exponents The Number System

Why kids mess up exponents

I’m trying very hard to get people as excited by exponent mistakes as I am. I just think that they’re really cool and interesting. I gave kids this survey today in class to 9th graders who have never seen negative or rational exponents before, just to see what they’d do.

survey 1

The results did not disappoint.  The mistakes they made will find their way to the site soon enough, but for now, drop by Rational Expressions and let me know what you think of the experiment and its results.

Here’s one result of the survey to whet your appetite:


If you decide to give your students the exponents survey, or make a survey of your own on exponents or any subject, I would sure love to see it. Send it my way, if you will.

2 replies on “Why kids mess up exponents”

Very interesting! Thanks for sharing the results of this survey. Based on these results, I’m not (yet) convinced that there is a fundamental difference in student thinking with negative exponents, positive integer exponents, and rational exponents. I see instead a lot of trying to apply rules that work for multiplication to exponents. You already noted this in that when taking 20 to the -3 many wanted to take 20 to the 3 and then make it negative (as they were “taught” to multiply by negative numbers). Other examples fall into this category, also, though. A few students also tried to use the rule that if there is a 0 at the end, just ignore it and tack it on the end so 20 to the -3 became 2 to the 3 and then tack on the – and the 0. I think the 100 to the .5 (at least possibly) falls into this category. To take 100 the .5, take 100 to the 1 and then cut it in half. An interesting question to ask would be 2 to the three-halves. If a student just replaces exponents with multiplication in strange situations, I would expect to see 3 (or six-halves) as a frequent answer. If a student is trying to use “rules” of multiplication to help with a more complicated problem I would expect to see 4 as an answer. By the way I saw this type of thinking at least once on your survey (and often from my own students) when faced with 3213 to the 43, one student tried raising it to the 40 and then adding 3213 raised to the 3, again a strategy that works when faced with a more complicated multiplication problem. It’s a great strategy for multiplication (and one which I wish I would see more often in that context) AND its one that can be adapted to exponents, but I think a key will need to be for students to understand WHY certain strategies work for multiplication so they can determine whether they apply directly in other situations (not often) or can be adapted to other situations (quite frequently).

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