Abstract:

This paper intends to analyse the characteristics of two pedagogical approaches – exploratory teaching (ET) and gallery walk (GW) – from the point of view of their potential for developing students' mathematical communication.

A lesson based on ET is structured in four phases: introducing the task, carrying out the task, discussing the task, and systematising learning (Canavarro et al., 2014). The first phase aims to ensure that students understand the task. Students collaboratively solve the task during the second phase. Next, following a sequence carefully chosen by the teacher, they present their work and discuss it collectively. The critical points of the whole activity and of the lesson’s goals are highlighted as a summary in the final phase.

A lesson based on a GW is organised into six stages, all of which take place in groups: solving the task, constructing posters, observing the posters, writing feedback, reflecting on the feedback received, and discussing how the posters can be improved (Vale & Barbosa, 2020). In the first stage, students solve the task. Afterwards, they display the solution process in a poster as clearly as possible. In the third and fourth stages, students observe the posters displayed as in a gallery, analyse their contents and write feedback to each poster with constructive questions and comments. In the fifth stage, each group reflects upon the feedback received. Finally, in a collective discussion, students present their posters and, based on the previous reflections, discuss how they could improve them.

These two pedagogical approaches have common aspects such as: the opportunity to access and understand different strategies for solving the same tasks, the opportunity to work collaboratively, and the promotion of reflection, critical analysis and communication between students. Both approaches make a strong contribution to developing students' communication skills, despite their significant differences (Guerreiro et al., 2015; Tomás Ferreira & Martinho, 2021). For example, there is more emphasis on writing (and reading) in the GW than in the ET approach, in which oral communication has a significant weight. We will present some examples that support these claims, with a focus on mathematical communication.

References:
[1] Canavarro, A. P., Oliveira, H., & Menezes, L. (2014). Práticas de ensino exploratório da Matemática: Ações e intenções de uma professora. In J. P. Ponte (Ed.), Práticas profissionais dos professores de matemática (pp. 217-233). IEUL.
[2] Guerreiro, A., Tomás Ferreira, R., Menezes, L., & Martinho, M. H. (2015). Comunicação na sala de aula: A perspetiva do ensino exploratório da matemática. Zetetiké, 23(4), 279-295. http://doi.org/10.20396/zet.v23i44.8646539.
[3] Tomás Ferreira, R. A., & Martinho, M. H. (2021). Using a gallery walk to promote prospective teachers’ written mathematical communication skills. Proceedings of the INTED2021 Conference (pp. 7878-7888). IATED. http://doi.org/10.21125/inted.2021.1585
[4] Vale, I. P., & Barbosa, A. (2020). Gallery Walk: Uma estratégia ativa para resolver problemas com múltiplas soluções. Revista de Educação Matemática, 17, e020018-e020018. http://doi.org/10.37001/remat25269062v17id260

Keywords:

Pedagogical approaches, exploratory teaching, gallery walk, mathematical communication.