Michael Pershan

Why Our Hints Don’t Help

Imagine staring at a math problem that you just don’t get. You want help, but you want the right kind of help – something that gives you a chance to be smart and leaves you with a tool to apply to other problems. In this talk I’ll explain why most hints let our students down and how we can do better by our kids.

Call to Action

For your next lesson, plan your hints in advance and share the ones that work. Together, we’ll create a collection of the very best hints to give.

About the Speaker

Michael Pershan teaches elementary and high school math in New York City. He tweets about teaching math from @mpershan and writes about student thinking at mathmistakes.org.

Updated 2015 Apr 21: Livetweeting

Check out the collection on Storify.

24 thoughts on “Michael Pershan”

  1. Will you post a detailed summary of your talk for those of us who were unable to attend NCTM Boston? I am sooooo curious about your thoughts on “hints” and how you use them

    1. Thanks Michael for a great talk! I think this is such an important issue in maths – too specific and maths is boring, too vague and no one understands.The need to get the right balance for each class, each student..comes with thoughtful experience. But I am going to think about this a lot more and reflect on what I do say. Also I agree primary maths reasoning is far ahead secondary….

    2. Thanks Sue!

      I’m curious to know what sort of things you think go into “thoughtful experience”? The big goal, someday, is for us to be able to help share our experience with other teachers, but it’s hard to know how to do that (I think) because we are often unsure what sort of experience is helpful to share. There’s almost a mirror-image of the hints problem when it comes to sharing teacher experience — sometimes we are too vague (“just listen to the students”) and sometimes we’re too specific (“here are my worksheets”).

      I’d be so curious to know your perspective on the teacher experience that is most important for getting hints and feedback right.

      Thanks so much for watching the talk and the comment!

  2. Lynn and Elizabeth: Thanks for the early comments.

    Pretty soon we’ll get the actual video from the talk up in this space, and then we’ll get to work on hints.

    In the meantime, you might whet your appetite on this collection of tweets from the entire shadowcon event.

  3. Hello to all the shadowconers, shadowconees, shadow cones and Shadow Connery’s out there.

    I’ve attached an image to this comment that’s a hacked up version of a few of my slides from the talk. The image contains a major claim of mine from the talk — that our hints will better foster learning and problem solving if they are rewritten to include context and reasons and are just specific enough for the hintee.

    Does that speak to you?

    I’m interested in your gut, but I’m also interested in stories from your teaching. If you have had moments when you reformulated a hint in a productive way, I would love to hear about it. Your comment would also be a great contribution to this project, so please offer it here.

    I’m also thinking that we need to hear your dissent. If part of this talk didn’t speak to you, please please please speak up here by leaving a comment.

    If you have a good hint to submit to the collection, you can send it off at bitly.com/goodhints. Or you can leave it as a comment here, and we’ll discuss it.

    OK thanks I’m done now. See you in comments!

  4. I’m curious…how do you find balance between giving a hint and doing the thinking for the student. For example, rather than the hint “make a table” might “find a way to organize your data” allow for more student thinking?

  5. I just watched the presentation. Thanks for making it available. So . . . the hint I gave the students for the horse problem in my last blog post [http://marilynburnsmathblog.com/wordpress/the-dealing-in-horses-problem/] was to have the students act out the problem. They didn’t have to contextualize it since it already had a context. Is this a hint? I used to worry it was giving too much away, but the blog comments posted are typical of what I’ve experienced in classrooms — even then people need validation of the correct answer.

  6. What a fantastic talk! Your message definitely resonates with me. And I agree that we really need to create the repository you described for HS math.

  7. I love the fact that everyone is thinking so deeply about how to maximize learning when a student is stuck, but I’m skeptical of the idea of being able to empirically identify “good hints” and “bad hints.” What a student needs to push his/her thinking forward is dependent on so many factors beyond just the problem and the step in the solution process they are on. For a hint (or guiding question, or probe, or whatever you call it) to land it has to meet the student where he or she is–which means it must take into consideration the students prior knowledge and experience. The perfect hint for one student might fall completely flat for another student who is coming at the problem with different background, even if the two students are ostensibly stuck in the same way. Would we be better off focusing on identifying where the student is at and what background knowledge they posses? Personally, I feel like that is the hard part. If we can do that, constructing an appropriate hint should be relatively easy.

    1. You’re spot on in addressing obtaining knowledge about students experiences and background information before delving into the best hint or guided questions to facilitate thinking. In my experience students are often hesitant or reluctant to divulge that personal information. This is the case even when encouraging risk-taking without condemnation occurs.

  8. There’s a great conversation brewing about hints between Anna Blinstein and Henri Picciotto.
    Anna shares her discomfort with hints. (link)

    As much as I agree that hints could be improved by these things, I also have a lot of discomfort around hints in general. Too often, I find that they funnel student thinking in a predetermined direction… as in, the student is stuck, and the teacher is trying to direct them onto a path that they think is productive by using hints, but it’s a predetermined path and therefore removes a lot of the exploration that one would presumably want a student doing in solving this problem.

    Henri offers a nuanced response. (link)

    As Deborah Ball says, requesting that students solve problems is not the same as equipping them to do it. A student-centered, problem-rich, investigative classroom requires a teacher who engages with the students, and supports them. Sometimes that support is manifested by just standing there, saying nothing. (Mysteriously, that is often enough.) Sometimes that support is manifested by saying something like “trust yourself”. Sometimes that support is manifested by providing a vague hint like “draw a picture” or “try it with smaller numbers.” Sometimes that support is manifested by out-and-out guidance, with the hope and intention of decreasing that over time. No one approach to hints will work in every situation.

  9. One hint that I’ve found to be equally successful with high school students and first grade students and every grade in between, doesn’t feel like a hint at all. I simply ask a student, “If you did know what to do, what would you do?”

    I know this may sound a bit crazy, but without fail, every student tells me what they would do and I simply say, “well, let’s give it a try” and walk away. It seems that posing a question in such a non-committal way, relieves enough tension to allow a student’s ideas to come out, even while they are still building their confidence as mathematicians.

  10. Lots of good stuff in the comments, people. Keep it up!

    There also continues to be good discussion on twitter and on blogs. Here’s a nice follow up to Anna and Henri’s back-and-forth from Mike Lawler. (link)

    So, thanks to Henri, I now see the connection better. If you get too caught up in general principles, you risk failing to improvise when you need to (or at least making it much harder to improvise). You also risk the possibility of dismissing hints that may well be useful in different situations.

  11. Do y’all know about hint cards? From Umussahar Khatri. (link)

    One of the strategies my math department has been using this year to scaffold lessons has been to offer hint cards to students that seem to be struggling on a given task. Unfortunately, I have found that many of my hint cards are either are too vague like, “create a table” and don’t help students any further or my hint cards become: “Fine, I’ll practically give you the answer” card — my cards give too much away of my thinking and limit the thinking of my students.

    Chris Shore is also thinking about hint cards. (link)

    This one resonated most with me, because I once heard that Japanese teachers have a small deck of cards with hints written on them. To draw a hint card, students have to first show effort and progress, then they may draw a hint card. They must use each hint before they may draw another.

    I also saw some great conversation on twitter about hint cards. See here and here.

    One nice thing about hint cards is that, since they’re in the hands of students, we might ask kids to rate how helpful they found the card. It could be a convenient way to get student input on our hints.

  12. On twitter, Kristin Gray and I have a conversation about hints for decimals. (link)

    Student struggling today with adding up from 3.12 to 3.2. Me,”Does it help to picture the grids when doing this?” He got it right away.

    An important question that I’m left with is, now that this hint helped, how do we help him internalize it so that he can give himself that hint, next time?

  13. Joe Schwartz blogs about hints in a 5th Grade volume lesson. (link)

    With Michael Pershan’s ShadowCon talk on hint-giving fresh in my mind, I had to do some thinking. What could I tell these kids to get them on the right track? […] While looking back at the pictures of the boxes they drew, I could ask something like, “How many of the first size boxes could fit inside the second box?” And if that didn’t work, I could try something more explicit: “The first box is 30 cubic cm and can hold 40 grams of clay. What if there were two of those boxes? What would be their volume? How many grams of clay could two boxes hold?”

    Go to Joe’s blog to read about the entire lesson.

  14. Dylan Kane blogs about hints and reaches a new conclusion about “hinting by telling.” (link)

    Hinting by telling can be an effective teaching move when the hint allows the student to continue productive struggle, while doing mathematical thinking.

  15. Annie Fetter nails it. (link)

    Hints that derail or jump over or shortcircuit thinking are not so helpful. Hints that put the student in a position to think about something they don’t realize they could think about are productive, and I think you’ve provided us with a great example.

  16. Annie (link) and Henri (link) have some more interesting thoughts about hints — not necessarily connected to my talk, but still relevant.


    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.


    But I digress. My point here is that there are many situations where generic hints are useless. Take the problem I worked on a few months ago, and reported on in this blog. I literally spent hours noticing, wondering, exploring, and experimenting. I tried it with small numbers. I decided drawing a picture would not help. I kept organized records of my investigation. I slept on it. Still, I could not crack it. Then I tried to write a computer program to complement my manual explorations, and again did not get very far.

    As I reported in the subsequent post, I asked for help.

  17. Dylan Kane (link) thinks there might be five ways in which hints can promote learning.

    Hints can promote learning in five ways:

    Redirect attention to features of the problem (What is it saying?)
    Redirect attention to student knowledge (What do I know?)
    Redirect attention to student cognition (How am I approaching it?)
    Promote students’ beliefs in their mathematical efficacy (I think I can solve it)
    Provide missing information (I know what I need to solve it)

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