Teachers' attention to task's potential for encouraging classroom argumentative activity

International audienceThis study investigated secondary school mathematics teachers’ attention to task’s potential for argumentative activity in the classroom. Analysis of the teachers’ choices of tasks and their explanations revealed categories that fall into two dimensions: (1) Attention to the mathematics in which the argumentative activity is embedded, focusing on three aspects: the mathematics inherent in the task; the mathematics related to the teaching sequence that the task is a part of; and meta-level principles of mathematics. (2) Attention to socio-cultural aspects related to the argumentative activity. Four attention-profiles of teachers were identified: Teachers who attended to both dimensions; teachers who were attentive only to the mathematics aspects inherent in the task; teachers who were attentive only to the socio-cultural dimension; and teachers who were attentive to neither of these dimensions

Fusionner des représentations mathématiques machinalement ou en réfléchissant : expériences d’utilisation de calculatrices graphiques

In designing mathematics learning with the mediation of computerized tools, one of the crucial questions to be considered is how much and in what way we would like the tool «to do the work » for the students. In problem situations where the solution is achieved mostly via graphical representatives, and algebraic models are mostly used as «keys » for obtaining graphical representatives on the screen, the algebraic representatives and their form seem minimized in importance, and students may tend to generate them from tables by mechanistic-algorithmic procedures. The above questions will be mainly demonstrated within the description and analysis of a case study involving a group of three 10th graders (about 16 years of age) working together to investigate and solve a problem situation on the topic of functions, having graphing calculators (TI-83 Plus) at their disposal. The role of contextual factors is highlighted by means of contrasts with the work of students on the same problem from another country.Dans l'élaboration de situations d’apprentissage en mathématiques s’appuyant sur la médiation d’outils informatiques, une des questions cruciales à considérer est jusqu’à quel point et de quelle façon voulons-nous que l’outil «fasse le travail » pour l’élève. Dans des situations problèmes où la solution est obtenue principalement à partir de représentations graphiques et où des modèles algébriques sont principalement utilisés comme «clés » pour obtenir des représentations graphiques à l’écran, les représentations algébriques et leurs formes semblent perdre de l’importance et les élèves risquent de les générer à partir de tableaux de valeurs par des procédures mécaniques-algorithmiques. Les questions ci-dessus sont principalement abordées à travers la description et l’analyse d’une étude de cas impliquant un groupe de trois élèves de dixième année (environ 16 ans) travaillant ensemble pour étudier et résoudre une situation problème portant sur les fonctions, en disposant de calculatrices graphiques (TI-83 Plus). Le rôle des facteurs contextuels est mis en évidence par contraste avec le travail, sur le même problème, d’élèves provenant d’un autre pays.Hershkowitz Rina, Kieran Carolyn. Fusionner des représentations mathématiques machinalement ou en réfléchissant : expériences d’utilisation de calculatrices graphiques. In: Sciences et techniques éducatives, volume 9 n°1-2, 2002. Logiciels pour l'apprentissage de l'algèbre (dir. Jean-François Nicaud, Elisabeth Delozanne, Brigitte Grugeon) pp. 201-218

Book review: a dialog in the footsteps of the book “A journey in mathematics education research—insights from the work of Paul Cobb”; Erna Yackel, Koeno Gravemeijer and Anna Sfard (Eds.); (2011); A journey in mathematics education research—insights from the work of Paul Cobb

Book review: a dialog in the footsteps of the book “A journey in mathematics education research—insights from the work of Paul Cobb”; Erna Yackel, Koeno Gravemeijer and Anna Sfard (Eds.); (2011); A journey in mathematics education research—insights from the work of Paul Cob

Abstraction in Context and Documenting Collective Activity

International audienceIn this report we advance the methodological and theoretical networking for documenting individual and collective mathematical progress. In particular, we draw together two approaches, Abstraction in Context (AiC) and Documenting Collective Activity (DCA). The coordination of these two approaches builds on prior analysis of grade 8 students working on probability problems to highlight the compatibility among the epistemic actions that ground each approach and drive the respective methodologies. The significance of this work lies in its contribution to coordinating what might otherwise be viewed as separate and distinct methodologies

First steps in re-inventing Euler's method: A case for coordinating methodologies

International audienceIn this report, we highlight the epistemic actions and concomitant discursive shifts of four students as they reinvent the fundamental idea and technique in Euler's method. We use this case to further the theoretical and methodological coordination of the Abstraction in Context (AiC) approach, with its associated model commonly used for the analysis of processes of constructing knowledge by individuals, and small groups and the Documenting Collective Activity (DCA) approach, with its methodology commonly used for identifying norma-tive ways of reasoning with groups of students. In this report, we show students' first steps towards re-inventing Euler's method and explicate the theoretical and meth-odological commonalities of AiC and DCA

Children's perception of ratios and fractions in Grade 5

Wachsmuth I, Behr MJ, Post TR. Children's perception of ratios and fractions in Grade 5. In: Hershkowitz R, International Group for the Psychology of Mathematics Education, eds. Proceedings of the Seventh International Conference for the Psychology of Mathematics Education. Rehovot: Dept. of Science Teaching, Weizmann Inst. of Science; 1983: 164-169

Reasoning in geometry

This chapter deals with the specific features of reasoning in geometry, including general aspects and specific case studies for different age groups carried out in different countries. The five sections of the chapter discuss and illustrate examples of main new trends in reasoning in geometry. The sections comprise a meta-cognitive analysis of geometrical reasoning processes and their interactions with other thinking processes, two sections that discuss theory and curriculum development that demonstrate what is called now “learning geometry from context”, a section on the roles of pupils’ spatial knowledge in geometry learning, and an analysis of how pupils interweave intuitive-visual reasoning and deductive reasoning. Together, the sections illustrate three main trends in learning geometrical reasoning; reasoning in building proofs, reasoning in geometry from contexts, and visual reasoning