., & Lupianez, J. L. (2009). Detecting psychological obstacles in teaching and learning the topics of reason and proportion in sixth grade pupils. Electronic Journal of Research in Education Psychology, 17, 7(1), 397-424.
Scharien, R., & Yackel, J. J. (2005). Analysis of surface roughness and morphology of first-year sea ice melt ponds: Implications for microwave backscatter. IEEE 122 Transactions on Geoscience and Remote Sensing, 43(12), 2927-2939.
Schliemann, A. D., & Carraher, D. W. (1992). Proportional reasoning in and out of school. In P. Light & G. Butterworth (Eds.), Context and Cognition (pp.47-73). Hemel Hempstead, Harvester-Wheatsheaf.
Schliemann, A. D., & Nunes, T. (1990). A situated schema of proportionality. British Journal of Developmental Psychology, 8, 259-268.
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
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, NY: MacMillan.
Sheffield, L. J. (1994). The development of gifted and talented mathematics students and the National Council of Teachers of Mathematics standards (RBDM 9404). Storrs, CT: The National Research Center on Gifted and Talented, University of Connecticut.
Schoenfeld, A. H. (1996). In fostering communities of inquiry, must it matter that the teacher knows “the answer”? For the Learning of Mathematics,16(3), 11-16.
Silver E. A. (1981). Recall of mathematical problem information: Solving related problems. Journal for Research in Mathematics Education, 12, 54-64
Singh, P. (2000). Understanding the concepts of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics, 43, 271-292.
Slivan, E. (1986). Motivation in social constuctivist theory. Educational Psychologist, 21(3), 209-233
Smith III, J. P. (2002). The development of student’ knowledge of fractions and ratios. In B. Litweller, & G. Bright (Eds), Making sense of fractions, and ratio, and proportions (pp. 3-17). Reston, VA: NCTM.
Sourviney, R. J. (1989). Learning to teach mathematics. Columbus, OH: Merrill.
Sousa, D.A. (2009). How the gifted brain learns, 2nd ed. Corwin Press.
Stake, R (1995). The art of case study research. Thousand Oaks, CA: Sage Publications.
Stake, R. (2003). Case studies. In N. K. Denzin & Y. S. Lincoln (Eds.), Strategies of qualitative inquiry (2nd ed., pp. 134-164). Thousand Oaks, CA: Sage Publications.
Stanley, J. S. (1991). An academic model for educating the mathematically talented. Gifted Child Quarterly, 35(1), 36-42.
Steen, L. A. (1999). Numeracy: The new literacy for a data-drenched society. Educational Leadership, 57(2), 8-13.
Steiner, H. H., & Carr, M. (2003). Cognitive development in gifted children: Toward a more precise understanding of emerging differences in intelligence. Educational Psychology Review, 15, 215-246.
Steiner, H. H. (2006). A microgenetic analysis of strategic variability in gifted and average-ability children. Gifted Child Quarterly, 50(1), 62-74.
Sternberg, R. J. (2003). Cognitive psychology (3rd ed.). Belmont, CA: Wadsworth.
Stonecipher, L. D. (1986). A comparison of mathematical problem solving processes between gifted and average junior high students: A clinical investigation. Unpublished doctoral dissertation, Southern Illinois University at Carbondale.
Swanson, H. L. (1990). Influence of metacognitive knowledge and aptitude on problem solving. Journal of Educational Psychology, 82, 306-314
Sweeney, C. M. (2010). The metacognitive functioning of middle school students with and without learning disabilities during mathematical problem solving. Doctoral dissertation, University of Miami, Retrieved September 11, 2011, from http://scholarlyrepository. miami.edu/cgi/viewcontent.cgi?article=1432&context=oa_dissertations.
Threlfall J., & Hargreaves M. (2008). The problem-solving methods of mathematically gifted and olderaverage-attaining students. High Ability Studies, 19(1), 83–98.
Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16, 181–204.
Treffinger, D. J. (1986). Fostering effective, independent learning through individualized programming. In J. S. Renzulli (Ed.), Systems and models for developing programs for the gifted and talented (pp. 429-460). Mansfield Center, CT: Creative Learning Press.
Udall, A. J., & Daniels, J. E. (1991). Creating the thoughtful classroom: Strategies to promote student thinking. Tucson, Arizona: Zephyr Press.
Van Dooren, W., De Bock, D., Evers, M., & Verschaffel, L. (2009). Students’ overuse of proportionality on missing-value problems: How numbers may change solutions. Journal for Research in Mathematics Education, 40(2), 187–211.
Van Luit, J. E. H., & Kroesbergen, E. H. (2006). Teaching metacognitive skills to students with mathematical disabilities. In A. Desoete & M. V. J. Veenman (Eds.), Metacognition in mathematics education (pp. 177-190). Hauppauge, NY: Nova Science Publishers.
Veenman, M., & Spaans, M. (2005). Relation between intellectual and metacognitive skills: Age and task differences, Learning and Individual Differences, 15, 159-176.
Veenman, M. V. J., Kerseboom, L., & Imthorn, C. (2000). Test anxiety and metacognitive skillfulness: Availability versus production deficiencies. Anxiety, Stress, and Coping, 13, 391-412.
Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127–174). New York, NY: Academic Press.
Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades: Vol. 2. (pp. 141–161). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics.
Vygotsky, L. S. (1962). Thought and Language. Cambridge, MA: MIT Press.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Translated by Knox and Carol. Cambridge, MA: Harvard University Press.
Wolfle, J. A. (1986). Enriching the mathematics program for middle school gifted students. Roeper Review, 9, 81–85.
Wood, D. J., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry, 17, 89-100.
Woolfolk, A. (2004). Educational psychology (9th ed.). Boston, MA: Allyn & Bacon.
Yin, R. K. (2003). Case study research: Designs and methods (3rd ed.). U.S.A.: SAGE.,
Yoon , C. H. (2009). Self-regulated learning and instructional factors in the scientific inquiry of scientifically gifted Korean. The Gifted Child Quarterly, 53(3), 203-216.