Article

Examination of modelling in K-12 STEM teacher education: Connecting theory with practice


  • Received: 01 September 2021 Revised: 01 November 2021
  • The goal of this paper is to examine the place of modelling in STEM education and teacher education. First, we introduce modelling as a cyclical process of generating, testing, and applying knowledge while highlighting the epistemological commonalities and differences between the STEM disciplines. Second, we build on the four well-known frameworks, to propose an Educational Framework for Modelling in STEM, which describes both teacher and student roles in the modelling cycle. Third, we use this framework to analyze how modelling is presented in the new mathematics and science school curricula in two Canadian provinces (Ontario and British Columbia), and how it could be implemented in teacher education. Fourth, we emphasize the epistemological aspects of the Educational Framework for Modelling in STEM, as disciplinary epistemological foundations may seem too abstract to both teacher educators and teachers of STEM school subjects. Yet, epistemologies are the driving forces within each discipline and must be considered while teaching STEM as a unified field. To nurture critical thinkers and innovators, it is critical to pay attention to what knowledge is and how it is created and tested. The Educational Framework for Modelling in STEM may be helpful in introducing students and future teachers to the process of modelling, regardless of if they teach it in a single- or a multi-discipline course, such as STEM. This paper will be of interest to teacher educators, teachers, researchers, and policy makers working within and between the STEM fields and interested in promoting STEM education and its epistemological foundations.

    Citation: Dragana Martinovic, Marina Milner-Bolotin. Examination of modelling in K-12 STEM teacher education: Connecting theory with practice[J]. STEM Education, 2021, 1(4): 279-298. doi: 10.3934/steme.2021018

    Related Papers:

  • The goal of this paper is to examine the place of modelling in STEM education and teacher education. First, we introduce modelling as a cyclical process of generating, testing, and applying knowledge while highlighting the epistemological commonalities and differences between the STEM disciplines. Second, we build on the four well-known frameworks, to propose an Educational Framework for Modelling in STEM, which describes both teacher and student roles in the modelling cycle. Third, we use this framework to analyze how modelling is presented in the new mathematics and science school curricula in two Canadian provinces (Ontario and British Columbia), and how it could be implemented in teacher education. Fourth, we emphasize the epistemological aspects of the Educational Framework for Modelling in STEM, as disciplinary epistemological foundations may seem too abstract to both teacher educators and teachers of STEM school subjects. Yet, epistemologies are the driving forces within each discipline and must be considered while teaching STEM as a unified field. To nurture critical thinkers and innovators, it is critical to pay attention to what knowledge is and how it is created and tested. The Educational Framework for Modelling in STEM may be helpful in introducing students and future teachers to the process of modelling, regardless of if they teach it in a single- or a multi-discipline course, such as STEM. This paper will be of interest to teacher educators, teachers, researchers, and policy makers working within and between the STEM fields and interested in promoting STEM education and its epistemological foundations.



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    [1]

    Government of Canada, The Government of Canada and STEM, Government of Canada, 2018, Ottawa.

    [2]

    Government of the United Kingdom, STEM Strategy, 2018, London, U.K.

    [3]

    Timms, M., et al., Challenges in STEM learning in Australian schools: Literature and policy review, Australian Council for Educational Research (ACER), 2018, Camberwell, VIC.

    [4]

    Hallström, J. and K.J. Schönborn, Models and modelling for authentic STEM education: Reinforcing the argument. International Journal of STEM Education, 2019. 6: 22. https://doi.org/10.1186/s40594-019-0178-z.

    doi: 10.1186/s40594-019-0178-z
    [5]

    Haines, C., P. Galbraith, and W. Blume. Mathematical Modelling: Education, Engineering and Economics - ICTMA 12. in Twelfth International Conference on the Teaching of Mathematical Modelling and Applications. 2007. City University London: Horwood Publishing.

    [6]

    Kaiser, G., M. Blomhøj, and B. Sriraman, Towards a didactical theory for mathematical modelling. ZDM, 2006. 38(2): 82-85. https://doi.org/10.1007/BF02655882.

    doi: 10.1007/BF02655882
    [7]

    Blum, W. and D. Leiss. How to students and teachers deal with modelling problems? in Twelfth International Conference on the Teaching of Mathematical Modelling and Applications. 2005, pp. 222-231. London, UK: Hrowood Publishing.

    [8]

    Etkina, E., D.T. Brookes, and G. Planinsic, Investigative Science Learning Environment, Morgan & Claypool Publishers, 2019.

    [9]

    Milner-Bolotin, M., Promoting Deliberate Pedagogical Thinking with Technology in physics teacher education: A teacher-educator's journey, in The Physics Educator: Tacit Praxes and Untold Stories T.G. Ryan and K.A. McLeod, Editors. 2016, pp. 112-141. Champaign, IL: Common Ground and The Learner.

    [10]

    Milner-Bolotin, M. Reimagining technology-enhanced STEM teacher education for 21st century: From more technology to increased quality of teaching and learning (Part 1). in Future Schools 2030. 2016. Beijing, China: Beijing Advanced Innovation Centre for Future Education: Beijing Normal University.

    [11]

    Martinovic, D., Z. Karadag, and D. McDougall, Proceedings of the Fifth North American GeoGebra Conference: Explorative learning with technology: GeoGebra-NA 2014 in GeoGebra_NA 2014. 2014, pp. 102. Toronto, ON, Canada: University of Toronto.

    [12]

    Blum, W. Quality Teaching of Mathematical Modelling: What Do We Know, What Can We Do? 2015, pp. 73-96. Cham: Springer International Publishing.

    [13]

    Windschitl, M., J. Thompson, and M. Braaten, Beyond the scientific method: Model-based inquiry as a new paradigm of preference for school science investigations. Science Education, 2008. 92(5): 941-967. https://doi.org/10.1002/sce.20259.

    doi: 10.1002/sce.20259
    [14]

    Hofer, B.K., Personal epistemology research: Implications for learning and teaching. Educational Psychology Review, 2001. 13(4): 353-383. https://doi.org/10.1023/A:1011965830686.

    doi: 10.1023/A:1011965830686
    [15]

    Kolb, D.A., Experiential learning: Experience as the source of learning and development. Vol. 1. 1984, Englewood Cliffs, NJ: Prentice-Hall.

    [16]

    Gardiner, P., Learning to think together: Creativity, interdisciplinary collaboration and epistemic control. Thinking Skills and Creativity, 2020. 38: 100749.

    [17]

    Carlson, M.A., et al., A case for mathematical modeling in the elementary school classroom, in Mathematical modeling and modeling mathematics, C.R. Hirsch and A.R. McDuffie, Editors. 2016, pp. 121-129. Reston, VA: National Council of Teachers of Mathematics.

    [18]

    Ben-David Kolikant, Y., D. Martinovic, and M. Milner-Bolotin, Introduction: STEM teachers and teaching in the era of change, in STEM Teachers and Teaching in the Era of Change: Professional expectations and advancement in 21st Century Schools, Y. Ben-David Kolikant, D. Martinovic, and M. Milner-Bolotin, Editors. 2020, pp. 1-18. Cham, Switzerland: Springer.

    [19]

    National Research Council, Next Generation Science Standards: For States, by States, ed. Q. Helen, S. Heidi, and K. Thomas. 2013, Washington DC: The National Academies Press, USA National Research Council.

    [20]

    Brown, J.R. Logic, Epistemology, Philosophy of Science The Canadian Encyclopedia. The Canadian Encyclopedia: Historica Canada 2012 August 24, 2014[cited 2021 September 3]; Available from: https://www.thecanadianencyclopedia.ca/en/article/logic-epistemology-philosophy-of-science.

    [21]

    Erduran, S., Nature of "STEM"? Science & Education, 2020. 29(4): 781-784. https://doi.org/10.1007/s11191-020-00150-6.

    doi: 10.1007/s11191-020-00150-6
    [22]

    Reynante, B.M., M.E. Selbach-Allen, and D.R. Pimentel, Exploring the Promises and Perils of Integrated STEM Through Disciplinary Practices and Epistemologies. Science & Education, 2020. 29(4): 785-803. https://doi.org/10.1007/s11191-020-00121-x.

    doi: 10.1007/s11191-020-00121-x
    [23]

    Kalman, C.S., The need to emphasize epistemology in teaching and research. Science & Education, 2009. 18: 325-348. https://doi.org/10.1007/s11191-007-9135-1.

    doi: 10.1007/s11191-007-9135-1
    [24]

    Martinovic, D. and M. Milner-Bolotin, Discussion: Teacher Professional Development in the Era of Change, in STEM Teachers and Teaching in the Era of Change: Professional expectations and advancement in 21st Century Schools, Y. Ben-David Kolikant, D. Martinovic, and M. Milner-Bolotin, Editors. 2020, pp. 185-197. Cham, Switzerland: Springer.

    [25]

    Ben-David Kolikant, Y., D. Martinovic, and M. Milner-Bolotin, STEM Teachers and Teaching in the Digital Era: Professional expectations and advancement in 21st Century Schools, in STEM Teachers and Teaching in the Digital Era. 2020, pp. 325. Cham, Switzerland: Springer.

    [26]

    Yuan, Z. -Q., M. Milner-Bolotin, and D. Anderson, Lessons Learned from Educating STEM Teachers in Canadian Universities: The Case of the University of British Columbia. Journal of Mathematics Education, 2021. 30(6): 96-102.

    [27]

    British Columbia Ministry of Education, British Columbia New Curriculum, Government of British Columbia, 2020, Victoria, British Columbia, Canada.

    [28]

    Milner-Bolotin, M. and R. Zazkis, A study of future physics teachers' knowledge for teaching: A case of sound level and a decibel scale. LUMAT: International Journal on Math, Science and Technology Education, 2021. Submitted March 2021: 29.

    [29]

    Ontario Ministry of Education, The Ontario Mathematics Curriculum: Elementary, Government of Ontario, 2020, Toronto, ON.

    [30]

    Techbridge. Techbridge Girls. 2017; from: http://www.techbridgegirls.org/index.php?id=28.

    [31]

    Annett, C., Girls and Women in Science, Technology, Engineering and Mathematics, Government of Canada, 2017, Ottawa, Canada.

    [32]

    Milner-Bolotin, M., Increasing girls' participation in physics: Education research implications for practice. Physics in Canada, 2015. 71(2): 94-97.

    [33]

    Herranen, J.K., E.C. Fooladi, and M. Milner-Bolotin, Editorial: Special Issue "Promoting STEAM in Education". LUMAT: International Journal of Math, Science and Technology Education, 2021. 9(9): 1-8. https://doi.org/10.31129/LUMAT.9.2.1559.

    doi: 10.31129/LUMAT.9.2.1559
    [34]

    Perignat, E. and J. Katz-Buonincontro, STEAM in practice and research: An integrative literature review. Thinking Skills and Creativity, 2019. 31: 31-43. https://doi.org/10.1016/j.tsc.2018.10.002.

    doi: 10.1016/j.tsc.2018.10.002
    [35]

    Ge, X., D. Ifenhaler, and J.M. Spector, Emerging Technologies for STEAM Education: Full STEAM ahead. Educational Communications and Technologies: Issues and Innovations. 2015, New York: Springer.

    [36]

    Hourigan, M. and J. Donaghue, The challenges facing initial teacher education: Irish prospective elementary teachers' mathematics subject matter knowledge. International Journal of Mathematical Education in Science and Technology, 2013. 44(1): 36-58. https://doi.org/10.1080/0020739X.2012.690897.

    doi: 10.1080/0020739X.2012.690897
    [37]

    Zazkis, R. and D. Zazkis, The significance of mathematical knowledge in teaching elementary methods courses: Perspectives of mathematics teacher educators. Educational Studies in Mathematics, 2011. 76(3): 247-263.

    [38]

    Ma, L., Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and in the United States. Studies in mathematical thinking and learning series, ed. A.H. Schoenfeld. 1999, Mahwah, NJ: Lawrence Erlbaum Associates.

    [39]

    Berlin, D.F. and A.L. White, A longitudinal look at attitudes and perceptions related to the integration of Mathematics, Science, and Technology education. School Science and Mathematics, 2012. 112(1): 20-30. https://doi.org/10.1111/j.1949-8594.2011.00111.x.

    doi: 10.1111/j.1949-8594.2011.00111.x
    [40]

    Lee, M. -H. and C. -C. Tsai, Exploring teachers' perceived self efficacy and Technological Pedagogical Content Knowledge with respect to educational use of the World Wide Web. Instructional Science, 2010. 38(1): 1-21.

    [41]

    Martinovic, D. and M. Milner-Bolotin, Problematizing STEM: What it is, what it is not, and why it matters, in 15 Years of MACAS (Mathematics and its Connections to the Arts and Sciences), C. Michelsen, et al., Editors. 2022: Springer.

    [42]

    Marder, M., A problem with STEM. CBE Life Sciences Education, 2013. 12(2): 148-150. https://doi.org/10.1187/cbe.12-12-0209.

    doi: 10.1187/cbe.12-12-0209
    [43]

    Martinez, M.E., Learning and Cognition: The Design of the Mind. 2010: Pearson.

    [44]

    Ortiz-Revilla, J., A. Adúriz-Bravo, and I.M. Greca, A framework for epistemological discussion on integrated STEM education. Science & Education, 2020. 29: 857-880. https://doi.org/10.1007/s11191-020-00131-9.

    doi: 10.1007/s11191-020-00131-9
    [45]

    Barquero, B., M. Bosch, and A. Romo, Mathematical modelling in teacher education: dealing with institutional constraints. ZDM, 2018. 50(1): 31-43. https://doi.org/10.1007/s11858-017-0907-z.

    doi: 10.1007/s11858-017-0907-z
    [46]

    Frejd, P., Teachers' conceptions of mathematical modelling at Swedish Upper Secondary school. Journal of Mathematical Modelling and Application, 2012. 1(5): 17-40.

    [47]

    Ortiz, J. and A.D. Santos, Mathematical Modelling in Secondary Education: A Case Study, in Trends in Teaching and Learning of Mathematical Modelling, K. G., et al., Editors. 2011. Dordrecht. : Springer.

    [48]

    Ärlebäck, J.B. and C. Bergsten, On the Use of Realistic Fermi Problems in Introducing Mathematical Modelling in Upper Secondary Mathematics, in Modeling Students' Mathematical Modeling Competencies: ICTMA 13, R. Lesh, et al., Editors. 2013, pp. 597-609. Dordrecht: Springer Netherlands.

    [49]

    Hestenes, D., Modeling Theory for Math and Science Education, in Modeling Students' Mathematical Modeling Competencies: ICTMA 13, R. Lesh, et al., Editors. 2010, pp. 13-41. Boston, MA: Springer US.

    [50]

    English, L.D. and N.G. Mousoulides, Engineering-Based Modelling Experiences in the Elementary and Middle Classroom, in Models and Modeling: Cognitive Tools for Scientific Enquiry, M.S. Khine and I.M. Saleh, Editors. 2011, pp. 173-194. Dordrecht: Springer Netherlands.

    [51]

    Gil, E. and A.L. Gibbs, Promoting modelling and covariational reasoning among secondary school students in the context of big data. Statistics Education Research Journal, 2017. 16(2): 163-190.

    [52]

    Healey, M. and A. Jenkins, Kolb's Experiential Learning Theory and Its Application in Geography in Higher Education. Journal of Geography, 2000. 99(5): 185-195. https://doi.org/10.1080/00221340008978967.

    doi: 10.1080/00221340008978967
    [53]

    Kolb, A. and D. Kolb, Eight important things to know about The Experiential Learning Cycle. AEL, 2018. 40(3): 8-14.

    [54]

    Abdulwahed, M. and Z.K. Nagy, Applying Kolb's Experiential Learning Cycle for Laboratory Education. Journal of Engineering Education, 2009. 98(3): 283-294. https://doi.org/10.1002/j.2168-9830.2009.tb01025.x.

    doi: 10.1002/j.2168-9830.2009.tb01025.x
    [55]

    Seaman, J., Experience, Reflect, Critique: The End of the "Learning Cycles" Era. Journal of Experiential Education, 2008. 31(1): 3-18. https://doi.org/10.1177/105382590803100103.

    doi: 10.1177/105382590803100103
    [56]

    Morris, T.H., Experiential learning – a systematic review and revision of Kolb's model. Interactive Learning Environments, 2020. 28(8): 1064-1077. https://doi.org/10.1080/10494820.2019.1570279.

    doi: 10.1080/10494820.2019.1570279
    [57]

    Bergsteiner, H., G.C. Avery, and R. Neumann, Kolb's experiential learning model: critique from a modelling perspective. Studies in Continuing Education, 2010. 32(1): 29-46. https://doi.org/10.1080/01580370903534355.

    doi: 10.1080/01580370903534355
    [58]

    Weinstein Webb, M., A definitive critique of experiential learning theory (Doctoral qualifying thesis), Case Western Reserve University, 1980.

    [59]

    Lesh, R., R. Young, and T. Fennewald, Modeling in K-16 Mathematics Classrooms – and Beyond, in Modeling Students' Mathematical Modeling Competencies: ICTMA 13, R. Lesh, et al., Editors. 2010, pp. 275-283. Boston, MA: Springer US.

    [60]

    British Columbia Ministry of Education, Curriculum Redesign, British Columbia Ministry of Education, 2021, Victoria, BC, Canada

    [61]

    Jensen, H.T., Communication: The essential difference between mathematical modeling and problem solving, in Modeling students' mathematical modeling competencies: ICTMA 13, R. Lesh, et al., Editors. 2010, pp. 255-264. New York, NY: Springer.

    [62]

    Driver, R., P. Newton, and J. Osborne, Establishing the norms of scientific argumentation in classrooms. Science Education, 2000. 84(3): 287-312.

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