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Pre-service teachers’ classroom stagings of proving-related activities and possible effects of Klein’s discontinuity

  • Thomas Bauer [1] ; Eva Müller-Hill [2]
    1. [1] Philipp University of Marburg

      Philipp University of Marburg

      Landkreis Marburg-Biedenkopf, Alemania

    2. [2] University of Rostock

      University of Rostock

      Kreisfreie Stadt Rostock, Alemania

  • Localización: Recherches en Didactique des Mathématiques, ISSN 0246-9367, Vol. 45, Nº 3, 2025, págs. 205-237
  • Idioma: inglés
  • Títulos paralelos:
    • Implementaciones en el aula de actividades relacionadas con la demostración por parte de profesores en formación y posibles efectos de la discontinuidad de Klein
    • Mise en scène par les enseignants en formation initiale des activités liées à la démonstration et effets possibles de la discontinuité de Klein
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  • Resumen
    • español

      La demostración es un elemento esencial de las matemáticas. Por lo tanto, desempeña un papel esencial en los estudios universitarios de matemáticas y también en la formación de los profesores de matemáticas en formación inicial. Sin embargo, se ha demostrado que los profesores en activo tienen problemas para implementar adecuadamente la demostración en su tarea docente. Consideramos esta ruptura entre los estudios universitarios y la práctica profesional como parte de lo que Klein denominó la «segunda discontinuidad». Empleando el marco teórico de la actividad, en este artículo analizamos la cuestión de cómo la implementación de las sesiones de los profesores en formación al final de su programa de estudios indica dificultades sistemáticas en la actividad relacionada con la demostración en el aula y cómo las experiencias de discontinuidad provocadas por las diferencias entre las prácticas relacionadas con la demostración en la escuela y la universidad podrían considerarse como una posible causa de ello. Presentamos los resultados de un estudio observacional con profesores en formación que revelan patrones específicos en su comportamiento relacionado con la demostración cuando planifican e imparten clases, y los relacionamos con las fuentes de posibles experiencias de discontinuidad de los profesores en formación. Como implicación práctica, nuestros resultados proporcionan indicaciones de cómo podría enfocarse el tema de la demostración en la formación didáctica del profesorado de matemáticas.

    • français

      La preuve est un élément central des mathématiques. Elle joue donc un rôle essentiel dans les études universitaires de mathématiques et, par conséquent, dans la formation des enseignants de mathéma-tiques en formation initiale. Cependant, il a été démontré que les enseignants en exercice rencon-trent des problèmes pour mettre en œuvre la preuve et la démonstration de manière adéquate dans leur enseignement. Nous considérons que cette rupture entre les études universitaires et la pratique professionnelle fait partie de ce que Klein a appelé la « deuxième discontinuité ». En utilisant un cadre théorique de l’activité, nous étudions dans cet article la question de savoir comment les mises en scène des leçons des enseignants en formation à la fin de leur programme d’études indiquent des difficultés systématiques dans la mise en scène d’activités liées à la preuve et la démonstration pour la classe et comment les expériences de discontinuité déclenchées par les différences entre les pratiques à l’école et à l’université pourraient être considérées comme une cause possible de ce phénomène. Nous présentons les résultats d’une étude d’observation menée auprès d’enseignants en formation qui révèlent des schémas spécifiques dans leur comportement lié à la preuve et la démonstration lorsqu’ils planifient et dispensent leurs cours, et nous les mettons en relation avec les sources d’éventuelles expériences de discontinuité des enseignants en formation. D’un point de vue pratique, nos résultats fournissent des indications sur la manière dont le thème de la preuve et de la démonstration pourrait être ciblé dans la formation des enseignants en didactique des mathématiques.

    • English

      Proof is a core element of mathematics. It therefore plays an essential role in university mathematics studies and thus also in the training of pre-service mathematics teachers. How-ever, it has been shown that in-service teachers face problems in adequately implementing proof in their teaching. We consider this break between university studies and professional practice as part of what Klein called the “second discontinuity”. Employing an activi-ty-theoretical framework, we investigate in this paper the question of how lesson stagings of pre-service teachers at the end of their study program indicate systematic difficulties in staging proving-related activity for the classroom and how discontinuity experiences triggered by differences between proving-related practices in school and university could be considered as a possible cause for that. We present results from an observational study with pre-service teachers that reveal specific patterns in their proof-related behavior when planning and delivering lessons, and relate these back to sources for possible discontinuity experiences of pre-service teachers. As a practical implication, our results provide indica-tions of how the topic of proof could be targeted in mathematics didactic teacher education.

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