Duos of Digital and Tangible Artefacts in Didactical Situations

Author(s):  
Sophie Soury-Lavergne
ZDM ◽  
2020 ◽  
Author(s):  
Frode Rønning

AbstractThis paper is based on data from two teaching sequences in primary school that are designed using principles from the theory of didactical situations (TDS). The following research question is addressed: “What opportunities can a teaching design based on TDS give a teacher to gain insight into pupils’ language use, and to use this insight to establish shared, and mathematically acceptable, knowledge in a group of primary school pupils?” Empirical data from one teaching sequence on geometrical shapes and another teaching sequence on combinatorial problems are used to answer this question. The research shows that a sharp focus on well-defined learning goals does not limit the pupils’ possibilities in expressing their thoughts and ideas in their own language. The research also shows that despite clear learning goals, the teacher has rich opportunities to build on pupils’ language to connect everyday and scientific language for the purpose of developing a mathematically accepted discourse.


1990 ◽  
Vol 21 (4) ◽  
pp. 258-272
Author(s):  
Nicolas Balacheff

This article presents the main features of the theoretical framework of French research known as recherches en didactique des mathématiques. The foundation of this approach consists mainly of the relationships between two hypotheses and two constraints, which are presented together with some specific key words. Outlines are given of Brousseau's théorie des situations didactiques (theory of didactical situations). An example is given that presents in some detail the rationale for the construction of a didactical situation and its analysis. This article ends with some questions addressed to research on mathematics teaching.


Author(s):  
Marianne Achiam ◽  
Bent Erik Kramer Lindow

Authentic science education has received increased attention in recent years, but it remains unclear what constitutes authenticity. Here, we use notions from the Anthropological Theory of the Didactic to approach authenticity. We take a point of departure in an existing education programme in a museum, and analyse it to pinpoint what constitutes its authenticity. We then use the theory of didactical situations as a way to construct a reference model; this reference model constitutes an authenticity-optimised version of the programme. We conclude by briefly discussing the implications of our findings.


Author(s):  
Santiago Palmas ◽  
Teresa Rojano ◽  
Rosamund Sutherland

Abstract This paper derives from a study which main purpose was to investigate how a group of adults with low schooling can have access to powerful mathematical ideas when working with activities that involve the use of technology resources and that take into account the adults’ previous experience with mathematics. Specifically, adults’ previous experience with area calculation was considered. Principles of the Theory of Didactical Situations (TDS) formulated by Brousseau guided the study design, and Pick’s theorem was recreated in a dynamic digital setting, with which it is possible to calculate the area of regular and irregular polygons. In this approach, intuitive notions of area and perimeter are resorted to, seeking to promote the experience with powerful ideas such as ‘the generality of a method’, ‘realizing the existence of different methods used for one and the same end’ and ‘realizing that each method possesses advantages and limitations’. Analysis of interview protocols from three noteworthy cases (which include both adults’ work in the digital setting and their discussions with the researcher) suggests the presence of powerful underlying mathematical ideas, such as the idea of generality and the power of a method and the features of the constituent elements of a geometric figure that are involved in calculating its attributes, attributes such as area.


Author(s):  
Erich Christian Wittmann

AbstractThe objective of this introductory chapter is to explain the common rationale behind the papers of this volume. The structure is as follows. The first section shows that learning environments are a natural way to address teachers in their main role, teaching, and that therefore this approach is promising for improving mathematics teaching in an effective way. The section ends with a teaching model based on Guy Brousseau’s theory of didactical situations.


Author(s):  
Gerson Pastre Oliveira

ResumoO presente artigo descreve uma investigação que ocorreu no âmbito de um grupo de mestrandos em Educação Matemática que cursavam a disciplina “Metodologia da Pesquisa” do Programa de Estudos Pós-Graduados em Educação Matemática da PUC-SP. A estratégia aplicada no desenvolvimento das aulas foi criada a partir de um planejamento que previa o uso de metodologias ativas, ensino híbrido e que tinha, como referência para as atividades propostas, a Teoria das Situação Didáticas. O principal objetivo era o de criar um contexto de discussões e um espaço de trabalho com interações presenciais e virtuais de modo a fornecer elementos para que os alunos iniciassem suas trajetórias como pesquisadores e começassem a escrever as respectivas dissertações, movimento classificado por eles como de grande dificuldade. O texto detalha as intervenções, em regime colaborativo, que os estudantes construíram, as discussões realizadas, os progressos alcançados, além de detalhes relativos à estrutura da disciplina que foram criados para incentivar o processo de formação pretendido.Palavras-chave: Colaboração, metodologias ativas, ensino híbrido, formação de pesquisadores, teoria das situações didáticas. AbstractThis article describes an investigation that occurred within a group of masters´ degree students in Mathematics Education that studied the discipline "Methodology of Research" of the Program of Postgraduate Studies in Mathematical Education of PUC-SP. The strategy applied in the development of classes was created from a planning that predicted the use of active learning methodologies, hybrid teaching and that had, as a reference for the proposed activities, the Theory of Didactic Situations. The main objective was to create a context of discussions and a workspace with face-to-face and virtual interactions in order to provide elements for the students to begin their trajectories as researchers as well as to begin to write the respective dissertations, a movement classified by them as very difficult. The text details the collaborative interventions the students have built, the discussions held, the progress made, as well as details of the discipline structure that were created to encourage the intended education process.Keywords: Collaboration, active learning methodologies, hybrid teaching, researchers’ education, didactical situations theory. ResumenEste artículo describe una investigación que se desarrolló en el ámbito de un grupo de estudiantes de maestría en Educación Matemática que cursaban la asignatura "Metodología de la Investigación" del Programa de Estudios de Postgrado en Educación Matemática de la PUC-SP. La estrategia aplicada en el desarrollo de las clases se creó a partir de una planificación que preveía el uso de metodologías activas, docencia híbrida y que tenía como referencia para las actividades propuestas, la Teoría de Situaciones Didácticas. El objetivo principal fue crear un contexto de discusiones y un espacio de trabajo con interacciones presenciales y virtuales con el fin de brindar elementos para que los estudiantes iniciasen sus trayectorias como investigadores y empezasen a escribir sus respectivas disertaciones, movimiento que calificaron como de gran dificultad. El texto detalla las intervenciones colaborativas que construyeron los estudiantes, las discusiones realizadas, los avances logrados, así como detalles relacionados con la estructura de la disciplina que se crearon para incentivar el proceso de formación pretendido.Palabras clave: Colaboración, metodologías activas, docencia híbrida, formación de investigadores, teoría de situaciones didácticas.


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