Mathematical Competencies in the Digital Era: An Introduction

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Mathematical Competencies in the Digital Era

Abstract

Mathematics education has been experiencing two rather distinct, yet related, ‘paradigm shifts’. The first is to do with the massive introduction of digital technologies (DT) in the teaching and learning of the subject (e.g., Trouche et al., 2013); the second is to do with a shift from the traditional focusing on mastering of skills and knowledge to being concerned with the possession and development of mathematical competencies (e.g., Stacey, 2010; Stacey & Turner, 2015). This book focuses on the potential interplay between these two paradigm shifts by considering the connection of different theoretical perspectives, e.g., by drawing on the notion of ‘networking of theories’ (e.g., Bikner-Ahsbahs & Prediger, 2010; Prediger et al., 2008).

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References

  • Bartolini-Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed.), (pp. 746–783). Routledge. https://doi.org/10.4324/9780203930236

  • Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking of theories—An approach for exploiting the diversity of theoretical approaches. In B. Sriraman, & L. English (Eds.), Theories of mathematics education: Seeking new Frontiers (pp. 483–506). Springer-Verlag. https://doi.org/10.1007/978-3-642-00742-2_46

  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work—Experiences from an in-service course for upper secondary teachers. ZDM Mathematics Education, 38, 163–177. https://doi.org/10.1007/BF02655887

    Article  Google Scholar 

  • Chevallard, Y. (2007). Un concept en émergence: la dialectique des médias et des milieux. In G. Gueudet, & Y. Matheron (Eds.), Actes du séminaire national de didactique des mathématiques (pp. 344–366), ARDM et IREM de Paris 7.

    Google Scholar 

  • Drijvers, P. (2015). Digital technology in mathematics education: Why it works (or doesn’t). In S. J. Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education (pp. 135–151). Springer Verlag. https://doi.org/10.1007/978-3-319-17187-6_8

  • Drijvers, P. (2019). Embodied instrumentation: Combining different views on using digital technology in mathematics education. In U. T. Jankvist, M. Van den Heuvel-Panhuizen & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 8–28). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

    Google Scholar 

  • Drijvers, P., Godino, J. D., Font, V., & Trouche, L. (2013). One episode, two lenses: A reflective analysis of student learning with computer algebra from instrumental and onto-semiotic perspectives. Educational Studies in Mathematics, 82(1), 23–49. https://doi.org/10.1007/s10649-012-9416-8

  • Geraniou, E., & Jankvist, U. T. (2019). Towards a definition of “mathematical digital competency.” Educational Studies in Mathematics, 102(1), 29–45. https://doi.org/10.1007/s10649-019-09893-8

    Article  Google Scholar 

  • Geraniou, E., & Misfeldt, M. (2022). The mathematical competencies framework and digital technologies. In U. T. Jankvist, & E. Geraniou, (Eds.), Mathematical competencies in the digital era (pp. 39–60). Springer.

    Google Scholar 

  • Guin, D., & Trouche, L. (1998). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195–227. https://doi.org/10.1023/A:1009892720043

    Article  Google Scholar 

  • Guin, D., & Trouche, L. (2002). Mastering by the teacher of the instrumental genesis in CAS environments: Necessity of instrumental orchestration. ZDM Mathematics Education, 34(5), 204–211. https://doi.org/10.1007/BF02655823

    Article  Google Scholar 

  • Jankvist, U. T., & Misfeldt, M. (2015). CAS-induced difficulties in learning mathematics? For the Learning of Mathematics, 35(1), 15–20.

    Google Scholar 

  • Jankvist, U. T., Misfeldt, M., & Aguilar, M. S. (2019). What happens when CAS-procedures are objectified?—The case of “solve” and “desolve.” Educational Studies in Mathematics, 101(1), 67–81. https://doi.org/10.1007/s10649-019-09888-5

    Article  Google Scholar 

  • Køppe, S. (2008). En moderat eklecticisme. [A moderate eclecticism.] Psyke & Logos, 29(1), 15–35.

    Google Scholar 

  • Matematikkommissionen (2016). Matematikkommissionen – afrapportering. Retrieved from: http://gymnasieskolen.dk/sites/default/files/matematikkommissionen_afrapportering.pdf

  • Niss, M., & Højgaard, T. (2011). Competencies and mathematical learning—Ideas and inspiration for the development of mathematics teaching and learning in Denmark (No. 485). IMFUFA, Roskilde University. English translation of part I-VI of Niss and Jensen (2002).

    Google Scholar 

  • Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9–28. https://doi.org/10.1007/s10649-019-09903-9

    Article  Google Scholar 

  • Niss, M., & Jankvist, U. T. (2022). On the mathematical competencies framework and its potentials for connecting with other theoretical perspectives. In U. T. Jankvist, & E. Geraniou, (Eds.), Mathematical competencies in the digital era (pp. 15–38). Springer.

    Google Scholar 

  • Niss, M., & Jensen, T. H. (2002). Kompetencer og matematiklæring—Ideer og inspiration til udvikling af matematikundervisning i Danmark [Competencies and mathematical learning—Ideas and inspiration for the development of mathematics teaching and learning in Denmark]. The Ministry of Education.

    Google Scholar 

  • O’Connell, D. C., & Kowal, S. (2012). Dialogical genres. Empractical and conversational listening and speaking. Springer. https://doi.org/10.1007/978-1-4614-3529-7

  • OECD. (2013). PISA 2012 assessment and analytical framework: Mathematics. OECD Publishing. https://doi.org/10.1787/9789264190511-en

    Book  Google Scholar 

  • OECD. (2015). Students, computers and learning—Making the connection. OECD Publishing.

    Book  Google Scholar 

  • Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches—First steps towards a conceptual framework. ZDM Mathematics Education, 40(2), 165–178. https://doi.org/10.1007/s11858-008-0086-z

    Article  Google Scholar 

  • Santos-Trigo, M., & Camacho Machín, M. (2013). Framing the use of computational technology in problem solving approaches. The Mathematics Enthusiast, 10(1–2), 279–302.

    Google Scholar 

  • Stacey, K. (2010). Mathematical and scientific literacy around the world. Journal of Science and Mathematics Education in Southeast Asia, 33(1), 1–16.

    Google Scholar 

  • Stacey, K., & Turner, R. (Eds.) (2015). Assessing mathematical literacy—The PISA experience. Springer. https://doi.org/10.1007/978-3-319-10121-7

  • Toulmin, S. E. (2003). The uses of argument: Updated edition (2nd ed.). Cambridge University Press.

    Google Scholar 

  • Trouche, L. (2005). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 197–230). Springer. https://doi.org/10.1007/b101602

  • Trouche, L., Drijvers, P., Gueudet, G., & Sacristán, A. I. (2013). Technology driven developments and policy implications for mathematics education. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 753–789). Springer. https://doi.org/10.1007/978-1-4614-4684-2

  • Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52(2), 83–94. https://doi.org/10.1159/000202727

    Article  Google Scholar 

  • Weigand, H.-G. (2014). Looking back and ahead—Didactical implications for the use of digital technologies in the next decade. Teaching Mathematics and Its Applications, 33(1), 3–15. https://doi.org/10.1093/teamat/hru006

    Article  Google Scholar 

  • Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U. (2016). Defining computational thinking for mathematics and science classrooms. Journal of Science Education and Technology, 25(1), 127–147. https://doi.org/10.1007/s10956-015-9581-5

    Article  Google Scholar 

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Ackowledgements

This book was partly prepared in the frame of project 8018-00062B under Independent Research Fund Denmark.

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Correspondence to Uffe Thomas Jankvist .

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Jankvist, U.T., Geraniou, E., Pedersen, M.K., Bach, C.C., Gregersen, R.M. (2022). Mathematical Competencies in the Digital Era: An Introduction. In: Jankvist, U.T., Geraniou, E. (eds) Mathematical Competencies in the Digital Era. Mathematics Education in the Digital Era, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-031-10141-0_1

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  • DOI: https://doi.org/10.1007/978-3-031-10141-0_1

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