Auteurs et bibliographie en mathématiques

Module 1 : Réapprentissage du sens des Nombres – Pr André Knops

https://www.lapsyde.com/membres/andre-knops

 

• Barbieri, Christina A., et al. "Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies." Journal of Educational Psychology 112.3 (2020): 628.
• Knops, A. (2018). Neurocognitive evidence for spatial contributions to numerical cognition. In Heterogeneity of function in numerical cognition (pp. 211-232). Academic Press.
• Park, J., and Brannon, E. M. (2014). Improving arithmetic performance with number sense training: an investigation of underlying mechanism. Cognition 133, 188–200. doi: 10.1016/j.cognition.2014.06.011
• Park, J., and Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychol. Sci. 24, 2013–2019. doi: 10.1177/0956797613482944
• Reinert, R. M., Huber, S., Nuerk, H. C., & Moeller, K. (2015). Multiplication facts and the mental number line: evidence from unbounded number line estimation. Psychological Research, 79, 95-103.
• Sobkow, A., Fulawka, K., Tomczak, P., Zjawiony, P., & Traczyk, J. (2019). Does mental number line training work? The effects of cognitive training on real-life mathematics, numeracy, and decision making. Journal of Experimental Psychology: Applied, 25(3), 372.
• Szkudlarek, E., and Brannon, E. M. (2018). Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers. Front. Psychol. 9:606. doi: 10.3389/fpsyg.2018.00606

 

Module 2 : Comprendre les notions de proportion et de fraction – Dr Laurianne Vagharchakian

 

• Abdul Aziz Alahmadati (2016). Autour du concept de fraction à l’école primaire, des représentations et des connaissances des élèves de cycle III. Thèse présentée et soutenue publiquement le 29 janvier 2016
• Ruggeri A, Vagharchakian L, Xu F. Icon arrays help younger children's proportional reasoning. Br J Dev Psychol. 2018 Jun;36(2):313-333. doi: 10.1111/bjdp.12233. Epub 2018 Jan 22. PMID: 29357112.

Module 3: Nombre et Calcul – Pr Emmanuel Sander

 

Module 4 : Calcul littéral – Pr Emmanuel Sander

 

Module 6 : Utiliser les grandeurs et mesures pour consolider la compréhension de notion de proportionnalité – Pr Emmanuel Sander

https://www.unige.ch/fapse/idea/equipe/sander

 

• Bassok, M., Wu, L.L., & Olseth, K.L. (1995). Judging a book by its cover: Interpretative effects of content on problem-solving transfer. Memory and Cognition, 23, 354-367.
• Bell, A., Swan, M., & Taylor, G. (1981). Choice of operation in verbal problems with decimal numbers. Educational Studies in Mathematics, 12(4), 399 420.
• Bonato, M., Fabbri, S., Umiltà, C., & Zorzi, M. (2007). The mental representation of numerical fractions: Real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33(6), 1410 1419.
• DeWolf, M., Grounds, M. A., Bassok, M., & Holyoak, K. J. (2014). Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance, 40(1), 71 82.
• DeWolf, M., & Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39 49.
• Fischbein, E. (1989). Tacit models and mathematical reasoning, For the Learning of Mathematics, 9, 9-14
• Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for research in mathematics education, 3-17.
• Frederick, S. (2005). Cognitive Reflection and Decision Making. Journal of Economic Perspectives, 19 (4), 25-42.
• Gamo, S., Nogry, S., & Sander, E. (2014). Apprendre à résoudre des problèmes en favorisant la construction d'une représentation alternative chez des élèves scolarisés en éducation prioritaire, Psychologie française, 59(3), 215-229.
• Gamo, S., Sander, E., & Richard, J-F. (2010). Transfer of strategies by semantic recoding in arithmetic problem solving. Learning and Instruction, 20, 400-410.
• Gros, H., Thibaut, J.-P., & Sander, E. (2020). Semantic congruence in arithmetic: A new model for word problem solving. Educational Psychologist, 55 (2), 69-87.
• Gvozdic, K., & Sander, E. (2018). When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ arithmetic word problem solving strategies. Educational Studies in Mathematics, 98(2), 157-175.
• Gvozdic, K., & Sander, E. (2020). Learning to be an opportunistic word problem solver: Going beyond informal solving strategies. ZDM Mathematics Education, 52 (1), 111-123.
• Hatano, G. (2003). Foreword. In A.J. Baroody, & A. Dowker (Eds.), The Development of Arithmetic Concepts and Skills (pp. xi–xiii). Mahwah, NJ: Lawrence Erlbaum Associates.
• Hersant, M. (2005). La proportionnalité dans l’enseignement obligatoire en France, d’hier à aujourd’hui. Repères IREM, (59), 5 41.
• Klahr, D., & Chen, Z. (2011). Finding one's place in the transfer space. Child Development Perspectives, 5, 196-204.
• Lakoff, G., & Núñez, R. (2000). Where mathematics comes from. How the embodied mind brings mathematics into being. New York, NY: Basic Books.
• Lautrey, J., Rémi-Giraud, S., Sander, E., & Tiberghien, A. (2008). Les connaissances naïves. Paris, Armand Colin.
• Nguyen-Xuan, A., Nicaud, J.-F., Bastide, A., & Sander, E. (2002). Les expérimentations du projet Aplusix. Sciences et Techniques Educatives, 9, 1-2, 63-91.
• Ni, Y., & Zhou, Y.-D. (2005). Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias. Educational Psychologist, 40(1), 27 52
• Sander, E. (2007). Manipuler l’habillage d’un problème pourévaluer les apprentissages, Bulletin de psychologie, 60, 119-124.
• Sander, E. (2008). Les connaissances naïves en mathématiques. Dans J. Lautrey, S. Rémi-Giraud, E. Sander et A. Tiberghien (Dir). Les connaissances naïves (pp 57-102). Paris : Armand Colin.
• Sander, E. (2017). Les connaissances issues de la vie quotidienne et les apprentissages scolaires. In R. Miljkovitch, F. Morange-Majoux and E. Sander (Eds.), Psychologie du Développement (pp. 217-225). Paris, Elsevier-Masson
• Sander, E. & Richard, J.-F. (2017). Les apprentissages numériques. In R. Miljkovitch, F. Morange-Majoux and E. Sander (Eds.), Psychologie du Développement (pp. 251-258). Paris, Elsevier-Masson
• Sander, E. (2018). La résolution de problèmes arithmétiques à énoncés verbaux. ANAE (Approche Neuropsychologique des Apprentissages chez l’Enfant), 156, 611-619.
• Sander, E., Nicaud, J-F, Chaachoua, H., Croset, M-C. (2005). From usage analysis to automatic diagnosis: The case of the learning of algebra. Proceedings of workshop Usage Analysis in Learning Systems. 12th International Conference on Artificial Intelligence in Education (AIED 2005) (pp. 45-52), Amsterdam, The Netherlands.
• Sander, E., Nguyen-Xuan, A., Nicaud, J.-F., & Bastide, A. (2000). Fine-tuning the pedagogical design of APLUSIX. Proceedings of workshop “Learning algebra with the computer”. ITS2000, Montréal, Canada.
• Scheibling-Sève, C., Pasquinelli, E., & Sander, E. (2017). Developing cognitive flexibility in solving arithmetic word problems. In B. C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 39th Annual Conference of the Cognitive Science Society (pp. 3076-3081). London, UK: Cognitive Science Society.
• Scheibling-Sève, C., Pasquinelli, E., & Sander, E. (2020) Assessing conceptual knowledge through solving arithmetic word problems. Educational Studies in Mathematics (103), 293-311.
• Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909 918.
• Sophian, C. (2007). Measuring spatial factors in comparative judgments about large numerosities. In International Conference on Foundations of Augmented Cognition ,157-165.
• Tirosh, D., & Graeber, A. O. (1991). The influence of problem type and primitive models on preservice elementary tearchers’ about division. School Science and Mathematics, 91, 157-163.
• Thagard, P., Holyoak, K.J., Nelson, G, & Gochfeld, D. (1990). Analog retrieval by constraint satisfaction. Artificial Intelligence, 46, 259-310
• Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and instruction, 28(2), 181-209.
• Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23(1), 57-86.

 

Module 5: Organisation et gestion de données, fonctions – Dr Valeria Giardino

http://www.institutnicod.org/membres/membres-statutaires/giardino-valeria/

 

• Cleveland, W., & McGill, R. (1985). Graphical Perception and Graphical Methods for Analyzing Scientific Data. Science, New Series, 229(4716), 828–833.
• Godau, C., Vogelgesang, T., & Gaschler, R. (2016). Perception of bar graphs – A biased impression? Computers in Human Behavior, 59, 67–73. https://doi.org/10.1016/j.chb.2016.01.036
• Khayat, N., & Hochstein, S. (2018). Perceiving set mean and range: Automaticity and precision. Journal of Vision, 18(9), 23.
• Panavas, L., Worth, A. E., Crnovrsanin, T., Sathyamurthi, T., Cordes, S., Borkin, M. A., & Dunne, C. (2022). Juvenile Graphical Perception: A Comparison between Children and Adults. CHI Conference on Human Factors in Computing Systems, 1–14. https://doi.org/10.1145/3491102.3501893
• Poulton, E. C. (1985). Geometric illusions in reading graphs. Perception & Psychophysics, 37(6), 543–548. https://doi.org/10.3758/BF03204920
• Solomon, J. A. (2010). Visual discrimination of orientation statistics in crowded and uncrowded arrays. Journal of Vision, 10(14), 19–19. https://doi.org/10.1167/10.14.19

 

Rôle de intuitions graphiques et des inférences statistiques

• Brehmer, B. (1971). Subjects’ ability to use functional rules. Psychonomic Science, 24(6), 259–260. https://doi.org/10.3758/BF03328999
• Carroll, J. D. (1963). Functional learning: The learning of continuous functional mappings relating stimulus and response continua. ETS Research Bulletin Series, 1963(2), i–144. https://doi.org/10.1002/j.2333-8504.1963.tb00958.x
• Chong, S. C., & Treisman, A. (2005). Statistical processing: Computing the average size in perceptual groups. Vision Res, 45(7), 891–900.
• Ciccione, L., & Dehaene, S. (2021). Can humans perform mental regression on a graph? Accuracy and bias in the perception of scatterplots. Cognitive Psychology, 128, 101406. https://doi.org/10.1016/j.cogpsych.2021.101406
• Ciccione, L., & Dehaene, S. (2022). Graphicacy skills across ages and cultures: a new assessment tool of intuitive statistics' abilities. In Proceedings of the Annual Meeting of the Cognitive Science Society (Vol. 44, No. 44).
• Ciccione, L., Dehaene, G., & Dehaene, S. (2022). Outlier detection and rejection in scatterplots: Do outliers influence intuitive statistical judgments? Journal of Experimental Psychology: Human Perception and Performance. https://doi.org/10.1037/xhp0001065
• Ciccione, L., Sablé-Meyer, M., & Dehaene, S. (2022). Analyzing the misperception of exponential growth in graphs. Cognition, 225, 105112. https://doi.org/10.1016/j.cognition.2022.105112
• Ciccione, L., Sable-Meyer, M., Boissin, E., Josserand, M., Potier-Watkins, C., Caparos, S., & Dehaene, S. (2022). Graphicacy across age, education, and culture: a new tool to assess intuitive graphics skills. bioRxiv.
• Curcio, F. R. (1987). Comprehension of Mathematical Relationships Expressed in Graphs. Journal for Research in Mathematics Education, 18(5), 382. https://doi.org/10.2307/749086
• Harvey, N., Ewart, T., & West, R. (1997). Effects of Data Noise on Statistical Judgement. Thinking & Reasoning, 3(2), 111–132. https://doi.org/10.1080/135467897394383
• Juslin, P., Winman, A., & Hansson, P. (2007). The naïve intuitive statistician: A naïve sampling model of intuitive confidence intervals. Psychological Review, 114(3), 678–703. https://doi.org/10.1037/0033-295X.114.3.678
• Meyer, J., & Shinar, D. (1992). Estimating Correlations from Scatterplots. Human Factors: The Journal of the Human Factors and Ergonomics Society, 34(3), 335–349. https://doi.org/10.1177/001872089203400307
• Rensink, R. A., & Baldridge, G. (2010). The Perception of Correlation in Scatterplots. Computer Graphics Forum, 29(3), 1203–1210. https://doi.org/10.1111/j.1467-8659.2009.01694.x
• Xu, F., & Garcia, V. (2008). Intuitive statistics by 8-month-old infants. Proceedings of the National Academy of Sciences, 105(13), 5012–5015. https://doi.org/10.1073/pnas.0704450105

 

Lien entre intuitions approximées et maitrise des formalisations symboliques et mathématiques (une sélection de la littérature pertinente)

• Ciccione, L., & Dehaene, S. (2020). Grouping Mechanisms in Numerosity Perception. Open Mind, 4, 102–118. https://doi.org/10.1162/opmi_a_00037
• Dehaene, S., Izard, V., Spelke, E., & Pica, P. (2008). Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures. Science, 320(5880), 1217–1220.
• Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q., & Germine, L. (2012). Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences, 109(28), 11116–11120. https://doi.org/10.1073/pnas.1200196109
• Ludewig, U., Lambert, K., Dackermann, T., Scheiter, K., & Möller, K. (2020). Influences of basic numerical abilities on graph reading performance. Psychological Research, 84(5), 1198–1210. https://doi.org/10.1007/s00426-019-01144-y

 

Module 7 : Espace et Géométrie – Dr Valeria Giardino

 

• J. Àdams, I. Resnick, T. Lowrie (2022). Supporting senior high-school students’ measurement and geometry performance: Does spatial training transfer to mathematics achievement? Math Ed Res J. 2022 Apr 25:1–22.
• D. Bessis (2022). Mathematica. Une aventure au coeur de nous-mêmes. Edition du Seuil.
• D. J. Bryant & B. Tversky (1999). Mental representations of perspective and spatial relations from diagrams and models. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25(1), 137. 
• D. J. Bryant, B. Tversky & N. Franklin (1992). Internal and external spatial frameworks for representing described scenes. Journal of Memory and Language, 31(1), 74–98. 
• S. Dehaene, V. Izard, P. Pica, E.S. Spelke (2006), Core Knowledge of Geometry in an Amazonian Indigene Group, Science CCCXI, 381–384.
• B. Tversky -B. Martin Hard (2009), Embodied and disembodied cognition: Spatial perspective-taking, Cognition, 110 (1), pp 124-129 
• R. Casati -V. Giardino (2013), Public Representations and Indeterminacies of Perspectival Content. Enacting Images : Representation Revisited, sous la direction de Z. Kondor, von Halem Verlag, Cologne, pp. 111 –126.
• E. K. Farran (2021). What role does spatial thinking play in STEM? Improving STEM skills by promoting the development of children’s spatial ability. Blog on Learning and Development. 
• N. Franklin, N., & B. Tversky, (1990). Searching imagined environments. Journal of Experimental Psychology: General, 119(1), 63. 
• N. Franklin, B. Tversky, & V. Coon (1992). Switching points of view in spatial mental models. Memory & Cognition, 20(5), 507–518. 
• K. Gilligan-Lee, Z. Hawes, K. Mix (2022). Spatial thinking as the missing piece in mathematics curricula. NPJ Sci Learn. 2;7(1):10.
• Y. Hamami, J. Mumma & M. Àmalricc  (2021), Counterexample Search in Diagram-Based Geometric Reasoning, Cognitive Science 45.
• Z. Hawes, J. Moss, B. Caswell, S. Naqvi & S. MacKinnon (2017) Enhancing Children's Spatial and Numerical Skills through a Dynamic Spatial Approach to Early Geometry Instruction: Effects of a 32-Week Intervention, Cognition and Instruction, 35:3, 236-264.
• Z. Hawes & D. Ànsari (2020), What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior, Psychonomic Bulletin & Review, 27, pp. 465–482.  
• M. Hegarty, & D. Waller (2004). À dissociation between mental rotation and perspective-taking spatial abilities. Intelligence, 32, 175-191. 
• A. Jamalian, A., V. Giardino, B. Tversky,(2013), ‘Gestures for Thinking’. Proceedings of the 
35th Annual Meeting of the Cognitive Science Society, pp. 645-650. 

• M. Kozhevnikov, & M. Hegarty (2001). À dissociation between object-manipulation and perspective-taking spatial abilities. Memory & Cognition, 29, 745-756. 
• T. Lowrie, T. Logan & M. Hegarty (2019), The Influence of Spatial Visualization Training on Students’ Spatial Reasoning and Mathematics Performance, Journal of Cognition and Development, 20:5, 729-751, DOI: 10.1080/15248372.2019.1653298
• T. Lowrie, T. Logan, D. Harris, M. Hegarty (2018), The impact of an intervention program on students' spatial reasoning: student engagement through mathematics-enhanced learning activities. Cogn Res Princ Implic. Dec 26;3(1):50.
• S. Soury-Lavergne (2020). La géométrie dynamique pour l’apprentissage et l’enseignement des mathématiques. CNESCO (Conseil national d’évaluation du système scolaire). hal-03853287 
• B. Tversky (2019), Mind in Motion. How Action Shapes Thought. New York, Basic books.
• B. Tversky, B. (1991). Spatial mental models. Psychology of Learning and Motivation, 27, 109–145. 
• B. Tversky, J; Kim, & A. Cohen (1999). Mental models of spatial relations and transformations from language. Àdvances in Psychology, 128, 239–258. 
• D. H. Uttal, N. G. Meadow, N. S. Newcombe, E. Tipton, L. L. Hand, Alison R. Àlden, C. Warren (2012). The Malleability of Spatial Skills: A Meta-Analysis of Training Studies, Psychological Bulletin, Vol. 139, No. 2, 352–402