Aisha Walker

Abstraction Through Game Play

This paper examines the computer game play of an 11-year-old boy. In the course of building a virtual house he developed and used, without assistance, an artefact and an accompanying strategy to ensure that his house was symmetric. We argue that the creation and use of this artefact-strategy is a mathematical abstraction. The discussion contributes to knowledge on mathematical abstraction: of non-traditional knowledge; without teacher mediation; through game play. The paper also considers learning without instruction/instructional design and questions received distinctions between scientific and everyday knowledge.

Mathematics and Non-School Gameplay

This chapter investigates the mathematics in the gameplay of three popular games (Angry Birds, Plants vs. Zombies and The Sims) that are unlikely to be played in mathematics lessons. The three games are different but each has been observed to provide opportunity for mathematical activity in gameplay. After describing each game, and the mathematics that can arise in gameplay, the chapter explores two questions: What kind of mathematics is afforded in these games? Can these games be used in/for school mathematics? Issues considered under the first question include: the nature of mathematics and the difficulty of isolating the mathematics in non-school gameplay; players’ strategic actions as mathematical actions; and ‘truth’ and its warrants in different mathematical worlds. Issues considered under the second question include: tensions between curricular expectations and the mathematics that arise in gameplay; and possible changes in gameplay when a game is moved from a leisure to an educational setting.