Roleplaying to develop students’ awareness and robust learning of advanced mathematical concepts

References

• Albano, G., & Pierri, A. (2014). Mathematical competencies in a role-play activity. In C. Nicol, P. Liljedhal, S. Oesterle, & D. Allan (Eds.), Proceedings of the 38th PME conference (Vol. 2, pp. 17–24). PME.
   Google Scholar
• Albano, G., Pierri, A., & Sabena, C. (2019). Enhancing formative assessment practices in undergraduate courses by means of online workshop. In B. Barzel, R. Bebernik, L. Göbel, M. Pohl, H. Ruchniewicz, F. Schacht, & D. Thurm (Eds.), Proceedings of ICTMT 14 (pp. 155–162). DuEPublico.
   Google Scholar
• Amendola, D., & Miceli, C. (2018). Online peer assessment to improve students’ learning outcomes and soft skills. Italian Journal of Educational Technology, 26(3), 71–84. https://doi.org/10.17471/2499-4324/1009
   Google Scholar
• Avital, S., & Libenskind, S. (1978). Mathematical induction in the classroom: Didactical and mathematical issues. Educational Studies in Mathematics, 9(4), 429–438. https://doi.org/10.1007/BF00410588
   Google Scholar
• Baldacci, M. (2006). Personalizzazione o individualizzazione? [Personalization or individualization?]. Erickson.
   Google Scholar
• Biza, I., Giraldo, V., Hochmuth, R., Khakbaz, A., & Rasmussen, C. (Eds.). (2016). Research on teaching and learning mathematics at the tertiary level. State-of-the-art and looking ahead. Springer Nature.
   Google Scholar
• Black, P., & Wiliam, G. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(1), 5–31. https://doi.org/10.1007/s11092-008-9068-5
   Web of Science ®Google Scholar
• Brumfield, C. (1974). A note on mathematical induction. Mathematics Teacher, 67(7), 616–618. https://doi.org/10.5951/MT.67.7.0616
   Google Scholar
• Bucholtz, M., & Hall, K. (2005). Identity and interaction: A sociocultural linguistic approach. Discourse Studies, 7(4-5), 585–614. https://doi.org/10.1177/1461445605054407
   Web of Science ®Google Scholar
• Chevallard, Y. (1992). Concepts fondamentaux de la didactique: Perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques, 12(1), 73–112. https://revue-rdm.com/1992/concepts-fondamentaux-de-la-didactique/
   Google Scholar
• Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: An attempt at a principled approach. Hiroshima Journal of Mathematics Education, 12(1), 71–114.
   Google Scholar
• Cusi, A., Morselli, F., & Telloni, A. I. (2020). Promoting formative assessment in mathematics teacher education: An experience of distance learning. In Demetrios G. Sampson, Dirk Ifenthaler & Pedro Isaías (Eds.), 17th International conference on cognition and exploratory learning in digital age (pp. 288–294). IADIS digital library.
   Google Scholar
• Di Martino, P., & Maracci, M. (2009). The secondary-tertiary transition: Beyond the purely cognitive. In M. Tzezaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd PME conference (Vol. II, pp. 401–408). PME.
   Google Scholar
• Double, K. S., McGrane, J. A., & Hopfenbeck, T. N. (2020). The impact of peer assessment on academic performance: A meta-analysis of control group studies. Educational Psychology Review, 32(2), 481–509. https://doi.org/10.1007/s10648-019-09510-3
   Web of Science ®Google Scholar
• Dubinsky, E. (1986). Teaching mathematical induction I. Journal of Mathematical Behavior, 5(3), 305–317.
   Google Scholar
• Dubinsky, E. (1989). Teaching mathematical induction II. Journal of Mathematical Behavior, 8(3), 285–304.
   Google Scholar
• Ernest, P. (1984). Mathematical Induction: A pedagogical discussion. Educational Studies in Mathematics, 15(2), 173–189. https://doi.org/10.1007/BF00305895
   Google Scholar
• Fazey, D. M., & Fazey, J. A. (2001). The potential for autonomy in learning: Perceptions of competence, motivation and locus of control in first-year undergraduate students. Studies in Higher Education, 26(3), 345–361. https://doi.org/10.1080/03075070120076309
   Web of Science ®Google Scholar
• Ferrari, P. L. (2004). Mathematical language and advanced mathematics learning. In M. Johnsen Høines & A. Berit Fuglestad (Eds.), Proceedings of the 33rd PME conference (Vol. 2, pp. 383–390). PME.
   Google Scholar
• Fishbein, E., & Engel, I. (1989). Psychological difficulties in understanding the principle of mathematical induction. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th PME conference (Vol. 1, pp. 276–282). PME.
   Google Scholar
• Frejd, P. (2017). Mathematical modelling as a professional activity: Lessons for the classroom. In G. A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 371–388). Springer.
   Google Scholar
• Grice, P. (1975). Logic and conversation. In P. Cole & J. Morgan (Eds.), Syntax and semantics (Vol. 3, pp. 41–58). Academic Press.
   Google Scholar
• Hammer, J., To, A., Schrier, K., Bowman, S. L., & Kaufman, G. (2018). Learning and role-playing games. In J. P. Zagal & S. Deterding (Eds.), Role-playing game studies: Transmedia foundations (pp. 283–299). Routledge.
   Google Scholar
• Harel, G. (2001). The development of mathematical induction as a proof scheme: A model for DNR-based instruction. In S. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 185–212). Kluwer.
   Google Scholar
• Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112. https://doi.org/10.3102/003465430298487
   Web of Science ®Google Scholar
• Kilgour, P., Reynaud, D., Northcote, M. T., & Shields, M. (2015). Role-playing as a tool to facilitate learning, self-reflection and social awareness in teacher education. International Journal of Innovative Interdisciplinary Research, 2(4), 8–20.
   Google Scholar
• Koen, K., Bitzer, E. M., & Beets, P. A. D. (2012). Feedback or feedforward? A case study in one higher education classroom. Journal of Social Sciences, 32(2), 231–242. https://doi.org/10.1080/09718923.2012.11893068
   Google Scholar
• Kuhn, T. (1979). The structure of scientific revolution. University of Chicago Press.
   Google Scholar
• Mason, J. (1998). Enabling teachers to be real teachers. Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243–267. https://doi.org/10.1023/A:1009973717476
   Google Scholar
• Nicol, D. J., & Macfarlane-Dick, D. (2006). Formative assessment and self-regulated learning: A model and seven principles of good feedback practice. Studies in Higher Education, 31(2), 199–218. https://doi.org/10.1080/03075070600572090
   Web of Science ®Google Scholar
• Reinholz, D. (2016). The assessment cycle: A model for learning through peer assessment. Assessment & Evaluation in Higher Education, 41(2), 301–315. https://doi.org/10.1080/02602938.2015.1008982
   Web of Science ®Google Scholar
• Ron, G., & Dreyfus, T. (2004). The use of models in teaching proof by mathematical induction. In M. Hőines & M. Fuglestad (Eds.), Proceedings of the 28th PME conference (Vol. 4, pp. 113–120). PME.
   Google Scholar
• Stefani, L. A. J. (1998). Assessment in partnership with learners. Assessment & Evaluation in Higher Education, 23(4), 339–350. https://doi.org/10.1080/0260293980230402
   Google Scholar
• Telloni, A. I., & Malara, N. A. (2021). A constructive and metacognitive teaching path at university level on the principle of mathematical induction: Focus on the students’ behaviours, productions and awareness. Teaching Mathematics and Computer Science, 19(1), 133–161. https://doi.org/10.5485/TMCS.2021.0525
   Google Scholar
• van Popta, E., Kral, M., Camp, G., Martens, R. L., & Simons, P. R. J. (2017). Exploring the value of peer feedback in online learning for the provider. Educational Research Review, 20, 24–34. https://doi.org/10.1016/j.edurev.2016.10.003
   Web of Science ®Google Scholar
• Vickermann, P. (2009). Student perspectives on formative peer assessment: An attempt to deepen learning? Assessment & Evaluation in Higher Education, 34(2), 221–230. https://doi.org/10.1080/02602930801955986
   Web of Science ®Google Scholar
• Vygotsky, L. (1978). Mind in society. Harvard University Press.
   Google Scholar
• Wiliam, D., & Thompson, M. (2007). Integrating assessment with instruction: What will it take to make it work? In C. A. Dwyer (Ed.), The future of assessment: Shaping teaching and learning (pp. 53–82). Erlbaum.
   Google Scholar
• Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25–48. https://doi.org/10.1007/BF03217394
   Google Scholar
• Wouters, P., van Nimwegen, C., van Oostendorp, H., & van der Spek, E. D. (2013). A meta-analysis of the cognitive and motivational effects of serious games. Journal of Educational Psychology, 105(2), 249–265. https://doi.org/10.1037/a0031311
   Web of Science ®Google Scholar