On Teaching Math Ed At Long Last

By a weird fluke, I’m running a section of Mathematics for Elementary Teachers. Some medical emergency has incapacitated the regular faculty member originally assigned to this section; since I was called on to sub when she was first hospitalized, the entire duty has fallen into my lap now that she’s out for a long recovery. I’ve never done anything at all like this class and there are reasons. Like many another math major, I’ve often been mystified by the Math Ed approach to pedagogy … specifically, the focus on (what can be called) presentation (as opposed to “content”). And it’ll probably be a long time before I ever say anything even resembling “Pedagogical Content Knowlege” without smirking.

But I sure feel like I’m doing worthwhile work and may even have convinced some of the students. There’ll be more about this down the line I expect …

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  1. Your first time?
    Is this math for math teachers, or methods for math teachers?

    Lots of real tensions here. Like they won’t know as much math as they should (maybe). Like what they know they may know from a procedural standpoint, only (maybe).

    Really, elementary math teachers should know a fair bit of mathematics, including some advanced stuff. A little abstract algebra, some number theory, those wouldn’t hurt.

    But what’s the chances?

    Jonathan

  2. I’ve never done anything at all like this class and there are reasons.

    Such as . . .?

  3. Ouch. Pedagogical Content Knowledge has been a rich construct for me to describe the competence that some teachers have and many do not to be able to craft a mathematically important experience out of the activities, questions, difficulties, detours etc. in regular classrooms.

    It helps explain why some very well educated folks are pretty useless in a classroom. I think it also highlights that you need a solid Math background in order to make the most of classroom interactions.

    So… whatcha got against it?

  4. @ jonathan (= jd2718):
    oh, for sure. and *logic*!
    number theory & logic (& sets)
    are among the topics that textbooks
    (and course designers) want to *pretend*
    are so easy that ordinary students should
    be able to pick up everything they need
    with a few hints … nobody wants to
    actually take time out of their crowded
    syllabus to actually *present* it
    (never *mind* provide carefully-worked-out
    exercise sets … you know, the kind of thing
    without which not even the pretty-darn-talented
    have much of a chance …). if we could
    somehow get a coherent theory of GCD & LCM
    into elementary mathematics, we might not
    have such problems with fractions (e.g.) …

    @mr. person (= joshua fisher):
    well, i’ll confess to having been pretty paranoid
    about taking such a thing on &’ve never included
    suchlike classes in my course requests …
    but at least one administration *other* than this
    has been known by me for sure to actively
    work to keep me *away* from the future teachers
    (i’ll probably post this story “up front” soon).
    & in general, the ed-school crowd sometimes seems
    pretty intent on insulating its students
    from mainstream undergraduate mathematics.
    often the hostility is even pretty out-in-the-open.

    @ross isenegger:
    what do you need a “rich construct” for
    if what you’re talking about translates
    readily into plain english (as “knowing
    something about how to teach”)?

    no, really: why couldn’t i just say
    (of those useless in the classroom),
    “they sure know the math … but they
    sure don’t know how to *present* it clearly”?
    in fact, don’t people say this kind of thing
    *all the time*? & *without* any technical terms?
    where’s the value-added?

    some educationists appear to believe
    that their investigations into epistimology
    can be somehow elevated (from philosophy–
    what they are–, into science–what they’re not)
    by pretending to a math-like precision.
    others think–very often rightly– that
    fancy words for simple things will wow the crowd.
    so on. i *don’t* include ross isenegger
    among their numbers — the creator of “mathfest”
    has gone so far as to engage the math-ed-hostile
    creators of “kitchen table math” (or for that
    matter, the creator of “vlorbik on math ed”)
    and has thereby displayed more good faith than
    we can expect from a wilderness of math-warriors.

    anyhow, in the exact example at hand,
    “pedagogy” is, in the popular imagination,
    *opposed* to “content” … so PCK looks like
    some weasel-word management trick to say,
    “no, look! they’re really the *same*!
    it’s a win-win! our consultant said so!”
    (and “knowledge” in this context actually
    means “opinion”). hence the smirking.

    of course i may be wrong ….

  5. oh, ps. jonathan. it’s sort of a mix:
    quite a lot of discussion of “how do i
    present this material to beginners” …
    but *without* any assumption that my
    students themselves have Profound Understanding.

    it can be kind of maddening.
    “why are we going to so much trouble;
    isn’t it easier to just …”
    (yes, this technique is probably more
    trouble than it’s worth; no, it’s not
    as simple as you think …).

    the trouble is many times compounded
    by the simple fact that *i’m no expert*:
    i’ve never taught this stuff to elementary
    school children and have to rely on the texts
    for information about where the difficulties
    tend to come up. since i’ve long been used to
    preaching the gospel of “nothing on authority”,
    this is a darned uncomfortable position to be in.
    (which, don’t get me wrong, is probably
    *good* for my teaching chops …)

  6. Maybe even using phrases like “rich construct” just show how long someone has been out of the classroom!

    Oh, and thanks for noticing some of my web activities and including mathfest in your blog roll.

    As for using the PCK phrase, I think it might be useful to indicate that teaching Mathematics is far more than presenting, telling, or even doing Mathematics (especially at the elementary level).

    In Ontario, students preparing to teach elementary mathematics get a course somewhere between 18 and 36 hours long. We have given our teachers more than that in some of our PD activities!

  7. You said you’ll have to “… rely on the texts for information about where the difficulties come up…” – I’m assuming your students will be able to tell you based upon their own difficulties with the topic (I had many el ed math folks in my classes when getting my degree).

    Good luck! I look forward to reading about your new endeavor.

  8. Vlorbik,

    Find out if your university has a “lab school” associated with it. If none, find out where the ed folks send their first year students to do observations and arrange observations with teachers. You will see right away some interesting topics to bring up in class. Also, perhaps, ask if any of your students already have classroom experience that they can contribute.

  9. Zac

    I’m still getting over my experiences with teaching math ed for elementary wanna-bes. It wasn’t math ed – it was math content.

    I spent considerable amounts of time doing straight basic content – at grade 6 level (yes, fractions, decimals, percents, all that fun stuff). When I tried to extend them just a tweak into some algebraic concepts, many of them burst into tears and the remainder threatened to take up arms.

    My colleague (who was supposed to be doing the method part) was fixated on the social psychology of math. She had neither content nor method to offer.

    So I’m still wondering how the students of my students are getting on. Right now, they are probably doing single digit additions on a calculator and learning all about how to evade math neurosis using Zen meditation. [Don’t get me wrong – the social psych part is important, but not at the expense of zero understanding in method.] I suspect they are getting no broader math concepts, no love of the subject, no sense of how and when it is used in the ‘real world’. Sigh.

    Just writing about it after a bunch of years still sends shudders down my spine…

    Abstract algebra and number theory? In my dreams.

  10. while it’s true that some of my students
    still struggle with topics that many teachers
    continue to think—& even to speak—of
    as “elementary”, their difficulties
    are presumably very *different* from those
    of an outright beginner.

    i’ve actually *been* on a couple classroom visits
    with student teachers (who had been *mathematics*
    students in classes run by me).
    this was back when i had a real job;
    i’m part-timing at a community college these days
    and such activities are right out of the question.
    it was a valuable experience for me (& i hope
    worthwhile for the student teachers).

    i’ll go ahead and remark now that it’s come up
    that this happened essentially *by accident*:
    the prof from the education department
    that arranged for me to make those visits
    contacted me directly and set these up;
    when the math department chair found out
    about it, she put a stop to it and made sure
    that such work would in future be handled
    by our resident math-ed specialist (i referred
    to this incident upthread in claiming to
    know for sure that an administrator had
    taken steps to keep me away from future teachers).

    anyhow, long story longer. i’ll stand by
    my comment: i’m counting on the book
    (to an uncomfortable extent) for information
    about what’s hard and easy about learning,
    say, “place value” for the first time.
    of course i’ve cared about this for a long time
    and can even remember some of my own experiences
    so i don’t have to trust ’em absolutely …
    and, while i’m at it, let me say right here
    that _mathematics_for_elementary_teachers_,
    by sybilla beckmann, is surprisingly good.
    i’m particularly impressed at the complete
    lack of non-math eye-candy (celebrity photos
    & comic strips & all the crap that’s reached
    well up into the college level & can be expected
    to infect springer’s GTM series any time now …).
    just the same, she appears to’ve
    elevated “hands-on” to some mystical principle
    (for example)and should probably be assumed
    to be as subject to blind spots as the next guy.

    there *is* at least one member of the class
    already working with actual schoolchildren.
    probably not by coincidence, she’s a terrific
    asset to our class: a natural leader in discussion,
    quick with an insight (and slow with impatience).
    if the rest of the class will only look to me
    for some “role modelling” in this one instance,
    they’ll learn a lot from *her* …

    social psych? what people seem never to get
    is that social science is *harder* than math
    (since there aren’t any “right answers”!).

  11. Sue

    In California, the math ed happens mostly at the 4-year schools, I think. Anyway, I haven’t managed to get a crop of students for the class I created. (Couldn’t get it approved for gen ed credit. Sigh.) So I also haven’t gotten to teach this, my favorite class, in many years.

  12. finally found this.
    i have theories.
    the good stuff has to happen
    off the radar. seems like
    some natural law or something.
    of course i tend to overstate things.
    sometimes. see recent blogging.
    yrs in the struggle.

  13. kibrolv

    backlink: cited by me here
    (as “pedagogical content knowledge”)




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