In a rapidly evolving world, fostering students’ ability to think critically, collaborate, communicate, and be creative is essential for their success. However, traditional mathematics education often fails to adequately engage students in these skills, relying on repetitive memorization and routine tasks rather than active learning and exploration. This study addresses the challenge of effectively integrating instructional strategies that promote deeper engagement, problem-solving, and higher-order thinking in mathematics education. To achieve this goal, our research explores the implementation of the Gallery Walk (GW) as an instructional strategy in elementary preservice teacher training. The research questions guiding this study are: (1) How does the use of a GW strategy impact students’ engagement and problem-solving skills in mathematics? (2) What problem-solving strategies do students employ when engaging with tasks that allow multiple solutions? (3) How do students react to the GW strategy in terms of motivation, collaboration, and cognitive engagement?

The organization of this study is embedded in active learning and inquiry-based instruction, all of which emphasize student-centered, interactive, and reflective engagement in learning. Research suggests that learning is most effective when students actively construct knowledge through meaningful tasks (NCTM, 2014; Vale & Barbosa, 2024). Traditional teacher-centered approaches, characterized by the ‘Triple X’ model of exposition, examples, and exercises (Evans & Swan, 2014), often limit students to low cognitive demand tasks. In contrast, an exploratory classroom encourages students to solve non-routine problems, engage in discussion, and develop reasoning skills. As inquiry-based learning fosters autonomy, allowing students to question, analyze, and use diverse strategies to solve mathematical problems (Maaß & Doorman, 2013). Additionally, cognitive development in mathematics is strongly linked to visualization. Students can be classified into three categories based on their problem-solving approaches: non-visual thinkers who rely on algebraic and numerical methods, visual thinkers who use diagrams and spatial reasoning, and harmonic thinkers who integrate both visual and analytical reasoning (Krutetskii, 1976; Presmeg, 2014). Furthermore, educational organizations emphasize that 21st-century students must be proficient in problem solving, critical thinking, communication, collaboration, and creativity (CCR, 2015; OECD, 2019). Problem solving involves higher order thinking, and research suggests that multiple-solution approaches to enhance students' flexibility (Leikin, 2016) being problem solving connected to the following skills: Critical thinking involves making informed decisions and solving complex problems; Communication entails sharing and understanding ideas effectively, Collaboration requires working in teams to achieve common goals; Creativity fosters innovative and original approaches to problem-solving or solutions. 

A GW embodies these principles by promoting cognitive, social, and physical engagement. It allows students to work collaboratively on multiple solutions tasks, present their solutions on posters around the classroom, provide and receive peer feedback, and participate in a collective discussion about their work. (Fosnot & Jacob, 2010; Prince, 2004). 

A GW supports deeper conceptual understanding and aligns with active learning principles (NCTM, 2014). Moreover, research highlights that movement enhances attention and learning (Braun et al., 2017), making the GW an effective strategy for sustained physical an intellectual engagement. This study explores how integrating a GW in preservice teacher education can foster problem-solving skills, and engagement in mathematics. By examining students’ problem-solving strategies and their reactions to this approach, we aim to contribute to the broader discourse on effective mathematics instruction, reinforcing the need for active, inquiry-based, and visually enriched learning experiences.

The research follows a qualitative and interpretive approach (Erickson, 1986) with an exploratory design, aiming to understand how preservice elementary teachers engage with a GW strategy in solving mathematical problems. The study was conducted with fourteen future elementary education teachers enrolled in a Didactics of Mathematics course. During the instruction, we adopted an exploratory approach, where we prioritized multiple-solution tasks that include visual approaches, promoting active student engagement through questioning, exploration, discussion, and movement. The GW strategy was implemented as a teaching and learning strategy in solving problems that address different contents (e.g. areas, fractions) challenging traditional teacher-centered instruction and fostering a more dynamic, student-centered learning environment. The research process followed a structured sequence of phases within the GW strategy (Vale & Barbosa, 2020) where students: (1) Task resolution, work collaboratively in groups to solve the multiple solutions tasks; (2) Construction of posters, display their solutions on posters, emphasizing clarity and originality; (3) Presentation and observations, affix the posters in the walls around the classroom; (4) Analysis and elaboration of comments, provide peer feedback through written notes on each group’s posters; (5) Group discussions, review their own poster, consider peer feedback, and synthesize key insights; (6) Collective discussions, highlight different problem-solving approaches, clarify misconceptions, and strengthen mathematical reasoning. Data collection involved multiple sources to gain a comprehensive understanding of student engagement and learning outcomes. These sources included classroom observations, students’ written solutions to mathematical tasks, posters created as part of the GW strategy, peer feedback through written comments on posters, and individual reflective written reports submitted at the end of the activity. Data analysis was conducted inductively, grounded in the various outputs produced by the future teachers, the research questions and the reviewed literature. Two main categories emerged: the diversity of problem-solving approaches, particularly visual solutions; and the reactions of future teachers to the GW experience.

This study highlights the effectiveness of GW as a strategy that fosters active participation, collaboration, and diverse problem-solving approaches among preservice teachers. The results indicate that these students engaged in mathematical problem-solving by discussing different strategies used, analyzing the most efficient ones, and presenting their solutions. This process encouraged the exploration of multiple solution pathways, enhancing mathematical reasoning (Vale & Barbosa, 2023). One of the key findings is the students’ preference for analytical solutions, which aligns with traditional teaching methods. However, through peer interactions and exposure to different strategies, some groups developed visual approaches, demonstrating flexibility. The emergence of visual strategies, led to a ‘Aha!’ moments (Liljedahl, 2016). Students reported that preparing posters helped them refine their explanations, making their reasoning clearer to their peers. The feedback process, conducted via anonymous post-its notes, facilitated reflection and allowed students to refine their problem-solving strategies. Many students acknowledged the importance of written mathematical communication, realizing that expressing mathematical ideas clearly and efficiently is a key skill for teaching (Vale & Barbosa, 2020). Overall, students expressed a positive reaction to the GW experience, highlighting its benefits in terms of engagement, motivation, and confidence-building. The structured yet open-ended nature of the activity allowed even the more reserved students to contribute and interact. Furthermore, students recognized its applicability in their future teaching, emphasizing the importance of integrating this approach in mathematics education (Prince, 2004; Vale & Barbosa, 2023). This study confirms that GW can enhance learning by promoting intellectual, social, and physical engagement. It also suggests that teacher education programs should incorporate innovative strategies to expose preservice teachers to diverse problem-solving methods, preparing them for more effective mathematics instruction. Additionally, it emphasizes the need to prepare future teachers to implement a similar GW experience with their own students (Vale & Barbosa, 2020).

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