Letting Kids Develop Their Own Graphical Vocabulary

...Ha! Lots of math posts today/this weekend. I guess you can tell that math is on my mind and that my boyfriend (who is usually the poor victim of my math blabbings) is busy with his own pet projects. :) :)

Anyway, I was planning a lesson to teach my precalculus kids some basic graph-analysis vocabulary -- things like concaving upwards/downwards, local minimum/maximum, inflection points. And I wondered: how much of this can the kids come up with on their own? When they are looking at a graph (or forced to look at it closely by describing it to their "blind-folded" friend), how many different features can they pick out without any assistance from me?

I guess we'll find out! This is modeled after a Geometry activity I had done in the past, where kids had to describe transformations in a coordinate plane in their own words before I taught them the proper ways of numerically specifying transformations. Except here, all my juniors will have to do is to get their friends to re-draw the graph without gesturing and without peeking at the original graph! --Easy?



I am interested in whether any group will develop ideas similar to concavity. At the minimum, they should figure out that they're going to need to specify slopes, "highest"/"lowest" points, some type of discussion of curvature, and (hopefully) roots! If they can already pick out all of these distinguishing features on their own, I have every reason to hope that the formal vocabulary will stick without too much trouble.

(Speaking of which, I don't teach middle-schoolers anymore, but it seems like this type of method of developing graphical vocabulary can be extended to middle school, when kids first learn to identify slope and y-intercept. If you give a kid a line and they have to get their friend to re-draw it based on verbal directions only, and they're not allowed to name (x, y) coordinates, what types of things would a kid pick out of the graph to describe??)