Abstract
In this paper we present a summary of the results of our research concerning 2-player combinatorial games and its applications used to teach the know-hows of the mathematical activity via certain a-didactical research situations, called SiRCs, that transpose to the classroom the activity of an actual researcher in mathematics. We use a specific kind of combinatorial game called Nim-type games and here we only present in some detail a game called the chocolate game. Our main conclusion is that SiRCs based on Nim-type combinatorial games are effective tools to introduce a genuine (but not necessarily original) mathematical research activity to students from high school and above.
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References
Berlekamp, E., Conway, J., & Guy, R. (2001). Winning ways for your mathematical plays. Natick, Wellesley, MA: A. K. Peters Ltd.
Brousseau, G. (1998). Théorie des situations didactiques. Grenoble: La pensée sauvage éditions.
Colipan, X. (2014). Étude didactique des situations de recherche pour la classe concernant des jeux combinatoires de type Nim (Thèse de Doctorat). Université de Grenoble.
Colipan, X. (2015). Desarrollo de la actividad científica en clases a través del estudio de juegos combinatorios, el ejemplo del juego del chocolate. Boletim de Educação Matemática. Bolema, Rio Claro (SP), 30(55), 691–712.
Colipan, X. (2016). A version of the game Euclid and Stacked b-Nim (preprint).
Colipan, X., & Grenier, D. (2015). Le jeu d’Euclide géométrique, une situation recherche pour construire et développer les savoir-faire fondamentaux de l’activité mathématique (preprint).
Coppé, S., & Houdement, C. (2002). Réflexions sur les activités concernant la résolution de problèmes à l’école primaire. Grand N, Grenoble, 69, 53–63.
Delahaye, J. (2009). Stratégies magiques au pays de Nim. Pour la Science, 307, 88–93.
Duchêne, E. (2006). Jeux combinatoires sur les graphes (Thèse de Doctorat). Université de Grenoble.
Giroud, N. (2011). Étude de la démarche expérimentale dans les situations de recherche pour la classe (Thèse de Doctorat). Université de Grenoble.
Godot, K. (2005). Situations recherche et jeux mathématiques pour la formation et la vulgarisation, exemple de la rue aux couleurs (407f. Thèse de Doctorat). Grenoble: Université Joseph Fourier.
Godot, K. (2006). La rue aux couleurs: Une situation recherche pour apprendre à chercher dès le cycle 3. Grand N, Grenoble, 78, 31–52.
Gravier, S., & Ouvrier-Buffet, C. (2009). Research-situations for teaching mathematics. In Challenging mathematics in and beyond the classroom (pp. 22–29).
Grenier, D., & Payan, C. (2002). Situations de recherche en classe: essai de caractérisation et proposition de modélisation. Actes du séminaire national de didactique de mathématiques. ARDM, pp. 189–205.
Grundy, P. (1939). Mathematiques and games. Eureka, 27, 9–11.
Rougetet, L. Machines designed to play Nim games (1940–1970): A possible (re)use in the modern French mathematics curriculum? In E. W. Hart & J. Sandefur (Eds.), Teaching and learning discrete mathematics in the school curriculum worldwide. Berlin: Springer.
Sprague, R. (1935). Über mathematische Kampfspiele. Tohoku Mathematical Journal, 41, 438–444.
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Colipan, X. (2018). Mathematical Research in the Classroom via Combinatorial Games. In: Hart, E., Sandefur, J. (eds) Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70308-4_14
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DOI: https://doi.org/10.1007/978-3-319-70308-4_14
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