Skip to main content

Sense-Making in Mathematical Modelling and Applications Educational Research and Practice

  • Chapter
  • First Online:
Mathematical Modelling Education and Sense-making

Abstract

This latest contribution from members of the ICTMA research community focusses on how students, teachers, tertiary educators, and researchers make sense of mathematical modelling and applications educational research and practice. Innovative approaches in modelling educational research and research into and evaluation of teaching practice are showcased; pedagogical issues, assessment, and applicability at different levels of education relating to modelling and applications are investigated; and examples of modelling and applications in educational practice are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), Proceedings of ICME 12 (pp. 73–96). Cham: Springer Open.

    Google Scholar 

  • Borromeo Ferri, R., & Blum, W. (2010). Mathematical modelling in teacher education-experiences from a modelling seminar. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of CERME 6 (pp. 2046–2055). Lyon: Institut national de recherche pédagogique.

    Google Scholar 

  • Bourdieu, P. (1972). Outline of a theory of practice. Cambridge: Cambridge University Press.

    Google Scholar 

  • Bourdieu, P. (1986). The forms of capital. In J. Richardson (Ed.), Handbook of theory and research for the sociology of education (pp. 241–258). Westport: Greenwood.

    Google Scholar 

  • Bourdieu, P. (1990). In other words, essays towards a reflexive sociology. Stanford: Stanford University Press.

    Book  Google Scholar 

  • Doerr, H. M., & Lesh, R. (2011). Models and modelling perspectives on teaching and learning mathematics in the twenty-first century. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 247–268). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Orienta-Konsultit: Helsinki.

    Google Scholar 

  • Greefrath, G., Hertleif, C., & Siller, H.-S. (2018). Mathematical modelling with digital tools—A quantitative study on mathematising with dynamic geometry software. ZDM Mathematics Education, 50(1–2), 233–244.

    Article  Google Scholar 

  • Hagena, M. (2015). Improving mathematical modelling by fostering measurement sense: An intervention study with pre-service mathematics teachers. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 185–194). Cham: Springer.

    Chapter  Google Scholar 

  • Hankeln, C., Adamak, G., & Greefrath, G. (2019). Assessing sub-competencies of mathematical modelling – Development of a new test instrument. In G. A. Stillman & J. P. Brwon (Eds.), Lines of inquiry in mathematical modelling research in education, ICME-13 monographs (pp. 143–160). Cham: Springer Open.

    Google Scholar 

  • Julie, C. (2015). Learners’ dealing with a financial application-like problem in a high-stakes school-leaving mathematics examination. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 477–486). Cham: Springer.

    Chapter  Google Scholar 

  • Keazer, L. M., & Menon, R. S. (2015/6)). Reasoning and sense making begins with the teacher. Mathematics Teacher, 109(5), 342–349.

    Article  Google Scholar 

  • Klein, G., Moon, B., & Hoffer, R. R. (2006). Making sense of sensemaking 1: Alternative perspectives. IEEE Intelligent Systems, 21(4), 70–73.

    Article  Google Scholar 

  • Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Research Journal, 32(3), 465–491.

    Google Scholar 

  • Lesh, R. A., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism (pp. 35–58). Mahwah: Erlbaum.

    Chapter  Google Scholar 

  • Malthus, T. (1798). An essay on the principle of population as it affects the future improvement of society, with remarks on the speculations of Mr. Godwin, M. Condorcet, and other writers. Available from https://oll.libertyfund.org/titles/malthus-an-essay-on-the-principle-of-population-1798-1st-ed

  • Mercer, N. (2013). The social brain, language, and goal-directed collective thinking: A social conception of cognition and its implications for understanding how we think, teach, and learn. Educational Psychologist, 48(3), 148–168.

    Article  Google Scholar 

  • National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author.

    Google Scholar 

  • NCTM. (2009). Executive summary. In Focus in high school mathematics: Reasoning and sense making. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Organisation for Economic Co-operation and Development (OECD). (2013). PISA 2012 assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. Paris: OECD Publishing. https://doi.org/10.1787/9789264190511-en.

    Book  Google Scholar 

  • Paulhan, F. (1928). Qu’est-ce le sens de mots? Journal de Psychologie, 25, 289–329.

    Google Scholar 

  • Psycharis, G., & Potari, D. (2017). Mathematics teachers’ learning at the boundaries of teaching and workplace. In G. A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 301–312). Cham: Springer.

    Chapter  Google Scholar 

  • Rosa, M., & Orey, D. (2015). Ethnomodelling as a research lens on ethnomathematics and modelling. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 117–127). Dordrecht: Springer.

    Google Scholar 

  • Rosa, M., & Orey, D. (2017). Ethnomodelling as the mathematization of cultural practices. In G. A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 153–163). Cham: Springer.

    Chapter  Google Scholar 

  • Schukajlow, S., Kolter, J., & Blum, W. (2015). Scaffolding mathematical modelling with a solution plan. ZDM Mathematics Education, 47(7), 1241–1254.

    Article  Google Scholar 

  • Schukajlow, S., Kaiser, G., & Stillman, G. (2018). Empirical research on teaching and learning of mathematical modelling: A survey on the current state-of-the-art. ZDM Mathematics Education, 50(1–2), 5–18.

    Article  Google Scholar 

  • Stevenson, A., & Waite, M. (2011). Concise Oxford English dictionary (12th ed.). Oxford: Oxford University Press.

    Google Scholar 

  • Treffert-Thomas, S., Viirman, O., Hernandez-Martinez, P., & Rogovchenko, Y. (2017). Mathematics lecturers’ views on the teaching of mathematical modelling. Nordic Studies in Mathematics Education, 22(4), 121–145.

    Google Scholar 

  • Vos, P. (2013). Assessment of modelling in mathematics examination papers: Ready-made models and reproductive mathematising. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 479–488). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Vygotsky, L. (1934/1986). Thought and language. (A. Kozulin, Ed. & Trans.). Cambridge, MA: The MIT Press.

    Google Scholar 

  • Weick, K. E. (2001). Making sense of the organization. Maldon: Wiley-Blackwell.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gloria Ann Stillman .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Stillman, G.A., Kaiser, G., Lampen, E. (2020). Sense-Making in Mathematical Modelling and Applications Educational Research and Practice. In: Stillman, G.A., Kaiser, G., Lampen, C.E. (eds) Mathematical Modelling Education and Sense-making. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-030-37673-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-37673-4_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-37672-7

  • Online ISBN: 978-3-030-37673-4

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics