How did this student end up with the answer he did?  What does it seem that he knows about complex numbers?

What is it about complex numbers that this student finds confusing? Do you think he would make an identical mistake on $(12 + 3x) + (2 - 3i)$? Why or why not?

What does this student know about composition of functions?

What’s going through the kid’s brain when he makes his mistake?

How would you help?

Last week we posted a somewhat similar mistake involving logarithms. Here’s the student work:

While you should feel free to comment on today’s mistake independent of the earlier one, I think it would be especially productive to compare these two pieces of student work. Could the same student have done both pieces of work? Are there differences between the way each student understands logarithms?

By the way, we now support equation editing in LaTeX, so feel free to write things such as $\frac{2\log(6x)}{\log}$ in the comments. This post is also tagged with a Common Core Standard and categorized according the hierarchy that you see in the menu on the left.

Today’s mistake is a classic, at least in my classroom.  What makes this mistake so tempting for students, and how do you help them see the light?

Why did this student divide by “e”? What does that say about the way they think about logarithms? How would you help the student?

This kid clearly knows some of the basics of composing functions. But check out that last line.

What is going through this kid’s brain, and how would you respond?