How would you help this student?

Another thought: would this student have made this mistake at the beginning of the problem? In other words, is this mistake more likely to happen as the problem goes on than at the beginning? If so, then what does that say about problem-solving?

Thanks to Anna for the submission!

What’s the fastest way of helping these students?

Thanks to Anna for the submissions.

There’s a lot going on here. What about this work do you find the most interesting? How would you help this student?

Thanks to Heather for the submission!

I think the temptation I have is to call this a “careless” mistake and urge more practice. Let’s probe deeper.

1. What does this kid know and understand about exponents?

2. What’s the fastest way to help?

3. What makes this mistake so tempting?

Thanks to Sadie Estrella for the awesome addition to our ever-mounting pile of exponents mistakes.

Kelli Prine submits the above, and asks “This student keeps factoring the terms and canceling.  What can I do to clarify the process?”

I expect some excellent comments on this one. Don’t disappoint.

Here are 7 mistakes. There represent all of the variety of mistakes from a selection of 36 students. The first two mistakes were repeated by several students, but the last 5 were unique in the sample.

Which of these mistakes would you predict? Which ones surprise you? Can you make sense of them all?

What’s the mistake? Diagnose the disease, and find the cure in the comments.

Thanks to Anna Blintsein for the submissions. Go follow her on twitter!

Here are two classic mistakes:

Whenever I see a mistake that recurs at all different levels, and with all different students, I wonder: what makes this mistake so attractive? What’s the misconception? And what can we do about it?

Say something smart in the comments, and then go check out this post from Fawn Nguyen.

In case you’re having trouble reading the kid’s work, and because the top of the question is cut off, I’m going to reproduce the problem in text below the image:

Question: What is the product of $\frac{x^2-1}{x+1}$ and $\frac{x+3}{3x+3}$?

Answer: $\frac{3x^2-3}{3x+3}*\frac{x+3}{3x-3}$

$\frac{3x^2+9}{9x+9} \rightarrow \frac{1x^2+3}{3x+3}$

The usual: What does he know, what doesn’t he know, and what would you do next?