I just presented the MiGen project at the ICALT 08 conference. We were accepted as a short paper so I had 15 minutes for the presentation and 5 minutes for questions. I gave a very brief overview of the project, introducing the three main components eXpresser, eGeneraliser and eCollaborator. I then showed ShapeBuilder and demonstrated the pond tiling task, introducing the idea of messing up. I then explained how we moved away from shape-based problems since this doesn’t cover many typical generalisation tasks in the National Curriculum. I then showed the latest version of the system that I had (v0-1004). I demonstrated basic shapes and creating a diagonal and then demonstrated the ‘footpath’ problem, showing the backward-c construction and the 2n+1 construction. (Note that this uses the new expression parsing facilities in 0-1004).
I was asked two questions at the end. The first was about whether the system was really teaching algebra. I agreed that it was only teaching part of it; for example, it does not help with the idea of doing the same thing to both sides of an equation. I emphasised that the system was about mathematical generalisation and that algebra is a useful tool for this. Admittedly the paper title includes the word ‘algebra’ so perhaps this is slightly misleading. The second question was about possibly displaying (essentially) a table of numbers so that the child can abstract the pattern. I explained that this was precisely what we were trying to avoid since suhc premature engagement with numbers is problematic in general. Also, table-based exploration is not scalable for problems of more than one variable (for example).
Another comment was also made saying that the system could automatically show how changing iterations (say) would make their pattern look more and more messed up. For example, imagine that their pattern is hard-wired to look okay for 5 iterations. If the user changes this to 6, it looks messed up but if system then changed it progressively to 7, 8, 9, etc the user would see that their construction getting more and more messed up.
Various people (after the session) felt that the system could be useful for age ranges far above our 11-14 age range.