Date: Nov 15, 2012 11:48 PM
Author: kirby urner
Subject: Re: How teaching factors rather than multiplicand & multiplier confuses kids!

On Thu, Nov 15, 2012 at 7:21 PM, Robert Hansen <> wrote:
> On Nov 15, 2012, at 9:48 PM, kirby urner <> wrote:
> This is what development looks like.
> I didn't see any development at all.

Fine, I didn't give you a cartoon comparing digital to analog and relating
that to discrete versus continuous. I don't have a budget for that right
now -- I should look on Youtube.

In STEM, I'd say there's a bias in favor of digital over analog. Two points
infinitely close together is like the reciprocal of two points infinitely far
apart. But do we really need "infinity" in either context. We may think
that we do. There's math for thinking that way.

There's also math for not thinking that way.

> Maybe it would help if you gave us the student's reaction. When you say "An
> analog clock has a sweeping second hand and a digital clock flips through
> the digits.", how do they respond?

Maybe I'm just showing what STEM teaching is like and leaving a lot
to the imagination. If I were trying to clear some lesson plan with a
committee of my peers, I might take a different approach, but that's not
what's going on here.

Making gasoline come off as discrete in terms of Avogadro's Number i.e.
thinking of gas (petrol) in terms of a discrete number of particles, was
somewhat funny / ironic, as usually fluids are treated as analog / continuous.
That's another example of "continuity" being a mere "approximation" of
the scientific facts.

You could say I'm more in the lineage of Democritus (atoms) than
Euclid (infinitely thin infinitely extended planes).

I think this tilt towards quantum or discrete is part of the zeitgeist of
our times and I'm merely echoing a well known theme here.

> It seems like you are doing nothing more than teaching through example the
> common use of the phrase "continuous motion", although, second hands
> generally jump, not sweep, because of the escapement. All of this dialog of

Yes, I thought of jumping second hands too. That would be part of the
banter. You're the kind of adult who'd bring that up, and I'd welcome it.

> yours looks very much like you showing the students common uses of the word
> "continuous". Given what you have posted so far, this is a language arts
> class, not a math class. Maybe if you provided the students' side of this
> dialog it might help us distinguish it from language arts.
> Bob Hansen

Yes, more of a language arts class in some ways, I agree, because working
to ground students in experience, to anchor in the everyday. Setting the stage.

To get more mathematical about it I might take those growing cuboctahedral
numbers 1, 12, 42, 92... and get the cumulative totals, getting a sense of how
many layer's we'd need to reach Avogadro's number. I've shared those
computations elsewhere.

Maybe I should just "go underground" with this program and stop sharing
so much about it here. What do I have to gain from always freely sharing?
There's no point trying to push it all through math-teach again, all the same

Thanks for helping persuade me to drop the frequency of my posting here.