Eid Carol - Representation Systems

I am truly amazed by the possibility of designing literacies that expand our ability to learn. diSessa speaks of the power of appropriate literacies and representational systems to transform what we think is learnable at a particular grade level. He presents Galileo’s proof of Theorem 1 (p. 17) and contrasts this proof with the simple way we currently deploy symbols to reflect the same theorem. Although I approve that studying concepts using the algebraic symbols that have been devised simplify the theorem and allows a larger, younger and less-skilled audience to have access to Galileo’s ideas, I nevertheless found Galileo’s way of explaining the system much more syntonic and meaningful than the way algebra presents the same ideas. For instance, consider the below way of thinking about distance and time and their relationship to velocity. Distance and time are presented on two different axes (wow!) that allow a visual perception of the relationship between distance and time on one hand, and among different times and distances on the other.  

Now compare this to:

                                  

What does this notation expose about distance as we perceive it in real life? It is a letter, a symbol that can represent anything. Compared to utilizing a “line” the way Galileo’s proof does, this approach conceals the “feel” of a distance and requires that one contemplates more and imagines further to understand how the relationships between time and distance actually unfold in real life.

I am not saying at all that the algebraic notations have not had a major impact in simplifying concepts and pushing innovation, but I think this simplification came with the cost of disempowering ideas (Papert’s concept). And although diSessa considers that algebraic systems have helped us become smarter, I think they have helped made the “use” of ideas easier but have not necessarily afforded a deeper understanding of these ideas for the majority of people (such as students).

Interestingly, I regard that computational literacies are attempts to de-abstract what representational systems, such as algebra, conceal. Moreover, they have the potential of explaining concepts in ways that are deeply rich, meaningful and syntonic. For instance, in the tool presented by diSessa, the student manipulates the velocity “v” through a program. For me, however, I would not have thought of manipulating v directly. Since I have learnt that v=d/t, velocity has always been this value that I calculate from distance and time (which felt more concrete for me), but that I cannot manipulate directly. Nevertheless, by presenting time as a “tick” (rather than “seconds”) and velocity as “a magnitude” v (rather than some abstract notion calculated as distance over time), velocity is made more concrete and the idea that velocity is the magnitude of a step covered in a tick, regardless of whether the tick is a second, an hour, or a year, the idea of velocity gains a much more concrete and meaningful sense and its relation to distance and time is revealed in a much clearer manner than what v=d/t can afford.  Let me know your thoughts on this!