Conceptualizing inquiry-based education in mathematics

The terms inquiry-based learning and inquiry-based education have appeared with increasing frequency in educational policy and curriculum documents related to mathematics and science education over the past decade, indicating a major educational trend. We go back to the origin of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the theory of didactical situations, the realistic mathematics education programme, the mathematical modelling perspective, the anthropological theory of didactics, and the dialogical and critical approach to mathematics education. In an appendix these frameworks are illustrated with paradigmatic examples of teaching activities with inquiry elements. The paper is rounded off with a list of ten concerns for the development and implementation of IBME.     

Pupils learning algebra with DERIVE

This article deals with the use of computer algebra systems in mathematics secondary education. First, we present the global framework of a research project carried out in France with pupils of grades 9 to 12, from 1993 through 1995. Then we focus on a specific part of this project concerning two grade 9 classes of different mathematical ability taught by the same teacher. We briefly present the aims and organisation of DERIVE's use in the two classes, before embarking with more details on a specific topic: systems of linear equations. Finally, we present the data provided by the pupils' answers to a questionnaire taken at the end of the academic year; we use them for investigating pupils' assumptions about DERIVE's potential for mathematics learning, and compare these representations with those emerging from the entire population.     

Connecting and Integrating Theoretical Frames: The TELMA Contribution

This paper presents the methodology developed within TELMA for connecting and integrating the theoretical frames used by the different teams for studying the design and use of interactive learning environments in mathematics education. Two case studies are then analysed and compared in order to illustrate the methodology and the results it can lead to. The papers ends by a more general discussion about the outcomes of the experimental work developed within TELMA and the perspectives it offers for approaching theoretical fragmentation.     

Editorial Note

Editorial Introduction

Editorial Note     

Billiards and Toy Gravitons

Journal of Statistical Physics - In this article we study the one-dimensional dynamics of elastic collisions of particles with positive and negative mass. We show that such systems are equivalent...     

Toward networking three theoretical approaches: the case of social interactions

We rely on discussions initiated at CERME4 and continued at CERME5 to compare, contrast and combine in a coherent way different theoretical frameworks currently used in mathematics education, with the eventual aim of networking between theoretical approaches. Specifically, we chose for this purpose the theory of didactic situations (TDS), the nested epistemic actions (RBC+C) model for abstraction in context (AiC), and the theoretical approach of interest-dense situations (IDS). As an example, we focus on how each of these frameworks is taking into account social interactions in learning processes. We identified not only connections and contrasts between the frameworks but also additional insights, which each of these frameworks can provide to each of the others. We also present some methodological reflections about the process of networking different theoretical approaches.     

Implementation of inquiry-based learning in day-to-day teaching: a synthesis

This synthesis is designed to provide insight into the most important issues involved in a large-scale implementation of inquiry-based learning (IBL). We will first turn to IBL itself by reflecting on (1) the definition of IBL and (2) examining the current state of the art of its implementation. Afterwards, we will move on to the implementation of IBL and look at its dissemination through resources, professional development, and the involvement of the context. Based on these theoretical reflections, we will develop a conceptual framework for the analysis of dissemination activities before briefly analyzing four exemplary projects. The aim of our analysis is to reflect on the various implementation strategies and raise awareness of the different ways of using and combining them. This synthesis will end with considerations about the framework and conclusions regarding needed future actions.     

Mathematical working spaces through networking lens

ZDM – Mathematics Education - This issue of ZDM collects research works sharing a common reference to the theoretical framework of Mathematical Working Spaces (MWS), a construction which...     

Learning Mathematics in a CAS Environment: The Genesis of a Reflection about Instrumentation and the Dialectics between Technical and Conceptual Work

The last decade has seen the development in France of a significant body of research into the teaching and learning of mathematics in CAS environments. As part of this, French researchers have reflected on issues of ‘instrumentation’, and the dialectics between conceptual and technical work in mathematics. The reflection presented here is more than a personal one – it is based on the collaboration and dialogues that I have been involved in during the nineties. After a short introduction, I briefly present the main theoretical frameworks which we have used and developed in the French research: the anthropological approach in didactics initiated by Chevallard, and the theory of instrumentation developed in cognitive ergonomics. Turning to the CAS research, I show how these frameworks have allowed us to approach important issues as regards the educational use of CAS technology, focusing on the following points: the unexpected complexity of instrumental genesis, the mathematical needs of instrumentation, the status of instrumented techniques, the problems arising from their connection with paper & pencil techniques, and their institutional management. This revised version was published online in July 2006 with corrections to the Cover Date.