Danish University Colleges Developing reasoning competence in inquiry-based mathematics teaching Larsen, Dorte Moeskær Publication date: 2019 Link to publication Citation for pulished version (APA): Larsen, D. M. (2019). Developing reasoning competence in inquiry-based mathematics teaching. Syddansk Universitetsforlag. 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Sep. 2021 Developing reasoning competence in inquiry-based mathematics teaching Prepared by Dorte Moeskær Larsen LSUL, IMADA, SDU Submitted: 14th September 2019 Supervisor: Claus Michelsen Co-supervisor: Thomas Illum Hansen 1 Duration of this Ph.D.: 15th of September 2016 – 14th of September 2019 2 1 Publication by the author of this thesis Peer reviewed and all written, submitted or published during this thesis. The papers include in this thesis is marked with * Dreyøe, J., Larsen, D. M., Hjelmborg, M. D., Michelsen, C., & Misfeldt, M. (2017). Inquiry-based learning in mathematics education: Important themes in the literature. Nordic Research in Mathematics Education, 329. (Dreyøe, Larsen, Hjelmborg, Michelsen, & Misfeldt, 2017) *Dreyøe, J., Larsen, D. M., & Misfeldt, M. (2018). From everyday problem to a mathematical solution-understanding student reasoning by identifying their chain of reference. In Bergqvist, E., Österholm, M., Grandberg, C., Sumpter, L. (Eds.) Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education. Umeå, Sweden (Dreyøe, Larsen, & Misfeldt, 2018) Gents, S., Christensen, M., Hjelmborg, M., Jensen, M., Larsen, D.& Hansen, R (2019). How do mathematics teachers interact with the mathematic book and how does the use of the mathematics book and other resources influence the teaching? Abstract to Iartem 15 International Conference, Odense, Denmark (Gents, Christensen, Hjelmborg, Jensen, Larsen & Hansen, 2019) Gissel, S. T., Hjelmborg, M., Kristensen, B. T., & Larsen, D. M. (2019). Kompetencedækning i analoge matematiksystemer til mellemtrinnet. MONA (3) p. 7- 27 Copenhagen, Danmark (Gissel, Hjelmborg, Kristensen, & Larsen, 2019) 3 Larsen, D.M. (2017). Testing Inquiry-based Mathematic Competencies. In Ann Downton, Sharyn Livy, & Jennifer Hall (Eds) Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA), University of Monash (Larsen, 2017) *Larsen, D.M., Dreyøe, J., & Michelsen, C. (2019) How argumentation in teaching and testing of an inquiry-based intervention is aligned. Manuscript submitted for Eurasia Journal of Mathematics, Science and Technology Education. (Larsen, Dreyøe & Michelsen, 2019) Larsen, D. M., Hjelmborg, M. D., Lindhardt, B., Dreyøe, J., Michelsen, C., & Misfeldt, M. (2019). Designing inquiry-based teaching at scale: Central factors for implementation. 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 (CERME11, February 6 – 10, 2019). Utricht: the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. (Larsen, Hjelmborg, Lindhardt, Dreyøe, Michelsen & Misfeldt, 2019) *Larsen, D. M., & Lindhardt, B. K. (2019). Undersøgende aktiviteter og ræsonnementer i matematikundervisningen på mellemtrinnet. MONA-Matematik-og Naturfagsdidaktik, (1). p. 7-21. Copenhagen, Danmark (Larsen & Lindhardt, 2019) *Larsen, D.M., & Puck, M.R. (2019). Developing a Validated Test to Measure Students’ Progression in Mathematical Reasoning in Primary School.Manuscript submitted for publication in International Journal of Education in Mathematics, Science and Technology (Larsen & Rasmussen, 2019) 4 *Larsen, D.M., & Misfeldt, M. (2019). Fostering mathematical reasoning in inquiry- based teaching – the role of cognitive conflicts, Submitted to Nordic Studies in Mathematics Education (NOMAD) (Larsen & Misfeldt, 2019) Larsen, D. M., Østergaard, C. H., & Skott, J. (2018). Prospective Teachers’ Approach to Reasoning and Proof: Affective and Cognitive Issues. In H. Palmér & J. Skott (Eds.) Students' and Teachers' Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms (pp. 53-63): Springer. (Larsen, Østergaard, & Skott, 2018) Larsen, D. M., & Østergaard, C. H. (2019). Questions and answers but no reasoning... In U. T. Jankvist, M. V. d. Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME 11, February 6 – 10, 2019). Utricht: the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. (Larsen & Østergaard, 2019) Skott J., Larsen, D.M., & Østergaard, C.H. (2017) Reasoning and proving in mathematics teacher education. In Zehetmeier, S., Rösken-Winter B., Potari, D. & Ribeiro, M., Berlin (Eds.), Proceedings of the Third ERME Topic Conference on Mathematics Teaching, Resources and Teacher Professional Development, European Society for Research in Mathematics Education p. 197-206 (Skott, Larsen, & Østergaard, 2017) Skott, J., Larsen, D.M., & Østergaard, C.H. (in press). Learning to teach to reason: Reasoning and proving in mathematics teacher education, In Zethetmeier, S. (Eds.), Routeledge. (Skott, Larsen & Østergaard, in press) 5 Non-peer reviewed: Dreyøe, J., Michelsen, C., Hjelmborg, M. D., Larsen, D. M., Lindhardt, B. K., & Misfeldt, M. (2017). Hvad vi ved om undersøgelsesorienteret undervisning i matematik: Forundersøgelse i projekt Kvalitet i Dansk og Matematik, delrapport 2. (Dreyøe, Michelsen, et al., 2017) Gissel, S. T., Hjelmborg, M. D., Skovmand, K., Kristensen, B. T., & Larsen, D. M. (2017). Kompetencedækning i analoge læremidler til matematikfaget: Evaluering af analoge, didaktiske læremidler til matematikfaget i forhold til Fælles Mål med særligt fokus på kompetencedækning. (Gissel, Hjelmborg, Skovmand, Kristensen, & Larsen, 2017) Michelsen, C., Dreyøe, J., Hjelmborg, M. D., Larsen, D. M., Lindhardt, B. K., & Misfeldt, M. (2017). Forskningsbaseret viden om undersøgende matematikundervisning, Undervisningsministeriet, København. (Michelsen et al., 2017) Larsen, D. M. (2017b) Problemopstilling som vurdering for læring. MONA-Matematik- og Naturfagsdidaktik, (2) (pp. 84-87) (Larsen, 2017b) Hansen, N. J., Vejbæk, L., Lindhardt, B., Jensen, M., Larsen, D. M., Hjelmborg, M., Jørgensen, A. S. (2018). Matematikdidaktiske tanker - mod en mere undersøgende dialogisk anvendelsesorienteret matematik: KiDM. (N. J. Hansen et al., 2018) Contributions: Hansen, T.I., Elf, N., Misfeldt, M., Gissel, S.T., Lindhardt, B. (2019). KVALITET I DANSK OG MATEMATIK. Et lodtrækningsforsøg med fokus på undersøgelsesorienteret dansk- og matematikundervisning. Slutrapport. (T. I. Hansen et al, 2019) 6 2 Content 1 Publication by the author of this thesis ................................................... 3 2 Content........................................................................................................ 7 3 Preface ...................................................................................................... 11 4 Acknowledgement .................................................................................... 14 5 Abbreviations & Acronyms .................................................................... 16 6 Abstract .................................................................................................... 17 6.1 English Abstract ........................................................................................................ 17 6.2 Danish Abstract (Dansk resume) ............................................................................... 18 7 Keywords .................................................................................................. 21 8 Introduction ............................................................................................. 22 8.1 Aim of the research - Theory into practice and practice into theory ......................... 24 8.2 Research questions .................................................................................................... 26 8.3 Reading guide ............................................................................................................ 27 8.4 Short summary of the five papers .............................................................................. 28 8.5 Theoretical considerations in this thesis .................................................................... 30 Networking the different theories ....................................................................... 30 Theories in research, practice and problems ..................................................... 34 9 Clarifications and theoretical background ........................................... 36 9.1 Reasoning in mathematics education .......................................................................