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

“Pinecone,” one of the kids says.

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.

I have so much more curiosity when my kid says something incorrect. I find it so fascinating that she decided to say that 1 + 9 = 30. Why?!?

I get so much more 1:1 time with her than with students in my classroom. I feel that spaciousness in a deep way.

— Bree Pickford-Murray (@btwnthenumbers) March 10, 2020

This is sort of alluded to in your already listed reasons, but maybe(?) another reason: You may feel as if you have more time to engage with the thinking of someone who [hopefully] will be in contact with you for the rest of your life. With students, time can feel [is?] shorter.

— Benjamin Dickman (@benjamindickman) March 10, 2020

2020 Jun 13. Other examples of early ideas about language from around my home.

• “Getting tangled out” a/k/a “getting untangled.”
• “Yesterday” as a placeholder word for any time in the past.
• “Foots” and “Gooses” as the plural for “Feet” and “Geese”.
• Them: What do cows eat? Me: Hay, I think. Them: No, horses eat hay.
• 6 looks a lot like a lowercase “g”.
• “After” is any time in the future. Me [beleaguered]: “We’ll do that later, kids.” Kids [combative]: “AFTER!”
• “More taller” is coming up a lot.
• These kids think that as they get older, they’ll get bigger and I’ll get smaller and turn into a baby.