It is SO difficult to correct a student when they arrive at the correct conclusion. For so many, the conclusion is the concern in math (and elsewhere)

I think I would ask a series of slightly modified questions with different bases (constants, not unknowns) and try to arrive at a realization of the problem with this representation.

I totally agree with both of mrdardy’s points here: first that answer-getting as a motivation can make students resistant to learning from this kind of mistake, and second that a good way to circle back around to this particular question is to ask a bunch of questions like “why is $frac{3^{14}}{3^2} = 3^{12}$” (3^14 / 3^2 = 3^12) and look at their explanations for that. Then you can compare steps throughout their work by punching the result into the calculator.

You could also ask about their work for the problem that appears just above here.

You could also emphasize when it is good to substitute an arbitrary number for a variable (say, when you’re trying to check your work and make sure something you’ve claimed to be an identity really is plausible) and when it is not good.

At least, that kid is thinking on his answer even if it perfectly wrong. Thus, it’s a good lesson for that kid to know that he or she should study in order to answer those questions correctly and be able to tackle question and answer perfectly.

## 4 replies on “Simplifying exponents”

I’d ask what the kid was thinking 🙂

It is SO difficult to correct a student when they arrive at the correct conclusion. For so many, the conclusion is the concern in math (and elsewhere)

I think I would ask a series of slightly modified questions with different bases (constants, not unknowns) and try to arrive at a realization of the problem with this representation.

I totally agree with both of mrdardy’s points here: first that answer-getting as a motivation can make students resistant to learning from this kind of mistake, and second that a good way to circle back around to this particular question is to ask a bunch of questions like “why is $frac{3^{14}}{3^2} = 3^{12}$” (3^14 / 3^2 = 3^12) and look at their explanations for that. Then you can compare steps throughout their work by punching the result into the calculator.

You could also ask about their work for the problem that appears just above here.

You could also emphasize when it is good to substitute an arbitrary number for a variable (say, when you’re trying to check your work and make sure something you’ve claimed to be an identity really is plausible) and when it is not good.

At least, that kid is thinking on his answer even if it perfectly wrong. Thus, it’s a good lesson for that kid to know that he or she should study in order to answer those questions correctly and be able to tackle question and answer perfectly.