My research is concern with what might be call the DECONSTRUCTION of mathematical activity. The term is use to allude to the work of Jacques Derrida on the metaphors and mechanisms at the heart of our human experience. In all modesty, my hope is to re-produce some aspects of his contributions to the study of philosophy and language, but to the domain of mathematics education.
This essentially means to me finding ways and occasions to provoke (thinking)!
I currently develop most of my work around the following topics:
Analyzing teachers and students mathematical activity (or anyone's really!) without ascribing thoughts or intentions... not an easy task! This part of my research efforts goes to developing a way to talk and think about doing mathematics by focusing only on what is visible, audible, sensible, etc. Drawing to ethnomethodology and cognitive studies à la Maturana and Varela, amongst other things, this theoretical development dwells on the idea that "mathematics is what we do, when we do mathematics... and vice versa!".
Most of this work is realize in close collaboration with Jerome Proulx. Here are some of our key publications:
Technology and mathematics are the closest friends. And while some argue that there is not mathematics without some sort of a tool (e.g. symbols), others wants to consider mathematics itself as the essence of technology. So how can such visions play in to disturb our everyday discourses and perspective on technology and mathematics, especially in the context of mathematics education? It is old story so argue that computers and calculators call for a rethinking of what we do in school, how and why. But so far, as Papert many times brilliantly explain it, much of our thinking goes toward adapting technologies to schools, affecting as little as possible the mathematics that is taught.
My work here is to imagine new mathematical possibilities for mathematics education, and without too much concern for the actual programs and various state of affair. So what I do is to try and conceptualize what is possibly at sake when technology and mathematics and thoughts together, and create some applets (see my Ressources section) featuring of those elements. In particular, I came to give great attention to the artistic aspect of doing mathematics.