本研究旨在探討國小四年級學童對於三種不同脈絡的解題表現差異探討，研究中以完成國小三年級而且剛開始學習四年級課業並結束第一次段考的100名學童為對象，依據目前已習得的數與計算概念為主軸來進行作業設計，檢視國小四年級的學童在學習過基本的運算能力後，面對這三種不同脈絡下的命題時的解題表現，研究中並進一步檢視不同數學成就的學童在此不同脈絡的解題差異表現。
結果顯示，在數字和解題策略同構的狀態下，不同脈絡對於學生的解題表現影響雖然未達統計上的顯著，但從描述統計上卻呈現了些微的差異，其中買賣問題對學生而言是較能意義內化的，高、低分組在越接近真實的脈絡之表現均較佳，但對於中分組學生而言，虛擬買賣問題與非買賣問題的兩者情境是沒有差異，真實情境則略為薄弱，可能原因在於真實買賣情境的文字陳述較長，對於中分組學生而言，語文的負荷可能是其解題表現較為薄弱的可能原因。
整體而言，教師在企圖提升學生的問題解決能力和數學學習動機時，可以考量與學生生活相關的脈絡進行問題設計，以促進學生對於問題解決的意義內化，提高其解題的表現。

This study aimed to explore the differences of problem-solving performances for different problem contexts for 4th graders. In this study, we focus on the number and operation concepts that have been taught in the third grade curriculum and design 3 context assessments of problem solving. There were 100 4th graders participated in this study.

The results showed that, the contexts were different but the mathematics concepts and problem solving strategies were isomorph, the students showed slightly different performances from descriptive statistics view, but there was no statistical significant, the students performance better on the money situation, especially on the real money situation. Further, considering the mathematics abilities, the highest and lowest achievement students, the real money situation was more sense making for their performance, the second context was virtual money situation, the non-money situation was not as well as money situation. For the middle achievement level students, their performances were different the other two groups.

Based on the results, when the teachers attempt to improve student math problem-solving ability and motivation for learn mathematics, they should consider the sequence of life-related issues for designing the problem-posing , in order to promote the students to solve the problem within the meaning of and enhance their problem-solving performance.

中文摘要 …………………………………………………… i
英文摘要 …………………………………………………… ii
目錄 …………………………………………………… iii
表目錄 …………………………………………………… iv
圖目錄 …………………………………………………… v
第一章 緒論………………………………………………… 1
第一節 研究動機與背景……………………………………… 1
第二節 研究目的與待答問題………………………………… 6
第三節 名詞解釋……………………………………………… 7
第四節 研究範圍與限制……………………………………… 8
第二章 文獻探討……………………………………………… 9
第一節 情境的理論……………………………………………… 9
第二節 數學解題的理論基礎………………………………… 20
第三章 研究方法……………………………………………… 33
第一節 研究架構……………………………………………… 33
第二節 研究樣本……………………………………………… 35
第三節 研究工具……………………………………………… 37
第四節 資料分析……………………………………………… 47
第四章 研究結果與討論……………………………………… 49
第一節 三種脈絡問題解題表現差異…………………………… 49
第二節 全體學生在不同脈絡測驗下的表現差異比較……… 69
第三節 不同數學成就學生在不同脈絡測驗下的表現差異比
較……………………………………………………… 75
第五章 結論與建議…………………………….……………… 79
第一節 結論…………………………………………………… 79
第二節 建議…………………………………………………… 81
參考文獻 …………………………………………………… 83
附錄一 …………………………………………………… 89
附錄二 …………………………………………………… 92
附錄三 …………………………………………………… 93
附錄四 …………………………………………………… 97
附錄五 …………………………………………………… 101

一、中文部分
王保進（2004）。多變量分析：套裝程式與資料分析。臺北市：王保進出版。
王淑嬌（2006）。國小四年級學童閱讀理解能力與數學解題歷程之相關研究。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。
吳明隆、涂金堂（2005）。SPSS與統計應用分析。臺北市：五南。
李俊秀譯（2005）。孩子數學不好怎麼辦？台北市：新手父母出版。
林文生、鄔瑞香（1999）。另類教與學：數學教育的藝術與實務。台北市：心理。
林碧珍（2003）。生活情境中的數學。新竹縣教育研究集刊，3，1-26。
林清山譯（1997）。教育心理學：認知取向。台北市：遠流。
施郁芬、陳如琇（1996）。情境脈絡與學習遷移。教學科技與媒體，29，23-31。
洪慧津（2004）。國小數學資優生和一般生數學解題的創造力與情意之探究。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。
孫名符、鄭素琴、王曄、孫傑遠、董小平（1996）。數學教育學原理。台北市：建宏出版社。
徐新逸（1995）。情境學習在數學教育上的應用。教學科技與媒體雙月刊，29，13-22。
張平東（1989）。國小數學教材教法新論。台北市：五南出版社。
教育部（1993）。國民小學課程標準。台北：教育部。
教育部（2000）。國民中小學九年一貫課程暫行綱要。台北：教育部。
教育部（2003）。九年一貫數學領域課程綱要。台北：教育部。
陳瑞中（2005）。強化連結能力之數學教學對國小學童數學信念與數學能力影響之研究。國立台南大學教育經營與管理研究所碩士論文，未出版，台南市。
陳慧娟（1998）。情境學習理論的理想與現實。「教育資料與研究」，25，47-55。
陸昱任（2002）。天啊！誰把小孩變笨了！。師友月刊，415，30-33。
喻平（2002）。數學教育心理學。廣西：廣西教育。
黃敏晃（2003）。人間處處有數學。台北：天下遠見出版。
楊順南（1997）。情境認知教學觀的衝擊與啟用。教育研究雙月刊，56，51-62。
蔡坤憲譯（2006）。怎樣解題。台北市：天下文化。
賴怡君（2002）。生活數學雙簧戲－生活化的數學問題解決教學。師友月刊，415，34-37。
劉秋木（1996）。國小數學科教學研究。台北市：五南。

二、西文部分
B. A. Bottge, & T. S. Hasselbring(1993). A comparison of two approaches for teaching complex, authentic mathematics problems to adolescents in remedial math classes. Exceptional Children, 59(6), 556-566.
B. S. D’Ambrosio (1991). The modern mathematics reform movement in Brazil and its consequences for Brazilian mathematics education. Educational Studies in Mathematics, 22(1), 69-85.
Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 21-29.
Civil, M. (1994, April). Connecting the home and the school: Funds of knowledge for mathematics teaching and learning. Paper presented at the annual meeting of the America Educational Research Association, New Orleans, LA.
Civil, M. (1995a, April). Bringing the mathematics to the foreground. Paper presented at the annual meeting of the America Educational Research Association, San Francisco, CA.
Civil, M. (1995b, April). Everyday mathematics, “mathematicians’ mathematics,” and school mathematics: Can we (and should we)bring these three cultures together？ Paper presented at the annual meeting of the America Educational Research Association, San Francisco, CA.
Civil, M. (1998, April). Bridging in-school mathematics and out-school mathematics. Paper presented at the annual meeting of the America Educational Research Association, San Francisco, CA.
Civil, M. (2001). Mathematics instruction developed from a garden theme. Teaching Children Mathematics, 7(7), 400-405.
Cohen, E. G. & Lotan, R. A. (Eds.). (1997). Working for equity in heterogeneous classrooms: Sociological theory in practice. New York: Teachers College Press.
D. H. Clements, Ph.D., & J. Sarama, Ph.D.(2006). Your child’s mathematical mind. Scholastic Parent & Child, 10(1), 32-38.
D. J. Brahier, M. Kelly, & J. Swihart(1999). This little piggy. Teaching Children Mathematics, 5(5), 274-278.
Diversity in Mathematics Education Center for Learning and Teaching (2007). Culture, Race, Power, and Mathematics Education. In F. Lester (Ed) Second Handbook of Research on Mathematics Teaching and Learning. (pp. 413-415). Greenwich CT：Information Age Publishing, Inc., and NCTM.
Gay, J., & Cole, M. (1967). The new mathematics and an old culture: A study of learning among the Kpelle of Liberia. New York: Holt, Rinehart, and Winston.
Gbuerman, S. R.(2004).A comparative study of children’s out-of-school activities and arithmetical achievements. Journal for Research in Mathematics Education, 35(2), 117-150.
Gonzalez, N., Andrade, R., Civil, M., & Moll, L. (2001). Bridging funds of distributed knowledge: Creating zones of practices in mathematics. Journal of Education for Students Placed at Risk (JESPAR), 6(1-2), 115-132.
Gonzalez, N., Moll, L., & Amanti, C. (2005). Funds of knowledge: Theorizing practices in households and classrooms. Mahwah, NJ: Erlbaum.
Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge, UK: Cambridge University Press.
Lave, J., Murtaugh, M., & de la Rocha, O. (1984). The dialectic of arithmetic in grocery shopping. In B. Rogoff & J. Lave(Eds.), Everyday cognition (pp. 67-94). Cambridge, MA: Harvard University Press.
Lipka, J. (1994). Culturally negotiated schooling: Toward a Yup’ik mathematics. Journal of American Indian Studies, 33(3), 1-12.
Lipka, J. (1998). Transforming the culture of schools: Yup’ik Eskimo examples. Mahwah, NJ: Erlbaum.
Lipka, J. (2002). Schooling for self-determination: Research on the effects of including native language and culture in the schools. ERIC Digest.
Lipka, J. (2005). Math in a cultural context: Two case studies of a successful culturally based math project. Anthropology Education Quarterly, 36(4), 367-385.
Lipka, J., Wildfeuer, S., Wahlberg, N., George, M., & Ezran, .D. R. (2001). Elastic geometry and storyknifing: A Yup’ik Eskimo example. Teaching Children Mathematics, 7(6), 337-343.
Moll, L. (1992). Bilingual classroom studies and community analysis: Some recent trends. Educational Researcher, 21(2), 20-24.
Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: A qualitative approach to connect homes and classrooms. Theory into Practice, 31(1), 132-141.
Moll, L., & Greenberg, J. (1990). Creating zones of possibilities: Combining social contexts for instruction. In L. C. Moll (Ed.), Vygotsky and Education (pp. 319-348). Cambridge, England: Cambridge University Press.
Moschkovich, J. N. (2002b). An introduction to examining everyday and academic mathematical practices. In M. E. Brenner & J. N. Moschkovich (Eds.), Everyday and academic mathematics in the classroom (pp. 1-11). Reston, VA: National Council of Teachers of Mathematics.
Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge, MA: Cambridge University Press.
Polya, G. (1971). HOW TO SOLVE IT-A NEW ASPECT OF MATHEMATICAL METHOD. Princeton, New Jersey: Princeton University Press.
Saxe, G. B. (1988a). Candy selling and math learning. Educational Researcher, 17(6), 14-21.
Saxe, G. B. (1988b). The mathematics of child street vendors. Child Development, 59(5), 1415-1425.
Saxe, G. B. (1989). Transfer of learning across cultural practices. Cognition and Instruction, 6(4),325-330.
Saxe, G. B. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale, NJ: Erlbaum.
Scribner, S. (1984). Studying working intelligence. In B. Rogoff & J. Lave (Eds.), Everyday cognition: Its development in social context (pp. 9-40). Cambridge, MA: Harvard University Press.
Simon, M. A.(1994). Learning mathematics and learning to teach: learning cycles in mathematics teacher education. Educational Studies in Mathematics 26: 71-94.
Taylor, E. V. (2004, April). Engagement in currency exchange as support for multi-unit understanding in African-American children. Paper presented at the annula meeting of the American Education Research Association, San Diego, GA.
Webster, J. P., Wiles, P., Civil, M., & Clark, S. (2005). Finding a good fit: Using MCC in a “Third Space.” Journal of American Indian Education, 44(3), 9-30.