159
Principal Results and Conclusions
A result of seventh graders playing against Robi was a rapid turn toward a different
winning strategy, one which consisted of trying to leave blank spaces, and counting out how
many were necessary according to which turn they had. They were able then to display their
arithmetical abilities to find a new and not expected winning strategy.
Concerning eighth grade students, they recognized that symmetry was the intended
structure of the game, in accordance with they had studied this topic the previous year. It is
likely that the structure and function of the artifact employed (Domino) in this context have
fostered cognitive development (Verillon and Rabardel, 1995), since it was observed that when
students used a strategy that they believed to be a winner, they continued to use it and perfected
it as long as it was functional, or discovered an alternative one.
Moreover, an opponent strategy, which began to be a winning one, was a cause for
reflection and reformulation or construction of the new winning strategy. This heuristic is a
characteristic for problem solving (Polya, 1954) promoted by the competition situation of the
game. Nonetheless, the potential of this type of psychological instrument is still to be
determined for solving specific math problems.
Endnote
1. The topic of symmetry is part of the curriculum for seventh graders; thus eighth grade
students should have encountered this topic the previous year. In effect, this situation might be
confirmed by applying the game in class with eighth students, since many of them quickly
noticed that one way to win was to mirror the opponent’s moves symmetrically.
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