The power of visual representations

In middle- and high-school math classes, we spend a lot of time helping students learn different representations of mathematical relations: words, equations, graphs, tables, etc. One of the big ideas is that a particular representation may be more powerful than others for a particular use or context. Examples start to become routine and repetitive after a while, so I was startled to see one today that I had never seen before: a graph of a function that immediately and dramatically shows the objective difference between the speech rhythms of Harriet Miers and George W. Bush. My erstwhile classmate, Mark Liberman, displays this graph of the waveform of Bush’s introduction followed immediately by Miers’s speech:

As Liberman points out, “it’s easy to see where Bush stops and Miers starts.”

So we’re not just imagining it when we think that Bush pauses between phrases too often and for too long.

Categories: Math, Teaching & Learning, Technology