re: scoring high school math textbooks according to their "CS friendliness"

[kirby urner]

CS means "computer science" BTW. 

BTW means "by the way".

....

Consider that place in the middle-to-high school curriculum
where the concept of "function" is first introduced.  The

"set of ordered pairs" definition often central, and is very
general. 

As long as a domain element maps to only one range
element (not more), it's a function and not a relation.

But which textbooks bother to give examples of functions
that are non-numeric in their domain and range? 

For example a function "to uppercase" a letter giving
ordered such pairs as in the set {("a", "A"), ("r", "R"), ("b", "B")}

and so on:  that's a non-numeric example.

Or perhaps concatenation is introduced as a binary
operation:  "A" + "B" gives "AB" or maybe we write it:

(+ "A" "B") putting the operator / function up front as

in Scheme with string-append [1], or add("A", "B") -> "AB".

This meaning of + is not commutative, which is helpful
when providing contrast, especially initially as all the
number sets we're used to in the early grades *are*

commutative w/r to addition.  Nice to have this familiar /

commonplace alternative.

I'd consider mathematics textbooks that go to the
trouble to introduce non-numeric examples of functions
are more CS-friendly than those that don't.  That's
because algorithms in computer science are frequently
only semi-numeric or non-numeric in nature. 

To think of computers as "number crunchers" is something
of a misnomer.  Sure, letters reduce to binary sequences,
but then these get used as letters, not numbers.  When
you "add" them, they concatenate, and "upper" may
well be defined.  Computers are "alpha crunchers"

or "string digesters" just as much as anything.

Textbooks that mention one or more computer languages
get a check in that column (vs. an X) -- picturing a chart
of several columns with checks or Xs.

Actually using a computer language for any reason:  another
CS-friendly check.  This attribute could be broken down
more e.g. is it only in an appendix they use some language,
or is a computer language is used throughout?

Here's another thread where I'm debating these points with
other discussants on math-teach:

http://mathforum.org/kb/thread.jspa?threadID=2620194

Robert thinks computer programs only provide "subroutines"
which are alien to the mathematical notion of a "function", a
kind of spin-off concept that branched away from mathematics

long ago.  He thinks CS and mathematics are very distinct

STEM areas.

Joe thinks I might not understand the generality of the ordered
pairs definition, thinking instead that any function is "computable". 

I attempt to address these countering viewpoints.

Kirby

PS: I link to one of Michel Paul's web pages in one of the posts.


[1] http://groups.csail.mit.edu/mac/ftpdir/scheme-7.4/doc-html/scheme_7.html

[Peter Farrell]

Hi, Kirby,

I find a lot of CS commands and conventions are learned and used, and only afterwards can be understood in their mathematical or logical sense. 

If you want to add an element to a set, you learn "append()" or whatever, and only when some bright Oregonian points it out do you realize that the operation "a.append(b)" is not commutative.

My opinion at the moment is that this 20/20 hindsight is preferable to the way we've always done it in schools: teach kids the commutative property long before they'll ever need to analyze an operation for commutativity. This may have to do with my desire to see all schooling reduced to one 6-week program. (Credit for the idea goes to this educational genius.)

Another of the broad generalizations clanging around in my skull must be blamed on Seymour Papert, whose Mindstorms I sum up in my mind as "Everything worth doing in math education can be done using a computer." Have kids do some real computer stuff and they'll look back on understanding commutative operations like the character in a Voltaire play who was delighted to learn he had been speaking prose all his life.

Upon rereading this, I'm not sure it's fit to post. But if I let that stop me I'd never post anything.

Peter Farrell

[Linda Fahlberg-Stojanovska]

i think the problem is not the rule, it is that our teachers are not given good strategies. I fail to see how talking about adding, i.e. walking the width and then the height of a rectangle is the same as vice versa or walking a triangle in one direction is the same distance as walking in the other direction and then later saying "this is called the commutative law" is not a good thing...., (btw nobody seems to care that the words "length" and "width" of a rectangle make no sense especially when the next area formula is for a triangle and the vertical is called height.)

 Question. is 'down'append'fall' the same as 'fall'append'down'? maybe i am mixing commands.

Warm regards, Linda

Sent from my iPad

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[Rakesh Biswas]

Dear Peter,

"...like the character in a Voltaire play who was delighted to learn he had been speaking prose all his life."

Perhaps you meant Molière, January 15, 1622 – February 17, 1673 and not Voltaire, 21 November 1694 – 30 May 1778?

PHILOSOPHY MASTER

		To make the point most terse.

What isn't verse is prose, and what's not prose is verse.

"MONSIEUR JOURDAIN
Oh, really? So when I say: "Nicole bring me my slippers and fetch my
nightcap," is that prose?

PHILOSOPHY MASTER
Most clearly.

MONSIEUR JOURDAIN
Well, what do you know about that! These forty years now, I've been speaking
in prose without knowing it!" http://moliere-in-english.com/bourgeois.html

SPIN..?


PHILOSOPHY MASTER (A Robot)

		To make the point most brief.

What is not math is code and without code i would never figure your prose...Good grief!

"MONSIEUR JOURDAIN
Oh, really? So when I say: "Nicole bring me my slippers and fetch my
nightcap," is that computer code?

PHILOSOPHY MASTER ( A Robot)
Most clearly.

MONSIEUR JOURDAIN
Well, what do you know about that! These forty years now, I've been speaking
in 'code' without knowing it!"

best,

rakesh

--

[kirby urner]

Hi Peter --

The gist of that thread on math-teach, about ranking math texts per criteria

for judging their "CS friendliness", is that in Oregon 2009 we (teachers,

activists, geeks) were looking at making room in the law for new high
school math classes that would:

(a) count towards the three years of math required for a high school
diploma and

(b) include more technology and programming skills, which could be
seen as importing from computer science, or as simply updating the
mathematics curriculum (for just these particular new classes) to use
technology well beyond calculators.

The status quo is the better schools that benefit from higher property
taxes in their zip codes, more parental involvement (e.g. only one parent
works, the other makes $200K/annum) etc. usually have computer science
electives, but these do *not* count towards the required 3 years of math,
whereas the poorer schools cannot afford anything CS, not because of
the hardware so much as faculty.  The math teachers are already over-
burdened and math is required after all, so the CS elective gets axed.

Now there have been changes in the tax code to supposedly level the

playing field more.  Our initiative would dovetail with that, as our alternative
math courses would potentially feature in all public schools.

The teachers I met with in 2009 were excited by the prospect of a
new genre of math class, which we could call "Digital Math" or

"Math in the Workplace" or "Math for the Digital Age" or "Computational

Thinking" or... you name it.  Most of them were thinking to use some
Python, but not necessarily exclusively. 

However our chief organizing lobbyest from Software Association
of Oregon, one Chris B., got hired by WebMD.  The economy was
soon to fall on hard times and the thread was lost.  Many teachers

with a CS background end up in private industry.  Organizational
memory is difficult to sustain. 

Note:  I was not then and have never been directly employed by SAO. 
I'm just a private citizen activist and joined some of these SAO-sponsored
meetings as a rep from Free Geek (freegeek.org) a Portland-based
NGO that recycles old computers, but also teaches classes and help
kids learn (kids and adults volunteer to learn how to break down and
rebuild computers, called the Build Program).

So our for-credit CS-friendly math courses are not yet a reality in Oregon.

I think the bottleneck is mostly in the journalism sphere.  There are
lots of moving parts to a story like this, and the objectives need to
be clear in the public mind, for enough citizens to care to get it on
the collective radar to a degree that legislators will care too.  But
that requires a rather high level of debating skill and conceptual

sophistication and I'm afraid our local press is just not up to the job.

The issues are too gnarly and well, mathematical, for journalists to
wanna tackle it for real.  Public debate stays focused squarely on
money only, as that's the one thing the 99% have very little of, but

will claim to understand and gladly talk and read about.  Money-
talk counts as news, then there's sports and weather.

Kirby

[Christian Baune]

Hi,

I know that in Belgium at least teachers are bound to a curriculum and even a methodology.

I used to be advanced in Maths due to two years of "special schooling". Having a broad interest in Maths, I learned all the 12 years in only two.(But French, my native language, was a pain for me)

At every Maths course I asked, when I dared to, "Why making it so complicated? Why asking to remember? Why being confusing? Why all of this wording? Why no puzzles? ..."

Answer was and always remains the same : "We can't really teach the way we want; We have to follow the program and instructions".

The fact is that Maths and fluid verbal skills (Which taint writing skills) are bound to IQ and more precisely the "g" factor.

Computer language are Maths. Programming is a subset of mathematics. You can turn it in any way, a program is only a big function. (Don't you have a "main()"?)

What's good also is to show mapping function using a lookup table and ask students to solve some equations.

By making the tables bigger,  students will be encouraged to look for function properties. (Or operator if you dare using infix)

Text books should include such exercises and puzzles.

KR,
P.

[kirby urner]

I'm sympathetic to your pleas.

Not sure what I think about the g-factor.  I think many studies show that better nutrition makes a difference and schools that eliminate junk food and Pepsi / Coke from their vending machines tend to get improved performance. 

It's partly that selling junk food to kids sends the wrong message.  It tells them adults don't care and just want to give them diabetes so they can make a buck, and that's discouraging. In many schools if you ask a student for an honest answer as to what's the biggest problem, it's:  the adults don't respect us.

Anyway, yes, a programming function may well be a function in a formal sense, meaning if you pair inputs with outputs it's either many-to-one or one-to-one but never one-to-many i.e. it's wrong to have an indeterministic outcome, a choice, and call it a function. 

Something to discuss and philosophize about. 

Obviously "function" is a multi-valent word with currency in many shoptalks.  It's important not to assume a particular shoptalk is working with the "global meaning" as if their were such.  It's for a reason that dictionaries enumerate meanings, and even that is not enough to capture the many nuances and spins a word may have in different circumstances ("function" being a word like that).

I'm very against the one-size-fits-all, everyone-on-the-same page cookie cutter approach to education.  It's cheap and convenient for bureaucrats but does an extreme disservice to the kids and future citizens. 

I'm sorry Belgium is so backward. 

I hope we never get there in our region, where diversity still thrives, but is under attack (as usual) from an alliance of big publishing (winner-take-all textbook publishers) and micro-manager control freaks of many ilks and species. 

I like The Lego Movie (even in 2D) because it pokes fun at such "can't handle non-conformity" types.

Kirby

[Rakesh Biswas]

Kirby, "I'm sorry Belgium is so backward.  I hope we never get there in our region..."

I wonder if that would a big generalization from an 'n of 1' experience? :-)

Belgium gave the world Poirot and Tintin and although both were mythical characters they were global leaders and surely didn't look backward.

BTW apologies for my 'Myth and Math' interjections of x-factors into this engaging CS and M (M=Math) discussion.

best,

rakesh

PS: The meaning of 'x-factor' is more amenable to google searching than perhaps the g-factor?

[kirby urner]

On Sun, Feb 23, 2014 at 6:04 PM, Rakesh Biswas <rakesh...@gmail.com> wrote:

Kirby, "I'm sorry Belgium is so backward.  I hope we never get there in our region..."

I wonder if that would a big generalization from an 'n of 1' experience? :-)

Belgium gave the world Poirot and Tintin and although both were mythical characters they were global leaders and surely didn't look backward.

Yes, I've definitely been a Tintin fan though my real crush might've been on Snowy (for Freudians to figure out).

Actually it was Captain Haddock who probably made the biggest impression.  I might a guy like him later in life, right down to wearing a captain's coat (with a boat to go with it).

I liked the Tintin movie too, amazing animation and the same frenetic pace of the comic.

Speaking comics, I highly recommend the graphic novel Logicomix, a link being Michel Paul's tag line (in his sig) about CS being the new math (I spell it "gnu math" sometimes, waving the flag, making a pun).

http://en.wikipedia.org/wiki/Logicomix

I consider the graphic novel or manga and entirely legitimate way to communicate technical content amidst lore (you need both).  From there it's a short hop to full fledged cartoons (anime), also a favored medium (in my mind -- I have high hopes for "didactic cartoons" continuing to mature / morph as a genre).

Kirby
 

[kirby urner]

On Sun, Feb 23, 2014 at 6:12 PM, kirby urner <kirby...@gmail.com> wrote:

On Sun, Feb 23, 2014 at 6:04 PM, Rakesh Biswas <rakesh...@gmail.com> wrote:

Kirby, "I'm sorry Belgium is so backward.  I hope we never get there in our region..."

I wonder if that would a big generalization from an 'n of 1' experience? :-)

Belgium gave the world Poirot and Tintin and although both were mythical characters they were global leaders and surely didn't look backward.

Yes, I've definitely been a Tintin fan though my real crush might've been on Snowy (for Freudians to figure out).

Actually it was Captain Haddock who probably made the biggest impression.  I might a guy like him later in life, right down to wearing a captain's coat (with a boat to go with it).

"... met a guy" sorry.  I might as well reveal his identity:

http://flic.kr/p/5DAVEe  (but not in his captain coat & hat)

Here's his boat:

http://flic.kr/p/Mp7XW

Our joke has been:

Don:  "Oh so if I'm Captain Haddock then you must be Tintin." 

Me:  "No, I'm Snowy".

He has a white beard whereas Haddock's is black.

Don helps spearhead a group named Wanderers that meets in the former boyhood home of Linus Pauling, 2x Nobel prize winner (the only one so far to have two unshared). 

Pauling was from our state of Oregon, his dad a pharmacist who died when Linus was young, but not before helping shape his love for chemistry, which he practiced in the basement beneath our meeting room (we meet every week, have been doing so for about a decade I think).  His mom made the house a boarding house to make ends meet.  Here's its picture:

http://flic.kr/p/dPnBgm  (that's the Alpha Helix in front, a molecule the structure of which Pauling determined)

Alpha Helix is by this artist:

http://flic.kr/p/5ASvDW  (Julian)

This group, of many scientist and engineer types, some retired some practicing some in and out of work, has been a goldmine for me, in terms of interesting facts and information. 

We have Dick Pugh some days, a world class scholar of meteorites and a steward of Portland State's respectable meteorite collection.  Talk about STEM on steroids!

The late Doug Strain, our main benefactor, studied under Linus personally and devoted a lot of his wealth, derived from the Silicon Forest company he co-founded, to helping to preserve Linus's legacy (that picture of Don, above, is from Doug's memorial service, where Don sang in his honor).

Kirby

[Peter Farrell]

Hi, Kirby,

I was also impressed with the new generation of 3D animation in the Tintin flick. I'll have to check out Logicomix.

My sons are great cartoonists and I'm trying to interest them in 3D graphics programs like Blender. In fact 3D graphics might hold some of the answers to many "math through technology" issues:

1. Most students in my CS classes are fascinated by and WANT to create 3D images with Sketchup or Visual Python. That hurdle is not to be underestimated, especially among high-schoolers and "underserved" populations. The "A" in STEAM might motivate a lot more potential technophobes than generating a list of Fibonacci numbers might.

2. The math involved in extruding, rotating and scaling objects is not trivial. However, one need not endure an entire year of Precalculus just to create a convincing Alphahelix. I've met many tech-competent people who got into programming to learn "just enough" to get what they needed out of a computer.

3. The demand for Python programmers shows no sign of stopping, so teaching it by any means is like giving away free money. Everything you can do by hand (ok, by mouse) in Blender can be programmed in Python, which alone makes it worth the cost. (It's free.) Yet another intersection of Math, Art and Python, the others being the fun Turtle module (an homage to Papert's Logo turtles) and Visual Python, where 3D objects are pre-loaded and ready to import. Blender can be used for animation and game programming, too.

You perfectly described the bottleneck to getting all this free technology to the students who would benefit from it. The textbook publishers (and now the online "one software fits all" marketing machines) would indeed have every math class in the US on the same (web)page on the same day of the school year, and the general public oscillates back and forth between "education using cutting edge technology" and "back to basics."

I would also welcome any more info on your free geek program, as I'm trying to stockpile a fleet of (linux) laptops to work with Raspberry Pi's.

Peter Farrell

SF Peninsula

On Thursday, February 20, 2014 9:35:22 PM UTC-8, kirby urner wrote:

[kirby urner]

On Sun, Mar 2, 2014 at 10:25 AM, Peter Farrell <peterfa...@gmail.com> wrote:

Hi, Kirby,

I was also impressed with the new generation of 3D animation in the Tintin flick. I'll have to check out Logicomix.

Yes, amazing animation.
 

My sons are great cartoonists and I'm trying to interest them in 3D graphics programs like Blender. In fact 3D graphics might hold some of the answers to many "math through technology" issues:

1. Most students in my CS classes are fascinated by and WANT to create 3D images with Sketchup or Visual Python. That hurdle is not to be underestimated, especially among high-schoolers and "underserved" populations. The "A" in STEAM might motivate a lot more potential technophobes than generating a list of Fibonacci numbers might.

Yes. 

My solution involves providing "scaffolding" by which I mean already working solutions amenable to altering, once at least partially understood.  We start "in the middle" with running code, rather than "at the beginning" with some intimidating "blank canvas".

For example, I just posted a couple Python programs to edu-sig.  The first "makes" a Fractal object, while the second writes out its information as a POV-Ray file, suitable for rendering.  Yes, POV-Ray scene description language is a huge topic and we're only scratching the surface.

https://mail.python.org/pipermail/edu-sig/2014-March/date.html

"Scratching the surface" in judicious, illuminating ways, is what I call "cave paintings".  A critic might call it "shallow".  But to actually read some source code and participate in a graphics-generating "pipeline" is more hands-on than any so-called math textbooks for these same students that I'm aware of.

With this scaffolding in place, and run, a student may then make some alterations.  In the case of a Fractal, a Mandelbrot in particular, the question is does a certain sequence converge or diverge, and if it diverges, how quickly?  Color code accordingly and you have a picture.  But exactly how these colors are applied, and what colors, is wide open to experimentation.

Even before we get to fancy rendered output, I start with an ASCII art version:

http://flic.kr/p/kCDaRB  (ASCII)
http://flic.kr/p/kCLp2F  (low rez rendered spheres)

2. The math involved in extruding, rotating and scaling objects is not trivial. However, one need not endure an entire year of Precalculus just to create a convincing Alphahelix. I've met many tech-competent people who got into programming to learn "just enough" to get what they needed out of a computer.

Funny you should mention AlphaHelix as I just last week got to visit with STEM artist Julian Voss Andreae after more than two years. 

His studio is in a completely different place from before, and his subject area has changed. 

Whereas he sculpted AlphaHelix in front of the Linus Pauling House, now it's about filling the human form with irregular tetrahedra, but with form-fitting facets on the surface.  He's using custom algorithms (plugins for WIngs 3D), and sculpting the results in metal.

http://flic.kr/p/kz1okK  (prototype)
http://flic.kr/p/kz1CD6 (Julian with alpha-helix-looking thingy)
http://flic.kr/p/bQNRJM (AlphaHelix in Google Earth rendering of Pauling Campus)

3. The demand for Python programmers shows no sign of stopping, so teaching it by any means is like giving away free money. Everything you can do by hand (ok, by mouse) in Blender can be programmed in Python, which alone makes it worth the cost. (It's free.) Yet another intersection of Math, Art and Python, the others being the fun Turtle module (an homage to Papert's Logo turtles) and Visual Python, where 3D objects are pre-loaded and ready to import. Blender can be used for animation and game programming, too.

We had Blender jocks deliver presentations at OSCON a couple years ago I think it was.  As a proposal ranker, I might have been influential in that regard. 

I picked up an undercurrent from the Blender pros of "we've put in hours and hours practicing drawing and visual sculpting and are really good at that, whereas you folks are really good at programming, but maybe not so good at drawing." 

All pretty true, i.e. programmers need to (and often do) form symbiotic relationships with visual artists to make their dreams come true, in a lot of cases.  Once over the hurdle of its bewilderingly complicated API, Blender is more about being good at drawing than programming, notwithstanding the fact that Blender is itself a result of brilliant programming.

I'm amazed at agog at the Blender movies out there, especially the one about the kid and her dragon.  Awesome.

 

You perfectly described the bottleneck to getting all this free technology to the students who would benefit from it. The textbook publishers (and now the online "one software fits all" marketing machines) would indeed have every math class in the US on the same (web)page on the same day of the school year, and the general public oscillates back and forth between "education using cutting edge technology" and "back to basics."

The technology is all in place to empower faculty; to make each school a *source* of curriculum materials, swapping with others, value-adding by editing-recombining, or sometimes just copying (legally, as copyleft is the new norm in education -- or the old norm as Stalling likes to point out, i.e. software was free before the money-makers invaded academe (he was at MIT's AI Lab then, pre GNU)).

http://en.wikipedia.org/wiki/Richard_Stallman  (for those reading who might not know who Stallman is)

 

I would also welcome any more info on your free geek program, as I'm trying to stockpile a fleet of (linux) laptops to work with Raspberry Pi's.

FreeGeek.org has been really successful here in Portland, largely because of its Build Program, which teaches kids and their guardians how to wipe hard drives clean, test components, and reassemble "Freek Boxen" with Ubuntu installed. 

Here's the lure:  build five and the sixth is yours to keep.  

The nonprofit gets bucks for the motherboards too (because of the metals), but I don't know anything about the margins.  Portlanders often take their computers to FreeGeek for recycling.  Whole companies offload when upgrading.  It's a thriving nonprofit I'd say.

Kirby

Peter Farrell

SF Peninsula

[kirby urner]

The technology is all in place to empower faculty; to make each school a *source* of curriculum materials, swapping with others, value-adding by editing-recombining, or sometimes just copying (legally, as copyleft is the new norm in education -- or the old norm as Stalling [sic] likes to point out, i.e. software was free before the money-makers invaded academe (he was at MIT's AI Lab then, pre GNU)).

http://en.wikipedia.org/wiki/Richard_Stallman  (for those reading who might not know who Stallman is)

Hah hah, I'm so careful to cite the right guy, and then spell his name wrong anyway.  See [sic].

That's because I know a Johnny Stallings, a fine actor / director who goes into prisons with Shakespeare.  Many mentions in my blogs.

Crossed wire, as the neuro-folk say.

Re "school as source", yes, I'm a big fan of "place based", meaning you tell history in a way that fans out from where you are, relating things back to the locale.  It's deliberately "centric" and that's OK.  Move somewhere else, and there's another center, as there should be.

Kirby

[Peter Farrell]

I thought maybe Carl Stalling, the genius behind the classic Looney Tunes music, had very modern ideas about software I never knew about!