Perceiving Fractions Through Failure: Punishment, Feedback, and Reflection

• In Event: 35.028 - Failure in the Learning Process: How Learners Experience and Overcome Obstacles Through Resources and Supports

Abstract

Mathematics plays the role of gatekeeper in the United States, guarding the doors to further success in both school and society (Moses & Cobb, 2001; Kaput, 1999). At the same time, mathophobia runs rampant (e.g., Papert, 1980), and the experience of failure in mathematics classrooms is perceived as an indicator of eventual absolute failure (Stevenson & Stigler, 1992). Yet empirical research on innovative organizations unanimously found that taking manageable risks and moving beyond failures are imperative for successful knowledge creation (e.g., Dunbar 1997, 1999; Harford, 2011; Puccio & Cabra, 2010). Similarly, game scholars note that players constantly construct new understandings by making use of and working through failures in the gaming context (e.g., Gee, 2006; Juul, 2009; Littz & Ramirez, 2014), since well-designed games purposefully mold failures so that they function as opportunities for learning (Gee, 2004; Schell, 2008).

This study explored how failure influenced players’ mathematical reasoning in the game Rolly’s Adventure (RA; Williams, 2015), designed to engage players in a playful and mathematical experience (Williams-Pierce, 2016a) that evoked a games-based sense of failure, rather than the type of failure often experienced in math classes. RA consists of 14 puzzles designed to support players in gradually building up knowledge on reversible multiplicative reasoning (Williams-Pierce, 2016b). We specifically define failure as the pairing of punishment and feedback, such that the punishment indicates to the player or learner that they need to attend to the feedback in order to successfully learn and progress. Consequently, failure results in reflection and adaptation, without the accompanying sense that the experience of failure indicates an inability to learn or succeed (Williams-Pierce, 2017).

Our participants consisted of fourteen middle school students recruited into four dyads and six solos, resulting in 10 males and 4 females from eleven to fourteen years who lived in a small Midwestern city. Video of their physical bodies, screencapture of their digital avatars, and audio of their spoken language were captured, synced, and analyzed for occurrences of failure and the resulting adaptations. Although our primary unit of analysis is failure within individual puzzles, we also categorize overall game trajectories and learning and identify patterns that led to a different type of failure – that is, failure to unpack and build up a coherent understanding about the underlying mathematical structure of the puzzles within RA.

Findings reflect that failure supported players in perceiving game elements that were previously not noticed, and in hypothesizing about and experimenting with the fractional situation within RA. We found that players who accumulatively made use of the feedback component of failures at various puzzles were more successful at building up and explicating knowledge on reversible multiplicative reasoning; while players who attended only to the feedback for individual puzzles – and did not develop a grand hypothesis to guide their problem-solving at subsequent puzzles – tended to struggle to understand the underlying structure of the game. This work has important implications for how to successfully incorporate failure into mathematical learning experiences.

Authors

• Caroline Cassie-Marie Williams-Pierce, University at Albany - SUNY

• Yan Tian, University at Albany - SUNY