J-‘s final exams were last week. We’d been helping her review physics, since she was okay with her other subjects. She solved many of the review questions on her own, and then asked us for help with the ones she didn’t know how to do. I was surprised to discover that I remembered enough of kinematics and other topics to be helpful (and to enjoy helping). Yay! =)
We walked her through solving the problems that stumped her. Lots of math and science problem solving is about pattern recognition: seeing how the problem you’re working on is similar to other things you’ve already done (possibly with help), and adapting your experience to the current situation. Having someone sketch out a map and provide quick feedback can make studying a much more productive and less frustrating experience.
Here are some notes on the sub-skills involved:
Algebra’s a big one. I’m not sure how you can develop fluency in that aside from practice and different ways of exploring it. Practising this seems pretty low on the priority list once homework’s finished and even lower priority during vacations. On the other hand, it’s hard to cram understanding when the pressure’s on. I think either John Mighton’s The End of Ignorance or The Myth of Ability had some tips on helping people develop a more intuitive understanding of algebra.
On a related note, there’s also the challenge of translating a word problem into the appropriate math, especially when multiple parts or equations are involved. Maybe we can think out loud more often, modeling the real-world applications of this skill.
There are the usual small mistakes related to doublechecking one’s work or getting the units straight, but she’ll get the hang of that.
J- will be taking more physics, chemistry, and biology next term, so it might be good to do a bit of this review during the summer. In general, I get the impression that she’s doing pretty well, especially compared with the rest of her class.