Research, practice and theory in didactics of mathematics: Towards dialogue between different fields (original) (raw)
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Didactics and History of Mathematics: Knowledge and Self-Knowledge.
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This chapter analyses specificities of the French field of 'didactics of mathematics', questioning its reasons, tracing the geneses of concepts related to artefacts and following influences on, and interactions with, the international communities of research. This complex genesis is traced in four sections: a first section on the roots of the didactics of mathematics in France, a second section on two founding theoretical frameworks (the theory of didactical situations of Brousseau, and the theory of conceptual fields of Vergnaud), a third section on the anthropological approach of Chevallard, a fourth focusing on specific approaches dedicated to artefacts and resources in mathematics education. Beyond historical and cultural specificities, the chapter aims to evidence the potential of interactions between teachers and researchers, as well as interactions between researchers in mathematics and mathematics education for improving our understanding of learning and teaching issues in mathematics. In this chapter, I analyse specificities of the French field of " didactics of mathematics " , questioning its reasons, tracing the geneses of concepts related to artefacts, and following influences on and interactions with the international communities of research. Questioning the dynamics of the theoretical frameworks, that we bear and that leads us, is complex, as each theory is a result of individual and collective pathways (Trouche, 2009), which meet a set of sometimes critical facts and are subjects to multiple influences. I have organized this chapter in four sections, giving voice to some main actors 1 involved in these complex geneses: a first section on the roots of the didactics of mathematics in France, a second section on two founding theoretical frameworks (the theory of didactical situations of Brousseau, and the theory of conceptual fields of Vergnaud), a third section on the anthropological approach of Chevallard, a fourth focusing on specific approaches dedicated to artefacts and resources in mathematics education
Recherches en Didactique des …, 2010
Les études comparatives internationales visent à identifier et expliquer les différences entre phénomènes homologues dans plusieurs contextes. Elles sont menées avec une variété d'objectifs et de méthodes, et leurs résultats ainsi que les interprétations de ces derniers font l'objet de débats parfois vifs, surtout pour ce qui concerne les évaluations quantitatives à grande échelle telles que PISA. Même si l'évaluation des compétences des élèves n'est pas sa préoccupation majeure, la recherche didactique ne peut manquer d'être concernée par ces débats. Dans cet article, nous présentons d'abord un modèle théorique, dérivé de la théorie anthropologique du didactique, qui nous servira à spécifier les niveaux auxquels une comparaison est effectuée. En nous servant de ce modèle, nous proposons ensuite une analyse synthétique d'une sélection d'études comparatives internationales en éducation mathématique (allant d'évaluations à grande échelle à des comparaisons binaires à petite échelle menées dans le cadre de thèses), dans le but spécifique de comprendre comment ces études diffèrent et peuvent s'articuler.
Re-construction of the mathematics curriculum in the context of the didactic knowledge of the primary teacher (Atena Editora), 2022
El presente artículo pretende socializar los avances de un estudio doctoral en curso que procura responder la pregunta ¿cómo un profesor de primaria (re) construye el currículo de matemáticas en el contexto de su Conocimiento Didáctico? El horizonte teórico considera ciertas investigaciones enfocadas en el currículo de matemáticas, determinando algunos asuntos asociados con el conocimiento y desarrollo profesional del profesor, asuntos que permiten un acercamiento al problema, en cuanto a lo que significa (re) construir el currículo de matemáticas y el conocimiento didáctico que debe exhibir un profesor de primaria para lograr gestionar el currículo en el aula. Otro aspecto relevante, es la metodología propuesta, que se enmarca en un paradigma de corte cualitativo, en el cual las tareas de formación constituirán una posibilidad para propiciar interacciones, reflexiones y posibles transformaciones en el conocimiento didáctico del profesor que enseña matemáticas en la educación básica primaria.
Didactics of Mathematics in Higher Education as a Scientific Discipline
2017
algebra is a well suited example for these categories: It is a conceptual framework that can be constructed in several distinct ways by horizontal mathematization and it requires a crucial step of integrating the concepts by vertical mathematization. For example, problems from arithmetics, geometry or combinatorics all give rise to concepts that can ultimately be integrated into the group concept (Leuders, 2015). Of course, the categories „horizontal“ and „vertical“ are by no means unequivocally defined, as Freudenthal already conceded (1991, 42): „To be sure, the frontiers of these worlds are rather vaguely marked. The worlds can expand and shrink – also at one another’s expense. Something may belong in one instance to the world of life and in another to the world of symbols [...] For the expert mathematician, mathematical objects can be part of his life in quite a different way but for the novice. The distinction between horizontal and vertical mathematising depends on the specifi...
The French Didactic Tradition in Mathematics
European Traditions in Didactics of Mathematics, 2019
This chapter presents the French didactic tradition. It first describes the emergence and development of this tradition according to four key features (role of mathematics and mathematicians, role of theories, role of design of teaching and learning environments, and role of empirical research), and illustrates it through two case studies respectively devoted to research carried out within this tradition on algebra and on line symmetry-reflection. It then questions the influence of this tradition through the contributions of four researchers from Germany, Italy, Mexico and Tunisia, before ending with a short epilogue.