MERIA – Conflict Lines: Experience with Two Innovative Teaching Materials

  • Željka Milin Šipuš Department of Mathematics, Faculty of Science, University of Zagreb, Croatia
  • Matija Bašić Department of Mathematics, Faculty of Science, University of Zagreb, Croatia
  • Michiel Doorman Freudenthal Institute, Utrecht University, Netherlands
  • Eva Špalj XV. gimnazija, Zagreb, and Department of Mathematics, Faculty of Science, Croatia
  • Sanja Antoliš XV. gimnazija, Zagreb, and Department of Mathematics, Faculty of Science, Croatia
DOI: https://doi.org/10.26529/cepsj.987
Keywords: inquiry-based mathematics teaching, realistic mathematics education, teaching scenarios, theory of didactic situations

Abstract

The design of inquiry-based tasks and problem situations for daily mathematics teaching is still a challenge. In this article, we study the implementation of two tasks as part of didactic scenarios for inquiry-based mathematics teaching, examining teachers’ classroom orchestra-tion supported by these scenarios. The context of the study is the Erasmus+ project MERIA – Mathematics Education: Relevant, Interesting and Applicable, which aims to encourage learning activities that are meaningful and inspiring for students by promoting the reinvention of target mathematical concepts. As innovative teaching materials for mathematics education in secondary schools, MERIA scenarios cover specific curriculum topics and were created based on two well-founded theories in mathematics education: realistic mathematics education and the theory of didactical situations. With the common name Conflict Lines (Conflict Lines – Introduction and Conflict Set – Parabola), the scenarios aim to support students’ inquiry about sets in the plane that are equidistant from given geometrical figures: a perpendicular bisector as a line equidistant from two points, and a parabola as a curve equidistant from a point and a line. We examine the results from field trials in the classroom regarding students’ formulation and validation of the new knowledge, and we describe the rich situations teachers may face that encourage them to proceed by building on students’ work. This is a crucial and creative moment for the teacher, creating opportunities and moving between students’ discoveries and the intended target knowledge.

Downloads

Download data is not yet available.

References

Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM - International Journal on Mathematics Education, 45(6), 797–810. https://doi.org/10.1007/s11858-013-0506-6

Brousseau, G. (1997). Theory of didactical situations in mathematics. Didactique des mathématiques 1970–1990. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2

Bruder, R., & Prescott, A. (2013). Research evidence on the benefits of IBL. ZDM - International Journal on Mathematics Education, 45(6), 811–822. https://doi.org/10.1007/s11858-013-0542-2

Doorman, M., Van den Heuvel-Panhuizen, M., & Goddijn A. (2020). The emergence of meaningful geometry. In M. Van den Heuvel-Panhuizen (Ed.), National reflections on the Netherlands didactics of mathematics (pp. 281–302). ICME-13 Monographs. Springer. https://doi-org.proxy.library.uu.nl/10.1007/978-3-030-33824-4_15

Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47202-3

Hersant, M., & Perrin-Glorian, M. (2005). Characterization of an ordinary teaching practice with the help of the theory of didactic situations. Educational Studies in Mathematics, 59, 113–151. https://doi:10.1007/s10649-005-2183-z

Holbrook, J., & Rannikmäe, M. (2014). The philosophy and approach on which the PROFILES project is based. CEPS Journal, 4, 9–29.

Gravesen, K.F., Grønbæk, N., & Winsløw, C. (2017). Task design for students’ work with basic theory in analysis: The cases of multidimensional differentiability and curve integrals. International Journal of Research in Undergraduate Mathematics Education, 3, 9–33. https://doi.org/10.1007/s40753-016-0036-z

Holzäpfel, L., Rott, B., & Dreher, U. (2016). Exploring perpendicular bisectors: The water well problem. In A. Kuzle, B. Rott, & T. Hodnik Čadež (Eds.), Problem solving in the mathematics classroom, perspectives and practices from different countries (pp. 119–132). WTM, Verlag für wissenschaftliche Texte und Medien.

Kieran, C., Doorman, M., & Ohtani M. (2014). Frameworks and principles for task design. In A. Watson, & M. Ohtani (Eds.), Task design in mathematics education. Proceedings of ICMI Study 22. ICMI Study 22, Oxford, United Kingdom (pp. 19–80). https://link.springer.com/chapter/10.1007/978-3-319-09629-2_2#citeas

Rott, B. (2020). Teachers’ behaviors, epistemological beliefs, and their interplay in lessons on the topic of problem solving, International Journal of Science and Mathematics Education, 18, 903–924. https://doi.org/10.1007/s10763-019-09993-0

Sherin, M.G. (2002). A balancing act: Developing a discourse community in a mathematics classroom. Journal of Mathematics Teacher Education, 5, 205–233. https://doi-org.proxy.library.uu.nl/10.1023/A:1020134209073

Winsløw, C. (ed.). (2017). MERIA practical guide to inquiry based mathematics teaching. https://meria-project.eu/activities-results/practical-guide-ibmt

Published
2022-03-25
How to Cite
Milin Šipuš, Željka, Bašić, M., Doorman, M., Špalj, E., & Antoliš, S. (2022). MERIA – Conflict Lines: Experience with Two Innovative Teaching Materials. Center for Educational Policy Studies Journal, 12(1), 103–124. https://doi.org/10.26529/cepsj.987
Issue
Vol 12 No 1 (2022): Problem Solving and Problem Posing: From Conceptualisation to Implementation in the Mathematics Classroom
Section
FOCUS

Authors who publish with this journal agree to the following terms:

  1. Authors are confirming that they are the authors of the submitted article, which will be published online in the Center for Educational Policy Studies Journal (for short: CEPS Journal) by University of Ljubljana Press (University of Ljubljana, Faculty of Education, Kardeljeva ploščad 16, 1000 Ljubljana, Slovenia). The Author’s/Authors’ name(s) will be evident in the article in the journal. All decisions regarding layout and distribution of the work are in the hands of the publisher.
  2. The Authors guarantee that the work is their own original creation and does not infringe any statutory or common-law copyright or any proprietary right of any third party. In case of claims by third parties, authors commit themselves to defend the interests of the publisher, and shall cover any potential costs.
  3. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under https://creativecommons.org/licenses/by/4.0/deed.en that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  4. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  5. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.