為探討教師在教學中使用模型與建模的知識與實踐，本研究以三位國中理化教師為研究對象（分別為一位科教博士與兩位科教碩士)。瞭解不同模型觀與建模教學經驗的教師在教授酸與鹼單元所呈現出的建模學科教學知識有何不同。
本研究含模型與建模的知識（Models and Modeling Knowledge；MMingK)（含教師對模型和科學建模型的觀點)與建模學科教學知識（Modeling-Pedagogical Content Knowledge；Ming-PCK)（含教師建模的教學目標與建模教學策略之知識與實踐)兩大面向。由教學前、中、後訪談、課堂觀察與問卷填答收集資料，並在教師教學後，對三位教師的某授課班級學生進行模型本質問卷與建模學習經驗問卷調查。在學生問卷填答之後由各教師推薦九位學生（高中低成就學生各三位)進行晤談，以深入瞭解學生的模型本質觀點與學習經驗感受，研究結果顯示如下：
一、建模教學經驗較豐富的教師能明確地說出模型與建模在科學教學上的應用（如：透過粒子動畫模型來讓學生瞭解酸鹼中和的過程)；在教學中能純熟溶入建模歷程且重視微觀與動態表徵模型以協助學生進行建立成分之間的聯結（如透過PhET互動軟體讓學生建構加水後的體積與莫耳濃度變化)。
二、建模教學經驗少於一年的教師在模型與建模的教學則多從巨觀與微觀的角度思考，對於動態過程的呈現（如動態模擬軟體以呈現稀釋或稀釋的過程)較少，在建模歷程的設計則較難考量到修正模型與重建模型的步驟。
三、無建模教學經驗的教師無法明確說出對模型的定義，課堂中多以文字與講述教學為主，較不重視微觀與圖像（如課程設計中很少呈現出微觀的酸鹼離子），建模步驟中則較注重應用模型（將酸鹼概念用來解題)的部分。
四、學生於兩份問卷的填答均無達到統計上的顯著差異，顯示出內隱式教學無法有效提升學生的一般化模型觀。從晤談資料可知，多數學生認為模型是實體，與問卷結果相符；五位中高能力組的學生提到模型可以用來解釋與檢驗（如耐震程度）。部分學生認為自行操作或設計實驗對學習科學理論有助益。

In order to explore teachers' practice of Models and Modeling Knowledge (MMingK), this study taked three middle school Physical Science teachers as research objects, one expert teacher with a Ph.D. in science education and two teachers with a MSc in science education. The purpose of this study was to investigate the differences in the presentation of Ming-PCK of teachers with different perspective on models and teaching experience in modeling when they were instructing the unit Acid and Base.
This study contained two major aspects of Models and Modeling Knowledge (MMingK) (Teachers' views on models and scientific models) and Modeling-Pedagogical Content Knowledge (Ming-PCK) (The teaching objectives of teacher modeling and the knowledge and practice of modeling teaching strategies.) Data were collected from interviews before, during and after the course, classroom observations and questionnaires. After the teaching, a nature of model questionnaire and modeling learning experience questionnaire were conducted for a class of three teachers. After the survey, nine students (Divided into high, medium and low level students) were recommended by the instructors to conduct an interview to look into the perspective and learning experience of models of the students. The result showed that,
1.Teacher with more experience in modeling could accurately and consistently state out the application in science teaching and learning. (Such as through the particle animation model to let students understand the process of Acid-base neutralization) The teacher was skilled in combing modeling process with teaching and he valued microscopic models and utilized dynamic models to assist students in constructing the links between the components of models. (For example, through the PhET interactive software, students could construct volume and molar concentration changes after adding water)
2.Teacher with no experience in modeling teaching could not clearly state out the definitions of models. In the classroom, his instruction primarily based on lectures and explaining scientific theories. He focused less on the microscopic and image (For example, microscopic acid-base ions were rarely present in course design.), and he concentrated more on the application of models (Used the acid-base concept to solve questions).
3.Teacher with no experience in modeling teaching could not clearly state out the definitions of models. In the classroom, his instruction primarily based on lectures and explaining scientific theories. He focused less on the microscopic and dynamic models, and he concentrate more on the application of models.
4.Students’ responses to the two questionnaires did not reach statistically significant differences. It showed that implicit teaching could not effectively improve students' generalized model view. According to the interview data, most students thought that the model was an entity, which was consistent with the results of the questionnaire; five students in the middle and high ability group mentioned that the models could be used to explain and test (such as the degree of earthquake resistance.) Some students believed that self-operation or design experiments were helpful for learning scientific theories.

吳明珠（2008)。科學模型本質剖析：認識論面向初探。科學教育月刊，307，2-8
宋元惟（2016）。探討日本與台灣學生之模型本質認識－以東京與台北地區為例（未出版碩士論文）。國立臺灣師範大學，臺北市。
宋志雄、林曦、徐順益（1993）。探究國三學生酸與鹼的迷思概念並應用以發展教學診斷工具。科學教育，4，1-23。
周金城（2008)。探究中學生對科學模型的分類與組成本質的理解。科學教育月刊，306，10-17。
林生傳（1992）。新教學理論與策略。臺北：五南圖書出版公司。
林靜雯、邱美虹（2008）。從認知／方法論之向度初探高中學生模型及建模歷程之知識。科學教育月刊，307，9-14。
邱柏融（2009）。建模教學對國小五年級學生酸鹼心智模式改變之探究（未出版碩士論文）。國立臺灣師範大學，臺北市。
邱美虹（2008）。模型與建模能力之理論架構。科學教育月刊，306，2-9。
邱美虹（2016）。科學模型與建模：科學模型、科學建模與建模能力。臺灣化學教育，11。取自http://chemed.chemistry.org.tw/?p=13898
邱美虹（2017）。再談科學模型與建模—從酸鹼模型發展史談起（上），臺灣化學教育，18。取自http://chemed.chemistry.org.tw/?p=22296
邱美虹（2017）。再談科學模型與建模—從酸鹼模型發展史談起（下），臺灣化學教育，18。取自http://chemed.chemistry.org.tw/?p=22363
邱美虹（2017）。再談科學模型與建模—從酸鹼模型發展史談起（中)，臺灣化學教育，18。取自http://chemed.chemistry.org.tw/?p=22310
邱美虹、江玉婷（1997）。初任與資深國中地球科學教師學科教學知識之比較。科學教育學刊，5(4)，419-459。
邱美虹、劉俊庚（2008）。從科學學習的觀點探討模型與建模能力。科學教育月刊，314，2-20。
國家教育研究院（2018）。十二年國民基本教育課程綱要－國民中小學暨普通型 高級中等學校（自然科學領域）。取自國家教育研究院網址https://reurl.cc/xzXQ4
張志康、邱美虹（2009）。建模能力分析指標的發展與運用—以電化學為例。科學教育學刊，17(4)，319-342。
陳瑞麟（2004）。科學理論版本的結構與發展。臺北：國立臺灣大學出版中心。
陳嘉成（1998）。合作學習式概念構圖在國小自然科教學之成效研究。教育與心理研究，21，107-128。
曾茂仁（2016）。探討建模本位探究教學於化學電池的學習成效與建模能力。（未出版碩士論文）。國立臺灣師範大學，臺北市。
黃文田（2013）。探討建模教學對八年級學生酸鹼概念發展與建模能力的影響。（未出版碩士論文）。國立臺灣師範大學，臺北市。
劉秀嫚（1998）。合作學習的教學策略。公民訓育學報，7，285-294。
劉俊庚（2011）。探討模型與建模對於學生園子概念學習之影響。（未出版碩士論文）。國立臺灣師範大學，臺北市。
簡紅珠（2002）。教師知識的不同詮釋與研究方法。課程與教學，5(3)，1-15。
鐘建坪（2013）。模型本位探究策略在不同場域學習成效之研究。（未出版碩士論文）。國立臺灣師範大學，臺北市。
Baird, D. (2004). Thing knowledge: A philosophy of scientific instruments. Berkeley and Los Angeles, California︰University of California.
Berry, A., Loughran, J., & Van Driel, J. H. (2008). Revisiting the roots of pedagogical content knowledge. International Journal of Science Education, 30(10), 1271-1279.
Buckley, B. C., & Boulter, C. J. (2000). Investigating the Role of Representations and Expressed Models in Building Mental Models. In J. K. Gilbert, & C. J. Boulter (Eds.), Developing Models in Science Education (pp. 119-135). Netherlands: Kluwer Academic Publishers.
Campbell, T., Oh, P. S., Maughn, M., Kiriazis, N., & Zuwallack, R. (2015). A review of Modeling Pedagogies: Pedagogical Functions, Discursive Acts, and Technology in Modeling Instruction. Eurasia Journal of Mathematics, Science & Technology Education, 11(1). 159-176.
Clement, J. (2000). Model based learning as a key research area for science education. International Journal of Science Education, 22(9), 1041–1053.
Crawford, B. A., &; Cullin, M. J. (2004). Supporting prospective teachers' conceptions of modelling in science. International Journal of Science Education, 26(11), 1379-1401.
Erduran, S., & Dagher, Z. R. (2014). Reconceptualizing the nature of science for science education: Scientific knowledge, practices and other family categories. Dordrecht: Springer.
Giere, R. N. (1988). Explaining Science: A Cognitive Approach. Chicago: University of Chicago Press.
Giere, R. N. (2004). How models are used to represent reality. Philosophy of Science, 71(5), 742–752.
Gilbert, J. K. (2004). Models and modelling: Routes to more authentic science education. International Journal of Science and Mathematics Education, 2(2), 115-130.
Gilbert, J. K. (2005). Visualization: A metacognitive skill in science and science education. In J. K. Gilbert (ed.), Visualization in Science Education (pp. 9-27). Dordrecht: Springer
Gilbert, J. K., & Justi, R. (2016). Learning Scientific Concepts from Modelling-Based Teaching. In J. K. Gilbert, & R. Justi (Eds.), Modelling-based Teaching in Science Education (pp. 81-96). Switzerland: Springer.
Gilbert, J. K., & Treagust, D. F. (2009). Introduction: Macro, submicro and symbolic representations and the relationship between them: key models in chemical education. In J. K. Gilbert, & D. Treagust (Eds.), Multiple representations in Chemical Education (pp. 1-8). Dordrecht: Springer.
Gilbert, J. K., Boulter, C. J., & Elmer, R. (2000). Positioning Models in Science Education and in Design and Technology Education. In J. K. Gilbert, & C. J. Boulter (Eds.), Developing Models in Science Education (pp. 3-17). Dordrecht: Springer.
Gilbert, S. W. (1991). Model building and a definition of science. Journal of research in science teaching, 28(1), 73-79.
Glynn, S. M., & Duit, R. (1995). Learning science in the schools: Research reforming practice. Mahwah, NJ: Lawrence Erlbaum Associates.
Graham, C. R., Borup, J., & Smith, N. B. (2012). Using TPACK as a framework to understand teacher candidates' technology integration decisions. Journal of Computer Assisted Learning, 28(6), 530-546.
Grant, G. E. (1992). The sources of structural metaphors in teacher knowledge: Three cases. Teaching and Teacher Education, 8(5), 433-440.
Grgurina, N., Barendsen, E., Suhre, C., van Veen, K., & Zwaneveld, B. (2017). Investigating informatics teachers' initial pedagogical content knowledge on modeling and simulation. In A. Hellas, & V. Dagienė (Eds.), Informatics in Schools: Focus on Learning Programming (pp. 65-76). Cham: Springer.
Grosslight, L., Unger, C., Jay, E., & Smith, C. L. (1991). Understanding models and their use in science: Conceptions of middle and high school students and experts. Journal of Research in Science Teaching, 28(9), 799-822.
Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
Grünkorn, J., zu Belzen, A. U., & Krüger, D. (2014). Assessing students' understandings of biological models and their use in science to evaluate a theoretical framework. International Journal of Science Education, 36(10), 1651-1684.
Günther, S. L., Fleige, J., zu Belzen, A. U., & Krüger, D. (2019). Using the Case Method to Foster Preservice Biology Teachers' Content Knowledge and Pedagogical Content Knowledge Related to Models and Modeling. Journal of Science Teacher Education, 30(4), 321-343.
Halloun, I. (1996). Schematic modeling for meaningful learning of physics. Journal of Research in Science Teaching, 33(9), 1019-1041.
Harrison, A. G., & Treagust, D. F. (2000). A typology of school science models. International Journal of Science Education, 22(9), 1011-1026.
Hartmann, S. (1999). Models and stories in Hadron physics. In M. S. Morgan, M. Morrison, & Q. Skinner (Eds.), Models as mediators: perspectives on natural and social science (pp. 326-346). New York: Cambridge University Press.
Henze, I., van Driel, J. H., & Verloop, N. (2007). Science teachers' knowledge about teaching models and modelling in the context of a new syllabus on public understanding of science. Research in Science Education, 37(2), 99-122.
Henze, I., Van Driel, J. H., & Verloop, N. (2008). Development of experienced science teachers' pedagogical content knowledge of models of the solar system and the universe. International Journal of Science Education, 30(10), 1321-1342.
Hestenes, D. ( 1995). Modeling software for learning and doing physics. In C. Benardini, C. Tarsitani, & M. Vincentini (Eds.), Thinking physics for Teaching (pp. 25-66). New York: Plenum Press.
Hestenes, D. (1987). Toward a modeling theory of physics instruction. American journal of physics, 55(5), 440-454.
Hodson, D. (1992). In search of a meaningful relationship: an exploration of some issues relating to integration in science and science education. International Journal of science education, 14(5), 541-562.
Hsu, Y. S., Lin, L. F., Wu, H. K., Lee, D. Y., & Hwang, F. K. (2012). A novice-expert study of modeling skills and knowledge structures about air quality. Journal of Science Education and Technology, 21(5), 588-606.
Johnson, D. W., Johnson, R. T., & Holubec, E. J. (1994). Cooperative learning in the classroom. Alexandria, VA: ASCD.
Johnstone, A. H. (1993). The development of chemistry teaching: A changing response to changing demand. Journal of chemical education, 70(9), 701-705.
Jong, J. P. (2016). The effect of a blended collaboratıve learnıng envıronment ın a small prıvate onlıne course (SPOC): A comparıson wıth a lecture course. Journal of Baltic Science Education, 15(2). 194-203.
Justi, R. S., & Gilbert, J. K. (2003), Teachers' views on the nature of models. International Journal of Science Education, 25(11), 1369-1386.
Justi, R. S., & Gilbert, J. K. (2002a). Modelling, teachers' views on the nature of modelling, and implications for the education of modellers. International Journal of Science Education, 24(4), 369-387.
Justi, R. S., & Gilbert, J. K. (2002b). Science teachers' knowledge about and attitudes towards the use of models and modelling in learning science. International Journal of science education, 24(12), 1273-1292.
Justi, R., & Van Driel, J. (2005a). A case study of the development of a beginning chemistry teacher's knowledge about models and modelling. Research in Science Education, 35(2-3), 197-219.
Justi, R., & Van Driel, J. (2005b). The development of science teachers' knowledge on models and modelling: promoting, characterizing, and understanding the process. International Journal of Science Education, 27(5), 549-573.
Justi, R., Chamizo Guerrero, J. A., García Franco, A., & Figueirêdo, K. L. (2011). Experiencias de formación de profesores de ciencias latinoamericanos sobre modelos y modelaje. Enseñanza de las Ciencias, 29(3), 413-426.
Kenyon, L., Davis, E. A., & Hug, B. (2011). Design approaches to support preservice teachers in scientific modeling. Journal of Science Teacher Education, 22(1), 1-21.
Knuuttila, T. (2011). Modelling and representing: An artefactual approach to model-based representation. Studies in History and Philosophy of Science Part A, 42(2), 262-271.
Lin, J. W. (2014). Elementary school teachers' knowledge of model functions and modeling processes: A comparison of science and non-science majors. International Journal of Science and Mathematics Education, 12(5), 1197-1220.
Lin, J. W., & Chiu, M. H. (2007). Exploring the characteristics and diverse sources of students' mental models of acids and bases. International Journal of Science Education, 29(6), 771-803.
Louca, L. T., Zacharia, Z. C., & Constantinou, C. P. (2011). In Quest of productive modeling‐based learning discourse in elementary school science. Journal of Research in Science Teaching, 48(8), 919-951.
Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources, and development of pedagogical content knowledge for science teaching. In J. Gess-Newsome, & N.G. Lederman (Eds.), Examining pedagogical content knowledge (pp. 95-132). Dordrecht, Netherlands: Kluwer Academics.
Maia, P. F., & Justi, R. (2009). Learning of chemical equilibrium through modelling‐based teaching. International Journal of Science Education, 31(5), 603-630.
Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.
Namdar, B., & Shen, J. (2015). Modeling-oriented assessment in K-12 science education: A synthesis of research from 1980 to 2013 and new directions. International Journal of Science Education, 37(7), 993-1023.
National Research Council. (1996). National science education standards. Washington, DC: National Academic Press.
National Research Council. (2012). A framework for K-12 science education: Practices, crosscutting concepts, and core ideas. Washington, DC: National Academic Press.
Nelson, M. M., & Davis, E. A. (2012). Preservice Elementary Teachers' Evaluations of Elementary Students' Scientific Models: An aspect of pedagogical content knowledge for scientific modeling. International Journal of Science Education, 34(12), 1931-1959.
Nersessian, N. J. (2002). The cognitive basis of model-based reasoning in science. In P. Carruthers, S. Stich, & M.Siegal (Eds.), The Cognitive Basis of Science (pp. 133-153) . Cambridge: Cambridge University Press.
Nicolaou, C. T., & Constantinou, C. P. (2014). Assessment of the modeling competence: A systematic review and synthesis of empirical research. Educational Research Review, 13, 52-73.
Oh, P. S., & Oh, S. J. (2011). What teachers of science need to know about models: An overview. International Journal of Science Education, 33(8), 1109-1130.
Oversby, J. (2000). Models in explanations of chemistry: The case of acidity. In J. K. Gilbert, & C. J. Boulter (Eds.), Developing Models in Science Education (pp. 227-251). Dordrecht: Springer.
Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in science Education, 38(3), 261-284.
Park, S., Jang, J. Y., Chen, Y. C., & Jung, J. (2011). Is pedagogical content knowledge (PCK) necessary for reformed science teaching?: Evidence from an empirical study. Research in Science Education, 41(2), 245-260.
Rolinick, M., Bennett, J., Rhemtula, M., Dharsey, N., & Ndlovu, T. (2008). The place of subject matter knowledge in pedagogical content knowledge: A case study of South African teachers teaching the amount of substance and chemical equilibrium. International Journal of Science Education, 30(10), 1365-1387.
Saari, H., & Viiri, J. (2003). A research‐based teaching sequence for teaching the concept of modelling to seventh‐grade students. International Journal of Science Education, 25(11), 1333-1352.
Schwartz, R. S., & Lederman, N. G. (2002). “It's the nature of the beast”: The influence of knowledge and intentions on learning and teaching nature of science. Journal of Research in Science Teaching, 39(3), 205-236.
Schwarz, C. (2009). Developing preservice elementary teachers' knowledge and practices through modeling‐centered scientific inquiry. Science Education, 93(4), 720-744.
Schwarz, C. V., & Gwekwerere, Y. N. (2007). Using a guided inquiry and modeling instructional framework (EIMA) to support preservice K-8 science teaching. Science education, 91(1), 158-186.
Schwarz, C. V., & White, B. Y. (2005). Metamodeling knowledge: Developing students' understanding of scientific modeling. Cognition and Instruction, 23(2), 165-205.
Schwarz, C. V., Reiser, B. J., Davis, E. A., Kenyon, L., Achér, A., Fortus, D., ... & Krajcik, J. (2009). Developing a learning progression for scientific modeling: Making scientific modeling accessible and meaningful for learners. Journal of Research in Science Teaching, 46(6), 632-654.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of new reform. Harvard educational review, 57(1), 1-23.
Sins, P. H. M., Savelsbergh, E. R., & van Joolingen, W. R. (2005). The Difficult Process of Scientific Modelling: An analysis of novices' reasoning during computer‐based modelling. International Journal of Science Education, 27(14), 1695–1721.
Tamir, P. (1988). Subject matter and related pedagogical knowledge in teacher education. Teaching and teacher education, 4(2), 99-110.
Thagard, P. (2010). How brains make mental models. In L. Magnani, W. Carnielli, & C. Pizzi (Eds.), Model-based reasoning in science and technology (pp. 447-461). Berlin, Germany: Springer.
Treagust, D. F., Chittleborough, G., & Mamiala, T. L. (2002). Students' understanding of the role of scientific models in learning science. International Journal of Science Education, 24(4), 357-368.
Tregidgo, D., & Ratcliffe, M. (2000). The Use of Modelling for Improving Pupils' Learning about Cells. School Science Review, 81(296), 53-59.
Upmeier zu Belzen, A., & Krüger, D. (2010). Model competence in biology class. Journal of Teaching Methods on Natural Science, 16, 41-57.
Van Driel, J. H., & Verloop, N. (1999). Teachers' knowledge of models and modelling in science. International Journal of Science Education, 21(11), 1141-1153.
Van Driel, J. H., & Verloop, N. (2002). Experienced teachers' knowledge of teaching and learning of models and modelling in science education. International Journal of Science Education, 24(12), 1255-1272.
Van Driel, J. H., Verloop, N., & De Vos, W. (1998). Developing science teachers' pedagogical content knowledge. Journal of Research in Science Teaching, 35(6), 673-695.
van Joolingen, W. (2004). Roles of modeling in inquiry learning. In IEEE Computer Society (ed.), ICALT 2004 - Proceedings of the IEEE International Conference on Advanced Learning Technologies (pp. 1096-1097). Joensuu, Finland: IEEE Computer Society.
Vieira, R. M., & Tenreiro-Vieira, C. (2016). Fostering scientific literacy and critical thinking in elementary science education. International Journal of Science and Mathematics Education, 14(4), 659-680.
Wang, Z., Chi, S., Hu, K., & Chen, W. (2014). Chemistry teachers' knowledge and application of models. Journal of Science Education and Technology, 23(2), 211-226.