Mental mathematics under the lens: Strategies, oral mathematics, enactments of meanings

The Journal of Mathematical Behavior - Tập 56 - Trang 100725 - 2019
Jérôme Proulx1
1Laboratoire Épistémologie et Activité Mathématique, Département de Mathématiques, Université du Québec à Montréal, C.P. 8888, Succ. Centre-Ville, Montreal, QC, H3C 3P8, Canada

Tài liệu tham khảo

Alain (1932/1967). Propos sur l’éducation. Paris: Les presses universitaires de France. Anghileri, 2001 Bass, 2003, Computational fluency, algorithms, and mathematical proficiency: One mathematician’s perspective, Teaching Children Mathematics, 9, 322, 10.5951/TCM.9.6.0322 Bednarz, 1992, ). L’enseignement de l’algèbre au secondaire: une caractéristique du scénario actuel et des problèmes qu’il pose aux élèves, 21 Butlen, 1990, Calcul mental, calcul rapide, Grand N, 47, 35 Butlen, 1992, Calcul mental et résolution de problèmes multiplicatifs, une expérimentation du CP en CM2, Recherches en didactique des mathématiques, 12, 319 Caracciolo, 2012, Narrative, meaning, interpretation: An enactivist approach, Phenomenology and the Cognitive Sciences, 11, 367, 10.1007/s11097-011-9216-0 Davis, 1995, Why teach mathematics? Mathematics education and enactivist theory, For the Learning of Mathematics, 15, 2 Davis, 1996, Cognition, co-emergence, curriculum, Journal of Curriculum Studies, 28, 151, 10.1080/0022027980280203 Di Paolo, 2010, Horizons for the enactive mind: Values, social interaction, and play, 33 Gattuso, 1997, La moyenne, un concept évident?, Bulleting AMQ, 37, 10 Gordon Calvert, 2001 Hamilton, 2007, What changes are occurring in the kind of problem-solving situations where mathematical thinking is needed beyond school?, 1 Hazekamp, 1986, Components of mental multiplying, 116 Heirdsfield, 2004, Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers, The Journal of Mathematical Behavior, 23, 443, 10.1016/j.jmathb.2004.09.005 Lave, 1988 Lockhart, 2017 Maturana, 1987, Everything is said by an observer, 65 Maturana, 1988, Reality: The search for objectivity of the quest for a compelling argument, The Irish Journal of Psychology, 9, 25, 10.1080/03033910.1988.10557705 Maturana, 1992 Murphy, 2004, How do children come tu use a taught mental calculation strategy?, Educational Studies in Mathematics, 56, 3, 10.1023/B:EDUC.0000028403.25781.79 Noss, 2002, Mathematical epistemologies at work, vol. 1, 47 Nunes, 1993 Osana, 2018, Commonalities, complementarities, and contrasts between an educational psychologist and a mathematics educator in an examination of mental computation and relational thinking, Journal of Numerical Cognition, 4, 59, 10.5964/jnc.v4i1.89 Plunkett, 1979, Decomposition and all that rot, Mathematics in Schools, 8, 2 Poirier, 1990, Évolution du rôle et de l’importance du calcul mental dans les programmes d’études québécois, Bulletin AMQ, 30, 5 Proulx, 2013, Mental mathematics, emergence of strategies, and the enactivist theory of cognition, Educational Studies in Mathematics, 84, 309, 10.1007/s10649-013-9480-8 Proulx, 2013, Le calcul mental au-delà des nombres : conceptualisations et illustrations avec la résolution d’équations algébriques, Annales de didactique et de sciences cognitives, 18, 61 Proulx, 2015, Mental mathematics with mathematical objects other than numbers: The case of operation on functions, The Journal of Mathematical Behavior, 39, 156, 10.1016/j.jmathb.2015.07.001 Proulx, 2015, Mental mathematics and enactment of specific strategies: The case of systems of linear equations, 173 Proulx, 2017, Le calcul mental en mathématiques : Quels potentiels pour l’activité mathématique ?, Canadian Journal of Science, Mathematics and Technology Education, 17, 288, 10.1080/14926156.2017.1378833 Proulx, 2017, From problem-solving to problem-posing, and from strategies to laying down a path in solving – Taking Varela’s ideas to mathematics education research, Constructivist Foundations, 13, 701 Proulx, 2013, On the emergence of mental mathematics strategies, 328 Proulx, 2017, Équations algébriques et activité mathématique en calcul mental : regard sur les défis d’enseignement, Annales de didactique et de sciences cognitives, 22 Reid, 1996, Enactivism as a methodology, Vol. 4, 203 René de Cotret, 1999, Perspective bio-cognitive pour l’étude des relations didactiques, 103 1994 Rezat, 2011, Mental calculation strategies for addition and subtraction in the set of rational numbers, 396 Richards, 1991, Mathematical discussions, 13 Schmidt, 1997, Raisonnements arithmétiques et algébriques dans un contexte de résolution de problèmes: Difficultés rencontrées par les futurs enseignants, Educational Studies in Mathematics, 32, 127, 10.1023/A:1002946500851 Siegler, 1996 Star, 2013, Procedural and conceptual knowledge: exploring the gap between knowledge type and knowledge quality, Canadian Journal of Science Mathematics and Technology Education, 13, 169, 10.1080/14926156.2013.784828 Thom, 2009, Perceptually guided action: Invoking knowing as enaction, vol. 1, 249 Thompson, 2009, Mental calculation, Mathematics Teaching, 213, 40 Threlfall, 2002, Flexible mental calculations, Educational Studies in Mathematics, 50, 29, 10.1023/A:1020572803437 Threlfall, 2009, Strategies and flexibility in mental calculation, ZDM, 41, 541, 10.1007/s11858-009-0195-3 Torrance, 2005, In search of the enactive, Phenomenology and the Cognitive Sciences, 4, 357, 10.1007/s11097-005-9004-9 Varela, 1987, Laying down a path in walking, 48 Varela, 1996 Varela, 1999 Varela, 1991 Vermette, 2017, Enseignants de mathématiques et connaissances statistiques: le cas de la variabilité, Canadian Journal of Science Mathematics and Technology Education, 17, 219, 10.1080/14926156.2017.1299892 Watson, 1980 Zack, 2003, Good-enough understanding: Theorising about the learning of complex ideas (part 1), For the Learning of Mathematics, 23, 43 Zack, 2004, Good-enough understanding: Theorising about the learning of complex ideas (part 2), For the Learning of Mathematics, 24, 24