A couple of weeks ago during the Sunday night #probchat on Twitter the topic of hints came up. (You can read the whole conversation at Storify.) A few people started talking about possible “good” and “bad” hints, and I wondered how we’d gotten onto the topic of hints, rather than talking about possible solution strategies (which was the current question posed in the chat). So I chimed in with
Why on earth is anyone giving anyone any hints? I don’t think we should be doing anything other than checking for understanding. #probchat
— Annie Fetter (@MFAnnie) May 18, 2015
I know hints are a hot Twitter topic right now, and I agree that you do, as a teacher, want to have a plan for what to say to kids who are stuck somewhere specific (that you expected them to get stuck). But most of the hints that we give are really shoves (some very gentle, some more forceful) in a particular direction. They often don’t do three things that I think are important:
- figure out what the student understands about the story
- honor where the student is and what they’ve thought of so far
- let the student do all the work and make all the decisions
As a sometimes coach in a wide range of schools/districts/populations, I don’t think that I work with students that are so unusual, and I find that when a kid asks me a question or tells me they’re stuck, probably 19 times out of 20 (or maybe more like 49 out of 50, though my colleagues would probably guess at 99 out of 100), what I say is, “Tell me something about the problem.” That’s it. There are small modifications – if they asked about question 3, I’ll say, “Tell me something about question 3.” Or, if I’m feeling radical and they’ve actually done some math, “Tell me about what you’ve tried so far.”
Yes, even if they say, “I don’t know how to start.” In #probchat, Kent asked:
— Kent Haines (@MrAKHaines) May 18, 2015
I didn’t mean to imply that you should offer nothing to students who aren’t sure how to get started. I just don’t think you’re doing them any good by making any decisions or doing any math for them. Sure, they might be sitting there quietly with no intention of doing math, because they know it will all be over soon and they can go to lunch. But it also might be that they honestly don’t know where to start. You know why? <Warning: Gross generalization ahead.> We probably haven’t taught them strategies for getting started with a problem when they don’t quickly “see” how to solve it. They might not know that any of their ideas are good. Heck, they might not even know they have ideas, or that making sense of the story would be useful. So I like to ask them about their ideas. It’s the rare student who doesn’t have any.
So, here’s an example of something I think is almost always a bad hint: “What’s the problem asking you to do?” or “What’s the question?”
The student might not even know what the story is about, because they might not have ways to engage in it and make meaning out of the story, or they might not even know that’s something worth doing. Or they haven’t even read it yet. But you’re already asking them to look at The Question and then find The Answer. Stop! Back up the truck! Unless you know they understand the story, completely, any content-related hint you give them may well be useless or, worse, confusing. In particular, a hint that focuses on The Question just perpetuates the point of math as Answer Getting, as opposed to understanding and making meaning.
Years ago, one of my colleagues, Steve Weimar (@sweimar), was working with some eighth grade students in a “low-performing” school. The students had learned the Noticing and Wondering strategy and, when Steve was visiting, were Noticing and Wondering the heck out of a math situation. Steve was watching and eventually said, “Wow! It looks like you have a lot of great ideas about this problem! How about you start thinking about the question?”
The students looked at him and said, “Whoa! Slow down. We are not done noticing and wondering.”
Those kids had figured out that if they did a really good job of Noticing and Wondering, they could tackle any question that came up about the situation. And they had some strong ideas about how to know when they were done Noticing and Wondering. Until then, don’t make them move on, because they aren’t ready!
Imagine how different their experience would have been had the teacher jumped in early in the process and asked, “What’s the problem asking?” I’m guessing that a lot less math might have happened in that room, and those kids wouldn’t have nearly as strong a sense of themselves as people who do math.