Is this a mistake? Incomplete, sure, but if the student had responded:

Because 5^0 = 5^(1-1) = 5^1/5^1 = 5/5, and 5 goes into itself once,

would there be any issue? I wouldn’t assume the student understands all this — students should be required to explain themselves for credit. But this is called “Math Mistakes”…

It’s a communication mistake I think, and communication is part of mathematics. While I think this student is likely to have an understanding of what an exponent of 0 means, this “proof” is far from complete.

l hodge

The crossed out work makes me skeptical that this student understands the 0 exponent. They may well just have remembered dividing a number by itself when originally doing this in class.

When I ask a student to explain or prove something we have previously done in class, I am often not so sure whether a good explanation is really just memorization, or a bad explanation is resulting from good understanding but poor communication skills. I think unfamiliar problems are better for checking understanding – like ask them to use the ideas involved in finding a value for 5^0 to find a value for 5^(-1).

If the question was framed to include a model as proof perhaps the student would have provided a more robust response. This suggestion is really a combination of David’s and I hodge’s ideas. However some may view this clarification of directions as leading the student. For middle school I think it’s ok.

If the question was reframed to include a model perhaps the student would have provided a more robust response. This is a combination of David’s and I hodge’s ideas. Now is that a clarification of directions or leading the student? I think for middle school it’s ok.