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Shunning algebraic formalism: Student teachers and the intricacy of percents

  • Autores: Heidi Strømskag
  • Localización: Recherches en didactique des mathématiques, ISSN 0246-9367, Vol. 40, Nº 1, 2020, págs. 55-96
  • Idioma: inglés
  • Títulos paralelos:
    • Rehuyendo el formalismo algebraico: Los profesores en formación y el laberinto de los porcentajes
    • Sans formalisme algébrique aucun: Des élèves professeurs face aux pièges des pourcentages
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  • Resumen
    • español

      Este artículo investiga cómo los estudiantes en formación inicial para profesores de educación primaria y secundaria obligatoria utilizan y dominan el formalismo algebraico al resolver la tarea de determinar la tasa de crecimiento del área de un cuadrado cuando el lado de éste se incrementa un p%. El material empírico consiste en una grabación en vídeo de una sesión de trabajo en pequeño grupo en la que un grupo de tres estudiantes resuelve la tarea (interactuando con la formadora). Se utilizan como herramientas de análisis nociones de la teoría de las situaciones didácticas en matemáticas y de la teoría semiótica. El análisis muestra cómo la notación de los porcentajes complica la tarea y cómo se evitan los cálculos algebraicos. Se muestra también cómo una evolución del medio da lugar a la creación de manipulativos que proporcionan a los estudiantes representaciones en distintos registros semióticos, el de las figuras geométricas planas, que se transforman en notación porcentual con el fin de resolver la tarea. Se discuten finalmente las implicaciones didácticas tanto en el diseño de tareas de este tipo como en la formación del profesorado.

    • English

      This paper investigates primary and lower secondary school student teachers’ use and mastery of algebraic formalism in solving the task of determining the rate of increase of a square’s area when the square’s side increases by p%. The empirical material consists of a video-recorded small-group session where a triad of student teachers was solving this task (with teacher interaction). Notions from the theory of didactical situations in mathematics and semiotic theory are used as analytic tools. The analysis shows how percent notation complicated the task, and how algebraic calculations were avoided. It is further shown how an evolution of the milieu gave rise to creation of manipulatives that provided the student teachers with representations from a different semiotic register, that of plane geometric figures, which were transformed into percent notation that enabled them to produce a solution to the task. Didactical implications are discussed regarding design of such a task on the one hand, and teacher education on the other hand.

    • français

      Cette étude porte sur l’emploi et la maîtrise, par de futurs professeurs du primaire et du début du collège, du formalisme algébrique dans la détermination du taux de croissance de l’aire d’un carré dont le côté croît de p %. Les données empiriques consistent en l’enregistrement vidéo d’une séance de travail d’une triade d’élèves professeurs s’efforçant de résoudre ce problème (en interaction avec leur professeur). Les outils d’analyse utilisés relèvent de la théorie des situations didactiques en mathématiques et de la théorie sémiotique. L’analyse montre comment la notation en termes de pourcentages complique la tâche visée et comment se trouve évité tout calcul algébrique. On montre en outre comment une évolution du milieu engendre la création d’un matériel fournissant aux élèves professeurs une représentation du problème relevant d’un autre registre sémiotique, celui des figures géométriques, dont la traduction en pourcentages permet d’arriver à une solution au problème étudié. La discussion des implications didactiques de cette étude porte sur la conception de la tâche considérée, d’une part, et sur l’apport possible en termes de formation des enseignants, d’autre part.

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