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Topic: Mathematician
Replies: 28   Last Post: Oct 15, 2010 8:47 AM

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Michael Dougherty

Posts: 148
From: Weatherford, OK
Registered: 5/18/10
Re: Mathematician
Posted: Oct 8, 2010 11:21 AM
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To me, math is almost automatically "discovery learning." Maybe all subjects are but I could argue math is more so. It's just a matter of how much of it you want them to discover on their own. If I teach trigonometric substitution or partial fractions decompositions, they will still have to "discover" the logic of it as they go, even if I completely explain the logic to them in my always brilliant lectures. I suppose if I want to give these two topics a month instead of a week (collectively), they might be able to "discover" it from something closer to first principles, but no matter how much I explain things they still have to work the problems to "discover" what works and what does not.

As they say, give a man a fish and you feed him for a day; teach him to fish and you feed him for a lifetime.

OK, but now they're asking us to let him discover for himself how to fish, perhaps out of desperation? He'll know some aspects of fishing better than if you teach him, but he'll miss out on a lot of details you could have taught him. And a lot of time will be consumed where it did not have to be.

As he gets older, it's good if we can teach him how to find the resources to "teach himself," but in the beginning it's better to present a logical context and let them work through it.

But I submit it's still "discovery," that they will make working through problems we give them. The rest is arguing about what level we want them to start, and how much guidance to give them. Also, how much of it we want to be a group activity.

So when I hear "discovery learning," I'm hearing that they think we explain too much. In math, that's almost impossible, if at some point you make them work problems on their own.

- --Mike D.

> Wayne,
> Certainly mandating discovery learning in these ways
> is a bad idea
> because it is not essential to good teaching and
> because it is
> easy to botch in the hands of inexperienced teachers.
> Teachers who
> do not feel comfortable using discovery learning
> should think
> twice before trying to use it. In short, discovery
> learning can
> be a useful approach to teaching and can be highly
> beneficial to
> students, but it is not essential to good teaching.
> And, like
> any approach to teaching, discovery learning is best
> seen as
> something that can augment teaching and learning and
> does not
> have to be seen as an "all or nothing" approach.
> Johnson and
> Rising's book "Guidelines for Teaching Mathematics"
> does not
> mention much about discovery learning, but they do
> point out that
> discovery learning is not appropriate in certain
> cases. It would
> be good if they had mentioned more specifics such as
> discovery
> learning is not appropriate for those ideas that
> would require
> a mathematical genius or near genius to discover with
> little or
> no assistance from the teacher or from others who
> already know
> those ideas. Perhaps the authors felt that such
> comments are
> not necessary. But they are necessary for those who
> want to
> try to push discovery learning too far. Any teaching
> method,
> whether discovery learning or anything else, used to
> extremes
> leads to problems.
> Jonathan Groves

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