I’m not a real stickler for simplifying. I also don’t much care if a student does something my way, as long as they do it a correct way. I want them to think for themselves, and if their way makes more sense to them and is mathematically sound, who am I to say my way is better?

My students are not used to this. Previous teachers have required simplifying completely – and that’s fine. Previous classes were focused on those skills. Mine aren’t, and I’d rather them focus on what I’m teaching them then hone previously taught skills. Plus, the College Board is ok with it, so there’s that.

The change takes all year long for them. Sometimes two years. I get a lot of “Can we leave it this way?” and “Is this ok?” and “Can I do it this way instead?” I’ve been saying things like, “No, I need a little more,” or “Yes, that’s great.” But yesterday, on a different question, I noticed myself asking a question back: “Does it make a difference?”

I like that more. It puts the thinking back on the student, and it emphasizes what I care about. In my mind, simplifying a fraction really doesn’t make a difference. I don’t care if a student gives me 2/3 or 4/6. 2/3 is a little more dressed up, and it might be easier to work with, but it’s the same number as 4/6.

I think this could go a long way, this new question.

“Should this distance in the volume formula be $1-x$ or $x-1$?” Does it make a difference?

“Do I need to include the plus or minus?” Does it make a difference?

“Is this good enough, or do I need to keep going?” Does it make a difference?

Of course, sometimes, they’ll need an answer. Yes, you do need to use words when justifying your answer. No, you do not need to put your full heading on your paper. What makes a difference to other teachers may not make a difference to me. This isn’t good for everything. But with mathematical questions, where it makes them think about why they’re doing steps, then it could help.