LittleBigPlanet 2: Designing for Multiplicative Reasoning With Fractions

• In Event: 35.069 - Fractions Learning: One Subject, Multiple Perspectives

Abstract

“I claim that using video games is the way Euclid would have taught basic mathematics had that technology been around in ancient Greece” (Devlin, 2011, p. 47).
This proposal shares the process of designing a game for middle school students in Little Big Planet 2 (LBP) that supports multiplicative reasoning with fractions. Given the complex nature of this process, I focused on three different design trajectories that interleave. First, game design principles (Gee, 2003, 2005; Salen & Zimmerman, 2004), as well as the unique affordances of designing with LBP, resulted in my game trajectory. Next, Brousseau’s (1997) recommendations for teaching mathematics with games, and literature on best practices for teaching fractions (Hackenberg, 2007, 2010; Steffe & Olive, 2010), informed my mathematics trajectory. My desire to create an overarching narrative goal resulted in my narrative trajectory (not shared here due to space constraints). Lastly, as this product will be available via the PlayStation Network to players of all ages and mathematical backgrounds, the game begins with doubling, which is widely considered to be a concept learned at a very young age (Lobato & Ellis, 2010; Moss, 2002). See Figure 1 for a screenshot of the prototyped initial task.
In Figure 1, jumping on the button on the left results in the light blue block disappearing then re-appearing (½ x 1 = ½) in the (w)hole. The middle button results in the blue block disappearing, then two appearing (½ x 2 = 1; the correct answer). The last button results in the blue block disappearing, then three appearing (½ x 3 = 1 ½). The outer buttons result in prompt visual feedback immediately prior to “death” – which, drastic though it sounds, is a common consequence in games and a respected method of feedback (e.g., Juul, 2013). The middle button allows the player to satisfy a pre-established goal of the narrative trajectory and progress in the game. The simplicity of the content in this task allows the player to focus on inferring the multiplicative relationship between the buttons and the blue blocks, and while this task in particular can be solved with an additive strategy, the games and mathematics trajectories quickly escalate to require multiplicative reasoning with unit, proper, and improper fractions.
Another goal in the design process was to create a rich experience that supports players’ attending to relevant quantities (Ellis, 2004), as a way to ground symbolic representations meaningfully. For example, in Figure 1, all the quantities and numbers are represented non-symbolically. I specifically designed the trajectory to go from purely perceptual to allowing (and then requiring) quantification because numerous researchers recommend building meaningful concrete experiences to support abstract understanding (e.g., Ellis, 2004, 2007; Huinker, 2002; Kieren, 1995; Lamon, 1995; Vanhille & Baroody, 2002). By the end of the game, both button labels and blue fraction blocks will have symbolic notation instead of circles (for the buttons) and solely height/area (for the blocks).
In conclusion, this presentation will focus on the design process of building a mathematics education game, as well as some preliminary results from data, time permitting.

Author

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