But what is striking me right now as a math teacher is a passage from Kaiser's book, describing how the

*teaching*of quantum mechanics in 1950s America had changed from pre-World War II era pedagogy. Prior to the dispersal of the European founders of quantum mechanics across the globe, they had had ample opportunities to argue, debate, discuss, and wonder about the philosophical implications of what they had invented-slash-discovered. Textbooks written in the 1930s included long philosophical asides on the interpretation of quantum mechanics. Famously weird phenomena such as Schrödinger's cat and the double-slit experiment became commonplace topics of conversation.

That all changed after the war, because physics was perceived as an applied field; it had helped win the war for the Allies, and as the Cold War became more heated, physics became more important. In order to keep up the supply of physicists, the style of teaching and the topics taught changed. From Kaiser:

Faced with such runaway growth, physics professors across the country revamped their teaching style. They began to accentuate those elements that could lend themselves to high-throughput pedagogy, pumping record numbers of students through their courses. First to go was the discussion-based, qualitative, philosophical inquiry into what quantum mechanicsmeant... A few years later, another critic [the physicist George Uhlenbeck] weighed in... he accused his American colleagues of confusing what was "easy to teach" - the "technical mathematical aspects" of quantum mechanics, which could be chopped up and parceled out on problem sets and exams - with the conceptual, interpretive material that students needed most. (pp. 17-18)

In short, the larger the class, the less time spent talking through the big issues at the heart of quantum mechanics... The quarter century during which this Cold War style reigned witnessed an extraordinary buildup of calculating skill. All the same, an intellectual trade-off slipped by unnoticed, with wide-ranging implications... The fundamental strangeness of quantum reality had been leeched out. (pp. 19-20)To my mind, this parallel is occurring right now in mathematics education. With more and more students taking more and more mathematics, we are devoting less and less time to investigating the strangeness within it alongside our students. We confuse what is "easy to teach" (that is, "easy to assess") with conceptual, interpretive material.

It required a bunch of frustrated young physicists in the 1970s to change the perspective of the larger physics community to any degree. And arguably, that philosophical way of thinking still has not re-entered the physics world, much to its loss. Calculation still rules physics, and it still rules math education. And when we lose math students because we've spent too much time on the "how" and not enough on the "why/what happened", that's an even greater loss.

Third try - pesky Internet and lack of iPad comfort...

ReplyDeleteMy feeling here is that your take on computation is sadly too true in the core level hs classes. However, I really do feel that our upper level classes have the ability to explore in a pretty deep way thanks to current technologies. Just this past week our BC class was working on probability density functions and discussing expected value. Thanks to geogebra and demos we were able to explore the graphs of the functions in ways that were impossible 30 years ago when I was in hs. I think that I ask my kids more theoretical questions than I was asked. I could be overstating what I do as a teacher AND underestimating what my calc teacher did, but my calc class sure feels different to me than it did even ten years ago.

This was going on in math education debates in the late '80s through the '90s when I did grad work in math education at University of Michigan, right through to the present day. Go onto Facebook, look for groups opposed to the Common Core, or just Google "Common Core mathematics" and you'll find lots of places where (most) contributors bemoan the "lack of basics," reliance on calculators, kids who can't make change at the restaurant, and all the other classic Math Wars anecdotes and arguments from 20 - 25 years ago. Little changes except that the stakes are higher now because of all the high-stakes testing affiliated with the Common Core.

ReplyDeleteIn my not at all humble opinion, the vast majority of people weighing in on the online debate about math ed don't know what they're talking about. They dislike the Common Core, but for reasons that have little to do with my own concerns (which have to do with the larger picture - the takeover of public education by billionaires and corporations) and focus instead on some valid details (developmental inappropriateness of primary grade materials and topics, horridly written materials that you really need a math education degree or at least a lot of professional development training in a particular curriculum to parse (which is why most teachers don't get it, either), test and homework questions that make no sense, etc.). Those are all serious concerns, but those who focus on them tend to want to confuse specific materials with the actual math content standards, and lump it all together as "Common Core Math," when no such thing exists. Shades of the Math Wars. Shades of the anti-New Math fight in the '60s.

But regardless of the history, most Americans WANT everything to be like what you describe post-WWII physics pedagogy and courses as focusing upon. Computational, gradable, and not in any way deep or philosophical.

Oh, of course you can get heady stuff in upper-level graduate math courses. Those are for the elite of the elite. But K-14 math has got to be stuff parents can recognize as math, even if it's math they can't do. For me, this is a war that never ends: trying to get them to stop fighting to give their kids the same crap they were fed.

Thanks to Jim & Michael for the replies. A couple of thoughts:

ReplyDelete1) I don't disagree that the

potentialfor greater exploration and thoughtfulness and depth is available now due to technology; I just haven't seen that enter into most classrooms yet. And even those that I have seen, where the computational aspect of mathematics is toned down somewhat, are in very upper-level HS courses. I am unaware of any elementary, middle, or early-grade HS mathematics programs that are in use (to any meaningful degree) in public school systems that promote exploration and depth of thought.2) When I think about the Common Core and how it is being implemented, I ask myself a simple question:

whyis it being implemented in this way? Surely any new, national (de facto if not de jure) set of mathematics standards would be field-tested, right? And then I remember: it's not about the standards, it's about the assessments and the consequences thereof. It never was about new standards, it was about producing more data to provide "evidence" that public schools are not cutting the mustard. And until enough Americans realizethat, I too hold out little hope for the change in philosophy that I (and you, I think) believe is so desperately needed in math education.Thanks for the post. You have a following; unfortunately only a few reply. Physics always intrigued me especially after I read Zukovs book in the late 1970s. Those were heady times when big ideas were so much fun to explore. I pontificated a lot about change in those days and I guess I continue today with my promotion of the "Wannado Curriculum" which Im thinking a lot about these days as I struggle with writing my book. Tests rule we know that; but teaching is still best when students get interested in what we're teaching. Back in 1980 I taught a history of math course at Columbia Prep in NYC. I was humbled by the students that signed up. I learned so much not only because the kids were smart, but they were INTERESTED. Being interested should not be strictly for the gifted students as was in my case, it is possible to do it for all kids. Don't give up on the one year course for those less interested, someday it will be reality. The strong anti-common core trend today gives me hope.

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