(It’s Presidents’ Day, so remember to vote!)
Razib over at Gene Expression offers some thoughts on the algebra issue, in which he suggests some historical perspective:
The ancient Greeks were not unintelligent, so the fact that many of us (rightly I believe) take symbolic algebra for granted as a necessary feature of our cognitive landscape is something to reflect upon. Maths that we assume to be fundamental elements of our mental toolkits would have been beyond the very conception of the most brilliant minds of our species over one thousand years ago.
I’m not really happy with this, because it seems a little too Steven Pinker– “our ape-like ancestors on the savannah didn’t need algebra, so we never evolved the brain module for it…” I’m not really comfortable with the claim that the relatively late development of an idea indicates that it’s somehow counter to our brain chemistry, and thus ok for people to not understand it.
I originally planned to note that Newton’s Laws post-date the invention of symbolic algebra, and that doesn’t make them incomprehensible to normal humans. This quickly runs into the previously noted problem that many people do have a hard time grasping Newton’s Laws…
I thought of another example, though, after a conversation with Patrick Nielsen Hayden at Boskone. In the course of explaining the origin of the quote “Plot is a literary convernstion, story is a force of nature,” he made reference to (I’m paraphrasing here) the fundamnetal narrative connectors of medieval literature, which are “And here’s another thing…” and “And I forgot to mention that…”
(More after the cut…)
It’s a description that rings pretty true, based on the medieval lit course I took in college (scholars of medieval lit are welcome to object in comments), and points out that our modern ideas of narrative structure are also relatively recent. As Patrick noted, these are the same story-telling conventioned used by five-year-olds today, but most adults move past them fairly quickly.
The idea that a story is something more than a series of events presented in the order in which they occur to the teller is arguably a fairly recent development (of about the same age as symbolic algebra), and yet, nobody expects students to struggle with it. An even more recent development is the idea that an imaginary-world story can be told without first spending a chapter on establishing the provenance of some fictitious manuscript that serves as the source– that didn’t really change until the early 20th century, and nobody expects students to have trouble picking it up. In fact, people who can’t cope with the modern conceptions of fiction are widely considered to have problems…
I don’t think you’d find literary scholars trying to excuse reading comprehension issues with references to cognitive development, and the relatively recent adoption of modern literary conventions. In fact, people usually go in the other direction– faculty teaching older works take some time to explain that narrative convetions were different in the past, and treat our current set of conventions as the natural state of affairs.
I don’t think this is an iron-clad argument– for one thing, works like The Iliad don’t use the “And another thing…” transition to the same degree as later works. But it’s a non-science illustration of why I’m uncomfortable with attempts to excuse struggles with mathematics by reference to history– there are lots of other subjects where we wouldn’t attempt to make a similar justification for student difficulties, so why do we go to such lengths to excuse struggles with mathematics?