Sue Van Hattum will be leading a webinar tomorrow to counterbalance the one I facilitated a week ago. Sue is the lo-fi to my hi-fi. Sue’s thesis is that we can have the engagement and challenge of WCYDWT without the multimedia.
This is undoubtedly true. Consider Polya, who offered engaging, challenging problems without degrading himself by walking up a down escalator. “Into how many parts will five random planes divide space?” for instance, is challenging and engaging and offers points of entry to learners of all abilities.
So an open question: what’s the point of multimedia? If it’s just amusing â€” which is to say, engaging in the worst, most superficial way â€”Â I can do without it. My sense, though, is that the feature common to all of these problems …
- into how many parts will five random planes divide space?
- how long will it take Dan to walk up the down escalator?
- how many tickets are on the roll?
- how long will it take to fill up the water tank?
- how fast is the runner?
- what is the killer’s shoe size?
… is that they “reveal their constraints quickly and clearly.” They’re Twitter-sized queries that unpack into full-bodied mathematical investigations.
Multimedia lets us reveal constraints quicker and more clearly, though that isn’t a given. Multimedia can have low information resolution. (I’m talking about your stock photography, your dogs in bandanas, etc.) But the information resolution on this single image of a ticket roll blows me away. When you put the quarter next to the roll for scale, the problem literally reveals its own constraints. The learner can gather any information she wants â€” circumferences, radii, diameters, ticket dimensions â€” without the teacher having to write or say anything.
I suppose I’m trying to slip Sue a question in advance: how do I reveal the constraints of the same problem that quickly and clearly without the multimedia?