Abstract:

In this report, we present the path followed in the construction of a teacher education task (TET), aimed at preparing teachers for junior high and secondary education in Portugal (students aged 12 to 17 years-old). The term TET refers to a task designed to provide learning experiences to preservice teachers (PSTs). The TET herein addressed was aimed at developing PSTs’ written mathematical communication skills, in connection with problem solving abilities. These two transversal mathematical skills (problem solving and mathematics communication) are highly emphasized in the current Portuguese curricular guidelines for teaching mathematics in basic education (Canavarro et al., 2021), meeting the recommendations of research (e.g., Carreira & Jacinto, 2019; Martins & Martinho, 2021).

We privileged the gallery walk (GW) as a teaching approach, because of its potential to engage students in meaningful learning of both mathematical content and transversal skills (e.g., Schendel et al., 2008; Vale & Barbosa, 2020). A GW provides opportunities for problem solving, mathematical communication, and peer assessment practices (Vale & Barbosa, 2020). In a nutshell, a GW involves the collaborative resolution of challenging tasks (such as mathematical problems), with potential to trigger the use of various strategies and representations. Problem resolutions are presented in posters, in which the processes followed to obtain the solutions are expected to be clearly and thoroughly communicated to others. The posters are displayed in or outside the classroom, allowing those who analyze them the opportunity to give constructive feedback on each one. Finally, the analysis of the feedback received serves as a springboard for participation in a collective discussion about the work carried out.

The TET whose design path is reported here is based on three experiences (cycles of implementation and refinement) we carried out, with a total of six cohorts of mathematics PSTs enrolled in two didactics of mathematics courses with very similar characteristics, offered in two higher education institutions. We describe those experiences, explain how they resulted in the design of a TET of interinstitutional nature, and share our reflections on the affordances of this TET.

References:
[1] Canavarro, A. P. (Coord.), Mestre, C., Gomes, D., Santos, E., Santos, L., Brunheira, L., Vicente, M., Gouveia, M. J., Correia, P., Marques, P. M., & Espadeiro, R. G. (2021). Aprendizagens essenciais de matemática para o ensino básico. DGE. https://www.dge.mec.pt/aprendizagens-essenciais-ensino-basico
[2] Carreira, S., & Jacinto, H. (2019). A model of mathematical problem solving with technology: The case of Marco solving-and-expressing two geometry problems. In P. Liljedahl, & M. Santos-Trigo (Eds.), Mathematical problem solving. ICME-13 Monographs (pp. 41-62). Springer Nature Switzerland. https://doi.org/10.1007/978-3-030-10472-6_3
[3] Martins, L. G., & Martinho, M. H. (2021). Strategies, difficulties, and written communication in solving a mathematical problem. Bolema, 35(70), 903-936. http://dx.doi.org/10.1590/1980-4415v35n70a16
[4] Schendel, J., Liu, C., Chelberg, D., & Franklin, T. (2008). Virtual gallery walk, an innovative outlet for sharing student research work in K-12 classrooms. In 38th Annual Frontiers in Education Conference (pp. F1A-1). IEEE.
[5] Vale, I., & Barbosa, A. (2020). Gallery Walk: Uma estratégia ativa para resolver problemas com múltiplas soluções. Revista de Educação Matemática, 1, 1-19.

Keywords:

Teacher education task, gallery walk, problem solving, written mathematical communication, peer assessment.