On Thu, Feb 27, 2014 at 12:02 AM, GS Chandy <email@example.com> wrote:
> The anecdote is not directly about criteria for 'CS-friendly math texts'. > It simply describes an incident from real life how 'problem solving in the > systems context' helped resolve an issue 'related to the application of CS > to real life' - and suggests how the underlying issues here really are: > > i) how to improve/enhance the 'learning+teaching' of math' (and how to > improve/enhance our education systems worldwide); >
Some of the non-educators amongst us may fail, for lack of experience, to distinguish between effective technique, and content.
There's no doubt that Euclid's Method is both a math topic, completely legit, suitable for pre-college, *and* it's embedded in Knuth's 'The Art of Computer Programming' (volume 3 to be precise).
But such overlaps in content do not *require* that we introduce any programming within the math classroom, or "math lab" as the case may be. The simple fact of overlaps, content-wise, Venn Diagram modelable, is not a prime mover of these reforms.
The impetus is not that "the content requires it" so much as "students find a programming language catalyzes comprehension". Writing a few for loops helps you understand sigma notation (capital Greek sigma, used as a summation symbol).
I'm far from the first or only educator to make this observation. I don't claim it's universally true. If you hate typing or have severe dyslexia or... any number of stumbling blocks. Or maybe you find the pre-computer notations perfectly intelligible as is and don't find alternative notations expand your horizons in any way. More power to ya.
The other prime mover is, I think, economic. Forking the existing math track with a CS-enabled branch has been a long time in coming, but I think US Bureau of Labor statistics will support the idea that industries hunger for computational thinkers, whether or not they're super duper power uses of the calculus -- power users of the GNU bash shell are just as needed.
Our technological civilization can afford more than one pathway in STEM studies, with a percentage of those newly CS-empowered rejoining the calculus track, from which they fled as refugees, feeling newly encouraged by their new level of comprehension, brought about by increased integration.
My high school offered stats and trig as elective math subjects (I took both), as well as IB Math (as an overseas school, we catered to the Euro-bound). My daughter's high school has IB Math and AP Math. So now I'm suggesting "CS Math" (the courses could be variously named -- not my goal to control local faculties as they innovatively recombine materials (lots of room for ray tracing / art)).
> ii) how (perhaps) progress in 'i' might lead to or enhance progress in > 'computer sciences' (CS) - and how it might also help us avoid the 'abyss' > lying just ahead for the human race (see below); >
I'm an integrationist, in terms of wanting the disciplines more dovetailed and shuffled together. Every age has its exponents for more inter-disciplinary traffic. That group I mentioned that meets in the Linus Pauling house, we have this motto:
"Science would be ruined if it were to withdraw entirely into narrowly defined specialties. The rare scholars who are wanderers-by-choice are essential to the intellectual welfare of the settled disciplines." -- Benoit Mandelbrot
What I think could lead to the abyss is over-specialization. This was RBF's story in Operating Manual for Spaceship Earth, and I thought he did a good job putting out a credible thesis: the "great pirates" of old, those able to command the construction, staffing and sailing of great ships, had a way of compartmentalizing responsibilities such that no one under them became a direct threat, and that this is what's behind the compartmentalizing of universities.
Once we left the visible spectrum in science, such that human senses were not enough, even the great pirates lost their overview, leaving us where we are today: everyone compartmentalized. It's just a story, a myth, a narrative. You may connect some dots with it.
> > iii) how (perhaps) progress in CS might lead to progress in the > 'learning+teaching' of math - and also how it could help us develop and > design effective education systems as a whole. >
At Winterhaven, a "geek Hogwarts", I used Google Earth a lot on the projector. Instead of Trivium / Quadrivium, my mental model tends to be Geometry / Geography as the two areas of concentration.
Geometry alone is the purely imaginative stuff (metaphysical), Platonic in the extreme, the realm of abstract math even if it isn't geometric (my categories are broad).
Geography adds time and place (time lines, time tunnels, scenarios) and is synonymous with our cosmos, the physical i.e. solar system, galaxies etc. (what Hubble sees -- I trained the Space Telescope Institute people in Python once -- now they've got someone full time doing Python).
Google Earth gives you this KML markup language, an excuse to discuss markup. Not for days and days. Giving the 10000 foot view falls under the "how things work" category. We share a little about HTML / CSS (topics Robert mocks as being unworthy on a math track, never mind MathML and LaTeX), just as we share a little about how the internal combustion engine works, or the jet engine: because this is the world they live in.
There's this knee-jerk thinking around math classes, because they're taught so vocationally (it's all about "exercises"), that if you mention a topic you must immediately dive in. I'm all for "hands on", but what about "judicious use of time"? Share lore.
Storytelling is about learning from the past, not acting it out verbatim. Share about the history of mathematics, computing, navigation, measurement -- without necessarily reliving it. Example: no you *don't* have to learn how to manually interpolate logarithms using a table in the back of the book -- yet we're at liberty to show you how that was done, for historical perspective, even as we show you the slide rule, and how it turns multiplication into addition (n * m = 10**a * 10**b = 10**(a+b)).
Planet Earth is not exactly spherical as you know, but it's ball-like enough to create a segue to spheres more generally, and polyhedrons: how they pack; how they subdivide (voronoi cells etc). That's where the number series 1, 12, 42, 92... comes in, featured elsewhere in this thread. Completely accessible to high school level students, including the proof. Dr. Coxeter told the New Yorker he thought that was a nifty formula (10*F*F + 2). It also appeared in the New York Tribune.
Here's a link to that Winterhaven course, which was for nine weeks once a week as I recall. I had the whole 8th grade (but not my daughter, who was in an earlier grade at the time).
Thanks for the anecdote which follows. I think I should put DemocracyLab.org in touch with your web sites, if you have any currently in existence. Or post a link to whatever PDF you think best summarizes how your thinking / practices support the values of democracy.