本研究旨在探討教師在實施課程遇到的困難與解決策略，以及五年級學生在STEAM課程發展數學建模的歷程與結果。本研究採質性研究方法，對象為桃園市星星國小五年級的25位學生。課程設計架構將參考STEAM課程設計模式、數學探究的概念以及數學建模之歷程。本研究主要結論如下：
（一） 學生學習興趣日漸低落，須引入數學提升動機
（二） 數據分析有助於發展科學概念，與建模課程形成交互作用
（三） 學生記錄的舒適度分數隨時間逐漸穩定
（四） 五年級學生大多能主動發現數學關係，亦有部分能形成數學模型
（五） 舒適度模型大多為函數式，亦有學生以比例關係表示
（六） 舒適度模型僅適用於有限案例，無法用以描述所有情況
（七） 舒適度情境雖複雜，卻有助於學生建模
（八） 數學建模需長時間且連貫的觀察歷程

The purpose of this study is to explore the difficulties encountered by teachers in implementing the curriculum and their solution strategies, as well as the process and results of fifth-grade students' development of mathematical modeling in the environmental comfort STEAM curriculum. In this study, qualitative research methods were used, and the subjects were 25 fifth-grade students from Xingxing Elementary School in Taoyuan City. The curriculum design framework will refer to the STEAM curriculum design model, the concept of mathematical inquiry and the process of mathematical modeling. The main conclusions of this study are as follows:
(1) Students’ interest in learning is declining day by day, and motivation to improve mathematics must be introduced.
(2) Data analysis helps develop scientific concepts and interacts with modeling courses.
(3) The comfort scores recorded by students gradually stabilized over time.
(4) Most of the fifth graders can actively discover mathematical relationships, and some can form mathematical models.
(5) Most of the comfort models are functional, and some students use proportional relationship tables.
(6) The comfort level model is only applicable to limited cases and cannot be used to describe all situations.
(7) Although the comfort level situation is complex, it is helpful for students to model.
(8) Mathematical modeling requires a long and coherent observation process.

摘要................................................i
Abstract...........................................ii
謝誌..............................................iii
目次...............................................iv
表次...............................................vi
圖次.............................................viii
第壹章 緒論..........................................1
第一節 研究背景與動機.................................1
第二節 研究目的與待答問題.............................2
第三節 名詞釋義......................................3
第四節 研究限制......................................4
第貳章 文獻探討......................................6
第一節 STEAM教育.....................................6
一、 STEAM教育的意涵..............................6
二、 STEAM的課程設計..............................9
三、 國小STEAM教學相關研究........................13
第二節 數學探究......................................18
一、 數學探究的意涵...............................18
二、 數學探究的教學...............................19
三、 數學探究教學相關研究..........................21
第三節 數學模型與數學建模.............................26
一、 數學模型的意涵...............................26
二、 數學建模的意涵...............................27
三、 數學建模的歷程...............................29
四、 數學建模教學相關研究..........................36
第參章 研究方法.......................................39
第一節 研究架構與研究流程..............................39
第二節 研究場域與研究對象..............................42
第三節 教學設計.......................................43
第四節 研究工具.......................................52
第五節 資料蒐集與分析..................................53
第肆章 研究結果.......................................55
第一節 教師實施STEAM課程建模之困難與解決策略............56
第二節 學生發展STEAM課程之探究歷程分析..................64
第三節 學生發展STEAM課程之建模結果分析..................86
第伍章 結論與建議......................................97
第一節 結論...........................................97
第二節 建議...........................................99
參考文獻.............................................101
一、中文部分..........................................101
二、西文部分..........................................104
附錄.................................................110

一、中文部分
王子華（2019）。「清華STEAM學校」之DDMT教學模式的建構。科學教育實作學門電子期刊，17。取自https：//esep.colife.org.tw/17/journal
王為國（2021）。STEAM教育之教師專業問題與因應建議。臺灣教育評論月刊，115。
李祥宇（2012）。數學建模教學對於高中生學習成效的影響之研究-以排列、組合為例（未出版之碩士論文）。國立高雄師範大學數學系教學研究所，高雄市。
吳政諺（2020）。以清華STEAM學校DDMT教學模式發展國小學生STEAM素養—從數學觀點切入（未出版之碩士論文）。國立清華大學數理教育研究所，新竹市。
吳銘祥（2017）。創造思考與批判思考融入數學建模教學對女高中生之教學效果（未出版之碩士論文）。國立臺灣師範大學教育學院創造力發展研究所，臺北市。
巫茲棋（2021）。探討STEAM課程統整模式對國小學生學習成效之影響—以「降溫小屋」為例（未出版之碩士論文）。國立清華大學人力資源與數位學習科技研究所，新竹市。
林坤誼（2018）。STEM教育在台灣推行的現況與省思。Journal of Youth Studies，21（1），41。
林宜珊（2020）。以DDMT教學模式實施STEAM課程之行動研究—「竹塹城的第一座城牆」主題為例（未出版之碩士論文）。國立清華大學教育與學習科技學系課程與教學組，新竹市。
林琬婷（2013）。數學建模教學對國三學生數學學習態度、機率迷思概念及機率學習成就之影響（未出版之碩士論文）。國立中正大學教育學研究所，臺中市。
周佳萩（2019）。發展國小簡單機械STEAM統整課程之歷程研究（未出版之碩士論文）。國立高雄師範大學工業科技教育學系，高雄市。
周淑惠（2018）。具STEM精神之幼兒探究課程紀實:〔一起創建遊戲樂園〕主題 （Vol.51197）。心理。
邱偉誌（2013）。PCDC融入數學建模教學於七年級數學課室之行動研究（未出版之碩士論文）。國立彰化師範大學科學教育研究所，彰化市。
洪甄苓（2020）。STEAM應用於國小昆蟲立體書創作課程設計之研究（未出版之碩士論文）。國立臺北教育大學理學院數位科技設計學系玩具與遊戲設計，臺北市。
姜啟源（2001）。數學實驗與數學建模（Doctoral dissertation）。
范斯淳、游光昭（2016）。科技教育融入STEM課程的核心價值與實踐。 教育科學研究期刊，61（2），153-183。
柳棟、吳俊杰、謝作如、沈涓（2013）。STEM、STEAM課程與可能的實踐路線。中小學訊息技術雜誌，6，39-41。
陳明峰（2012）。高中數學建模教學及學生數學建模之研究（未出版之碩士論文）。國立彰化師範大學科學教育研究所，彰化市。
陳英娥、林福來（1998）。數學臆測的思維模式。科學教育期刊，6（2），191-218
陳怡倩（2017）。跨科統整的STEAM教育探究。教育參考，（3），5-11。
陳珮珊（2013）。數學探究教學對七年級學生數學素養影響之研究（未出版之碩士論文）。國立彰化師範大學科學教育研究所，彰化市。
陳榮德（2020）。矽谷STEAM教育對新課綱的教材編製與使用之啟示。臺灣教育評論月刊，9（3），41-46。
陳瑩（2015）。〈STEAM教育，玩的就是學科「跨界」〉。擷取自https://read01.com/mQGokP.html#.WZp7x_gjGzc
張斐宜（2016）。以臆測活動為主的數學探究教學對學生後設認知能力與學習成就影響之研究（未出版之碩士論文）。國立彰化師範大學科學教育研究所，彰化市。
張詩敏（2019）。四年級自然與生活科技領域融入STEAM元素科學課程之學生學習成效—以「有趣的力」單元為例（未出版之碩士論文）。國立臺北教育大學理學院自然科學教育學系，臺北市。
黃玟姿（2013）。實施數學探究教學對高職工業類科學生數學學習動機影響的行動研究（未出版之碩士論文）。國立彰化師範大學科學教育研究所，彰化市。
黃怡玲（2013）。發展與實踐數學探究教學模組之研究－以二次函數單元為例（未出版之碩士論文）。國立彰化師範大學科學教育研究所，彰化市。
黃沛錚（2019）。能源教育融入偏鄉國小STEAM課程統整教學之行動研究（未出版之碩士論文）。國立高雄師範大學工業科技教育學系，高雄市。
黃暄閔（2020）。一位國小教師實施數學探究教學之個案研究（未出版之碩士論文）。國立屏東大學科普傳播學系，屏東縣。
楊子錕（2010）。以數學建模教學方式進行國中三年級學生相似形概念之補救教學（未出版之碩士論文）。國立彰化師範大學科學教育研究所，彰化市。
葉秀玲（2020）。數學探究教學對學生數學學習的影響—以國中八年級學生為例（未出版之碩士論文）。國立屏東教育大學應用數學系，屏東縣。
趙慧臣、陸曉婷（2016）。開展STEAM教育，提高學生創新能力—訪美國STEAM教育知名學者格雷特．亞克門教授。開放教育研究，22（5），4-10。
趙慧臣、周昱希、李彥奇、劉亞同、文潔（2017）。跨學科視野下“工匠型”創新人才的培養策略─基於美國STEAM教育活動設計的啟示。擷取自https://www.jianshu.com/p/e42188a428c4
賓靜蓀（2017）。5大精神，培養STEAM新素養。擷取自https://flipedu.parenting.com.tw/article/3393
劉善德（2020）。環境教育中的STEAM教案設計與評估之行動研究─以臺南市國小高年級為例（未出版之碩士論文）。國立臺南大學生態暨環境資源學系，臺南市。
蕭翔文（2021）。仿生機器人STEAM課程對六年級學童的科學探究能力與對科學的態度之影響研究（未出版之碩士論文）。國立清華大學數理教育研究所，新竹市。
謝孟琪（2012）。實施數學探究教學於七年級課室之行動研究（未出版之碩士論文）。國立彰化師範大學科學教育研究所，彰化市。
戴咏秀（2013）。數學探究教學對國小二年級學生解題能力影響之研究（未出版之碩士論文）。國立屏東教育大學數理教育研究所，屏東縣。
關超然、李孟智（2009）。PBL問題導向學習之理念。方法，實務與經驗。臺北市: 臺灣愛思唯爾。
蘇琳（2019）。天氣與生活STEAM課程對國小三年級學童的天氣概念、探究能力與科學態度之影響研究（未出版之碩士論文）。國立清華大學數理教育研究所，新竹市。

二、西文部分
Asempapa, R. S.（2015）. Mathematical modeling: Essential for elementary and middle school students. Journal of Mathematics Education, 8（1）, 16-29.
Baroody, A. J., ＆ Coslick, R. T.（1993）.Problem solving, reasoning, and communicating, K-8: Helping children think mathematically. New York, NY:Macmillan Publishing.
Bliss, K., Levy, R., Teague, D., Giordano, F., ＆ Garfunkel, S.（2016）. GAIMME: Guidelines for assessment ＆ instruction in mathematical modeling education. Consortium for Mathematics and Its Applications and Society for Industrial and Applied Mathematics.
Blomhøj, M., ＆ Jensen, T. H.（2003）. Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching mathematics and its applications, 22（3）, 123-139.
Blum, W., Galbraith, P. L., Henn, H. W., ＆ Niss, M.（2007）. Modelling and applications in mathematics education（pp. 3-33）. New York：Springer.
Blum, W., ＆ Leiß, D.（2007）. Investigating quality mathematics teaching: The DISUM project. Developing and researching quality in mathematics teaching and learning, proceedings of MADIF, 5, 3-16.
Blum, W., ＆ Borromeo Ferri, R.（2009）. Mathematical modelling: Can it be taught and learnt?Journal of Mathematical Modelling and Application, 1（1）, 45-58.
Borasi, R. （1992）. Learning mathematics through inquiry. Portsmouth, NH: Heinemann.
Brown, N., Wilson, K., ＆ Fitzallen, N.（2007, November）. Using an inquiry approach to develop mathematical thinking. Paper presented at the meeting of AARE 2007 International Educational Research Conference-Fremantle, Adelaide,Australia.
Bybee, R. W.（2010）. Advancing STEM education：A 2020 vision. Technology and engineering teacher, 70（1）, 30.
Chapman, O.（2007）. Preservice secondary mathematics teachers’ knowledge and inquiry teaching approaches. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education（Vol. 2, pp. 97-104）.
Cobb, P., Yackel, E., ＆ Wood, T.（1991）. Curriculum and teacher development: Psychological and anthropological perspectives. In E. Fennema ＆ S. J. Lamon （Eds.）, Integrating research on teaching and learning mathematics（pp. 92–131）. Albany, NY: State University of New York Press.
Connor, A., Karmokar, S., ＆ Whittington, C.（2015）. From STEM to STEAM: Strategies for enhancing engineering ＆ technology education.
Cramer, K. A.（2003）. Using a translation model for curriculum development and classroom instruction: Models and modeling perspectives on mathematics pr. In Beyond constructivism: Models and modeling perspectives on mathematics pr （pp. 449-464）. Lawrence Erlbaum Associates.
Department for Education and Skills.（2001）. National strategy for key stage 3. London: DfES.
Erbas, A. K., Kertil, M., Çetinkaya, B., Çakiroglu, E., Alacaci, C., ＆ Bas, S. （2014）. Mathematical Modeling in Mathematics Education： Basic Concepts and Approaches. Educational Sciences： Theory and Practice, 14（4）, 1621-1627.
English, L. D.（2003）. Reconciling theory, research, and practice： A models and modelling perspective. Educational Studies in Mathematics, 54（2）, 225-248.
English, L. D., Fox, J. L., ＆ Watters, J. J.（2005）. Problem posing and solving with mathematical modeling. Teaching Children Mathematics, 12（3）, 156-163.
English, L. D.（2010）. Modeling with complex data in the primary school. In Modeling students' mathematical modeling competencies（pp. 287-299）. Springer, Boston, MA.
Ferri, R. B.（2006）. Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38（2）, 86-95.
Fibonacci（2012）. Learning through inquiry, http://fibonacci.uni-bayreuth.de/resources/resourcesfor-implementing-inquiry.html.
Fibonacci（2012）. Inquiry in Mathematics Education, http://fibonacci.uni-bayreuth.de/resources/resources-for-implementing-inquiry.html.
Flevares, L. M., ＆ Schiff, J. R.（2013）. Engaging young learners in integration through mathematical modeling: Asking big questions, finding answers, and doing big thinking. In Learning Across the Early Childhood Curriculum. Emerald Group Publishing Limited.
Force, S. T.（2014）. Innovate： A blueprint for science, technology, engineering, and mathematics in California public education. Dublin, CA：Californians Dedicated to Education Foundation.
Freudenthal, H.（1991）. Revisiting Mathematics Education（Dordrecht: D. Reidel Publishing, Co）.
Gravemeijer, K., ＆ Stephan, M.（2002）. Emergent models as an instructional design heuristic. In Symbolizing, modeling and tool use in mathematics education（pp. 145-169）. Springer, Dordrecht.
Haines, C., ＆ Crouch, R.（2007）. Mathematical modelling and applications: Ability and competence frameworks. In Modelling and applications in mathematics education（pp. 417-424）. Springer, Boston, MA.
HarlEn, W.（2013）. Inquiry-based learning in science and mathematics. Review of science, mathematics and ICT education, 7（2）, 9-33.
Hawking, S.（1988）. A Brief History of Time Bantam Press. London-1988, Çev. Selma Öğünç,“Zamanın Kısa Tarihi”, Doğan Kitapçılık, İstanbul-2000.
Henningsen, M., ＆ Stein, M. K.（1997）. Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for research in mathematics education, 28（5）, 524-549.
Herschbach, D. R.（2011）. The STEM initiative: Constraints and challenges. Journal of STEM Teacher Education, 48（1）, 96-122.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., ... ＆ Wearne, D.（1996）. Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational researcher, 25（4）, 12-21.
Kaiser, G.（2005）. Mathematical modelling in school -- Examples and experiences. In G. Kaiser ＆ H. W. Henn（Eds.）, Mathematikunterricht im spannungsfeld von evolution und evaluation（pp. 99-108）. Hildesheim, Deutschland: Franzbecker
Lakatos, I.（1976）. Proofs and refutations: The logic of mathematical discovery. Cambridge, UK: Cambridge University Press. doi: 10.1017/CBO9781139171472
Lederman, N. G., ＆ Niess, M. L.（2000）. Problem solving and solving problems: Inquiry about inquiry.School Science and Mathematics, 100（3）, 113-116.
Lesh, R., ＆ Heger, M.（2001）. Mathematical abilities that are most needed for success beyond school in a technology based age of information. The New Zealand Mathematics Magazine 38, 1-17.
Lehrer, R., ＆ Schauble, L.（2003）. Origins and evolution of model-based reasoning in mathematics and science. Beyond constructivism： Models and modeling perspectives on mathematics problem solving, learning, and teaching, 59-70.
Lesh, R. E., ＆ Doerr, H. M.（2003）. Beyond constructivism：Models and modeling perspectives on mathematics problem solving, learning, and teaching. Lawrence Erlbaum Associates Publishers.
Lesh, R.（2007）. Problem solving and modeling. Second handbook of research on teaching and learning.
Lesh, R., ＆ Zawojewski, J. S.（2007）.Problem solving and modeling. In F. K.Lester （Ed.）, Second handbook of research on mathematics teaching and learning（pp.763-804）. Greenwich, CT: Information Age.
Livshits, I., ＆ Coleman, N.（2008）. Mathematical Modeling.
Maeda, J.（2013）. Stem+ art= steam. The STEAM journal, 1（1）, 34.
Mason, J., ＆ Davis, J.（1991）. Modelling with mathematics in primary and secondary schools. Deakin University.
Marzano, R. J., Brandt, R. S., Hughes, C. S., Jones, B. F., Presseisen, B, Z., Rankin, S. C., ＆ Suhor, C.（1988）. Dimensions of thinking: A framework for curriculum and instruction. Alexandria, VA:Association for Supervision and Curriculum Development.
McNeal, B. ＆ Simon, M. A.（2000）. Mathematics culture clash: Negotiating new classroom norms with prospective teachers. Journal of Mathematical Behavior, 18（4）, 475-509.
Mote, C., Strelecki, K., ＆ Johnson, K.（2014）. Cultivating high-level organizational engagement to promote novel learning experiences in STEAM. The STEAM Journal, 1（2）, 18.
Mousoulides, N., Sriraman, B. H. A. R. A. T. H., ＆ Christou, C. O. N. S. T. A. N. T. I. N. O. S.（2007）. From problem solving to modelling. Education, 12（1）, 23-47.
National Council of Teachers of Mathematics.（2000）Principles and standards for school mathematics. Reston, VA: Author
National Research Council.（1996）. National science education standards. National Academies Press.
National Research Council.（2014）. STEM integration in K-12 education：Status, prospects, and an agenda for research. National Academies Press.
Niss, M.（2003, January）. Mathematical competencies and the learning of mathematics: The Danish KOM project. In 3rd Mediterranean conference on mathematical education （pp. 115-124）.
Organization for Economic Co-operation andDevelopment.（2009）. PISA 2009Assessment Framework Keycompetencies in reading, mathematicsand science. Paris: Author.
Peressini, D. ＆ Knuth, E.（2000）. The role of tasks in developing communities of mathematical inquiry. Teaching Children Mathematics, 391-397.
Pollak, H. O.（2003）. A history of the teaching of modeling. A history of school mathematics.
Lambros, A.（2004）. Problem-Based Learning in Middle and High School Classrooms: A Teacher’ s Guide to Implementation. Corwin Press.
Reusser, K., ＆ Stebler, R.（1997）. Every word problem has a solution—The social rationality of mathematical modeling in schools. Learning and instruction, 7（4）, 309-327.
Richards, J.（1991）. Mathematical discussion. In E. von Glaserfeld （Ed.）, Radical constructivism in mathematics education（pp. 13-51）.Dordrecht, The Netherlands: Kluwer.
Rolling Jr, J. H.（2016）. Reinventing the STEAM engine for art+ design education. Art Education, 69（4）, 4-7.
Schmidt, H. G., ＆ Moust, J. H.（2000）. Factors affecting small-group tutorial learning: A review of research. Problem-based learning: A research perspective on learning interactions, 19-52.
Schoenfeld, A. H.（1992）. Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. A. Grouws（Ed.）, Handbook of research on mathematics teaching and learning （pp. 334-370）. New York: Macmillan.
Schorr, R. Y. ＆ Lesh,（2003）. A modeling approach for providing teacher development. In R.Lesh ＆ H. Doerr（Eds.）Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning and Teaching（pp. 141-158）. Mahwah, NJ: Erlbaum.
Shaughnessy, J. M.（2013）. Mathematics in a STEM context. Mathematics Teaching in the Middle school, 18（6）, 324-324.
Siegel, M., Borasi, R., ＆ Fonzi, J.（1998）. Supporting students' mathematical inquiries through reading.Journal for Research in Mathematics Education, 29（4）, 378-413.
Sriraman, B., ＆ English, L. D.（Eds.）.（2010）. Theories of mathematics education: Seeking new frontiers（pp. 309-331）. New York, NY: Springer.
Stein, M. K., Grover, B. W., ＆ Henningsen, M.（1996）. Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American educational research journal, 33（2）, 455-488.
Trowbridge, L. W., ＆ Bybee, R. W.（1990）. Becoming a secondary school science teacher（5th ed.）.New York, NY: Macmillan.
Whitin, P.（2006）. Meeting the challenges of negotiated mathematical inquiry. Teaching ＆ Learning:The Journal of Natural Inquiry and Reflective Practice, 21（1）, 59–83
White, D. W.（2014）. What is STEM education and why is it important. Florida Association of Teacher Educators Journal, 1（14）, 1-9.
Yakman, G.（2008）. STEAM education. Research on Technology, Innovation, Design ＆ Engineering Teaching, 19, 1-28.
Yakman, G.（2010）. What is the point of STE@ M?–A Brief Overview. Steam: A Framework for Teaching Across the Disciplines. STEAM Education, 7.
Young, V. M., House, A., Wang, H., Singleton, C., ＆ Klopfenstein, K.（2011, May）. Inclusive STEM schools：Early promise in Texas and unanswered questions. In Highly Successful Schools or Programs for K-12 STEM Education：A Workshop. Washington, DC：National Academies. Retrieved May （Vol. 1, p. 2014）.