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Topic: Square root of six
Replies: 21   Last Post: Aug 31, 2012 12:47 PM

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kirby urner

Posts: 1,753
Registered: 11/29/05
Re: Square root of six
Posted: Aug 29, 2012 11:43 AM
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On Wed, Aug 29, 2012 at 4:52 AM, Robert Hansen <bob@rsccore.com> wrote:
> I want to make sure that my points aren't twisted any further.
>
> 1. I am not against teaching CS in school, I am for it.


Usually it's an elective that offers no math credit so worthless in
terms of counting towards that diploma, for which math credit is
required.

> 2. There is no trend, even an infinitesimally small one, towards treating CS and Math as the same.

There's a trend towards teaching something called computational math
which inherits from discrete math, and adding to that more topics that
would have only seen light of day in CS in recent memory within K-12.

You may use Google to study this trend, which is well beyond
infinitesimal at this point. This trend goes back to Seymour Papert,
Kenneth Iverson and many others.

http://dl.acm.org/citation.cfm?id=2170913

Note that the Litvins book 'Mathematics for the Digital Age and
Programming in Python' may be used for math credit or CS credit (at
Phillips). Something you brought up yourself.

I would say the trend is small but easily detected.

Its size also depends on how it's measured of course, like if you go
outside the US (which you should) and include initiatives like One
Laptop per Child.

If you go outside formal / conventional school and look at the
educational *function* of culture, versus the institutions to which
official lip service is given, then CS and math are way more
completely blended.

> 3. There is no trend (period) towards re-defining SQL as math.
>


http://publib.boulder.ibm.com/infocenter/soliddb/v6r5/topic/com.ibm.swg.im.soliddb.sql.doc/doc/the.mathematical.origins.of.sql.html

SQL *is* a math language, just like Python *is* a math notation,
albeit a machine executable one.

http://dl.acm.org/citation.cfm?id=358899 (the PDF spells it out)

> I looked up Riverdale High. They require 4 years of math. So I think to myself "Well maybe this is SQL and REGEX math like what Kirby keeps talking about." So I dig deeper and look up the state math assessments for Oregon and Riverdale in particular. I don't find SQL questions. I don't find REGEX questions. I find math questions. If we look at their class catalog, I don't even find a CS class. We do find a discrete class.
>
> http://www.riverdale.k12.or.us/site/Default.aspx?PageID=198
>


What Riverdale School District is well known for is helping to spread
Linux on thin client computers to K12 schools across the land:

http://hs.riverdale.k12.or.us/terminal/press.html (from 2002, yes a
decade ago i.e. this is not a new phenomenon by now)

You may have seen in Wikipedia that Linus Torvalds and family are in
this district, with kids enrolled in said school.

> Finally, I have no problem at all with the Python / Discrete / Numerical Methods class at Phillips or at any school. I am all for it. I just point out the obvious when I say that you can't really start that up till after the student has conquered algebra. We have dealt enough in the past with the MYTH that it is magical to put students and computers together in a math class. When you do that too early you don't do justice to math or to CS. But after a student has successfully navigated algebra, geometry and a few elementary functions. Then they have enough foundation and reason to explore numerical methods. That doesn't rule out the use of a computer in the classroom occasionally, until you get to numerical methods. It does rule out SQL and web pages development.
>
> Bob Hansen


Thanks for being clear on your positions, however wrong and misguided
they appear to me to be.

Short interactive computer "programs", called functions in Python,
look just like what's in the algebra books.

>>> def f(x): return x*x # 2nd power
>>> f(10)

100

That's easier to use than a calculator, which, if it's programmable at
all, uses a low level more difficult less flexible language on a tiny
screen.

Adding a line or two:

>>> \
def s(x):
if x==0: return 1
else: return 10*x*x + 2

Using interactively, immediately, with function still displayed (eat
your heart out calculator users):

>>> list(s(x) for x in range(1,10))
[1, 12, 42, 92, 162, 252, 362, 492, 642, 812]

Hmmm, important sequence: http://oeis.org/A005901 (with a link to my web site)

Looks a lot like algebra in that variables are used, functions, domain
and range, ordered pairs, graphing, ideas of bijectional, "into"
(injective), "onto" (surjective)...

Why would you "wait to know algebra" before tackling topics in algebra
itself with these tools? What a mind-numbing proposal. As I was
showing above, if you add permutations and operator overloading, such
that these may be multiplied, then you're well on your way to group
theory and CAIN (closure, associativity, inverse and neutral element).
Is abstract algebra not really algebra then?

My position is there's a gap between what the better thinkers are
doing to guide education forward, and what the laggards are doing, the
poor slobs in the rear.

I'm in the vanguard (obvious to me at least), collaborating with
peers. The poor slobs would include most rank and file teachers and
certainly most students.

What holds people back, a lot, is the mediocre thinking of the self
appointed "experts" who just haven't done enough homework and/or
haven't sufficient imagination to usher in a real future. A lot of
these dim bulbs have been busy on common core standards of late, which
offers zero synchronization across S,T,E and M. The idea these should
be integrated *at all* doesn't cross their minds. Over-specialization is
something they take completely for granted (a big part of their
dimness).

Kirby


Message was edited by: kirby urner



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