“I can teach them more math than they have done in their entire lives”

Here are two conversations for which I have no patience at all…

  1. “They should know X”
  2. “You should teach X in manner Y.”

Conversation number 1 is the reason they are students, and the reason you are a teacher. What they should know is not relevant here; only what they do know is. So let’s factor that into our instruction.

But I need to focus on conversation number 2 today. EdSurge reposted an article today that struck me the wrong way. An excerpt:

Of course, the problem is deeper than a handful of students who accidentally say ironically stupid things. The problem is that American high school students are taught something named “math” for four years which is not even close to math.

Pretty sweeping generalization here. But I don’t disagree with the basic premise, which is that we aren’t doing the job of bringing mathematics to students (and students to mathematics) that we should be doing. I do disagree that the K-12 system is the only place this problem exists, but let’s get back to the matter at hand.

I fear my rant may disguise my true intentions: the problem is not the content. Geometry and calculus and algebra are very fine subjects of mathematics. The problem is that they’re taught in a way that strips out all the math and leaves a vapid husk of an education.

Now things are starting to spin a little bit out of control. Vapid husk of an education? Wow.

And the solution?

[I]f you give me an hour with a group of disillusioned but otherwise motivated high school students, I can teach them more mathematics than they have ever done in their entire lives. I can give them a dose of critical thinking and problem solving like no algebra problem can.

Child, please.

I teach at the college level these days, so I am accustomed to this sort of bravado. I try (perhaps unsuccessfully) to avoid it in my own writing because it is (a) unproductive, and (b) false.

But my beef isn’t so much with the author (although…) No, my beef is with EdSurge.

Why not feature the vibrant work that is going on in K—12 math education?

Why not republish Fawn Nguyen’s brilliant reformulation of a crappy textbook problem?

Why not post Andy Schwen’s video of a kid talking about the relationship between slope and rate of change while working on Function Carnival?

 

Why not feature the work of people trying to bring real mathematics to young children? Moebius Noodles, Math in Your Feet, Talking Math with Your Kids, Math Munch—these are projects where people are working on a daily basis to help parents, teachers and caregivers to support meaningful mathematical thinking for children. No bravado. No blame. Just hard working, thoughtful people working to solve a problem.

Because there is a problem. For sure there is a problem.

But an hour with Professor Awesome isn’t going to solve it.

 

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11 responses to ““I can teach them more math than they have done in their entire lives”

  1. I suspect the answer to your “Why not feature the vibrant work that is going on in K—12 math education?” is: because we are Young And Smart and on our happy Silicon Island. It would be *awesome* if some of ‘em came out of their cloister to see what’s happening…

  2. I note that there’s no way to make a response other than using FB, which I’m not on. So I’ll have to put my rant here.

    Jeremy,

    You have some good points, but really? You could teach a “disillusioned but otherwise motivated” group of students more math “in an hour” than they’ve ever done? I don’t usually say this, but: time to put up or shut up. Convince those of us in the real K-12 world of real students that you can do better teaching math. Because it’s tiresome in the extreme to hear pontifications from college/university people how we’re doing it wrong.

    Oh, and one more thing: once colleges and universities stop requiring students to take courses called algebra, geometry, algebra 2, precalculus, and calculus, then we can talk about all of the other stuff you describe. Because what we have to do is to a large extent driven by what you all claim you want.

  3. Thank you for the kind words about my Moebius Noodles!

    If I put my active listening aid and my andragogy goggles on, here is the message I hear and see behind Jeremy Kun’s essay:
    “– I know some math and computer science ideas that could surprise the vast majority of teachers and students. I find these ideas very valuable, and I believe this opinion is shared by other mathematicians. Moreover, I can produce these surprises quickly, so quite a few of them can happen in an hour.”

    At least that would be the statement I would find meaningful. It’s not quite what Jeremy said, and the tone’s very different. The key to the tone of the essay is this quote, I think: “…the stuff we teach in calculus isn’t really math either.” Jeremy’s looking for a way to cope with what HE feels forced to do, as a college instructor. I hope he finds a solution to his problem, and some opportunities that would allow him to teach in the manner he can respect, as a mathematician interested in education.

  4. My issue with EdSurge is that this features not just a “borrowed” analogy of Paul Lockhart, but the premise of “A Mathematician’s Lament” as a whole.. So we have an article by an admittedly worse author, summarizing the superior author, followed by an ad for his blog. But this is often the M.O. of EdSurge.

  5. The simplest way to say it is that mathematics (especially at the elementary and secondary level) is about recognizing and reasoning about patterns. These patterns can come from anywhere: shapes, numbers, relationships at a party, physical systems, tournaments, card games, knotted rope, doodles with colorful pens, literally anything!

    Take as a premise that weaker students are going to need more time with important ideas. Take as another premise that weaker students aren’t going to learn as much content as stronger students. How do you design a course so that (a) it’s rigorous and challenging for top students while (b) helping weaker students gain understanding of the most important ideas?

    Answer 1: Let’s just talk about puzzles and patterns, and let’s talk about physics and Vi Hart and card games and tricks and pentominos!

    Answer 2: Let’s keep the content as focused and connected as possible by focusing on rich, core mathematical strands, say, numbers, algebra, and geometry, and then let’s go deep into these.

    The fairest thing to do is to mine the most important content areas for everything that they’re worth. Studying the patterns found in games and graph theory and puzzles in elementary and secondary school is a sometimes thing.

    In addition: It looks like edSurge probably publishes anything. Someone should pitch an article to them about edTech or STEM education.

  6. What a great moment! Awesome video

  7. I don’t know what an EdSurge is (sounds dangerous!), but I find the article a good gauge of how teachers view each other. With bravado, they often claim they can create ex nihilo – that they can swoop in and turn what was poor instruction into badass-ness very quickly. Perhaps even in an hour!

    Amateur teachers think like this, and it really stems from an inflated sense of self coupled with a healthy amount of insecurity. When I was a first year teacher, it was easy to roast other teachers I observed. The answers always seemed so obvious.

    This pride and ego extended into this year, when I saw our resident Obi-Wan Kenobi observe another teacher. Even in a dull, lifeless class, he was able to find where a teacher was shining, connecting with kids and being excellent. He did give the teacher the feedback about where he could grow, but it was couched within those moments of doing well.

    It’s easy for Jeremy to nitpick at strawmen, especially when there’s no examples, no specifics. Just like Christopher said, sweeping generalizations.

    But regardless of the snarkiness above, coming in for a 1 hour presentation can be incredibly informative, engaging, and could even make curious mathematics creators. But following that up with another 1 hour the next day, and the next day, and the next day… .that daily grind of *performing* is way more difficult. In fact, the two couldn’t even be classified as the same job.

    And +1 to Pershan – I think maybe we should publish something about this “STEM” or perhaps even “STEAM” (cuz math is an art obvi).

    Last thing – the header “A mathematician’s perspective on secondary math education” drives me insane because it plays on my ego. Am I not a mathematician as well?

  8. Oh boy. Christopher, perhaps you are the better man for not picking apart Jeremy’s statements.

    All in all, speaking about math content, I get the impression he is on a similar path as I (and probably differs from his Uni colleagues)–he want’s his students to arrive understanding math and not just being skilled manipulators of this language. Great!

    But throughout, he drops words and creates a tone that has absolutely no place in education–k12, higher ed, at home with our children, etc–no place.

    “The problem is deeper than a handful of students who accidentally say ironically stupid things.” Barf.

    “Just as the pitiful music student from before, there is no evidence that the student was ever any good at mathematics. That’s not to say he can’t be good, but that he has just been misled his whole life.” BARF!

    I know there are a lot of people out there that get sick of the ego-boosting, good-feeling education us middle level teachers promote, but there is no place to say things like this. Words like “pitiful” have no place in a conversation about a child or young adult struggling to be better. I would guess that Jeremy would never call a student pitiful. But his arrogance is so thick, any middle school student would see right through him.

    My 5 year old is learning to play piano. Twinkle Twinkle is “pitiful” if heard after her teacher has played it through. But I nearly cried after her first lesson when she advanced from merely pounding the keyboard like an animal. At the risk of making a sweeping generalization here (scold me if needed Trianglesman!), teacher cred drops to zero when you say such arrogant things about and to kids who are struggling to become better, smarter, or more talented.

    I hope I don’t see you on the pre-school basketball court putting smack-down on shots on the short net.

  9. Pingback: Neat coin flipping problem found on Twitter yesterday | mikesmathpage

  10. In response to Brandon: “Last thing – the header ‘A mathematician’s perspective on secondary math education’ drives me insane because it plays on my ego. Am I not a mathematician as well?”

    I am an educator at a teaching-focused college. My initial reaction to Jeremy’s post was somewhat similar: if you’re going to pontificate on pedagogy, you should state your claim as an educator, not a mathematician. The implication that a mathematician should take precedence just adds to the arrogance. (Perhaps he didn’t originate the article title?) The words “mathematician” and “educator” are both best stenciled on hats, not houses.

  11. Just re-read this, and it still rings of awesome. It’s so tempting to meet bravado statements with defensive rebuttals, but not as easy to respectfully (but not condescendingly) refute the premise entirely.

    Again, well done.

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