Abstract:

As teacher educators, we strive to provide learning experiences to our prospective mathematics teachers (for pupils aged 12 to 17 years-old) that engage them in the kind of mathematical activity that they are expected to develop with their own students in the future. It is important that prospective teachers engage and reflect on worthwhile mathematical tasks since these play a crucial role in introducing important mathematical ideas and in challenging pupils intellectually. In particular, collaboratively solving challenging problems, communicating (in writing) their reasoning, and giving peer feedback offer prospective teachers the kind of experiences in which they question their beliefs about teaching and learning mathematics, and think about how they can become effective teachers and promote students’ relational understanding.

A gallery walk is an instructional strategy that provides opportunities for students to engage in problem solving, (written) mathematical communication, and peer assessment practices. Students collaboratively solve a set of challenging tasks and convey their solutions and reasoning processes in the clearest and most complete way in a poster format. Posters are displayed as if they were paintings in an art gallery. Students visit the gallery, analyze their classmates’ solutions and thinking processes, and give feedback to each poster, searching to provide constructive and helpful comments to improve the posters. Afterwards, students engage in a collective discussion to reflect on the feedback received.

In this paper, we share the results of an ongoing exploratory qualitative research, in which we analyzed prospective teachers’ work within a gallery walk attending to three dimensions:
i) correctness of the problems’ solutions;
ii) clarity and completeness of the written mathematical communication; and
iii) the role of visualization in the written productions (posters and peer feedback).

Two cohorts of prospective teachers from two large universities in Portugal participated in the study, engaging in a gallery walk based on three problems were aimed at school pupils from 5th through 8th grade (10 to 13 years-old). Given the current constraints due to the COVID-19 pandemic, we experienced several obstacles regarding in situ collaborative work; thus, all collaboration was made possible by videoconference platforms, including our own class sessions with the prospective teachers. The posters were exhibited in each university courses’ platforms. Peer feedback was collaboratively made available in an anonymous mode. A whole class discussion occurred within each cohort of participants and all of them answered a questionnaire delivered using google forms.

The data gathered included the participants’ written productions – digital posters and comments to each other’s posters, audio recordings of the two whole-class discussions (one in each university), and the participants’ answers to the questionnaire. Our analysis has yielded some preliminary results, which suggest a significant variability in problem solving strategies, in clarity and comprehensiveness of the expression of solution processes, and in foci of the peer feedback. The main challenges found in the whole activity are related to being able to solve and express the solution process in a clear, correct, simple, and complete manner, which we believe reinforces the need of providing prospective teachers with similar experiences in their teacher education programs.

Keywords:

Gallery walk, mathematical communication, peer feedback, preservice teacher education.