[IAEP] How can we help kids get into the habits of looking for all possible causes and counter examples to problems?

Maria Droujkova droujkova at gmail.com
Mon Oct 3 07:38:08 EDT 2011

On Sun, Oct 2, 2011 at 5:59 PM, <forster at ozonline.com.au> wrote:

> Maria wrote:
> > Looking back at my life, I have never had to do anything with REASONS for
> > seasons or phases of the moon, outside of curriculum design. Have you?
> No, I doubt that > 0.001% of us have any reason to understand these things.
> The reason to teach about these things is that in practicing developing and
> testing hypotheses, it builds up our skills to understand other systems. So
> this kind of material should not be rote learned, it should be investigated.
> As Maria suggests, it might be even better practicing hypothesis testing on
> systems more relevant to us. The seasons probably made more sense a century
> ago as a system on which to practice understanding. We were much more
> affected by the seasons then and lived in a far simpler world. Today, maybe
> we should practice understanding on the internet or television or whether
> the moon landing was an elaborate hoax on a sound stage.

The point I am making: learning tasks, and learning questions, should have
some built-in means for students testing reasonableness of their hypotheses.
For example, students may plan settling Mars and investigate the role of
eccentricity in seasons there and on Earth.

The question, "Why are there seasons?" should be answered with, "Why do you
need to know?" - which allows students to investigate the matter in some
context, for themselves, and check their answers for REASONable-ness within
that context.

> The challenge for teachers is to share our love of understanding things,
> not so much a love of learning but a love of understanding. The joy of
> building robust hypotheses of how things work.

Tony, the pure joy of building robust hypotheses of how things work, just to
understand, is mostly a male thing. The joy of figuring out reasons why
things work, so as to make sense of personally and socially relevant
contexts, is mostly a female thing. I call for balance, and for
accommodations to students who prefer one over the other.

> PS
> Another challenge: why is it colder in the mountains?
> Tony

Can you pose this as a contextualized challenge? Where understanding WHY is
relevant and important to know?

Maria Droujkova

Make math your own, to make your own math
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