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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: 3,690
Registered: 11/29/05
Re: Square root of six
Posted: Aug 28, 2012 1:37 PM
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On Tue, Aug 28, 2012 at 9:41 AM, Robert Hansen <> wrote:
> Kirby, just a couple of weeks ago, on your advice, we checked out Beverly Hills High. They barely even had a digital offering at all and by no means did they offer (what they barely even had) in place of math. Since you will not offer accurate examples of this Math/CS thing then I will.

What was offered is math. The computational math teacher there
discusses his program, what he does, on other world-readable lists.
He and I talk to one another (on the record). I know what he does.

He's not the only one doing that kind of thing. I was giving you an example.

> Here is something interesting. That Python Math course offered at Phillips. You either get CS credit or Math credit, but not both.

Notice how you can get math credit. That's interesting isn't it. One
of the better schools, I think you'll agree.

> "COMP-470, Introduction to Discrete Mathematics and Programming
> Five class periods. This course blends a study of programming (using the Python programming language) with mathematics relevant to computer science. Students learn how to design simple algorithms and write and test short programs in Python. The course covers Python syntax and style, as well as data types, conditional statements, iterations (loops), and recursion. Selected mathematical topics include sets, number systems, Boolean algebra, counting, and probability. A student in this course is eligible for credit in either mathematics or computer science. A student who wishes to receive mathematics credit should sign up for MATH-470; a student who wishes to receive computer science credit should sign up for COMP-470. Prerequisite: MATH-340 or permission of the department."

However, why step into that cold? Why not start down that course
quite a bit earlier. The prompt (>>> ) is friendly, the language as
easy to work with as a calculator's.

> And you must complete math through pre-calculus (or get permission from the department) to take XXXX-470.

Right, not through calculus. It's OK to treat these earlier segments
as an on ramp to digital math. Given more time, the lead ins will get
better. Already some schools are using Scratch with 6th graders. But
I think you need to get more lexical, less graphical. This dream of
making everything left brain become a right brain activity is bogus.
Better to keep switching back and forth, between code on the one hand,
and the exciting visualizations and/or auditory and/or other phenomena
they create.

> I think they have the formula just about right with regards to CS/Math. Replace calculus with CS, for some students.

Remember you can keep calling it math and get math credit. In
Florida, they have this barbed wire fence maybe, with CS on the one
side, math on the other. That's Florida. Cut other states some
slack: they don't all want to be clones of your state. Just because
there's computer language involved doesn't suddenly mean "this is no
longer math".

> But this is if you are talking about classical programming which was math based.
> Creating applications like Facebook is neither mathy nor classical. I hate to break this to you like this, but the craft of writing software left its math origins decades ago. Saying that writing software is mathy is like saying that playing music is mathy. They all share a similar and energizing craftiness, but only math is mathy.

I'm saying you have no idea whatsoever with "math" is. You think
elaborate symbolic record-keeping and searching, connecting,
communicating, ala Facebook, can't be "math" because it's not what's
in math textbooks. I see more flexibility in language. We can call
that math if we want to. We can call it STEM as well and not be too
clear on whether it's E, S, T or M that we're talking about, when we
talk about Facebook.

You needn't "break" anything to me about computers and programming by
the way, as I've been in the field way longer than you have, plus
Portland is a high technology capital. Our company has partners etc.
etc., just like yours. I look at resumes and so on. When it comes to
"what industry wants and needs", I'm nationally published on that
topic, in FoxPro Advisor, March 1999, a trade mag for Microsoft
programmers, back in the day.

Not only have I been a professional high school math teacher, through
calculus, but I have been a professional programmer and continue to
teach STEM to this day. Yet you're always trying to let me in on
these inner circle viewpoints you claim to have. Sorry, but I've
already got a front row seat and know what I'm talking about.


> Bob Hansen
> On Aug 28, 2012, at 11:52 AM, kirby urner <> wrote:

>> Yes, I'm all in favor of roots and root finding. Raising to powers is
>> an important concept. I'm also a big believer in "infinite series"
>> i.e. the sums and sequences portion of precalc, where you're both
>> converging and/or your partial sums are converging... I'm a big fan of
>> that stuff.
>> However, I think it's very important that we get away from numbers,
>> meaning anything in the N, Z, Q, R, C pool, and focus on other objects
>> that many also be multiplied, such as permutations.
>> A permutation, in this namespace, is like a mapping of the letters A
>> to Z unto themselves, such that each letter is paired with another (or
>> itself). The identity permutation points every letter to itself.
>> When you multiply two permutations, you get the one that does the work
>> of both, e.g. if A -> R in the first and R -> K in the next, then
>> their product goes from A to K in one step.
>> These kinds of object are somewhat tedious to work with by hand and
>> students rapidly get carpel tunnel or throw fits in frustration,
>> twirling and foaming on the floor, as if possessed by demons.
>> We don't get that behavior with bright talking screens are enlisted,
>> and when we let computers do the guts of the operations. We program
>> though, which means we take control, have insight. Programming your
>> permutations, teaching them how to "multiply" is not just "for
>> programmers" (the way they say in Florida), it's for anyone learning
>> math, as this is group theory / abstract algebra, right at the core of
>> the disciplines.
>> So the nth root of a permutation: that makes sense. We can do "power
>> tables" which show how often permutations cycle, when multiplied by
>> themselves.
>> There's this thing about using the GCD (greatest common divisor
>> algorithm) to get the totatives of a number, those positive numbers <
>> N with no factors in common with N. If you multiply totatives modulo
>> N, you get a group. You are also laying some stepping stones for
>> understanding cryptography, RSA in particular, within reach by senior
>> year. This is the digital math track I talk about, used in the better
>> schools with state of the art STEM curricula.
>> There's a gap between schools with digital savvy and real STEM, and
>> lower quality laggard schools that don't have such quality curricula.
>> The USA is for the most part far behind, but here and there has some
>> pockets of excellence. We can't really break it down by race though,
>> as the better STEM schools are not furnishing us with exactly those
>> kinds of statistics. They're not even really "schools" in many cases,
>> just learning environments in cyberspace with no zip code, so more
>> like Facebook (a socially engineered meeting space).
>> Kirby

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