How mathematical games shape pre-service teachers' generalization processes: a qualitative case study
Timur Koparan, Ezgi Taylan Koparan
article (Uluslararası, Hakemli) | Yazar(lar): Timur Koparan, Ezgi Taylan Koparan | Yıl: 2026 — Özet: This study investigates how pre-service mathematics teachers engage in mathematical generalization within game-based learning environments. Although game-based learning has gained increasing attention in mathematics edu
This study investigates how pre-service mathematics teachers engage in mathematical generalization within game-based learning environments. Although game-based learning has gained increasing attention in mathematics education, existing research has largely emphasized engagement, motivation, and achievement, with comparatively limited focus on how such environments support the development of mathematical generalization processes. In particular, little is known about how pre-service teachers transition from concrete gameplay experiences to symbolic reasoning and formal mathematical generalizations, or how these processes relate to justification and proof. Addressing this gap, the study employed a qualitative multiple case study design involving 28 pre-service mathematics teachers enrolled in a Teaching Mathematics with Games course at a public university. Grounded in constructivist and problem-solving perspectives, the study examined how participants' actions, representations, and discussions during gameplay contributed to emerging generalizations. Data were collected through classroom observations, audio-recorded whole-class and small-group discussions, participants' written artifacts produced during gameplay, and researcher field notes. Participants played mathematical games, documented observations, identified patterns, and attempted to formulate and justify generalizations. The data were analyzed using qualitative analysis techniques supported by illustrative excerpts from participants' discourse and written work. Findings indicate that most participants actively generated predictions, drew inferences, and relied on intuitive reasoning during gameplay. However, many experienced difficulties in constructing valid and general mathematical statements and in justifying their conclusions through formal reasoning. These results reveal persistent challenges in the interconnected practices of generalization and proof, despite the exploratory and engaging nature of game-based environments. The study highlights the need for structured pedagogical support to help pre-service teachers transform exploratory insights into mathematically justified generalizations.