A study of the role of data in statistical and mathematical modelling
DOI:
https://doi.org/10.7146/nomad.v30i4.164194Keywords:
mathematicsAbstract
This paper examines the role of data in mathematical and statistical modelling, addressing its importance for students’ inquiry in mathematics education. The study focuses on how students’ actions with data contribute to delimiting problems, constructing models, and validating results. We revisit two Danish case studies: grade five students investigating physical activity with TinkerPlots and upper secondary students designing a facial recognition system with GeoGebra. Using the anthropological theory of the didactic, we analyse students’ question–answer processes, milieus, and data moves. Findings show that data served as a driver for inquiry, enabling autonomy and innovation, but also highlighted the need for orchestration and teacher support to develop conceptual understanding. The study underlines potentials and challenges of integrating data-driven modelling in school settings.
References
Ärlebäck, J. B., Frejd, P., & Doerr, H. M. (2021). Exploring students’ models of sampling and inference with nominal variables. Quadrante, 30(1), 158–177. https://doi.org/10.48489/quadrante.23655
Artigue, M., Bosch, M., Doorman, M., Juhász, P., Kvasz, L., & Maass, K. (2020). Inquiry based mathematics education and the development of learning trajectories. Teaching Mathematics and Computer Science, 18(3), 63–89. https://doi.org/10.5485/TMCS.2020.0505
Bakker, A. (2018). Design research in education: A practical guide for early career researchers. Routledge. https://doi.org/10.4324/9780203701010
Barquero, B., Bosch, M., & Gascón, J. (2013). The ecological dimension in the teaching of mathematical modelling at university. Recherches en didactique des mathématiques, 33(3), 307–338.
Barquero, B., & Jessen, B. E. (2020). Impact of theoretical perspectives on the design of mathematical modelling tasks. Avances de Investigacion en Educacion Matematica, 17, 98-113.
https://doi.org/10.35763/AIEM.V0I17.317
Berget, I. K. L. (2022). Mathematical modelling in textbook tasks and national examination in Norwegian upper secondary school. Nordic Studies in Mathematics Education, 27(1), 51-70.
Blomhøj, M. & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. ZDM Mathematics Education, 38, 163–177.
https://doi.org/10.1007/BF02655887
Bosch, M. & Winsløw, C. (2016). Linking problem solving and mathematical contents: the challenge of sustainable study and research processes. Recherches en Didactique des Mathématiques, 35(3), 357–401.
Bosch, M., Florensa, I., Markulin, K., & Ruiz-Munzon, N. (2022). Real or Fake Inquiries? Study and Research Paths in Statistics and Engineering Education. In R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, & C. Winsløw (Eds.), Practice-Oriented Research in Tertiary Mathematics Education. Advances in Mathematics Education. Springer.
https://doi.org/10.1007/978-3-031-14175-1_19
Büscher, C. (2019). Students’ development of measures. In G. Burrill & D. Ben-Zvi (Eds.), Topics and Trends in Current Statistics Education Research: International Perspectives, ICME-13 Monographs (pp. 27–50). Springer International Publishing. https://doi.org/10.1007/978-3-030-03472-6_2
Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 22-30). FUNDEMI IQS – Universitat Ramon Llull and ERME.
Chevallard, Y. (2008). Afterthoughts on a seeming didactic paradox. Cadre du Colloque International’Efficacité y équité en éducation (pp. 1-6).
Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: An attempt at a principled approach. Hiroshima Journal of Mathematics Education, 12, 71–114. https://doi.org/10.24529/hjme.1205
Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American Mathematical Monthly, 104(9), 801–823.
https://doi.org/10.1080/00029890.1997.11990723
Danish Ministry of Education. (2017). Matematik B – stx, august 2017, Bilag 112. https://www.uvm.dk/-/media/filer/uvm/gym-laereplaner-2017/stx/matematik-b-stx-august-2017-ua.pdf
Danish Ministry of Education. (2019). Matematik fælles mål. https://emu.dk/sites/default/files/2020-09/GSK_F%C3%A6llesM%C3%A5l_Matematik.pdf
Danish Ministry of Education. (2022). Vejledning til de tværgående kompetenceområder på de gymnasiale uddannelser. https://www.uvm.dk/-/media/filer/uvm/udd/gym/pdf22/juni/220629-vejledning-til-de-tvaergaaende-kompetenceomraader-paa-de-gymnasiale-uddannelser.pdf
Edwards, D. & Hamson, M. (2007). Guide to Mathematical Modelling. 2nd Ed. Industrial Press, Inc.
English, L.D. (2012) Data modelling with first-grade students. Educational Studies in Mathematics, 81, 15–30. https://doi.org/10.1007/s10649-011-9377-3
Fitzallen, N. E. (2013). Characterising students’ interaction with TinkerPlots. Technology Innovations in Statistics Education, 7(1).
https://escholarship.org/uc/item/5pv5j7m2
Freixanet, M. J., Alsina, M., & Bosch, M. (2023). Statistics inquiry and the students’ engagement in the change of paradigm. In P. Drijvers, C. Csapod, H. Palmér, K. Gosztonyi, & E. Kónya (Eds.), Thirteenth Congress of the European Society for Research in Mathematics Education. Alfréd Rényi Institute of Mathematics and ERME.
Frejd, P. (2013). An analysis of mathematical modelling in Swedish textbooks in upper secondary school. Nordic Studies in Mathematics Education, 18(3), 59–95.
Frejd, P. & Bergsten, C. (2016). Mathematical modelling as a professional task. Educational Studies in Mathematics, 91, 11–35.
https://doi.org/10.1007/s10649-015-9654-7
Garcia, F. J., Pérez, J. G., Higueras, L. R., & Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM Mathematics Education, 38, 226–246. https://doi.org/10.1007/BF02652807
Gattuso, L., & Ottaviani, M. G. (2011). Complementing mathematical thinking and statistical thinking in school mathematics. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics: Challenges for teaching and teacher education (pp. 121–132). Springer.
https://doi.org/10.1007/978-94-007-1131-0_15
GeoGebra Team. (2023). GeoGebra Classic (Version 6.0) [Computer software]. GeoGebra. https://www.geogebra.org/
Groshong, K. (2016). Different types of mathematical models. In C. R. Hirsch & A. R. McDuffie (Eds.), Annual Perspectives in Mathematics Education 2016: Mathematical modeling and modeling mathematics (pp. 17–24). National Council for Teachers of Mathematics.
Hakamata, R., Otaki, K., Fukuda, H., & Otani, H. (2022). Statistical modelling in the Brousseaunian guessing game: A case of teacher education in Japan. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics. Leibniz Universität.
Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic inquiry with data: Critical barriers to classroom implementation. Educational Psychologist, 27(3), 337–364. https://doi.org/10.1207/s15326985ep2703_5
Hansen, B., & Winsløw, C. (2011). Research and study course diagrams as an analytic tool: The case of bi-disciplinary projects combining mathematics and history. In Bosch, M., Gascón, J., Ruiz Olarría, A., Artaud, M., Bronner, A., Chevallard, Y., Cirade, G., Ladage, C. & Larguier, M. (Eds.) 3rd Conference of the Anthropological Theory of Didactics (pp. 685–694). Centre de Recerca Matemàtica
Houston, K., Ireland, N., Galbraith, P., & Kaiser, G. (2009). The first twenty-five years: The first century of the International Commission on Mathematical Instruction (1908–2008). http://www.icmihistory.unito.it (retrieved april 15, 2024)
Jablonski, S. (2023). Is it all about the setting?—A comparison of mathematical modelling with real objects and their representation. Educational Studies in Mathematics, 113(2), 307–330. https://doi.org/10.1007/s10649-023-10215-2
Jessen, B. E. (2017). How to generate autonomous questioning in secondary mathematics teaching? Recherches en Didactique des Mathematiques, 37(2/3), 217–245.
Jessen, B. E. (2019). Teachers learning to design and implement mathematical modelling activities through collaboration. 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. 1182-1189). Freudenthal Group & Freudenthal Institute.
Jessen, B. E., & Kjeldsen, T. H. (2021). Mathematical modelling in scientific contexts and in Danish upper secondary education: are there any relations?. Quadrante, 30(2), 37-57. http://doi.org/10.48489/quadrate.23658
Jessen, B.E. (2024). Media and Milieu Dialectics and New Resources Available for Students. In I. Florensa, N. Ruiz-Munzón, K. Markulin, B. Barquero, M. Bosch, Y. Chevallard (Eds), Proceedings of the 7th International Conference on the Anthropological Theory of the Didactic (CITAD7) (pp. 293–302). Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-55939-6_23
Kawakami, T., & Mineno, K. (2021). Data-based modelling to combine mathematical, statistical, and contextual approaches: Focusing on ninth-grade students. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modelling education in East and West: International perspectives on the teaching and learning of mathematical modelling (pp. 389–400). Springer International Publishing.
https://doi.org/10.1007/978-3-030-66996-6_32
Kidron, I., Artigue, M., Bosch, M., Dreyfus, T., & Haspekian, M. (2014). Context, milieu, and media-milieus dialectic: A case study on networking of AiC, TDS, and ATD. In A. Birkner-Ahsbahs & S. Prediger (Eds.), Networking of theories as a research practice in mathematics education (pp. 153–177). https://doi.org/10.1007/978-3-319-05389-9_10
Konold, C., & Higgins, T. L. (2003). Reasoning about data. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 193–215). National Council of Teachers of Mathematics.
Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305-325.
https://doi.org/10.1007/s10649-013-9529-8
Konold, C., & Miller, C. (2021). TinkerPlots: Dynamic data exploration (Version 3.3) [Computer software]. Data Description, Inc.
Lesh, R., Middleton, J. A., Caylor, E., & Gupta, S. (2008). A science need: Designing tasks to engage students in modeling complex data. Educational studies in Mathematics, 68, 113-130.
https://doi.org/10.1007/s10649-008-9118-4
McLean, J.A., Brady, C., Jung, H., Dominguez, A., & Glancy, A.W. (2023). Seeing the Forest for the Trees: Investigating Students’ Data Moves in a Citizen Science Based Model-Eliciting Activity. In Greefrath, G., Carreira, S., & Stillman, G.A. (Eds) Advancing and Consolidating Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 193–204). Springer, Cham.
https://doi.org/10.1007/978-3-031-27115-1_12
Niss, M. (2018). National and international curricular use of competency based Danish ”KOM project”. In Y. Shimizu & R. Vithal (Eds.), Proceedings of ICMI Study 24: School mathematics curriculum reforms: Challenges, changes and opportunities (pp. 69–76). University of Tsukuba.
Niss, M. & Højgaard, T. Mathematical competencies revisited (2019). Educational Studies in Mathematics, 102, 9–28.
https://doi.org/10.1007/s10649-019-09903-9
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]. Copenhagen: The Ministry of Education. Available electronically—search for ”Kompetencer og matematiklæring”.
Noll, J., Schnell, S., Gould, R., & Makar, K. (2022). New ways of interacting with data, context, and chance in statistical modeling processes. Mathematical Thinking and Learning, 24(4), 331–335.
https://doi.org/10.1080/10986065.2021.1922855
Østergaard, C. H. (2022). An Inquiry Perspective on Statistics in Lower Secondary School in Denmark and Japan–An Elaboration and Modelling of the Anthropological Theory of the Didactic Through Two Statistics Classrooms. European Journal of Science and Mathematics Education, 10(4), 529-546. https://doi.org/10.30935/scimath/12401
Østergaard, C. H., & Larsen, D. M. (2023). Questioning the world–A dialectic of study and research. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi & E. Kónya (Eds.), Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) (No. 25). Alfréd Rényi Institute of Mathematics, ERME.
Østergaard, C. H. & Larsen, D. M. (submitted). More than inquiry – Analysing two inquiry approach in statistical education. Statistics Education Research Journal.
Pfannkuch, M., Ben-Zvi, D., & Budgett, S. (2018). Innovations in statistical modeling to connect data, chance and context. ZDM Mathematics Education, 50(7), 1113-1123. https://doi.org/10.1007/s11858-018-0989-2
Serrano, L., Bosch, M., & Gascón, J. (2010). Fitting models to data: The mathematising step in the modelling process. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the 6th Conference of the European Research on Mathematics Education (pp. 2186–2195). ERME.
Verbisck, J., Bittar, M., Bosch, M., Barquero, B., & Benito, R. (2022). Study and research paths for statistics teacher education at secondary school level: An exploratory study. In S. Peters (Ed.) Eleventh International Conference on Teaching Statistics (ICOTS-11), IASE.
Wild, C. J. & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248.
https://doi.org/10.1111/j.1751-5823.1999.tb00442.x
Winsløw, C. (2011). Anthropological theory of didactic phenomena: some principles of its use in the study of mathematics education. In M. Bosch Casabo, J. Gascón, A. Ruiz Olarría, M. Artaud, A. Bronner, Y. Chevallard, G. Cirade, C. Ladage, & M. Larguier (Eds.), Un panorama de la TAD (pp. 117-140). Centre de Recerca Matemàtica.
Winsløw, C., Matheron, Y., & Mercier, A. (2013). Study and research courses as an epistemological model for didactics. Educational Studies in Mathematics, 83, 267–284. https://doi.org/10.1007/s10649-012-9453-3
Yin, R. K. (2013). Validity and generalization in future case study evaluations. Evaluation, 19(3), 321–332. https://doi.org/10.1177/1356389013497081
Yin, R. K. (2014). Case study research: Design and methods (5th ed.). Sage Publications.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
