I often find myself at a desk, agonizing over whether or not it’s worth it to give comments on student work. I have a similar worry that arises when kids are working in class. Should I say something? What should I say? Will it help?
Clearly, sometimes comments don’t work. Sometimes hints help. Sometimes they don’t. True, there’s always going to be some guesswork involved in teaching. Nothing works, at least not all the time. But come on! There has got to be some trends, some patterns that I can lean on.
A few weeks ago, I was talking to a kid about whether 3x^2 or (3x)^2 is equal to 9x^2. She wasn’t sure, and I found myself in that agonizing moment: what do I say? should I give a hint? let her flail?
I decided to speak up, and I found myself offering the following hints:
- “For this sort of problem, you’re probably looking to either use number testing or an area model.”
- “Why don’t you try number testing?”
- “Can you find a shortcut using the area model?”
These hints worked for this kid, and I’m left wondering why?
I wasn’t trying to do a whole lot of conceptual development during this one-on-one discussion. These were comments that were just asking this kid to connect strategies she had thought about in a whole-group setting to her personal work. I was using my hints/comments to draw a connection, not to develop an idea.
I was hoping that this idea would help me make decisions about when to give feedback in other situations. Today, I was trying to figure out whether to give comments on the work of my 4th Graders, who are working on multiplication. As I stared at the pile, I felt my gut say “AVOID!” Were my instincts right, or was I just being lazy?
I realized that I had no special language with which to give comments to my 4th Graders. I wanted to do for them what I did for my algebra student: refer them back to models or strategies that they had some understanding of already. Otherwise comment-writing gets insanely laborious and tricky. (How do you teach a kid to use a new strategy in two lines?) I wanted to leave them comments like “try doubling!” or “what if you broke apart this number by 10s?” or “put this multiplication in a word problem.”
I couldn’t do any of this, though, because we hadn’t focused on these strategies and we hadn’t named them, yet. So I didn’t write comments.
Instead, I ran a opening mental-math lesson. I asked this series of questions:
- 8 x 3
- 20 x 3
- 28 x 3
We named the strategy that many of them used: it’s splitting up the numbers, or breaking then numbers apart. Then I asked them to practice it with a new problem:
- 13 x 12
And we collected a few different ways of doing this, and talked about why it works.
And then, when they were working alone on practice with multiplication, I went up to A. She was using laborious doubling methods for her multiplication. I said to her, “Could you try breaking these numbers apart?” She said, “I prefer to use doubling and adding.” I said, “Well, that’s good too, but if you were going to break them apart, how would you?”
And she said 37 x 4 is the same as 30 x 4 and 7 x 4, and she solved it, and now we’re in business.
So, in short, one thing that works for me is giving hints that refer back to strategies we’ve already talked about.