Next: Modelling the response of Up: Empirical Modelling for Learning Previous: References Contents
I'm impressed by the scholarly orientation of this submission: there's excellent potential in considering different types of understanding, and in exploring philosophical perspectives. It will be important in developing these themes to use language very carefully - beware of the kind of transition from one expression to another that you have in your second sentence, where you don't seem to be distinguishing 'types of understanding' from 'types of knowledge'. Your abstract already promises a well-conceived format for the paper, and is oriented towards the kinds of issues that are most appropriate for discussion.
I think that the general themes of your paper fit well in the context of thinking about what Chris Roe describes in his thesis as the Experiential Framework for Learning (EFL). The EFL is intended as a map of learning activities that range from the experiential to the formal - it should be possible to interpret different specific instances of learning relative to it, and your case-study should suit the purpose quite well. For instance, it will most likely be appropriate for a child to learn about non-decimal bases through practical experience of arithmetic exercises of some kind, whereas a more abstract formal introduction would serve the conceptual needs of a more mature learner. There is also the issue of understanding in principle how non-decimal bases work, and being familiar with a particular base (for instance, I can know how base 7 operates in principle without being able to readily identify what 2364 is in base 7). Questions such as what it means to know numbers in context (is this the attendance at a football match, or the airfare to Budapest, or the speed of a car? etc) may fall within the scope of your discussion if not the practical work. In general, I think that making sure that there's a strong link between the thinking in the paper and the model-building activity will be the most challenging issue.
Probably will be useful to refer to Computer Support for Constructionism in Context - the latest of the papers authored by Chris Roe and myself. The heapsort model introduced in the lectures may also be relevant to the theme of modelling 'much more abstract subjects'. Appropriate to include more formal references to where papers have appeared in conferences etc, rather than citing them as originating from the University of Warwick.