Design and research for developing local instruction theories

• Michiel Doorman ^[1]
  1. [1] Utrecht University

     Utrecht University

     Países Bajos

     
• Localización: Avances de investigación en educación matemática, ISSN-e 2254-4313, Nº. 15, 2019, págs. 29-42
• Idioma: inglés
• DOI: 10.35763/aiem.v0i15.266
• Títulos paralelos:
  • Desenho e pesquisa para o desenvolvimento de teorias de instrução local
  • Conception et recherché pour le development de théories de l’instruction locale
  • Diseño e investigación para el desarrollo de teorías de instrucción local
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    La innovación en educación matemática necesita de la implicación de profesores, autores de libros de texto, legisladores e investigadores. Este artículo esboza el papel y la importancia del diseño instruccional orientado hacia nuevas teorías de instrucción local en educación matemática. Muestro esta aproximación con un estudio donde se investigó cómo apoyar a los estudiantes en el desarrollo de los principios básicos de las matemáticas del cambio. El estudio combina diseño e investigación en tres fases sucesivas. En la primera fase se diseña una trayectoria hipotética de aprendizaje y actividades de enseñanza, en la fase del experimento de enseñanza se implementa la trayectoria, y en la fase de análisis retrospectivo se reflexiona sobre las hipótesis adoptadas. Así se estructura un proceso cíclico de (re)diseño y desarrollo de enseñanza innovadora. Se espera que la teoría de instrucción local resultante cree oportunidades para que profesores, autores de libros de texto e investigadores puedan adaptar los resultados a su investigación o práctica de aula, teniendo en cuenta el contexto en el que trabajan.

  • English

    Innovation in mathematics education needs the involvement of teachers, textbook authors, policy makers and researchers. This paper sketches the role and importance of instructional design aiming at new local instruction theories in mathematics education. The approach is shown with a study that investigated how students can be supported in the development of the basic principles of the mathematics of change. The study combines design and research in three successive phases. In the first phase a hypothetical learning trajectory and instructional activities are designed, in the teaching experiment phase the trajectory is acted out, and in the phase of the retrospective analysis the articulated hypotheses are reflected upon. In this way, a cyclic process of (re)design and development of innovative teaching is structured. The resulting local instruction theory is expected to create opportunities for teachers, textbook authors and researchers to consider contextual factors and to adapt results for their research or teaching.

  • français

    L’innovation en didactique des mathématiques nécessite l’implication des professeurs, des auteurs de manuels, des législateurs et des chercheurs. Cet article propose une esquisse du rôle et de l’importance de la conception pédagogique orientée vers de nouvelles théories de l’instruction locale pour l’enseignement des mathématiques. Nous illustrons cette approche à travers une étude qui s’est donné pour but d’explorer comment les étudiants peuvent être soutenus dans le développement des principes fondamentaux des mathématiques du changement. Cette étude combine conception et recherche en trois phases successives. Dans la première phase, nous proposons la conception d’une trajectoire d’apprentissage hypothétique ainsi que d’activités pédagogiques; dans la phase d’expérimentation de l’enseignement, la trajectoire hypothétique est mise en œuvre ; enfin, dans la phase d’analyse a posteriori, les hypothèses avancées sont analysées. De la sorte se structure un processus cyclique de (re)conception et de développement d’enseignements innovants. La théorie de l’instruction locale qui en résulte devrait permettre aux enseignants, aux auteurs de manuels et aux chercheurs d’adapter les résultats à leurs recherches ou à leurs enseignements, en tenant compte du contexte dans lequel ils travaillent

  • português

    A innovação em educação matemática carece do envolvimento de professores, autores de manuais, legisladores e investigadores. Este artigo esboça o papel e a importância do esquema educacional orientado para as novas teorias de educação local em educação matemática. Apresento esta abordagem mediante um estudo onde se investigou a forma de apoiar os alunos no desenvolvimento de princípios básicos da matemática para a mudança. O estudo combina esquematização e investigação em três fases sucessivas. Na primeira fase esquematiza-se um percurso hipotético de aprendizagem e atividades de ensino, na fase de experiencia de ensino implementa-se o percurso e, na fase de análise retrospetiva, reflete-se sobre as hipóteses adotadas. Estruturou-se um processo cíclico de (re)esquematização e desenvolvimento de métodos inovadores de ensino. Espera-se que a teoria de educação local resultante crie oportunidades para que professores, autores de manuais e investigadores possam adaptar os resultados às suas investigações ou prática letiva, tendo em consideração o contexto no qual trabalham.

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