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Re: When math makes sense - w/ cooking, consruction
Posted:
May 25, 2013 2:02 PM
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The proposed exercise is to try matching a color using successive
approximation, where you mix red, green and blue to get there. As just a
snap shot, an activity, I don't see that it provides a basis for judging
and convicting some straw man curriculum presumed to be in the background.
True, the same activity would make sense in a science class, or an art
class, but to me that simply signals the interdisciplinary flavor of STEM,
which I welcome.
Where I might take such a lesson is into the subject of "pixel depth" and,
more generally, the need to develop a coordinate system or naming system
for addressing permutations. If we get down to a two value binary system,
then every color needs an associated pattern of 1s and 0s. How many things
can one name, with say three slots for a 1 or 0? (000, 100, 010, 001, 011,
101, 110, 111}.
It's starting to look a lot more like math now, in the conventional sense.
2**n (** for exponentiation or __pow__) is how many objects you might name
in this language game, with 2**3 = 8. We could use some kind of visual
proof.
So how many slots do we devote to color if we have 0..255 for each of three
slots, R G and B. And why 0..255, what's the significance in that? We can
count 0...7 in base 2: 000 001 010 011 100 101 111. That's 8
possibilities including 000. The number 8 actually needs a new slot. How
might we count to 256 (the number of possibilities)? Is that a power of
2. What's log to the base 2 of 256?
Using our trusty calculator... (actually more an interactive "chat window"):
>>> import math
>>> help(math.log)
Help on built-in function log in module math:
log(...)
log(x[, base])
Return the logarithm of x to the given base.
If the base not specified, returns the natural logarithm (base e) of x.
>>> log(256,2) # oops, forgot the namespace 'math'
Traceback (most recent call last):
File "<console>", line 1, in <module>
NameError: name 'log' is not defined
>>> math.log(256,2)
8.0
OK, so RGB would be like 8 slots for each of R, G and B.
<< pause to insert the color matching game we've been reading about,
perhaps a YouTube on the language game of paint color matching in the house
painting industry >>
Now lets talk about "pixel depth" in a different sense. Instead of the
color of each pixel on your screen, we're talking about characters and
strings of characters. What if you only had 256 permutations for all your
letters. That's just about right for Katakana + Hiragana (Kana) but so
what? We need to quote English on occasion, and Russian. We need room for
maybe millions of symbols, potentially. So what's the equivalent of RGB
when it comes to selecting characters?
<< segue to segments on Unicode >>
<< regular expressions >>
<< permutations and group theory >>
<< crypotography >>
<< logarithms >>
<< bases >>
<< functions as mappings >>
<< Pascal's Triangle >>
<< Tractor Math >>
The pointy brackets show like "buttons" you could press next to continue a
"train of thought". As a learner, you're pretty much in charge of the
order, at least a lot of the time.
If you're a speaker at a podium, you are maybe guiding the viewing of lots
of people and they may not see your button pushing as you may have
pre-selected the topic sequence. However it's important to give that sense
of a network now and then, a terrain we call STEM.
I'd often focus next on that 2x2 matrix we call a "canvas" with pixels
addressable using XY coordinates. That's what I do in my Tractor Math,
which replaces Turtles with Tractors and has them plow in XY fields,
reading and writing from cells, each with "depth" (like character or pixel
depth).
I presented Tractor Math in outline at PyCon 2013 during a Lightning Talk
(actually two, one at the EduSummit beforehand and once at the all hands on
Saturday). The 2x2 matrix easily becomes the complex plane and a subclass
of Tractor, the CropCircleTractor, makes these pretty patterns in the
fields.
Link to my slides for said Lightning Talk:
http://prezi.com/hw9gjvrfeizo/using-tractors-to-teach-python/
(only most of them, the complete set is at 4dsolutions.net/presentations as
pycon2013.pdf)
Kirby
On Sat, May 25, 2013 at 7:05 AM, Robert Hansen <bob@rsccore.com> wrote:
> And as usual, there is no development. It isn't just avoidance of
> mathematics (and computer science) going on here, it is avoidance of
> structured reasoned thought in everything they do. If this were a music
> class I fully expect that they would avoid the theory of music like the
> plague, just as they are doing here with mathematics (and computer
> science). I will admit, with many students that is unfortunately a workable
> formula, but is that what school should be doing? Acquiescing to students'
> lack of desire and/or ability with the real meat of these subjects and
> spending the year developing virtually nothing? And doesn't this just fuel
> the students' false sense of accomplishment in mindful pursuits that later
> leads them into decades of college tuition debt they have no chance of
> freeing themselves from?
>
> Bob Hansen
>
> On May 24, 2013, at 11:49 PM, Wayne Bishop <wbishop@calstatela.edu> wrote:
>
> > I'm not Kirby, of course, but I find it to be completely irrelevant to
> the teaching of mathematics, the nominal title of our thread. As usual, it
> is closer to mathematics avoidance than to mathematics teaching.
> >
> > At 10:06 AM 5/24/2013, Richard Strausz wrote:
> >> Kirby, I thought you would enjoy this blog post.
> >>
> >> http://blog.mrmeyer.com/?p=17112
> >>
> >> Richard
>
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