Entre desafios e potencialidades: processos formativos em proposição e resolução de problemas abertos de matemática como espaços de desenvolvimento da criatividade docente

Abstract

This thesis investigates how creative approaches, embodied in the Proposition and Resolution of Open Problems, foster the development of teachers’ creativity in professional development processes with mathematics teachers. Grounded in a theoretical framework that integrates cognitive and sociocultural perspectives on creativity, the study adopts the Four-C Model of Creativity (Kaufman & Beghetto, 2009), which expands the concept beyond extraordinary achievements and recognizes creative manifestations in everyday school contexts. The research also draws on Guilford’s (1950) notion of divergent thinking, emphasizing the skills of fluency, flexibility, originality, and elaboration. Methodologically, this qualitative study is based on the analysis of three editions of an original continuing education program (Brazil/2024, Argentina/2024, and Brazil/2025), which incorporated reflective, guided, and autonomous practices in both virtual and face-to-face settings. The activities involved proposing and solving open-ended mathematical problems connected to real and simulated teaching and learning situations. Throughout this process, creative approaches emerged, characterized by elements such as contextualization, student authorship, the use of images and narratives, diversity of strategies, visualization and modeling, variations, and argumentation, elements that enrich the concept of “creative approaches” as a formative outcome. The qualitative analysis, informed by Bardin’s (2016) content analysis and Braun and Clarke’s (2006) thematic analysis, revealed that open-ended problems enhance divergent thinking, promoting multiple forms of creative engagement and the development of more innovative pedagogical practices. The findings indicate shifts in participants’ understandings of creativity, highlighting its relevance as a central organizing principle of Mathematics teaching. The study also shows that designing and solving open-ended problems serves as a powerful strategy for fostering teacher creativity, supporting authorship, critical reflection, and professional autonomy. By recognizing teachers as creative agents, this research establishes connections among teacher creativity, open-ended problems, and transformative pedagogical practices, contributing to the advancement of a more creative, contextualized, and collaborative Mathematics Education.