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MIDDLE GRADERS’ EMERGENT STRATEGIES USING
ELECTRONIC MATHEMATICAL BOARD GAMES
Veronica Hoyos
Universidad Pedagogica Nacional
Guadalupe Rodriguez
Universidad Pedagogica Nacional
Here we present the results of an exploratory study into the functionality of a digital board
game called Domino, in the learning of mathematics at middle school. In particular, we have
some results from possible mathematical connections that students establish with other notions
or processes of Math curriculum arising from playful experience. Although the intended
mathematical structure of the game is symmetry, the actual structure defines a potential
organization that the children concretize in different ways once they are engaged in the task
for winning strategies.
To accomplish the exploratory study presented here, the digital board game Domino was
designed (Raggi, 2006). Symmetry is the underlying mathematical structure for this game.
When playing, a winning strategy is to place your dominos symmetrically opposite the
opponent’s placements. This computer game was introduced into the classroom as an
exploratory material to advance knowledge of how use of this type of concrete materials
mediates the development of mathematical activity among middle students. In this case, each of
the students had to initially play against the computer, called here Robi. The task asked of them
was to find a way to beat Robi or, if Robi won, to try to explain why Robi was able to beat
them.
Theoretical Underpinnings and Methodology
Although the potential of digital games as rich learning tools is widely recognized (Sanford,
2006), the great improvements at schools have not yet materialized (Wijekumar et al., 2005).
According to Wijekumar et al. (2005), it is still necessary to work moving students from a
game affordance of a computer to a learning mode.
However among the initiatives of using games to try to encourage students to learn specific
topics, are those that try to foster visual reasoning and self-engaging tasks designing a game
construction kit (Kahn et al. 2006), or to explore the affordances of the utilization of
mathematical electronic board games (Rodriguez, 2007), even to promote general action
patterns for solving math or science problems.
Applying Saxe and Bermudez’s (1996) theoretical constructs, RodrĂguez (2007) analyzed
children’s mathematical activity in relation with the affordances of the Dominó computer game.
Saxe and Bermudez (1996) pointed out that, even though there is an intended structure in a
board game (in their investigation they used the specially designed treasure hunt,) another
actual structure emerges as children play. In fact, artifacts and conventions used, reformulation
of rules, and also children’s prior understanding will give form to an alternate structure, which
could partially respect the previously intended, to establish new emergent mathematical
environments.
According to Saxe and Bermudez (1996), a mathematical environment is built by the
constructions the child performs in interaction with the tools or materials available. These
constructions must be understood or analyzed in that same environment, without overlooking
the child’s previous knowledge, so that we may understand how that child comprehends the
new knowledge or how a new conception of a mathematical object occurs.
Lamberg, T., & Wiest, L. R. (Eds.). (2007). Proceedings of the 29
th
annual meeting of the North
American Chapter of the International Group for the Psychology of Mathematics Education.
Stateline (Lake Tahoe), NV: University of Nevada, Reno.
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