Pattern recognition [cKą , Learning] A short story (non-fiction) drew recently my attention to the role of pattern recognition as part of the activity of reading and interpreting algebraic expressions. What is often seen as a technical weakness may have this time to be considered at a conceptual level.Posted on Friday 12th, September 2008
Close to the end of my carreer and looking back, I can see two periods: one dedicated to Mathematics Education (from 1974 to 1988) and another one dedicated to Technolgy Enhanced Learning (since 1988), with a non-empty intersection: to understand and to enhance the learning of mathematical proof. I am unsure about what I have found as a researcher, but it is clear that the problems I considered are now clearer although still rather open. Actually, one difficult issue in these areas is to find a large enough consensus on criteria to support the claim for validity of any statement, any result. It may be this issue -- which has both an epistemological and a social dimension -- which drives my current activity. I have taken up this challenge in two ways which I summarize here after.
In the case of Technology Enhanced Learning (TEL), I promote the adoption of an encyclopaedic approach based on the new tools that Science 2.0 provides us with. The first step is to gather the words we use and to make explicit the concepts to which they are related, to understand their variety, and identify the discrepencies in understanding them. The outcome will be a thesaurus and a dictionnary. Given the importance of culture and epistemology in the Learning Research area we have to be prepared to face differences (even disagreement) due to the differences between our languages (what is often hiden by an unquestionned use of English by non-Anglospeaker) or even of our disciplines. The forum attached to this site is an attempt to engage in this direction. Once the creation of a thesaurus will have made significant progress, then the next step will be the creation of an encyclopaedia to describe and support the TEL knowledge base, very likely based on a wiki and the TeLearn OA. This project will be carried out involving communities in the context of the Stellar EC FP7 Network of Excellence and the scientific association TELEARC.
In the case of mathematics education, I dedicate what remain of my activity to the writing of a wikibook on cK¢ , a knowledge model which aims at building two bridges at once! not less... first, a bridge between knowing and proving, using the notion of "control" as a pivot. Second, a bridge between mathematics education and computer-science by constructing a model which can be meaningful (and usable) for the former, and usable (and meaningful) for the latter.
Both projects will be web-based, using the so-called Web2.0 tools. These tools will be mainly this website with its forum, blog and repository and a wiki. For the rest, I leave to my friend Théo Rifortel the burden of discovering what migh be the value for academics of services like Twitter, Netvibes, Linkedin, etc.
We breathe without noticing until we run up the hill
We learn the way we breathe, until we have a will