Les différentes fonctions de la résolution de problèmes sont-elles présentes dans l’enseignement primaire en Communauté française de Belgique ?

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Approche par problème et formation d'enseignants de mathématiques : comment se diffusent, en formation, les résultats de la recherche?

peer reviewedBased on the framework of meta-didactic transposition analysis (Arzarello et al., 2014) and specifically the concepts of brokering and boundary object, this paper studies how knowledge to teach algebra is exchanged during a training program involving nine mathematics teachers and two researchers specialised in algebra teaching and learning. Organized in three half-day sessions, this program is based on a problem pointed out in the research literature as particularly rich to develop algebraic thninking. In addition, the materials used in training are come directly from the classes of the teachers participating in the programme. In this sense, the program values knowledge that makes sense in both research and teaching practice. The analysis of interactions between researchers and teachers highlights three types of collaborative activities between the two groups and thus questions the potential of such a mechanism to foster integration of research results by teachers

L’impact de l’introduction de schémas « range-tout » sur les démarches de résolution de problèmes arithmétiques en 4e année primaire

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Conceptualisation, symbolisation et interactions enseignante/enseignant-élèves dans les apprentissages mathématiques: l’exemple de la généralisation

Partant de la définition de l’apprentissage et des objets mathématiques selon Radford (2008), cet article propose une réflexion sur l’interdépendance des objets mathématiques, leurs symbolisations et les interactions sociales dans le processus d’apprentissage. Il vise à interroger la manière dont s’articulent ces trois composantes indissociables et présente, sur cette base, un modèle intégratif de l’apprentissage des mathématiques. Il vise à examiner en particulier l’importance des interactions entre l’enseignant ou l’enseignante et les élèves. Si l’importance des interactions sociales est démontrée depuis de nombreuses années, ce sont en effet principalement les interactions entre les élèves qui ont été étudiées (Schubauer-Leoni et Perret-Clermont, 1997; Iiskala, Vauras, Lehtinen et Salonen, 2011). Ce n’est qu’assez récemment que l’importance des interactions entre l’enseignant ou l’enseignante et les élèves a été mise en évidence. Dans notre article, nous proposons donc d’analyser plus particulièrement les interactions entre l’enseignant ou l’enseignante et les élèves, dans le contexte d’une activité de généralisation en algèbre. Nous montrons l’importance d’interventions de qualité de la part de l’enseignant, sur la base du modèle de Jacobs et al. (2010, dans Callejo et Zapareta, 2016), pour faire émerger les savoirs mathématiques des pratiques sociales de la classe.Starting from the definition of learning and mathematical objects according to Radford (2008), this article proposes a reflection on the interdependence of mathematical objects, their symbolization, and social interactions in the learning process. It aims to question the way in which these three indissociable components are articulated, and on this basis presents an integrative model of mathematical education. It aims to specifically examine the importance of interactions between the teacher and the students. Although the importance of social interactions has been demonstrated for many years, the interactions that have been studied are mainly those between students (Schubauer-Leoniand Perret-Clermont, 1997, Iiskala, Vauras, Lehtinen and Salonen, 2011). Only recently has the importance of teacher-student interactions been highlighted. In our article, we therefore wish to do a more specific analysis of interactions between teacher and students, in the context of a generalization activity in algebra. We show the importance of quality interventions on the part of the teacher, based on the model of Jacobs et al. (2010, in Callejo and Zapareta, 2016), to bring out mathematical knowledge through social practices in the classroom.A partir de la definición del aprendizaje y de los objetos matemáticos según Redford (2008), este articulo propone una reflexión sobre la interdependencia de los objetos matemáticos, sus simbolizaciones y las interacciones sociales en el proceso de aprendizaje. Su objetivo es cuestionar la manera en que se articulan estos tres componentes indisociables y sobre esta base presenta un modelo integrativo del aprendizaje de las matemáticas. Busca examinar, particularmente, la importancia de las interacciones entre maestro o maestra y los alumnos/alumnas. Si desde hace mucho tiempo se ha demostrado la importancia de las interacciones sociales, han sido principalmente las interacciones entre alumnos que se han estudiado (Schubauer-Leoni y Oerret-Clermont, 1997, Liskala, Vauras, Lehtinen y Salonen, 2011). La importancia de las interacciones entre maestro o maestra y los alumnos/alumnas, sólo muy recientemente han sido evidenciadas. En nuestro artículo nos proponemos pues analizar en particular las interacciones entre maestro o maestra y los alumnos/alumnas, en el contexto de una actividad de generalización en álgebra. Mostramos la importancia de intervenciones de calidad de la parte del maestro, basándonos en el modelo de Jacobs et al. (2010, en Callejo y Zapareta, 2016), para hacer surgir los saberes matemáticos de las prácticas sociales en la clase

Making sense of zero to make sense of negative numbers

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The role of algebraic thinking in dealing with negative numbers

peer reviewedTo date, of the many studies on early algebraic thinking, none, to our knowledge, has examined the relationships between algebraic thinking and negative numbers. Students encounter persistent difficulties in dealing with these numbers, and we believe that these could be addressed through the development of algebraic thinking. We are particularly interested in relational thinking, a form of algebraic thinking involved in generalised arithmetic, characterised by the ability to identify the structure of an expression as well as the relationships between numbers. The idea of the ‘subtractive number’ has been highlighted in this context. The aim of the study was to investigate the role of relational thinking in dealing with negative numbers. We submitted a paper-and-pencil test to 166 grade 6 students in order to analyse their skills in operations with integers, as well as their relational thinking in questions relating to the compensation strategy in subtraction. We then examined the extent to which the students who answered the compensation questions correctly performed the operations with integers better than those who answered them incorrectly. Our results showed that students’ ability to see the subtraction operation as a ‘transformation’ involving a unary use of the minus sign appears to be a factor in their success in operations with negatives. Few students demonstrated this ability, yet it can be seen as an essential stage on which to base the progressive development of relational thinking