In the midst of a very good post, Julie writes:
They also distributed the exponent to both numbers inside the parenthesis. I have no idea why they would do this, because I don’t even teach them the power to a power exponent rule. I have them expand any set of parenthesis with an exponent. They do love the distributive property, but we-e have never, ever, ever, distributed an exponent. Sigh. I failed.
There are a lot of wonderful reflective moments in that post, but I find the above fascinating. Kids are distributing exponents inside the parentheses. You might be tempted to explain this mistake as confusion between the power rule for exponents and the distributive property, but seeing as the kids haven’t yet learned the power rule that explanation seems false, at least for Julie’s kids.
Distributing exponents is tempting for kids. Why?
Julie has a strategy for helping her kids move past these sorts of mistakes:
So, starting Monday, I am going to have one problem of the day for both classes posted on the board. It will look like a variation of this. Evaluate -3x^2 – 2x + 5 when x = -2. I’ll throw in fractions, decimals, and any other basic, easily forgettable concept. This should help them quickly practice evaluating algebraic expressions, exponents, and the order of operations, EVERYDAY. And we will go over it, together, everyday.
Will repetition work? Will she need something else? Here’s hoping that there’s a follow up post from Julie letting us know how her experiment goes. The question for me is, what are the returns on any given genre of problem? Do they diminish with repetition? How different does a problem need to be in order to promote real learning?