Last week I posted a short video from a tutoring session I had with a kid. We were solving equations, and he had some interesting ideas, and it was nice to have those ideas and his mental workings become explicit.

Here’s another chunk of that video:

Comment on whatever you like, but here are some prompts:

1. Help me understand his thinking. How did he devise his test for whether his solution is correct?

Or jump in with whatever you like in the comments.

Question: Evaluate the expression $-z^{2} + x(3-y)^2$  when $x = 10$,   \$latex y = -2\$, and  \$latex z = -2\$.

What happened?  First, I HATE PEMDAS AND ANYONE WHO USES IT.  This starts early, and students are already brainwashed by 6th grade when I get them.  All of the GEMS in the world can’t seem to fix this.  I hate PEMDAS because students see parenthesis and go into “I must do that first” mode, even when there is only ONE number inside the parenthesis.  Just because it is in parenthesis, one number, for example (2), does NOT a group make.

Discuss her evaluation of the problem, and her next steps, either in the comments or at her place.

Chris Shore passes on the above, and he thinks that things just aren’t clicking for this kid. I’m inclined to agree. What would you all recommend? What’s the next step for this kid?

What task or problem would you have this student attempt? Or would you follow this up with an explanation?

Thanks to John Weisenfeld for the submission!

What does the kid think the distributive property is?

It’s easy to say: “Well, I’d avoid this mistake in my class by teaching the distributive property correctly.” Well, what’s the wrong way to teach this thing, then? What’s the smartest possible way to teach this, and still end up with your kids making that mistake?

After you’re done writing an awesome comment to this post, go check out Josh Weisenfeld’s blog. He spotted and submitted this gem of a mistake.