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!

• The most interesting part to me was the student turning “x+4” into “(x+2)(x+2)”. There might be some conflation with x^2-4 there, but I like the student’s hope that an (x+2) should show up there, since it would help with the (x+2) on the other side.

This is further proof that rational expressions just SUCK. In this case it sucked the math skill (present in the first few steps) right out of the student…

• Heaven help me, but if anything this example seems to show the futility of teaching these types of problems at all. What is learned here? What is the goal?

If anything, I’d start with the line with the blue arrows. Write that (as a teacher) first, then have the students deconstruct what is going on.

But at the end of the day, I totally agree with @bowenkerins. The student knows some algebra, but what do they learn by falling apart halfway through the problem?

• gfrblxt, I always thought the goal of the rational expressions and equations work in Algebra 1 was to say “you need more practice with fractions and more practice with factoring, but that would be insulting to make you do, so we’ll pretend we’re teaching you a new topic while you get that practice”.

The problem, as here, is that the understanding of all those things gets mingled up so much that it becomes hard to tell what the student understands or doesn’t understand, and what the student is doing as a memorized procedure correctly versus knowing meaningfully.

Maybe the cure is to not have them do all those steps in a single problem, but instead to show them lots of examples with well-chosen mistakes and have them find the errors? I hear there’s a blog that sometimes has examples like that.