Index. B Balance beam, 26 Bourbaki, 167 Bracket, 33, 36 38, 40, 41, 49, 134 Brossard, M., 189

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1 Bibliography Broin, D. (2002). Arithmétique et algèbre élémentaires scolaires. Unpublished Thèse Université Bordeaux 1. Brousseau, G. (1965). Les mathématiques du cours préparatoire. Paris: Dunod. Brousseau, G. (1970). Processus de mathématisation, Exemple de processus de mathématisation: l addition dans les naturels: CP-CE1, La mathématique à l école élémentaire (pp , ). Paris: APMEP (1972). Brousseau, G. (1980). Problèmes d enseignement des décimaux (Recherche en didactique des mathématiques, Vol. 1.1, pp ). Grenoble: La pensée Brousseau, G. (1981). Problèmes de didactique des décimaux (Recherches en didactique des mathématiques, Vol. 2.1). Grenoble: La pensée Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes en mathématiques. In Recherches en Didactique des Mathématiques. Vol 4, n 2, (pp ). Grenoble: La pensée Brousseau, G. (1995). Notes à propos de l article de Thurston. On Proof and Progress in mathematics. Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Trans.). Dordrecht: Kluwer Press. Brousseau, G. (1998). La théorie des situations didactiques. Recueil de textes de Didactique des mathématiques présentés par M. Cooper, N. Balacheff, R. Sutherland, V. Warfield. Grenoble: La pensée Brousseau, Guy & Antibi, André (2000). La dé-transposition des connaissances scolaires. In Recherches en Didactique des Mathématiques Vol. 20/1, (pp. 7 40). Grenoble: La pensée Brousseau, N., & Brousseau, G. (1987). Rationnels et décimaux dans la scolarité obligatoire. de Bordeaux: IREM. Brousseau G. & Warfield V.M. (1999). The case of Gaël. Journal of Mathematical Behavior, 18(1), 7 52(46). Elsevier. Brousseau, G., Brousseau, N., & Warfield, V. (2002). An experiment on the teaching of statistics and probability. Journal of Mathematical Behavior, 20, Elsevier. Brousseau, G., Brousseau, N., & Warfield, V. (2004). Rationals and decimals as required in the school curriculum Part 1: Rationals as measurement. Journal of Mathematical Behavior, 23, Elsevier. Brousseau, G., Brousseau, N., & Warfield, V. (2007). Rationals and decimals as required in the school curriculum Part 2: From rationals to decimals. Journal of Mathematical Behavior, 26, Elsevier. G. Brousseau et al., Teaching Fractions through Situations: A Fundamental Experiment, DOI / , Springer Science+Business Media B.V

2 212 Bibliography Brousseau, G., Brousseau, N., & Warfield, V. (2008). Rationals and decimals as required in the school curriculum. Part 3: Rationals and decimals as linear functions. Journal of Mathematical Behavior, 27, Elsevier. Brousseau, G., Brousseau, N., & Warfield, V. (2009). Rationals and decimals as required in the school curriculum. Part 4: Problem-solving, Composed Mapping and Division. Journal of Mathematical Behavior, 28, Elsevier. Flanders, Ned A. (1976). Analyse de l interaction et formation. In Morrison, A. & Mc Intyre (eds) Psychologie sociale de l enseignement. Paris: Dunod. Gonseth, F. (1974). Les mathématiques et la réalité, (1936). Paris: Librairie Albert Blanchard. Gras R., et Kuntz P. (2008). An overview of the Statistical Implicative, Statistical Implicative Analysis, R. Gras, E. Suzuki, F. Guillet and F. Spagnolo, Eds, Springer-Verlag, Berlin- Heidelberg, p Lebesgue, H. (1975). La mesure des grandeurs, ( ). Paris: Librairie Albert Blanchard. Odier, Antoine. (1955). Souvenirs d une vielle tige. Arthéme Fayard. Ratsimba-Rajohn, H. (1982). Eléments d étude de deux méthodes de mesures rationnelles (Recherches en didactique des mathématiques, Vol. 3.1). Grenoble: La pensée Rouchier, A., et al. (1980). Situations et processus didactiques dans l étude des nombres rationnels positifs (Recherches en didactique des mathématiques, Vol. 1.2). Grenoble: La pensée Thurston, W. P. (1994). On proof and progress in mathematics. Bulletin of the American Mathematical Society, 30, , with commentary on pp Warfield, Virginia McShane. (2007). Invitation to Didactique. USA: Xlibris. Whitney, H. (1968). The mathematics of physical quantities, Part I Mathematical model for measurement. The American Mathematical Monthly, 75, Whitney, H. (1968). The mathematics of physical quantities, Part II Quantity, structure and dimensional analysis. The American Mathematical Monthly, 76,

3 Index A Addition, 12, 18 20, 43, 48, 63, 74, 159 A-didactical, 147, , 157 A-didactical situations, 148, 149, 201 Algorithms, 19, 65, 78, 84, 92, 100, 125, 131, 148, 155, 206 Analogy(ies), 88, 205 Approximation, 23, 26, 49, 65, 162 Arrows, 85, 99, 118, 120, 121, 206, 207 Assessment(s), 20, 25, 130, 141, , 207 B Balance beam, 26 Bourbaki, 167 Bracket, 33, 36 38, 40, 41, 49, 134 Brossard, M., 189 C Cabri geometry, 201 Castelnuovo, E., 170 Centre des Observations pour Recherches en Éducation en Mathématiques (COREM), 1, 6 8, 100, 127, 128, 166, 168, 175, 179, 182, 184, 197 Choquet, G.A.A., 170 Codes, 10 11, 28 Colmez, 170 Comenius, 190 Commensuration, 6, 10 15, 26, 29 31, 93, 131, 161 Communication(s), 11 12, 15, 27 30, 148, 152, 156, 199 Connaissance(s), 89, , 135, 136, , 155, 156, 163, 189, , , Construction, 26 Construction paper, 28 Constructivist, 5, 49, 128, 129 COREM. See Centre des Observations pour Recherches en Éducation en Mathématiques (COREM) Cultural knowledge, 54 D Decimal filters, Decimal fractions, 45, 47, 48, 78 Decroly, O., 169 Devolution, 149, 151 Dewey, J., 169 Didactical, 2, 7, 8, 18, 20, 23, 88, 89, 92, 99, 129, , 136, 138, , , 159, 161, , 174, 178, 181, 184, 185, , , , 204, 208 contract, 197, situation, 89, Distributivity, 74 Division, 24 25, 42, 48 50, 54, 55, 58, 59, 85, , 112, , 163, 178, 204 Drill, 20, 47, 59 Dunod, 191 Dunot, 170 E Eiffel, 180 Epistemological obstacles, Equivalence, 6, 16 17, 30, 93, 95 Equivalent, 15 16, 22, 40, 99 Evaluation(s), 25, 36, 121, 132, , , 184, G. Brousseau et al., Teaching Fractions through Situations: A Fundamental Experiment, DOI / , Springer Science+Business Media B.V

4 214 F Félix, L., 170 Freinet, C., 169 G Gattegno, C., 170 Glaeser, G., 181 Glasses, 6, 26, 27 Gonseth, F., 190 Gréco, P., 170, 185 H Hennequin, P.L., 185 Heuristics, 88 I Implicit models, , 200, 201 Institutes for Research in Mathematics Education (IREM), 4, 7, , 185, 186 Instituteur, 188 Institutionalization, 2, 138, , 148, 201, 202 Institutionalized, 49, 50, 57, 65, 77, 82, 96, 120, 132, 151 IREM. See Institutes for Research in Mathematics Education (IREM) L La Borderie, R., 170 Lichnerowicz, , 175, 176, Linear, 51, 70, 78 89, 93, 94, , 114, 115, 117, 119, , 158, 159 Linearity, 70, 106, 158 Linear mappings, 51, 79, 81, 93, 94, 107, 110, 114, 115, 117, , 160, 161 M Malgrange, B., 185 Mathematical situations, 132, , 200, 202, 205 Mathematical slippages, 206 Mathematization, 86, 189, 196 Mental calculations, 19, 21, 61 Metadidactical slippage, 88, 89, 99, 121 Metaphor(s), 30, 91, 100, 136, 193, 205 Meta-situation, 205 Milieu, 138, 147, 191, 200, 201, 205 Multiplication, 18, 24, 30, 48, 57, 59, 62, 74, 75, 78, 86, 90, 94 98, 100, 110, 113, 159, 163, 178 N Number line, 41 45, 139 O Obsolescence, Odier, A., 180 Operator, 56 Optimist, 63 65, 67, 69, 78, 97, 98, 100, 136, 163 Ordered pairs, 15 17, 29, 97, 161 P Papy, G., 169, 170 Partitioning, 28, 92, 93 Pedagogy, 170, 171, 187, 188 Pescarini A., 170 Piaget, J., 169, 172, , 193 Pisot, C., 169 Pluvinage, F., 181 Polya, G., 88 Precision, 2, 15, 26, 28, 86, 91, 142, 144, 153, 155, 159 Proportional, 63, 64, 69, 70, 72, 73 Puzzle, 6, 51 55, 61, 69, 70, 136, 159 R Ratio, 63, 66, 68, 81, 82, 86, 93, 119 Reciprocal, 73, 94 96, 98, , 160 Representation, Index S Savoirs, 89, , 135, 137, , , 152, 153, 155, 156, 163, 189, 191, 192, , , 203, 205, 206 Servais W., 170 Situations of actions, 140, , 192, 201, 202 of communication, 68, 140, 152, 192 of evaluation, of formulation, 140, , 201, 202

5 Index 215 of institutionalization, 139, , 192, 196 of validation, 140, 151, 192, 201, 202 Spiral method, 174, 176 Strategies, 12, 17, 19, 21, 34, 38, 40, 42, 52, 53, 60, 61, 64 66, 76, 92, 139, 151, 153 Sum, 18 21, 36, 70, 81, 85, 90, 91, 94, 159 T Tessellation, 60, 137 Touanet, H., 185 Tournament of problems, 79 U Unsaid, 2, 157 V Vergnaud, G., 183 Vocabulary, 12, 16, 30, 100, 120, 152, 161, 171, 175, 178 Vygotsky, L.S., 169 Z Zamanski, M., 169