Clever Hans

Ben Blum-Smith:

Take-home lesson: never underestimate your ability to fool yourself into believing your students understand something when really what they are doing is watching you. To force them to engage the material it is often necessary to restrict their access to you or systematically confound the signals they get from you.

I think this is a central issue for modern math teachers. We need to explicitly develop ways of question-posing and interacting with our classes and individual students that hide or disguise our intentions for how they are supposed to respond. This needs to be part of the core training of math teachers, much more than it already is.

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I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Something I work really hard on with my Special Ed students, and don’t always succeed, is asking “Are you sure?” with a completely straight face all the time, even at times when they have the right answer. it’s really hard in this earlier part of the year, because the kids are so used to being questioned only when they get things wrong, but it pays off later in the year when they immediately justify their answers. It helps them learn to better explain what they do know, and helps me to understand their thought processes in order to fix up problem areas when they occur.

  2. I’ve been trying something similar during my student teaching, except usually I ask something like, “Why is that true?” or “Where did you get that answer from?” And yeah, almost every time I’ve said that students started second-guessing and thinking they got the wrong answer.

    If they get too deer-in-the-headlights then sometimes I let them know that they have the right answer, I just want them to explain how they got there. But that’s a short-term fix for poor self-efficacy and risks turning into a new cue. (Revised student algorithm: answer, look scared when asked to explain, wait to see if you are told you’re correct.)

  3. Right on both. It is kind of staggering to me that in the midst of an otherwise solid ed program, this sort of teacher response system was never discussed.

    We got into wait time. Like, “don’t just answer your own question when there’s silence,” but nothing like this kind of utterly essential Jedi mind trick.

    I’d like to trade notes on one point with both of you: it takes me a matter of months to rid most students of their dependence on my reaction for their response. Months. The process is much quicker than I’d imagine.

  4. Great post. Three thoughts:

    The ‘think-pair-share’ strategy helps here – youngsters discuss their ideas with a partner first, before sharing with class. No teacher involvement until they have already vocalised their thinking.

    It is much harder to get a ‘tell’ when you are communicating online. Maybe online learning has an edge here.

    This whole issue is a symptom of “teacher as priest”. Do we need learners to need us as arbiters of correctness and truth?

  5. Another good question we use in physics is “how do you know?” It does not imply an answer is incorrect, and requires an explanation from the student.

  6. Robert: Do we need learners to need us as arbiters of correctness and truth?

    Seems like they can get that anywhere, doesn’t it.

    I feel the most useful to my classes when I can ask a question, receive their explanation of an answer, ask another question to illustrate a soft spot in their argument, and then put them in a position to self-correct. Those moments aren’t common for me.

  7. It would help a lot if we started this sort of thing at a much earlier age. I try to do this with my first graders and some of them respond similarly to your students. Others immediately explain their thinking.

    I have also noticed this with my daughter. We’ve always asked her how she knows something or how she figured it out. Now she begins to explain how she did it without us asking. She seems to take pride in her explanation as much as in the correct answer. It does a mom proud.

  8. Teaching students how to write “leveled questions” using Bloom/Marzano/Costas models provides challenges at all levels and usually results in better questions than those provided by publishers because the students find their own relevance. The best part is that the responsibility for demonstrating the process required to answer the question(s) and to explain their thinking lands squarely on the shoulders of the students and not the teacher. “How do you know if this process is correct” can be the teacher’s question leading to proof.