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
Keywords: inquiry-based mathematics teaching, realistic mathematics education, teaching scenarios, theory of didactic situations


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 orchestration 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.


Download data is not yet available.


Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM - International Journal on Mathematics Education, 45(6), 797–810.

Brousseau, G. (1997). Theory of didactical situations in mathematics. Didactique des mathématiques 1970–1990. Kluwer Academic Publishers.

Bruder, R., & Prescott, A. (2013). Research evidence on the benefits of IBL. ZDM - International Journal on Mathematics Education, 45(6), 811–822.

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.

Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic Publishers.

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.

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).

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.

Sherin, M.G. (2002). A balancing act: Developing a discourse community in a mathematics classroom. Journal of Mathematics Teacher Education, 5, 205–233.

Winsløw, C. (ed.). (2017). MERIA practical guide to inquiry based mathematics teaching.