National Science Education Standards

The Silent Language

This paper arises from ongoing research undertaken by the Economics team of the ESRC/ TLRP Project ‘Enhancing Teaching and Learning Environments’ (ETL) 1 . This forms part of the large scale ESRC Teaching and Learning Research Programme Phase 2. ETL is seeking to identify factors leading to high quality learning environments within five disciplin ary contexts across a range of HE institutions. Mey er’s notion of a threshold concept was introduced into project discussions on learnin g outcomes as a particular basis for differentiating between core learning out comes that represent ‘seeing things in a new way’ a nd those that do not. A threshold concept is thus seen as something distinct within what university teach ers would typically describe as ‘core concepts’. Furthe rmore, threshold concepts may represent, or lead to , what Perkins (1999) describes as ‘troublesome knowledge’ — knowledge that is conceptually difficult, counter-intuitive or ‘alien’. The paper attempts to define characteristics of threshold concepts and, in the light of Perkins’ work, to indicate correspondences between the notion of threshold concepts and that of ‘troublesome knowledge.’

Threshold Concepts and Troublesome Knowledge: linkages to ways of thinking and practising within the disciplines

This paper examines how secondary teachers of the core subjects of English, mathematics, and science have begun to integrate information and communication technology (ICT) into mainstream classroom practice in English schools. It draws on an analysis of 18 focus‐group interviews with subject departments in these fields. Evident commitment to incorporating ICT was tempered by a cautious, critical approach, and by the influence of external constraints. Teacher accounts emphasized both the use of ICT to enhance and extend existing classroom practice, and change in terms of emerging forms of activity which complemented or modified practice. A gradual process of pedagogical evolution was apparent; teachers were developing and trialling new strategies specifically for mediating ICT‐supported learning. In particular, these overcame the potentially obstructive role of some forms of ICT by focusing pupils’ attention onto underlying learning objectives.

/pdf/teacher-perspectives-on-integrating-ict-into-subject-3uh6g20r0j.pdf

Teacher perspectives on integrating ICT into subject teaching: commitment, constraints, caution, and change

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.

/pdf/learning-mathematics-in-a-cas-environment-the-genesis-of-a-8hypbnan8j.pdf

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.

Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work

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.

/pdf/conceptualizing-inquiry-based-education-in-mathematics-3nz8r3uddm.pdf

Conceptualizing inquiry-based education in mathematics

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.

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

This chapter will highlight the interest and necessity of considering a plurality of perspectives (or dimensions) when addressing the issue of the integration of information and communication technologies (JCT) into the teaching and learning of mathematics. It will also show how this multidimensional perspective can be efficient for an analysis of the existing literature.

Michèle Artigue

Papers

Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work

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

Conceptualizing inquiry-based education in mathematics

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

Technology and Mathematics Education: A Multidimensional Study of the Evolution of Research and Innovation