Designing for Peer Learning : Mathematics, Games, and Peer Groups in Leisure-time Centers

Abstract: Constrained by national tests and the mathematics curriculum, teachers have problems finding time for exploratory and hands-on mathematical activities, especially so in classes with a reduced pace of progression, for example because of a large proportion of second-language learners. Could the leisure-time center, where time is not earmarked, provide such opportunities? The conclusion of this thesis is that this can be done, on the condition that designed activities build on the central premise of the leisure-time center: children have the right to choose which activities to engage with. The thesis is interdisciplinary, combining design research, situated cognition/embodied interaction, and pedagogy. The empirical material comes from a design project conducted in collaboration with the Rook, a multicultural school with an integrated leisure-time center. The participating children were 7-9 years old. The games studied were card and board games, especially combinatorial mathematics games (Set and Nim). The situated and embodied approach towards design is reflected in the analysis, which approaches visual artifacts as parts of multimodal communicative scenes with many co-present participants engaged in playing games or solving problems. It is shown that children learn the game through observation and participation, either as players or in non- playing roles. For many games, rules are written in a format that is inaccessible to children. One of the design tasks in the project has been to develop secondary artifacts related to games: graphic guides, conceptual maps, and paper-based exercises that can be used by children without adult support. The premise of the learners’ right to choose has many consequences for the design of learning activities. One is that motivation changes from being a property of the learner to a property of the activity. In order to highlight this difference, this thesis proposes the notions of learnability and learnworthiness to describe those aspects of an activity and its context which make it motivating from the learner’s perspective. The thesis concludes with a discussion of how design can increase the learnability and learnworthiness of a learning activity. Watching the activity being practiced is the most important resource for potential participants to determine its learnability and learnworthiness. The qualities determining the learnworthiness of an activity are reciprocity, mastery, and the potential for closure. Watching a peer successfully solving a task increases the learnability for the observers as well. If problem-solvers think aloud and use their hands to move or point at cards, collaboration and learning by observers is facilitated. Providing games with non-competitive side activities creates opportunities for deliberate practice, and offers a safe entry for children who are reluctant to engage as players.