Thursday, November 13, 2014
Relearning Algebra with The Boy
If you had told me at age thirteen that I’d bond with my future son while helping him study for an algebra test, I would have laughed out loud. Yet here we are. If x equals spending time making The Boy laugh and helping him learn, then I’m happy to solve for it.
That technique of speaking math out loud is really powerful. The pros can get an entire class to do it.
Some approaches try to get them to write it out as a essay, like the Arabs did back in the beginning, but I find writing is too slow for most students. Algebra is, after all, just a shorthand for words. I've also noticed that many college students struggling with beginning algebra have the right instincts, that is, they say the right thing for the next step, but lack the confidence to follow through. Emphathy is key with them.
If it helps, feel free to tell TB that I use algebra every single day. I think the only tools from math of that era that I don't use are synthetic division and the solve-by-hand square root algorithm.
Of course, xkcd has a relevant comic for your post.
I played it with my daughter who didn't know algebra and she couldn't quite make the connections between the game and real algebra (she was 10/11 yo). However, I actually thinks it makes more sense to play it as the same time as a person is learning algebra.
I'm glad we don't use "s" for slope, though, because s has a tendency to turn into a 5 if you're not careful and have handwriting like mine. Similarly, the only time I use cursive is when I'm using a letter like "b" (which turns into a 6) or "l" (which turns into a 1) in a math problem. I haven't found a good solution for "s" and "o" so I tend to avoid them as variable names.
The thing that helped me the most with algebra as a middle schooler was that I'd been writing computer programs for years, so I was able to transfer over some of my understanding of the concept of variable from there. This was less useful when I was just supposed to be finding some specific number to make a statement true, but it helped quite a bit with functions since I'd been writing functions in C for years by that point.
I mean, the history's fine -- it's fun to learn the history of timetelling, too. But some things are just arbitrary, because any answer is correct, as long as we all stick with it.
For example, I don't think we use m because the babylonians did. On the other hand, we use 12 hours and 60 minutes because of divisibility by integers (2,3, and 4, as well as 5 and 6 for 60) that led the babylonians to use that system for numbers. That is why there are 12 inches as well as 12 hours. Ever try dividing 10 exactly by 3?
The best we have, according to math historian Frederick Rickey is that it's not based on any historical reason (such as derivation from a French or German source). His hypothesis is that an influential algebra text from the US made that the choice for the parameter at one point and it just stuck.
That is... it appears to be arbitrary.
Would just love to have folks with a humanities/ English background and an open mind to teach some of our Dev Math courses.