Pattern: Guess my X (GmX)

Summary	Sustaining a mathematical discussion is vital to the establishment of socio-mathematical norms (Yackel & Cobb, 1995) and to the collaborative construction of knowledge in the community. This goal is especially difficult to achieve in geographically distributed communities. This pattern addresses this by a challenge exchange game of build this puzzles.
Status	beta	Confidence	0
details...		Group	Participatory learning

Problem

(Migrated from http://lp.noe-kaleidoscope.org/outcomes/patterns/Guess_my_X)

Learning mathematics is fundamentally learning to be a mathematician. It requires the learner to internalize a range of mathematical skills as regular habits: computation, analysis, conjecturing and hypothesis testing, argumentation and proof. For this to happen, the learner needs to take ownership of a meaningful mathematical inquiry, and engage in activities of problem solving and discussion. Games provide a natural setting for the kind of “flow” needed, but how do we ensure that the focus of this flow is mathematical activity and discourse?

Context

A teacher wants to design a game for learning concepts, methods and meta-cognitive skills in a particular mathematical domain. This game should use a combination of available technologies.

Solution

Guess my X is a pattern of game structure, which can be adapted to a wide range of mathematical topics. At is core is a challenge exchange of build this puzzles, using mathematical game pieces as objects to talk with in a narrative space, using a league chart to orchestrate sustained social interaction.

GmX involves players in two roles, proposers and responders, and a facilitator. An implementation of the game would specify a domain of mathematics and rules for constructing processes in that domain. A proposer sets a challenge, in the form of a mathematical object which she constructed. The explicit rules of the game define the nature of the process by which this object can be created, but not its details. The proposer would construct such a process, and capture its product. She then saves the process model in a private space and publishes the product as a challenge. Responders then need to “reverse engineer” the process from the product. If they succeed, they publish their version as a response to the challenge. The proposer then needs to confirm the responder’s solution of provide evidence for the contrary.The game is not a sugar-coating to disguise the mathematics: it is a game with mathematical game-pieces. The rules of the game are intentionally left vague. This requires students to negotiate what constitutes a correct answer, and in doing so collaboratively refine the underlying mathematical concepts. These negotiations can lead to discussions of issues such as proof, equivalence and formal descriptions. The quality and extent of these discussions depends on the scaffolding and provocations provided by the teacher, but a necessary condition for them to emerge is that the medium of the game provides a narrative space, where the mathematical game-pieces of the game can become objects to talk with.

Related Patterns

list other patterns related to this one, under categories such as component, assisting, conflicting, uses this, etc.

Notes, Links and References

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Licensing

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