Development of pre-service mathematics teachers’ professional knowledge and identity in working with information and communication technology

This paper describes the work undertaken in a course in communication and information technology in a pre-service program for secondary school mathematics teachers. This course aimed to help pre-service teachers develop a positive attitude regarding ICT and use it confidently. It focused on the exploration of educational software and of the Internet’s potential as a means of research and production of web sites. We discuss how the pre-service mathematics teachers evaluate their work concerning their commitment, difficulties they found, learning they identified, and personal relationship. We also analyse the effects of the course on the development of their professional knowledge and identity

Graphic Thinking and Digital Processes: Three Built Case Studies of Digital Materiality

Think strategic link between computer programming; digital modeling; the data; matter and CNC manufacturing in the various stages of the architectural project is key to update our discipline with new technologies. Our proposal to articulate and digital graphic thought processes; developable folded geometries and compositions is rooted in an expanded graphic thinking through multiple conceptual tools that are already part of the operational structure of our discipline

Exploring the mathematics of motion through construction and collaboration

In this paper we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models – in the form of programs – to formalise and thus extend their existing knowledge. In these activities, students controlled the movement of objects in a programming environment, recording the motion data and plotting corresponding position-time and velocity-time graphs. They shared their findings on a specially-designed web-based collaboration system, and posted cross-site challenges to which others could react. We present learning episodes that provide evidence of students making discoveries about the relationships between different representations of motion. We conjecture that these discoveries arose from their activity in building models of motion and their participation in classroom and online communities

The Possibilities of the Parabola

The present study details an investigation into the provision of opportunities for secondary school students to develop an understanding of visual aesthetics by manipulating a single mathematical curve: the parabola. The study documents the establishment of a robust cross-curricular relationship between Mathematics and Visual Design by providing a pedagogical model for learning that relies on the conduit between the two subject areas being explicitly linked. Although the central concept is the marriage of disparate themes, it was operationalised by the development and delivery of activities sequenced to grow appreciation and understanding of the links between unrelated curricula. While this account aims to foster cross-curricular discourse and action, the product output simultaneously provided avenues for the presentation and exhibition of student work; a gallery of which is included in the study. Documenting the inter-disciplinary approach to learning and teaching has resulted in an exploration of the complexities we employ to discover meaning in a range of contexts not singularly reliant on art or language. A convergence is presented in that mathematical rules unite with the rules of art and design in the attempt to project new concepts into new situations where a space for originality exists. Here, the students have been encouraged to imagine new, effective ways of bringing ideas to form (Richmond, 2009). Naturally, developing explicit appreciation/action situations required critical and creative thinking to coincide with lateral and literal approaches to gaining knowledge and understanding of aesthetics. The study presents a reflexive account of the delivery of coursework entitled The Possibilities of the Parabola, from concept to completion

Thinking and acting both locally and globally: new issues for school development planning

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The quantitative approach to business cycle in « X-Crise » group in the 1930's

To construct models and to apply quantitative techniques in order to explain the cyclical movements of the economy is one of the main aims of “X-Crise” group (nickname of “Centre Polytechnicien d'Etudes Economiques”) at the “Ecole Polytechnique” in Paris. Indeed, french polytechniciens' engineers hope that mathematical economics, and especially empirically based modelization, will be helpful first to build a true economic science, and second, to find solutions to the 1930's crisis. These hopes are developed in the methodological debate that Polytechniciens began even before the creation of the association X-Crise. They explain in particular their rejection of "pure” economics and their defence of an approach which mixes economic concepts, statistical facts and mathematical model – such as econometrics. Overall, these hopes are expressed through models constructed by X-Crise members, such as Polytechniciens like François Moch and Maurice Potron or non-polytechniciens like brothers Georges and Edouard Guillaume. Attempts were done to include business cycle in their models. But, finally, they failed to confront them to empirical data.French Engineers - Business Cycles - history of econometrics