[Edu-sig] number-line graphics for teaching arithmetic

[Kirby Urner]

>> I like to go for a more complete vector concept, and not make the
>> number line too front and center initially.  Space first, planes and
>> lines second, is my approach (take freedoms away later, but start
>> with what's most familiar and real i.e. volume).
>
>That sounds cool, but I'm not convinced about how well it actually
>plays out.  Worth a try though.
>

Just an addendum:  vectors are like dashed lines on a map.  
Because of topography, the actual path goes up and down too.
It's every day experience.  If you think of little arrows 
showing your path from the kitchen to the bedroom, or from
your house to the grocery store, then that's tip-to-tail 
vector addition.  It's just a matter of adding those arrows
to the picture (a thought experiment).

Number line motion is more constrained, like a window in 
a frame -- opens or closes.  So you could take a closed 
window (starting state) and to W+ W+ W+ W+, then W- W-.  
These are increments in the "more open" and "more closed" 
direction.

I guess you could say my approach is to deliberately get
away from the very abstract little pictures and go for real
world situations when possible.  Then back to the pictures
(after a decent interval talking up the real world special
cases -- not "word problems" necessarily, just analogous
concepts).

I tend to think of these demos as "Sesame Street shorts" -- 
like all those video clips about the letter A and number 9, 
except here about vectors, great circles, polyhedra, whatever.
E.g. I imagine kid voice in chorus saying "Open" "Open",
"Closed" and this window slides a bit each time.  Then you
do the same thing with some valve-looking thing (circular
motion).

To this end, I think the Flash format might be very useful,
but haven't had time to master the relevant apps myself.

I imagine a huge collection of "math clips" being archived
to a DVD juke box (or single DVDs if the juke box is too
expensive/fancy in a given context).  

The teacher can pull up these clips in a sort of "stream of 
consciousness" manner, i.e. because they're quite short (many
under a minute), you keep the narrative threads going, plus
the teacher is in control of sequencing (much of the time)
-- not like traditional AV, where you devote pretty much
the whole class, or half of it, to some documentary or other.

Just sort of rambling here.  Python is part of the mix in 
these idealized math classes.  Again, it's often a matter of
the teacher simply typing a few lines of code as she or he
presents, as in:

"Let's take prime numbers between 60,000 and 60,500..."

>>> pri = filter(lambda x: x<=60500 and x>=60000,primes.get2nb(60700))
>>> pri
[60013, 60017, 60029, 60037, 60041, 60077, 60083, 60089, 60091, 
60101, 60103, 60107, 60127, 60133, 60139, 60149, 60161, 60167, 
60169, 60209, 60217, 60223, 60251, 60257, 60259, 60271, 60289, 
60293, 60317, 60331, 60337, 60343, 60353, 60373, 60383, 60397, 
60413, 60427, 60443, 60449, 60457, 60493, 60497]

"Now lets run a Fermat test on them, using 2 as a base..."

>>> >>> map(primes.fermat,map(long,pri))
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

... and so on.

NOTE:  in this case, running get2nb(60700) or so before 
class might have been a good idea, as it took a minute or
so to generate 'em using trial-by-division.  But they're
cached, so the 2nd time, the the function returns quasi-
instantaneously.

Kirby