The Emergence of the “FlexTech” Orchestration of Inferential Reasoning on Pattern Generalization

The purpose of this study is to further our understanding of orchestrating math-talk with digital technology. The technology used is common in Swedish mathematics classrooms and involves personal computers, a projector directed towards a whiteboard at the front of the class and software programs for facilitating communication and collective exploration. We use the construct of instrumental orchestration to conceptualize a teacher’s intentional and systematic organization and use of digital technology to guide math-talk in terms of a collective instrumental genesis. We consider math-talk as a matter of inferential reasoning, taking place in the Game of Giving and Asking for Reasons (GoGAR).The combination of instrumental orchestration and inferential reasoning laid the foundation of a design experiment that addressed the research question: How can collective inferential reasoning be orchestrated in a technology-enhanced learning environment? The design experiment was conducted in lower-secondary school (students 14–16 years old) and consisted of three lessons on pattern generalization. Each lesson was tested and refined twice by the research team. The design experiment resulted in the emergence of the FlexTech orchestration, which provided teachers and students with opportunities to utilize the flexibility to construct, switch and mark in the orchestration of an instrumental math-GoGAR.

An instrumental orchestration for online course at the university level

In this article, we present a proposal for instrumental orchestration that organizes the use of technological environments in online mathematics education, in the synchronous mode for the concepts of eigenvalue and eigenvector of a first linear algebra course with engineering students. We used the instrumental orchestration approach as a theoretical framework to plan and organize the artefacts involved in the environment (didactic configuration) and the ways in which they are implemented (exploitation modes). The activities were designed using interactive virtual didactic scenarios, in a dynamic geometry environment, guided exploration worksheets with video and audio recordings of the work of the students, individually or in pairs. The results obtained are presented and the orchestrations of a pedagogical sequence to introduce the concepts of eigenvalue and eigenvector are briefly discussed. This work allowed us to identify new instrumental orchestrations for online mathematics education.

Ayudar a aprender matemática sin enseñar: la construcción del conocimiento didáctico matemático en profesionales de la psicopedagogía

In this article we share the basics, planning and example of a professional training course for psychopedagogy professionals in Argentina. We characterize the proposal as a mathematical workspace (Kusniak, 2011), energized by an instrumental orchestration process (Trouche, 2018) where participating professionals can build specialized knowledge (Carrillo et. al, 2013). We promote a critical and democratic reflection on the teaching and learning of mathematics (Skovsmose, 1999) and the construction of mathematical didactic knowledge in those who do not have the function of teaching this discipline in school.

When bibliometrics met mathematics education research: the case of instrumental orchestration

Thanks to digital technology, methods for finding and analysing research literature have become dramatically more powerful over the last decades. Also, new bibliometric techniques have been developed and applied to the results of such literature search queries. The application of these bibliometric tools to mathematics education research, however, is rare. In this paper, we explore the value of these techniques for mathematics education research through triangulating bibliometrics and expert findings. To do so, we address the case of instrumental orchestration, and want to know how this notion developed over time and was used in research practices. The results show that bibliometric clustering techniques provided a sense-making sketch of the ‘landscape’ of instrumental orchestration research. Triangulating the bibliometric findings with expert interpretations seemed an appropriate method to set up compact ‘identity cards’. In the case of instrumental orchestration, we identified five main clusters in research literature, characterized by the following labels: Managing teaching complexity, Designing living resources, Teaching with technology, Adult learners, and Interacting with computers. The paper ends with some reflections on the potential of bibliometrics in our field and on future research on instrumental orchestration.

GeoGebra como herramienta mediadora de un fenómeno físico

RESUMENUna de las dificultades en la enseñanza de las ciencias está relacionada con la ausencia de prácticas de laboratorio, debido a esto, el presente artículo propone el uso de GeoGebra como un recurso mediador para la experimentación del fenómeno de caída libre y la modelización de la energía mecánica, generando una propuesta de laboratorio portable a través de la creación de un escenario virtual. La metodología aplicada de tipo cualitativo describe por medio de algunos puntos de la orquestación instrumental, cómo configurar y utilizar un escenario virtual para la experimentación simulada. Resultados sobre la orquestación instrumental del uso de GeoGebra, evidencian que éste software es una alternativa de laboratorio portable que brinda recursos para la simulación. Por otra parte, el uso de un escenario virtual con GeoGebra, permitió a un grupo de estudiantes de secundaria mediar procesos de modelización matemática de la energía mecánica de manera experimental, promoviendo la comprensión de conceptos físicos y matemáticos a través de los diversos registros de representación. Palabras claves: escenarios virtuales; simulación, modelización matemática. RESUMOUma das dificuldades no ensino das ciências está relacionada com a ausência de práticas laboratoriais, devido por um isto, o presente artigo propicia o uso da GeoGebra como um recurso de mediador para a experimentação do fenômeno da queda livre e a modelagem da energia mecânica, gerando uma proposta de laboratório portátil através a criação de um cenário virtual. A metodologia aplicada de tipo qualitativo descreve por meio da orquestração instrumental, como configurar e usar um cenário virtual para a experiência simulada. Resultados sobre a orquestração instrumental de uso da GeoGebra, evidência de que este software é uma alternativa de laboratório portátil que fornece recursos para simulação. Por outro lado, o uso de um cenário virtual com a GeoGebra, permitiu que um grupo de estudantes secundários mediará processos de modelagem matemática da energia mecânica de maneira experimental, promovendo a compreensão de conceitos físicos e matemáticos a partir de vários registros de representação.Palavras-chave: cenários virtuais; simulação, modelagem matemática. ABSTRACTOne of the difficulties in teaching Sciences is related to the absence of laboratory practices, due to this, this article proposes the use of GeoGebra as a mediating resource for the experimentation of the phenomenon of free fall and mechanics energy modeling, generating a portable laboratory proposal through the creation of a virtual scenario. The qualitative methodology applied describes through some points of instrumental orchestration, about how to configure and use a virtual scenario for simulated experimentation. Results on the instrumental orchestration of the use of GeoGebra show that this software is a portable laboratory alternative that provides resources for simulation. On the other hand, the use of a virtual scenario with GeoGebra, allowed a group of secondary school students to mediate processes of mathematical modeling of mechanical energy in an experimental way, promoting the understanding of physical and mathematical concepts through the various representation registers.Keywords: virtual scenarios; simulation, mathematical modeling