But Artichokes Aren’t Pinecones: What Do You Do With Wrong Answers?

I have very small children which means my life is measured by little games and distractions stretched across the day. “What’s that called?” is one of those games. Point at a thing and ask for its name. Do that for another thing. Hey – it’s almost nap time!

So recently we pointed at an artichoke. “What’s that called?”

“Pinecone,” one of the kids says.

a drawing of a pinecone and an artichoke

That’s a factually incorrect answer, which is the same as lots of student answers in math class. But when my kid calls a pinecone an artichoke, I have a very different emotional, physical, and pedagogical response than when a student says something factually incorrect in math class.

With my kid, I am fine with the error. Delighted, even. I am quick to point out all the ways that answer is correct. “Oh! I see why you’d say that. They both have the kind of leafy-looking things. They both have the same-ish shape.”

I find it easy to build connections from their answer to the correct answer. “But an artichoke is greener, larger, and softer. People often eat it and people don’t often eat pinecones.”

However, if I’m teaching a math lesson and a student answers a question about math incorrectly, my reflex is to become …

… evaluative … “What did I just hear? Is it right or wrong?”

… anxious … “Oh no it’s wrong. What do I do now?”

… corrective … “How do I fix this answer and this student?”

I find it much harder to celebrate and build from a student’s incorrect answer in math class than I do an incorrect answer from my kids about artichokes. The net result is that my kids feel valued in ways that the students don’t and my kids have a more productive learning experience than the students.

I can give lots of reasons for my different responses but I’m not sure any of them are any good.

  • This is my kid so I feel warmer towards his early ideas than I do towards ideas from kids I see for only a small part of the day.
  • This kid looks like me so I’m more inclined to think of him as smart and brilliant and wonderful than I am a student with a different race, ethnicity, or gender.
  • The stakes are smaller. What’s the worst consequence of my kid referring to an artichoke as a pinecone? That he doesn’t get invited back to the Governor’s Ball? Who cares. This will work out. I’m not preparing him for an end-of-course exam in thistle-looking stuff.
  • I know the content better. I can build conceptually from a pinecone to an artichoke much more easily than I can build from early math ideas to mature math ideas.

But I find that every aspect of my professional and personal life improves when I try to neutralize those excuses.

  • I am a member of faith and educator communities that help me dissolve my conviction that my kid is more valuable or special than your kid, communities that help me dissolve my sense of separateness from you. We are not separate.
  • I am working with a team to develop experiences in math class that lead to student answers that are really hard to call right or wrong, or ones that at least lead to lots of interesting ways to be right or wrong. I am learning that it’s more helpful to ask a question like, “How are you thinking about this question right now?” than “What is your answer to this question?” because the first question has no wrong answer.
  • I am trying to develop pedagogical tools that make use of differences between student answers to replace ones that try to reconcile or flatten them. Tools like “How are these answers the same and different?” or “For what question would this answer be correct?”
  • I am trying to learn more math more deeply so I can make connections between a student’s early ideas and the later ones they might develop.

I am thinking about this idea from Rochelle Gutierrez more often:

All teaching is identity work, regardless of whether we think about it in that way. We are constantly contributing to the identities that students construct for themselves …

Whether my kid calls an artichoke a pinecone or a student offers an early idea about multiplication, they’re offering something of themselves just as much as they’re offering a fact or a claim. My goal is to celebrate those early ideas and build from them so that students will learn better math, but also so they’ll learn better about themselves.

Featured Comments

Several people mention that we have more time to enjoy our kids and their thinking than we do students in math class.

About 
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.

11 Comments

    • Pete Capewell

      March 10, 2020 - 2:22 pm -

      God bless your beautiful heart Dan Meyer. You always try try to see inside the error and look beyond the shortcoming. Thank you.

  1. Reply

    And how comfortable are your kids (your own, and your students) with you in these interactions?

    It feels related to your previous post(s) citing Dr. Gutierrez. With each encouraging and inviting interaction you build more trust. With your own kids you can build that trust from the beginning. But in classrooms, you have students who have learned to distrust invitations to share thinking. Rightfully, if their interactions have been with the evaluative/anxious/corrective versions of teachers!

    I have been that evaluative/anxious/corrective teacher myself. I think many teachers might add to your list of factors: pressure to cover content, pressure to not confuse kids, difficulty in managing the class discussion and attention. Maybe more?

    Your neutralizers may still apply. Can we weave together lots of content so each day is richer than a sequence of dry discrete ideas? It feels like learning more content and connections between content is applicable here.

    Worried about confusing kids by not calling out factually wrong things? Ask more questions that are those hard-to-say-right-or-wrong. But perhaps there’s more to say here. Like, why might we feel such evaluation of an idea is automatically a part of a class discussion? In other words, not only ask more hard-to-say questions but also ask fewer right/wrong questions, at least in the discussion setting.

    And maybe that ties into the classroom management worries. I certainly remember feeling stressed managing discussions because I felt I was risking derailing the class. I’d seek the students who I thought were likely to move the conversation “forward” and intermittently scold distracted students. Looking back, these were not actually discussions, right? I wasn’t really asking for student ideas, and I certainly wasn’t building much trust.

    I feel like very experienced teachers and non-teachers can look back and do a lot of reflection on best practices they should have done, but what does it look like to grow these ideas earlier in the teaching corps?

    I wonder how we can support teachers taking on these ideas, especially beginning teachers. Of course the tools and content that Desmos offers are in this vein. What else is possible here?

  2. Reply

    Agreed! The strong focus on the correctness of answers is what has lead to the unhealthy attitude that general public has towards math. They figure, “I’m always wrong, therefore I am not good at math.” Their conclussion, however, is based on the false premise that *math is about answers* when actually *math is about thought*.

    • Chester Draws

      March 13, 2020 - 3:43 pm -

      What a lovely thought. Except that Maths is about answers.

      To a problem there might be a number of correct answers, a range of answers, an uncertainty about the answers or even no correct answer at all. But without answers, Maths is useless. We might as well be teaching interpretive dance if we are going to go down the road that “math is about thought”. Let’s at least keep one subject that is not subject to relativism and subjectivity.

      Dan article discusses how we might steer a misconception into a correct understanding. So that we can get correct answers.

      My concern is that asking “How are you thinking about this question right now?” can actually be a lot more stressful to kids than merely correcting them — depending on the kid in question.

      A lot of my students know enough that when I am probing them as to their thinking that they must have made a mistake — and so they clam up. They find the process of having their failings displayed at length to the rest of the class much more stressful than merely being wrong. So I never go that route with anxious ones, whereas I am prepared to do it with the bold and brash.

  3. Reply

    Thought-provoking post, Dan!

    Is it also partly that as *teacher* of your students, you feel you have to *teach* something, whereas being a parent is more about sociability, passing the time in a nice way? Most of us know that if our young kid says something wrong, it will be corrected without our intervention. Or even that if we start using our child’s funny way of saying something because it’s cute, they will, disappointingly, somehow learn the right way anyway!

    Correction can be wrong not just because it impacts identity and ego, but because it isn’t how we learn. We move on, we have new experiences that expand our previous knowledge; they don’t always need to hit our areas of ignorance head-on. We as teachers try to bring about those new experiences.

    Featured Comment

    For instance, if it was in a primary class, like you say, a teacher might respond, ‘oh yes, these are really like pine cones! Have you seen this pattern on both of them when you look at them from above? {shows picture] What do you notice about that?…’

    I sometimes think about this story of the eastern joke-character Nasrudin in this context:

    Two men were quarrelling outside Nasrudin’s window at dead of night. Nasrudin got up, wrapped his only blanket around himself, and ran out to try to stop the noise. When he tried to reason with the drunks, one snatched his blanket and both ran away.
    ‘What were they arguing about?’ asked his wife when he went in.
    ‘It must have been the blanket. When they got that, the fight broke up.’

  4. Reply

    Love this move.

    For instance, if it was in a primary class, like you say, a teacher might respond, ‘oh yes, these are really like pine cones! Have you seen this pattern on both of them when you look at them from above? {shows picture] What do you notice about that?…’

  5. Reply

    When I first saw the pictures of the pinecone and artichoke, I expected a lesson in the Fibonacci series. Perhaps in a few years when the children are older. It was still a good lesson.

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