This was one student;s take on the front of my homework last night. We’re wrapping up graphing quadratics right now, and it’s mixed practice (see my homework philosophy here) from the whole year.

I’m fascinated by mistakes like these graphs — where a student takes one concept and projects it onto a number of unrelated concepts. What is the best way to approach this student. Oh, and how do you address the mistake on #5?

The struggle.

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howardat58No. 5: He has correctly expanded the term on the left. He sees 12x on each side but subtracting 12x from each side leaves him with no x’s at all. he doesn’t like this so he leaves the x in on the right, just subtracting (bad move) the 12 by removing it. Now he has an x and some numbers, which he deals with correctly. I think that he thinks that every equation should have an x in it, and fixes things. problem here for him, if he checked his answer it would satisfy the equation !

katenerdypooI like the mixed review of graphing. Maybe it would be helpful if you asked the students first what type of graph they were asked to graph:linear, quadratic, other, and had them give a brief reason why. That might ease the rushing mindlessly through syndrome that so many students fall prey to. Plus it helps constantly reinforce the concept of form.