以建模觀點詮釋國中資優生的數學解題活動：以問題解決及專題研究為例_

:::

詳目顯示

第 1 筆 / 總合 1 筆

/1頁

論文基本資料
摘要
外文摘要
參考文獻

題名：	以建模觀點詮釋國中資優生的數學解題活動：以問題解決及專題研究為例
作者：	顏富明
作者(外文)：	Fu-Ming Yen
校院名稱：	國立彰化師範大學
系所名稱：	科學教育研究所
指導教授：	張靜嚳
學位類別：	博士
出版日期：	2011
主題關鍵詞：	問題解決；專題研究；建模；資優生；詮釋；problem solving；mathematic project；modeling；gifted student；interpretation
原始連結：	連回原系統網址
相關次數：	被引用次數:期刊(0) 博士論文(0) 專書(0) 專書論文(0) 排除自我引用:0 共同引用:0 點閱:42

本研究目的是以建模觀點詮釋國中資優生的數學問題解決與數學專題研究的解題活動，包含思維內涵、模型、建模循環與模型發展系列的關係。本研究採個案研究法，整個個案是由問題解決的四個個案與專題研究的一個個案所形成。在問題解決方面，是在一班30人的國中資優生進行小組合作解題，全班共分成八組，每組3至4人，以其中四組為本研究之個案，而在專題研究方面，是在一班37人的國中資優生進行小組合作專題研究，全班共分成九組，每組4至5人，以其中一組為本研究之個案。資料收集包含小組討論及其發表、學生的學習日誌、教學現場摘記、教學日誌及任務導向的臨床晤談。研究者將上述多元的質性資料加以編碼，並採用詮釋學的資料分析程序進行分析詮釋，以獲致研究結論。研究結果發現：1.國中資優生的解題活動是建模思維取向甚於描述式或規範式的歷程。2.以建模觀點詮釋國中資優生數學解題活動，有助於了解國中資優生的數學思維特徵。3.模型、建模循環與模型發展系列也有一些特定的關係與蘊涵，包括(1)模型與建模循環的一對一對應關係；(2)在每個問題的模型發展系列的主要活動中，所建構的模型數量是依問題解決者所經歷的建模循環次數而定；(3)問題的本質與模型建構、模型發展系列的關聯性；(4)所建構的模型數量的多寡，不是代表題目的難易，而是代表不同解題者企圖貼近問題，所經歷的建模循環次數的差異。4.個案小組學生在模型調整活動及模型探索活動所建構的模型，扮演不同模型發展鏈結圖之間的關鍵連結角色。5.關於高階數學思維特徵方面，個案小組學生在數學專題研究活動較在問題解決活動更易產生綜合面向的思維特徵。6.個案小組學生所建構的複雜系統的模型，擁有合適的解釋力。7.個案小組學生的解題是一種數學化的活動，而不是解碼的活動。8.個案小組學生的建模活動中的探究符合Dewey實用主義的論點，即探究是一組過程與結果。9.個案小組學生的建模活動符合Lakatos準經驗主義的論點。10. 結構不佳的真實生活問題，有助於促進資優生發展數學能力。

以文找文

The purpose of this paper was to interpret the mathematical problem solving and project activities of junior high school gifted students from modeling perspectives, focusing particularly on the relationships among the intension of thinking, models, modeling cycles and model-development sequences. Using a case study approach, the study consists of 4 cases of problem solving and 1 case of mathematic projects. Regarding problem solving, the study examined the cooperative problem solving of a class of 30 students. The subjects were divided into eight small groups of 3 to 4 students. Four groups were chosen as the cases. Regarding mathematic projects, the study examined the cooperative project of a class of 37 students. The subjects were divided into nine small groups of 4 to 5 students. One group was chosen as the case. Data were collected from the discussions and presentations of the groups, the students’ learning journals, the teaching notes, the teaching journals, and the task-based clinical interviews. Researcher coded the above multifaceted qualitative data, analyzed and interpreted the coded data through the analytical procedure of hermeneutics, and then inducted the conclusions. The main findings of the study were as follows. 1. The problem solving activities of junior high school gifted students were more a modeling-thinking-oriented process than a descriptive or prescriptive process. 2. Interpreting the mathematical problem solving activities of junior high school gifted students from modeling perspectives, the study also provided an insight into the characterizations of the students’ mathematical thinking. 3. There were some specific relationships and implications among models, modeling cycles and model-development sequences, including (1) the one-to-one correspondences between models and modeling cycles; (2) the dependence of the quantities of constructed models on the number of times of modeling cycles that problem solvers experienced during the main activities of model development sequences of each problem; (3) the relationships among the nature of the problem, model construction and model-development sequences; (4) the various quantities of constructed models, which represent the discrepancy of times of modeling cycles experienced by different problem solvers who attempt to approach problems, rather than the difficulty levels of problems. 4. The models constructed by the students in these cases during model-adaptation activities and model-exploration activities play a crucial connective role among the model development chain figure. 5. In terms of characterizations of advanced mathematical thinking, it is easier for the students in these cases to generate synthesizing thinking in mathematic project than in problem solving. 6. The models of complex systems constructed by the students in these cases had adequate explanatory power. 7. The problem solving activities of the students in these cases were a mathematizing activity, rather than a decoding activity. 8. The students’ inquiry during the modeling activities conforms to Dewey’s pragmatism perspectives, which means that inquiry is a set of processes and outcomes. 9. The modeling activities of the students correspond with Lakatos’s Quasi-empiricism perspectives. 10. The ill-structured real-life problems facilitate the development of junior high school gifted students’ mathematical competencies.

以文找文

參考文獻
中文部分

Heppner, P. P., & Heppner, M. J. (2010). 研究論文寫作(Writing and publishing your thesis, dissertation & research，王麗斐、杜淑芬、吳麗琴、王玉珍、吳育沛、簡華妏、喬虹和王敬元譯)。台北：洪葉。(原著出版於2004年)
李源順、余新富和李勇諭 (2006)。同分母分數加減法的教學研究。科學教育研究與發展季刊，2006專刊，114-141。
秦爾聰、林勇吉和陳俊源(2009)。探討高二學生在三角探究教學中的解題表現。科學教育學刊，17(5)，433-458。 new window

張靜嚳 (1995)。問題中心教學在國中發展之經過、效果及可行性之探討。科學教育學刊，3 (2)，139-165。 new window

郭靜姿(1993)。如何指導資優生進行獨立研究。資優教育季刊，48，5-15。
陳英娥和林福來 (1998)。數學臆測的思維模式。科學教育學刊，6 (2)，191-218。
陳蕙茹和柳賢 (2008)。從建模觀點初探學生關於資料之數學推理。花蓮教育大學學報，26, 21-47。
黃國勳和劉祥通 (2006)。一個情境認知取向教學活動的發展與實踐－以「因數大老二」為例。科學教育學刊，14 (1)， 1-27。
楊凱琳和林福來 (2006)。探討高中數學教學融入建模活動的支撐策略及促進參與教師反思的潛在機制。科學教育學刊，14 (5)，517-543。
詹秀玉 (2006)。指導資優兒童做好科展作品PBS模式的理論與應用。資優教育季刊，99，1-14。
劉宏文(2001)。高中學生進行開放式科學探究活動之個案研究。國立彰化師範大學科學教育研究所博士論文，未出版，彰化縣。 new window

劉秋燕(1993)。資優生獨立研究的理念與做法。資優教育季刊，47，10-12。
顏瓊芬(1999)。職前生物教師進行開放式科學探究過程之研究。國立彰化師範大學科學教育研究所博士論文，未出版，彰化縣。 new window

西文部分

Antonius, S., Haines, C., Jensen, T. H., & Niss, M. (with Burkhardt, H.) (2007). Classroom activities and the teacher. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 295-308). New York: Springer.
Barron, B. J. S., Schwartz, D. L., Vye, N. J., Moore, A., Petrosino, A., Zech, L., Bransford, J. D., & The Cognition and Technology Group at Vanderbilt (1998). Doing with understanding: Lessons from research on Problem- and Project-Based Learning. The Journal of the Learning Sciences, 7(3 & 4), 271-311.
Blomhøj, M., & Jensen, T.H. (2007). What’s all the fuss about competencies? In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 45-56). New York: Springer.
Blumenfeld, P. C., Soloway, E., Marx, R. W., Krajcik. J. S., Guzdial, M., & Palincsar, A. (1991). Motivating Project-Based Learning: Sustaining the doing, supporting the learning. Educational Psychologist, 26(3 & 4), 369-398.
Bonotto, C. (2007). How to replace word problems with activities of realistic mathematical modelling. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 185-192). New York: Springer.
Borasi, R., & Siegel, M. (1992). Reading, writing, and mathematics: Rethinking the “basics” and their relationship. Paper Presented at the 7th International Congress on Mathematics Education, Quebec City, Canada.
Burke, C., & Harste, J. (1992). Teacher as researcher: classrooms that support teacher and student inquiry. Workshop Presented at the third Annual International Whole Language Umbrella Conference, Niagara Falls, NY.
Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp.547-590). Mahwah, NJ: Lawrence Erlbaum Associates.
Confrey. J., & Maloney, A. (2007). A Theory of mathematical modelling in technological settings. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 57-68). New York: Springer.
Dreyfus, T. (1991). Advanced mathematical thinking processes. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 25-41). Dordrecht, The Netherlands: Kluwer.
Dreyfus, T., & Eisenberg, T. (1996). On different facets of mathematical thinking. In R. J. Sternberg & T. Ben-Zeev (Eds.), The Nature of Mathematical Thinking (pp. 253-284). Mahwah, NJ: Lawrence Erlbaum Associates.
Ernest, P. (1991). The Philosophy of mathematics education. Basingstoke, Falmer Press.
Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal of Research in Science Teaching, 35, 258-291.
Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht, Netherlands: Freudenthal Institute.
Gravemeijer, K., & Doorman, D. (1999). Context problems in realistic mathematics education: A Calculus course as an example. Educational Studies in Mathematics, 39, 111-129.
Greeno, J. G., & Middle School Mathematics through Applications Project Group. (1998). The Situativity of knowing, learning, and research. American Psychologist, 53, 5-26.
Haines, C., & Crouch, R. (2007). Mathematical and applications: ability and competence frameworks. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 417-424). New York: Springer.
Hemmi, K. (2010). Three styles characterising mathematicians’ pedagogical perspectives on proof. Educational Studies in Mathematics, 75, 271-291.
Henn, H. W. (2007). Modelling pedagogy – overview. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 321-324). New York: Springer.
Henning, H., & Keune, M. (2007). Levels of modelling competencies. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 225-232). New York: Springer.
Herron, M. D. (1971). The Nature of scientific inquiry. School Review, 79, 171-212.
Hershkowitz, R., Friedlander, A., & Dreyfus, T. (1991). Loci and visual thinking. In F. Furinghetti (Ed.), Proceedings of the 15th International Conference on the Psychology of Mathematics Education (pp. 181-188). Genova, Italy: U Press.
Hmelo, C. E., Holton, D. L., & Kolodner, J. L. (2000). Designing to learn about complex systems. The Journal of the Learning Sciences, 9(3), 247-298.
House, P. A. (1987). Providing opportunities for the mathematically gifted. Reston, VA: National Council of Teachers of Mathematics.
Jurow, A. S. (2005). Shifting engagements in figured worlds: middle school mathematics students’ participation in an architectural design project. The Journal of the Learning Sciences, 14(1), 35-67.
Kehle, P. E., & Lester, F. K. (2003). A Semiotic look at modeling behavior. In R. Lesh & H. M. Doerr (Eds.), Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 97-122). Lawrence Erlbaum Association, Mahwah, New Jersey.
Koichu, B., & Berman, A. (2005). When do gifted high school students use geometry to solve geometry problems? The Journal of Secondary Gifted Education, 16(4), 168-179.
Kolodner, J. L., Camp, P. J., Crismond, C., Fasse, B., Gray, J., Holbrook, J., et al. (2003). Problem-Based Learning meets case based reasoning in the middle-school science classroom: putting learning-by-designTM into practice. The Journal of the Learning Science, 12, 495-548.
Krajcik, J., Blumenfeld, P. C., Marx, R. W., Bass, K. M., Fredricks, J., & Soloway, E. (1998). Inquiry in Project-Based science classrooms: initial attempts by middle school students. The Journal of the Learning Science, 7( 3 & 4), 313-350.
Lakatos, I. (1976). Proofs and refutations. Cambridge, Cambridge University Press.
Lesh, R. (2006). Modeling students modeling abilities: the teaching and learning of complex systems in education. The Journal of the Learning Sciences, 15(1), 45-52.
Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 3-33). Lawrence Erlbaum Association, Mahwah, New Jersey.
Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual Development. Mathematical Thinking and Learning, 5( 2 & 3 ), 157-189.
Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5( 2 & 3 ), 109-129.
Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 763-804). National Council of Teachers of Mathematics, Information Age Publishing, Charlotte, NC.
Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In R. Lesh & H. M. Doerr (Eds.), Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 35-58). Lawrence Erlbaum Association, Mahwah, New Jersey.
Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp.591-646). Mahwah, NJ: Lawrence Erlbaum Associates.
Lesh, R., Yoon, C., & Zawojewski, J. (2007). John Dewey revisited—making mathematics practical VERSUS making practice mathematical. In R. A. Lesh, E. Hamilton & J. J. Kaput (Eds.), Foundations for the Future in Mathematics Education (pp. 315-348). Lawrence Erlbaum Association, Mahwah, New Jersey.
Lester, F. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25, 660-675.
Lester, F. K., & Kehle, P. E. (2003). From problem solving to modeling: the evolution of thinking about research on complex mathematical activity. In R. Lesh & H. M. Doerr (Eds.), Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 501-518). Lawrence Erlbaum Association, Mahwah, New Jersey.
Maker, C. J., & Schiever, S. W. (2005). Teaching models in education of the gifted (3rd ed.). Austin, TX: PRO-ED.
Meyer, D. K., Turner, J. C., & Spencer, C. A. (1997). Challenge in a mathematics classroom: students’ motivation and strategies in Project-Based Learning. The Elementary School Journal, 97(5), 501-521.
Mousoulides, N. G., Christou, C., & Sriraman, B. (2008). A Modeling perspective on the teaching and learning of mathematical problem solving. Mathematical Thinking and Learning, 10, 293-304.
Muller, E., & Burkhardt, H. (2007). Applications and modelling for mathematics—overview. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 267-274). New York: Springer.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and Standard for School Mathematics. Reston, VA: Author.
Niss, M. (2002). Mathematical competencies and the learning of mathematics: The Danish KOM project. Retrieved February 8, 2011, from http://www7.nationalacademies.org/mseb/mathematical_competencies_and_the_learning_of_mathematics.pdf
Niss, M., Blum, W., & Galbraith, P.(2007). Introduction. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 3-32). New York: Springer.
Organisation for the Economic Co-operation and Development (2003). PISA 2003 Assessment framework: mathematical literacy. Retrieved September 20, 2010, from http://www.pisa.oecd.org/dataoecd/38/51/33707192.pdf
Pólya, G. (1957). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.
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. (2003). Handbook of gifted education. Boston, Pearson Education, Inc.
Romberg, T. A. (1992).Perspectives on scholarship and research methods. In D. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 49-64). New York, Macmillan.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 334-370). New York: Macmillan.
Singer, J., Marx, R. W., Krajcik, J., & Chambers, J. C. (2000). Constructing extended inquiry projects: curriculum materials for science education reform. Educational Psychologist, 35(3), 165-178.
Singer, M. (2007). Modelling both complexity and abstraction: A paradox? In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 233-240). New York: Springer.
Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: the problem-solving experiences of four gifted students. The Journal of Secondary Gifted Education, 14(3), pp.151-165.
Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, 17(1), 20-36.
Steen, L. A., & Turner, R. (with Burkhardt, H.) (2007). Developing mathematical literacy. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 285-294). New York: Springer.
Steiner, H. H., & Carr, M. (2003). Cognitive development in gifted children: Towards a more precise understanding of emerging differences in intelligence. Educational Psychology Review, 15(3), 215-246.
Stylianou, D. (2011). An examination of middle school students’ representation practices in mathematical problem solving through the lens of expert work: Towards an organizing scheme. Educational studies in Mathematics, 76, 265-280.
Swan, M., Turner, R., & Yoon, C. (with Muller, E.) (2007). The roles of modelling in learning mathematics. In W. Blum, P. L. Galbraith, H.W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education, The 14th ICMI Study (pp. 275-284). New York: Springer.
Threlfall, J., & Hargreaves, M. (2008). The problem-solving methods of mathematically gifted and older average-attaining students. High Ability Studies, 19(1), 83-98.
Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proof: An exploratory study. Educational Studies in Mathematics, 76, 329-344.
Wilhelm, J., & Walters, K. (2008). Project-Based Learning environments: Challenging preservice teachers to act in the moment. The Journal of Educational Research, 101(4), 220-233.
Wubbels, T., Korthagen, F., & Broekman, H. (1997). Preparing teachers for realistic mathematics education. Educational Studies in Mathematics, 32, 1-28.
Yang, D. C. (2006). Developing number sense through real-life situations in school of Taiwan. Teaching Children Mathematics, 13(2), 104-110.
Zawojewski, J. S., & Lesh, R. (2003). A models and modeling perspective on problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond Constructivism. Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 317-336). Lawrence Erlbaum Association, Mahwah, New Jersey.

推文
推薦
引用網址
引用嵌入語法
轉寄

top

:::

相關期刊
相關論文
相關專書
相關著作
熱門點閱

1.	遊戲融入通識教育的課程設計與學習成效
2.	問題導向學習在觀光活動課程之設計與實踐
3.	文化情境融入「整數運算規則」之補救教學研究
4.	輕度認知障礙國中生乘法公式表徵與運算學習成效之探討
5.	數學建模教學對國三學生數學學習態度的影響--以「機率」學習為例
6.	數學探究之意義初探與教學設計實例
7.	數學建模--社會文化與集體論證的觀點
8.	從建模教學推敲數學補救教學的可能面向
9.	大學普通生物學實驗課程應用探究鷹架自我評估策略對學生探究能力表現之影響
10.	數學建模評量規準之研究
11.	小組建立假設的合作探究策略--以網路環境為例
12.	以真實數學教育觀點談設計數學史融入課室之解題活動經驗分享
13.	從學生的表現與觀點探討引導發現式教學作為發展探究教學之折衷方案角色的成效--以密度概念為例
14.	探究教學的專業成長歷程--以十位國中科學教師的觀點為例
15.	開發數學建模的教材

1.	國小學童學習三角形邊長關係之個案研究
2.	學習共同體與講述教學對國小高年級學童社會學習領域學習成效之比較研究
3.	問思-解釋教學對交互主體性與分散認知影響之研究
4.	國民中學學習領導、學習環境與學習成效關係之研究
5.	八位數學教師從傳統教學趨向建模教學之研究
6.	以探究式學習導入高職化工群學生「專題製作」核心能力指標建構與驗證之研究
7.	模型本位探究策略在不同場域學習成效之研究
8.	iEARN專案式學習教師信念、專案認知與專案教學取向之關係研究
9.	參與學習社群之科學教師其探究教學專業成長轉變之研究
10.	提升學童批判思考能力之5E探究式教學研究
11.	融入後設認知鷹架策略於開放式探究之合作式行動研究
12.	輔導國中數學實習教師學習問題中心教學之行動研究
13.	數學建模活動下國小五年級學生代數思考及其發展歷程之研究
14.	國小教師之教學專業發展研究：以閱讀策略教學為例
15.	學佈脈絡數學問題：探討二位國中數學教師佈題行為的改變

1.	建構主義的認識論觀點及其在科學教育上的意義

無相關著作

無相關點閱

QR Code

臺灣人文及社會科學引文索引資料庫系統

詳目顯示

臺灣人文及社會科學引文索引資料庫