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Middle graders’ emergent strategies using electronic mathematical board games
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Concerning the Domino computer game, it was introduced in two middle school Math
classes, each with approximately 25 students. In fact the game proved to serve as a tool to diagnose the state of the knowledge of symmetry among seventh and eight grade students, previous to the instrumentation of other teaching cycles with other computational material, (a dynamic geometry software). Figure 1 shows the screen the game displays:
Figure 1: Screenshot of the Domino computer board game
The work sessions with the game were video-recorded, as were some of the instructor-
student interviews when the games ended. These interviews aimed to record student hypotheses, conjectures, and explanations of the possible winning strategies; and important data was obtained after transcribing the protocols extracted from both video sources.
The fact should be highlighted that when the game was first shown to them the theme of
symmetry had not yet been presented to the seventh graders. They did not recognize symmetry in Robi’s way of playing or winning. Rather, they developed another winning strategy, one based on counting and building inaccessible spaces on the board. Such was not the case with eighth graders (1), who had had symmetry presented to them the year before. In general, student performance of the eighth school year reveal that, as long as they experiment with the game and during execution of the task, they were able to activate mental processes that allowed them to demonstrate a pattern of behavior as such that characteristic to the mathematical activity related with problem solving (see Polya, 1954).
From a Verillon and Rabardel (1995) point of view, an artifact’s structure and function will
foster certain knowledge or effect in cognitive development. It is to say that the introduction and use of instruments, whether material or psychological (language, computational means, symbols, diagrams, maps, etc.) leads to consummating many structural and functional changes in the learner’s cognition. Vygotsky confirms this in these affirmations:
A complete series of new functions tied to the use and control of the chosen instrument are activated; the labor performed by the instrument makes an entire series of natural process worthless and replaces them; [the instrument] transforms the development and particular aspects (intensity, duration, continuity, etc.) of all the processes involved in the composition of the instrumental act. [In this way the instrument constitutes itself as] a new interceding element situated between the object
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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| | Authors: Hoyos, Veronica. and Rodriguez, Guadalupe. |
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157
Concerning the Domino computer game, it was introduced in two middle school Math
classes, each with approximately 25 students. In fact the game proved to serve as a tool to
diagnose the state of the knowledge of symmetry among seventh and eight grade students,
previous to the instrumentation of other teaching cycles with other computational material, (a
dynamic geometry software). Figure 1 shows the screen the game displays:
Figure 1: Screenshot of the Domino computer board game
The work sessions with the game were video-recorded, as were some of the instructor-
student interviews when the games ended. These interviews aimed to record student
hypotheses, conjectures, and explanations of the possible winning strategies; and important
data was obtained after transcribing the protocols extracted from both video sources.
The fact should be highlighted that when the game was first shown to them the theme of
symmetry had not yet been presented to the seventh graders. They did not recognize symmetry
in Robi’s way of playing or winning. Rather, they developed another winning strategy, one
based on counting and building inaccessible spaces on the board. Such was not the case with
eighth graders (1), who had had symmetry presented to them the year before. In general,
student performance of the eighth school year reveal that, as long as they experiment with the
game and during execution of the task, they were able to activate mental processes that allowed
them to demonstrate a pattern of behavior as such that characteristic to the mathematical
activity related with problem solving (see Polya, 1954).
From a Verillon and Rabardel (1995) point of view, an artifact’s structure and function will
foster certain knowledge or effect in cognitive development. It is to say that the introduction
and use of instruments, whether material or psychological (language, computational means,
symbols, diagrams, maps, etc.) leads to consummating many structural and functional changes
in the learner’s cognition. Vygotsky confirms this in these affirmations:
A complete series of new functions tied to the use and control of the chosen
instrument are activated; the labor performed by the instrument makes an entire series
of natural process worthless and replaces them; [the instrument] transforms the
development and particular aspects (intensity, duration, continuity, etc.) of all the
processes involved in the composition of the instrumental act. [In this way the
instrument constitutes itself as] a new interceding element situated between the object
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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