Abstract
We study the experts’ practices developed with the support of digital technologies (DT), when they take aware in-the-moment decisions during classroom discussions to promote the development ...of effective formative assessment (FA) processes. In this investigation, we complement a macro-analysis of paradigmatic examples of classroom activities, focused on the functionalities of DT and on the implemented FA strategies, with a micro-analysis, developed with reference to a theoretical construct useful for interpreting and analysing expert teachers’ roles during classroom discussions (the Model of Aware and Effective Attitudes and Behaviours, M
AE
AB). More specifically, we explore how the expert uses DT to empower these roles with the aim of promoting FA processes. This study has two implications: (1) at the theoretical level, the study will introduce a model aimed at characterising the ways in which the expert can promote FA during classroom discussions when they are mediated by the use of DT; (2) at the pragmatic level, the use of this model to analyse paradigmatic examples from teaching experiments will introduce potential guidelines for teacher professional development aimed at promoting teachers’ autonomous use of DT to carry out effective FA practices.
This open access book, inspired by the ICME 13 topic study group “Affect, beliefs and identity in mathematics education”, presents the latest trends in research in the area. Following an introduction ...and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main sections: motivation and values, engagement, and identity in mathematics education. Each section comprises several independent chapters based on original research, as well as a reflective commentary by an expert in the area. Collectively, the chapters present a rich methodological spectrum, from narrative analysis to structural equation modelling. In the final chapter, the editors look ahead to future directions in the area of mathematics-education-related affect. It is a timely resource for all those interested in the interaction between affect and mathematics education. ; Presents a selection of current empirical studies, and a visionary chapter on future directions Includes recent developments in the areas of motivation, engagement, and identity Provides a broad spectrum of theoretical and methodological approaches
Nous présentons une méthode mise en œuvre en Italie à propos de la démarche d’investigation (DI) au collège. Nous souhaitons, à travers cet article, contribuer au débat issu du groupe de travail « La ...démarche d’investigation dans la classe de mathématiques : fondements et pratiques » (Matheron, Morselli, René de Cotret, Schneider, 2012) notamment en ce qui concerne les questions suivantes : caractériser les typologies de questions à poser et les responsabilités des acteurs (enseignant, élèves, chercheurs).Tout d’abord, la DI est insérée dans le contexte de l’institution scolaire italienne. Nous présentons ensuite un cas spécial de DI, c’est-à-dire la Démarche d’investigation et explication, mise en œuvre dans le contexte d’un projet qui vise à la formation professionnelle des enseignants « pour et à travers » la mise en place de la DI. Nous présentons quelques repères théoriques qui sont à la base de la Démarche d’investigation et explication, notamment les fonctions de l’explication et les dimensions de la rationalité selon Habermas. Ces repères théoriques sont la référence pour la conception et gestion des séquences d’apprentissage. Cela est montré à travers l’analyse d’épisodes issus d’une séquence d’apprentissage au sujet des rectangles isopérimétriques.
We present a special case of inquiry based learning implemented in Italy in lower secondary school, the « Investigation and explanation activities ». At first we present the theoretical framework for the planning and implementation of the activities: the fonctions of explanation and the construct of rational behaviour. Afterwards, we present and analyze (by means of the theoretical tools) some episodes from a teaching experiment on isoperimetric rectangles. With this article we aim at contributing to the debate on inquiry based learning. More specifically, we tackle two crucial issues: how to characterize the tasks and questions to be posed during inquiry based learning activities; how to charaterize the roles of teachers, stduents and researchers.
This paper is based on a design-based research project investigating how to use digital resources to help activate formative assessment processes in the classroom. Performed as part of FaSMEd, a ...European Union project, our own project adopts a comprehensive theoretical framework, including the different functionalities of technology, formative assessment strategies, the agents involved, and teacher practices in classroom discussion management. Through this framework we analyze the design and implementation of specific digital worksheets that can be sent from teacher to students and vice versa, as well as displayed on the students’ tablets, on the teachers’ computer and/or on interactive whiteboards, by means of connected classroom technology. These digital resources are meant to help students share their results, opinions and reflections with their classmates and teachers during or at the end of mathematical activities. In this paper we focus on how to exploit digital worksheets supported by connected classroom technologies in order to help activate formative assessment (FA) strategies, especially during class-wide activities. Our analysis reveals that formative assessment strategies emerge in the shape of typical patterns of their interaction when digital worksheets are implemented in the lessons. Hence we have outlined several criteria for the design and implementation of digital worksheets in support of FA processes.
It is widely recognized that purely cognitive behavior is extremely rare in performing mathematical activity: other factors, such as the affective ones, play a crucial role. In light of this ...observation, we present a reflection on the presence of affective and cognitive factors in the process of proving. Proof is considered as a special case of problem solving and the proving process is studied adopting a perspective according to which both affective and cognitive factors influence it. To carry out our study, we set up a framework where theoretical tools coming from research on problem solving, proof and affect are present. The study is performed within a university course in mathematics education, where students were given a statement in elementary number theory to be proved and were asked to write down their proving process and the thoughts that accompanied this process. We scrutinize the written protocols of two unsuccessful students, with the aim of disentangling the intertwining between affect and cognition. In particular, we seize the moments in which beliefs about self and beliefs about mathematical activity shape the performance of our students.
In this paper, we report on a study aimed at describing the way secondary school teachers treat proof and at understanding which factors may influence such a treatment. This study is part of a wider ...project on proof carried out for many years. In our theoretical framework, we combine references from research on proof with those from research on teachers in relation to their beliefs. The study was carried out through interviews with secondary school teachers aimed at learning how they describe their work with proof in the classroom, and to elicit beliefs and other factors that shape this work. Through the interviews we were able to detect reasons behind teachers’ choices in planning their work in the classroom. In the present paper, we concentrate on four cases that, among other factors, offer elements suitable to unravel the problem of inconsistencies using the construct of leading beliefs, i.e., beliefs (whose nature may vary from teacher to teacher) that seem to drive the way each teacher treats proof.
In the chapter on proof in the previous PME Research Handbook, Mariotti (2006) observed that there had seemed to be “a general consensus on the fact that the development of a sense of proof ...constitutes an important objective of mathematics education” and also “a general trend towards including the theme of proof in the curriculum” (p. 173).
Nous présentons une méthode mise en œuvre en Italie à propos de la démarche d’investigation (DI) au collège. Nous souhaitons, à travers cet article, contribuer au débat issu du groupe de travail « La ...démarche d’investigation dans la classe de mathématiques : fondements et pratiques » (Matheron, Morselli, René de Cotret, Schneider, 2012) notamment en ce qui concerne les questions suivantes : caractériser les typologies de questions à poser et les responsabilités des acteurs (enseignant, élèves, chercheurs).Tout d’abord, la DI est insérée dans le contexte de l’institution scolaire italienne. Nous présentons ensuite un cas spécial de DI, c’est-à-dire la Démarche d’investigation et explication, mise en œuvre dans le contexte d’un projet qui vise à la formation professionnelle des enseignants « pour et à travers » la mise en place de la DI. Nous présentons quelques repères théoriques qui sont à la base de la Démarche d’investigation et explication, notamment les fonctions de l’explication et les dimensions de la rationalité selon Habermas. Ces repères théoriques sont la référence pour la conception et gestion des séquences d’apprentissage. Cela est montré à travers l’analyse d’épisodes issus d’une séquence d’apprentissage au sujet des rectangles isopérimétriques.
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