What we’re debating when we debate “misconceptions”

Is ‘misconceptions’ a bad word? I’ve had the conversation about misconceptions a number of times, most recently when I wrote this post. Here is a bit from the conclusion:

We see misconceptions in children because it really is true that there’s stuff that they don’t yet know. Noticing this doesn’t have to be an act of violence — in fact, I don’t think that it usually is. Usually it’s like me playing with my son and noticing there’s stuff he doesn’t yet know how to do, even as my mind is blown because oh my god my son is into puzzles! When did our baby turn into a kid?

Is it good pedagogy to ask people who don’t already see their pedagogy as abusive to forswear from using words that they use all the time? Isn’t this exactly the sort of “intellectual violence” that we’re being urged to refrain from? Shouldn’t we start with the way people actually see the world, rather than asking them to use language that is not their own?

That excerpt did not convince anybody at all, but my goal here isn’t to convince. Really all I want to do is bring up something I learned about the constraints of this argument.

There are a couple people I’ve met who have flirted with the idea of cutting out all evaluative language from discussions of teaching, but it’s largely an unsustainable position. You can’t cut out value from teaching, and the thought that you can is a bad mistake. Even if you don’t talk of “misconception” you’re still in need of language to describe thinking that isn’t yet what it could be. Maybe there are no misconceptions, but there is thinking that is e.g. inflexible, procedural, memorized, additive-but-not-yet-multiplicative, trick-reliant, stage one, whatever it is you want to say.

Plus, the math education community very clearly want to be able to understand problematic language and ideas for what they are. We want to be able to call ideas or patterns of thought racist, sexist, colonialist, etc. That’s very different than the “all thinking is just thinking” position.

And so the discussion is only ever about what is particularly harmful (or not) about the term “misconception” and its popular usage. Though people frequently talk about the issues with evaluative language in general when discussing misconceptions, that argument just confuses things. We need to be able to talk about thinking in terms of what it could, even should ideally be.

So there are really just two questions that are relevant for this discussion. Is the term “misconception” particularly harmful, compared to other evaluative language? And even if the term is intrinsically fine, is it used in particularly harmful ways?

I’ve shared my answers, but I’d make the case that those are the right questions.

6 thoughts on “What we’re debating when we debate “misconceptions”

  1. Thought experiment: How far *can* we get without evaluative language?

    1. You’re teaching Spanish. A kid says, “I call that a table.” You can pretty easily say, “Well, in Spanish, we call that una mesa” without declaring the English word worse or inferior. Learning a new language doesn’t wipe out the old one. It’s just a new discipline to master. In fact, saying “table is wrong” will probably confuse and alienate the student.

    2. You’re teaching Spanish. A kid repeatedly uses the present tense instead of the subjunctive. This kid isn’t speaking their own home version of Spanish; they’re speaking our version incorrectly. Still, if you like, you can frame this as “mastering arbitrary conventions.” Seems a little weird to me – I have no problem saying that using the subjunctive is “correct,” and failing to use it is “wrong” – but it’s true that languages are, at root, arbitrary, so you can fall back on the same approach as in #1.

    3. Say you’re teaching science. A kid says, “We only use 10% of our brain.” Or, “It was colder when the dinosaurs lived.” Or, “Medicine can’t help with cancer.” I can’t imagine how you’d avoid discussing these ideas without, sooner or later, calling them errors, mistakes, or misconceptions. In science, there is such a thing as truth, and the whole job of a scientist is to sift wrong from right.

    4. So, what does this tell us about math?

    Insofar as math is fact-based, like science or history, then evaluative language is unavoidable.

    Insofar as math is a set of conventions, and the students understand it as such, then evaluative language can be avoided, though I’m not sure it’s worth the trouble.

    And insofar as math is a set of conventions, and the students *don’t* understand it as such, then evaluative language *ought* to be avoided.

    (In my view, math is a difficult-to-parse mixture of conventions and truths. Truths that we access via conventions; conventions so powerful that they yield truths. I’m not sure where that leaves us.)

    (Also, in practice, I avoid “misconception” with students – I think it’d sound harsh to them – but have no problem using it in conversation with other teachers, or in my own thinking.)

    • This is sensible and interesting!

      I’ll quibble a bit. When you say “In Spanish we call that una mesa” that is implicitly evaluative. It’s clearly a response to what the student said. It’s not saying that their word was wrong, but it would be correct for the student to take that as a kind of correction, and if the student totally ignored the statement (in Spanish class!) they’d probably have missed the point. (In philosophy of language classes they called this the ‘pragmatics’ that accompany the statement.)

      I think this matters because it’s possible to think you’re not evaluating student thinking when, really, you are. You might say to your whole class, “Hey so I noticed that most people added for this problem. But Becky multiplied. Isn’t that interesting! Becky, can you explain to everyone what you did?”

      Well, you didn’t use the word misconception. You didn’t say “better” or “more efficient.” You didn’t say “right” or “wrong” but students would be quite correct to see Becky’s idea as worth knowing and of particular value to their teacher. (It depends on the way the classroom works, I guess.)

      But I really think the whole project of avoiding evaluation is not quite right. Instead I’d frame the entire thing in terms of attention. What are you drawing the student’s attention to at any given moment? Is it to new, valuable facts or ways of thinking? Or are you drawing attention to the student’s deficiencies? There are sometimes tensions here, to be sure, but tensions are inevitable in teaching.

      • Mmm, so I guess the question is what a teacher means by statements of the form: “I like how you said X; here, we’re learning a new system, where we say Y.” The anti-“misconception” crowd views this as qualitatively different from calling X wrong. To them, it’s honoring X, while saying there’s something new to learn. But to you, it boils down to saying “X is wrong in this context,” or, “I want you to say Y,” which isn’t categorically different.

        I’m not sure where I stand on that distinction, but overall I think I come down where you are. It’s important to send the messages “I value your thinking” and “We’re in a new system here, and it doesn’t mean your old system is bad or wrong.” But I’m not interested in avoiding evaluation for its own sake. Instead, I want to create a learning environment where students feel they *can* be wrong, where they *can* make mistakes, where something can be a “misconception” and still have a lot of value and internal consistency and insight to it.

        (And, as I think you’ve pointed out in the past, this is a tension in progressive educator rhetoric right now – we want to normalize mistakes, but also to carefully police our language around mistakes.)

        • One thing I want to add is that I don’t think this “debate” is really a debate. It’s about a particular moral practice that is extremely meaningful to many people. I wrote this as a comment on Rachel’s post:

          I totally agree that the instinct to wait and see how a student’s work makes sense is a productive teaching move. But it is a move! I think when I do that it involves a conscious choice not to REFUSE to see the misconception as a misconception, but to dig deeper into the student’s thinking. It’s something you can learn the habit of — of seeking to explain things, to not dismiss the thinking of others, to build on what they already know, to be kind.

          I think some people would then say, “Exactly! that’s why I want to keep myself from using the word misconception. To remind myself to live up to those practices.”

          In other words, for many this is not about whether there are “really” misconceptions or not. Rather it’s about a personal moral practice: by taking great care with one’s language, one can change the way they react to students. Not the Sapir-Whorf hypothesis (that changing your language necessarily changes your thinking, or something) but a personal-improvement hypothesis: changing your language CAN help you change your actions and thinking.

          So, maybe. Live and let live. It’s still true that, as a matter of fact, you absolutely need some evaluative language to make sense of teaching and learning. But if someone wants to be cautious with their words for the sake of changing their ways? Who am I to say that won’t work?

          This is my take; many people who would rather we change our language would resist this framing. But from my point of view we have people for whom this practice is deeply significant and want it to become universal. Then you have people like me who don’t want to adopt this practice. I think there are other ways to come to valuing student thinking but, I admit, I don’t have any systematic practice that helps me keep this in mind. I don’t think I need one, but maybe I’m wrong.

  2. Pingback: Quick thought on “misconceptions” – Arithmetic Plus

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