Habit of Mind

12/04/2005 08:31:00 pm

Dean's recent post The Theory of Relativity got me thinking. Dean writes:

My recently adopted criteria of "Relevant, Engaging and Ownership" as a criteria for learning is definitely in its infancy. I've been saying that teachers need to address the ever popular question of "why do we have to learn this?" as part of how we do business .... I can agree that some things we learn may not completely link to our lives but offer a rich experience that will in some way enhance our lives.

He ends his post with:

So there are times when students may not see the relevance but we need to. So if you believe Calculus is going to be important for kids, make sure that at least you know why it's relevant. Stephen Downes says he's still waiting for it to be relevant. Not sure it will ever be.

That's twice recently that I've read the suggestion calculus is not relevant to student's lives. Lots of people feel that way. Whenever I meet someone for the first time and they learn I'm a math teacher they always reply either:

(a) I hated math; or
(b) I like math.

95% of the time it's (a). I think they've missed the point of what an education is all about.

I've been telling my classes for years now that by the time I'm finished with them at the end of grade 12 I hope they come to realize that I haven't really been trying to teach them math; I've been trying to teach them a habit of mind. Studying mathematics is just the vehicle for that purpose.

I think there are a great many courses we take that are not relevant in the way that Dean or Stephen describe. I also think that the educational value in those courses is the "habit of mind" they foster.

The relevance criterion will be a tough one. How do we determine that a particular course has no value? I think there is value in learning, no matter what it is you are learning. The value is in the habit of mind the learning facilitates. Each discipline facilitates a different habit of mind.

For all that, I think showing kids the relevance of what they're learning is to real life helps to motivate them. One question I ask my classes is:

"Y'know all those police dramas where the coroner arrives on the scene and says, 'The victim was murdered between 2:00 and 2:15 am.' How does she know that? Was she there?"

Well, one way she might have done that is using calculus to solve a first order differential equation. Let's learn how she did that. ;-)

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  1. Darren,

    I'm glad there are Calculus teacher's like yourself that are prepared to adequately answer questions of relevance.

    The questions I'd pose to you are:

    1. Are you happy with the current Manitoba Calculus curriculum? How could it be more relevant? Would it be better taught as an integrated subject....maybe an investigative crime class?

    2. Is Calculus relevant for everyone? Do those who enroll in Calculus do it because they see the relevance or is it just a way to gain acceptance into another program?

  2. Anonymous4/12/05 22:20

    (1) No, I'm not happy with the Manitoba Curriculum. I feel it is far too constrained by WNCP. The curriculum we have is a loose patchwork of topics strung together in such a way as to enable us to say that our local curriculum is globally competitive; "Look, we teach that too."

    My main beef is with the design of the curriculum. Calculation skills are emphasized outside the context of problem solving. Problem solving is given lip service, often attached to the end of a unit of study as opposed to being woven into the fabric of the curriculum. Conceptual understanding falls victim to calculation and manipulation skills which students struggle to memorize instead of developing an integrated understanding of how seemingly disparate concepts actually ARE related conceptually. Students end up developing a concept of mathematics as a dry rule driven subject. You've got to figure out which rule applies in a given situation, roll your eyes up into the back of your head, accessing your memory to recall the appropriate formula to plug the numbers into. That's not math!!

    Math is the creative application of problem solving skills. Good math isn't knowing how to solve any problem you're given. Good math is knowing what to do when you don't know what to do. It is a habit of mind.

    It could be more relevant if it was taught as part of an integrated curriculum as they do at High Tech High. This year all the students efforts are focused towards designing a human powered submarine.

    Then again, some stuff has to be learned and it's just plain boring -- like your multiplication tables; you just have to memorize that. In order to learn the interesting, more advanced applications, you first have to have a good grasp of the basics.

    Something I neglected to mention in my post is another bit of advice I give all my students -- "What you get out of every course you take is directly proportional to the amount of time, energy and effort that you put into it.

    An investigative crime class sounds like a neat idea. It might be a way to make relevant the material students learn in math, science, language arts, law, political science, industrial arts, etc. Hmm ... now you've got me thinking again ... Maybe our school could start such a project? ... hmmm ....

    (2) The content of calculus is relevant only to those who need to pass it as a "gateway" course or who will actually use it in their future education and careers. But the study of calculus is relevant to everyone as regards developing a habit of mind. Wrestling with the concepts and stuggling thorough the problem solving is a worthwhile exercise for any person interested in an intellectual challenge and growth. Dean, if you took calculus today from a teacher who really emphasized it's conceptual underpinnings you'd find it facinating -- anyone would.

    Whew! I'll step off my soap box now. ;-)

  3. I don't think it's a soapbox, sounds more like a passion. That's hard to argue with.

    I'm going to have to come up with a new subject as I consider irrelevance.

    I think in general our entire curriculum needs a makeover. I think there is still way too teaching in isolation in high schools. While we talk about relevance and the need to prepare kids for the future, we have failed to recognize that few lots in life deal with isolated learning requirements. Your student weblogs represent the use of writing and oral discussion that are often missing in a mathematics environment. I'd like to see this kind of learning normalized in schools. Your situation strikes me as somewhat unique.

  4. Anonymous4/12/05 23:55

    I don't know if my situation is unique unless by unique you mean I have a supportive administration. And if that is what you mean by unique, can the state of education in this country be that beleaguered? Ouch.

    So far, everyone who has seen what my students are doing (teachers, parents, administrators, former and current students) immediately sees the value in it. In light of the recent conversations we've had here I'm concerned that someone might want to "pull the plug." As an informed community of educators we need to articulate a defensible position .... and yet .... shouldn't the quality of my students work be a sufficient argument in favour of this pedagogy?