
Re: Square root of six
Posted:
Aug 29, 2012 11:43 AM


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 K12.
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 redefining 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 mindnumbing 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. Overspecialization is something they take completely for granted (a big part of their dimness).
Kirby
Message was edited by: kirby urner

