@Stephen – I envy you your ability to write significant comments to your students in a timely fashion (or perhaps your class size… or perhaps your energy level. :) ). I have >185 students, so it’s just not practical for me to write & turn around comments like this in a timely way. Perhaps that’s why I’ve had to expand my repertoire of in-class techniques like this. It’s a little painful because until my current school, I had always had small enough classes to be able to establish powerful relationships with students through writing comments.

So I say good for you and keep going!!!

@Evan – I actually ask them to analyze the text of the prompt/question, as in asking them What is the verb in the instruction/prompt? Circle it in red. What does that verb mean?

I ask them about prefixes and suffixes and roots (they are often SHOCKED that math teachers might know this strange wizardry) and I will ask them (as Dan often does) to write a guess in their notebook.

I will also do a whole-class group noticing (thank you, Math Forum) if I need to, asking each person to say something they noticed and writing it on the board. I have actually been known to fill up more than one whiteboard with these noticings – but this practice is important to communicated to them that I am not going to fold. THEY ARE GOING TO HAVE TO GO BACK TO THE TEXT AND THEY ARE GOING TO HAVE TO ANSWER MY Q BEFORE WE MOVE ON!

I have even assigned this as a graded HW assignment when I’ve had to.

A lot of being the language support as you put it (I like that framing) involves out-stubborning them. This communicates to them that this is IMPORTANT, that they are responsible for their learning, and that I am not going to let them off the hook for this. Does that help at all?

– Elizabeth (@cheesemonkeysf)

Thanks for the thoughtful comment here, Michael. Your perspective from studying in yeshivas is a particularly helpful lens on your last comments. At this point I don’t mean to say much more than this:

That we should be able to train our ears to hear what’s valuable and correct in a student’s thinking, that we should be able to communicate that, but while also telling our students how to improve?

I tend to think the implicit definition of “mistake” in math class works against that specialized hearing, and that the growth mindsetization of mistakes amounts to doing the wrong thing in the right way.

Thanks Cheesemonkeysf. I’m with you about the “right answer” mindset. Such thinking is a precursor to focusing on grades, not learning. Something that always leaves a bad taste in my mouth. The guy who teaches science two doors and I independently stopped putting scores on assignments this year and have started to write far more comments trying to direct students to the part of their own written thinking where unclarity is present. The task for the student is to revisit their own thinking.

1. It still seems to me that the meaning of “mistake” we’re dealing with is new and designed to conform to the distinction. We might as well have invented a new word.

2. There is a small but important movement to entirely remove language that applies any sort of evaluation on student thinking. So no misconception, no mistake, no incorrect, no wrong. These last two posts seem to me uneasily balanced on the edge of this movement. The arguments of these posts are really arguments for removing much more than “mistake” from teacher talk, and likewise “So, if we don’t call it a mistake, then what do we call it? THINKING.”

…but then why are we comfortable using the language of correct or incorrect? And why are we comfortable saying kids are bad at expressing their ideas but uncomfortable talking about whether they’ve made a mistake or not?

3. The premise of the last bit of the post — that correct/incorrect can’t apply to complex mathematical questions — doesn’t match with my experience of mathematics. Proofs can be correct or incorrect…though of course there can be amazing, beautiful ideas contained in flawed proofs! And isn’t that the point, ultimately? That we should be able to train our ears to hear what’s valuable and correct in a student’s thinking, that we should be able to communicate that, but while also telling our students how to improve? Beyond this, what are we talking about? (I agree: we shouldn’t kick off the conversation by telling kids “You’ve made a mistake!”)

4. These last two posts are implicitly a critique of growth mindset culture in math edu. Hear hear! Too many math teachers are in the business of shutting down students’ ideas but putting a cherry on top. (Stronger you make do mistakes, young Jedi.) But that critique hasn’t quite been made explicit. Isn’t that what we’re talking about here?

5. The math that most benefits from frank talk of correctness is the math of skills. This is a lot of what we do in the classroom! The end of this post says that these types of questions — the ones that can be judged correct/incorrect easily — don’t matter. (Or don’t very much matter?) I think that’s wrong, and it’s signing away a lot of wonderful math. I’ve seen kids come alive with beautifully complex questions and with simple questions too. (Can’t Three Act Problems be simply judged to be correct or not? Isn’t that the point of a video — it’s the answer key?)

6. As usual in these sorts of things, as we get more specific I find more agreement. I use something like the script you offer a couple times a day, at least. (Compliment — Restatement — Correction — Try Again).

But the advice to always find a question that the student answered correctly is not always useful. The point isn’t to randomly find a question that the kid correctly answered — the point is to value the students’ thinking. Knowing more math (so that we can match kids’ thinking with mathematical questions) seems to me of dubious value. Kids want to know that there is something valuable about their thinking for THIS question, not some other one.

7. I strongly suspect that this is a cultural thing, and that different groups of students (/teachers) in this large country and larger world have different relationships to all this language. In the yeshivas that I attended, we always talked about this and that great sage and the mistakes they made or their incorrect assumptions. In the schools that I’ve taught in with the math that I’ve taught, I strongly sense that my students value forthright, explicit information about when they’ve made a mistake (so they can improve). It’s even sort of funny when people are shy or implicit about when a mistake has been made.

I suspect that these last two posts are optimized to resonate with a particular culture that I don’t have access to, and that this partly explains my tin ear.