On Fri, May 14, 2010 at 9:04 AM, Haim <email@example.com> wrote: > Jonathan Groves Posted: May 14, 2010 8:19 AM > >>It is ironic that K-12 science education at least makes >>some attempt to show students how science is discovered >>and how scientists work. But why not mathematics as >>well? > > Jonathan, > > Science, almost by definition, is "hands on". If you have any reason to believe that science education in our public schools is especially effective, please share it with us. If it is not especially effective, why should we consider "hands on" pedagogy in the teaching of mathematics? > > I have given a similar challenge to Kirby Urner. In the past, he has made a big deal of the role of "narrative" in education. I have pointed out to him that there are disciplines, like literature and history, that are nothing but narrative. I am not aware that they are especially effective, either, in teaching K-12 students, and I have asked him for evidence to the contrary. (Kirby has not even acknowledged the question.) >
Note that your above paragraph does not contain a question. When the premise is your "awareness" of this or that, we're somewhat at a disadvantage, unless our "awareness" also counts for something. Some free ranging argument over whether history teaching is effective or not could consume miles of bytes to no avail.
Conjuring the picture of a bored distracted student, tuned out, not engaged, is not a difficult trick.
Anyway, yes, I believe in weaving history and mathematics together, also some philosophy, in general working to integrate across the compartments to improve students' mnemonic access to various timelines, as well as to past, contemporary and possible future concepts.
Anchoring these concepts and developing skills around them requires hands-on exercise and mathematics has always been hands-on in that respect. The nature of the exercises may change, but not the need for interactivity.
When looking at SQL, for example, I talk about "keeping tabs" with tabulation machines. Plenty of history, a lot of it dark and ugly, worth exploring here (I'm out there on BlipTV doing just that, in a talk for math teachers (3 hr workshop) recorded in some Hyatt Regency near O'Hare in 2009).
There's a "how things work" aspect to teaching about tabulation and record keeping, but also a hands on aspect, e.g. import sqlite3 is enough to give cursory access to a simple SQL engine in Python.
Of course SQL isn't part of the Underwood Duddley sequence, or is it? What if we access a store of polyhedra in some relational structure? Venn diagrams, boolean filters... it's all here, both free and open source, just need a teacher with relevant training, perhaps from South Africa or the Philippines. For home schoolers, or just to give the flavor: http://showmedo.com/videotutorials/video?name=1510240&fromSeriesID=151
My detractors say I'm just relabeling "computer science" as "mathematics" and then giving out math credits for what amounts to a shop class. That's sort of right, but then it's an over-specializing bureaucracy that electrifies the fences between disciplines in this way. If you have no access to historical time lines you might not see this.
A graphical novel, tracing recent history of mathematics through Russell, Frege, Wittgenstein, Peano, Cantor, Godel etc., and ending up in computers (Von Neumann) is 'Logicomix: An Epic Search for Truth' by Apostolos Doxiadis and Christos H. Papadimitriou (Bloomsbury, NY: 2009). There's some fictional material in terms of who met whom and how things unfolded, so I wouldn't call this literal history. I like the Athena connection though, given Python (if you know some Greek mythology, you know these icons go together).
Note that I'm no champion of the "reform" tomes routinely trashed by Mathematically Correct. For one thing, those have no mention of the simple whole number volume ratios you might get when using a tetrahedron as unit volume.
This segment needn't dominate but it *does* need to be included, along with ideas about sphere packing. This is just basic training for the imagination, low level like mental arithmetic (call it "mental geometry" if you like).
The payoff, in terms of having stronger spatial geometry concepts, is obvious so I use the presence or absence of this content as a litmus test to rank curricula (one of several).
It's easy to supplement with the missing ingredients of course, so I don't throw away a perfectly good curriculum just because of this one glaring omission (gaping hole).
>>So many students little idea of many of the modern >>applications and modern ideas in mathematics. > > Were you not persuaded by Underwood Duddley, > http://www.ams.org/notices/201005/rtx100500608p.pdf > that there are very few real-world applications of mathematics? >
Underwood Duddley makes the case that the current curriculum is outmoded. He says right at the top that he's talking about the status quo, not the more intelligently designed stuff that I'm talking about.
> Perhaps you and some of your colleagues are confused between "many" and "important". There are certainly important applications of mathematics, but how many such applications are there and, more to the point, how many scientists and engineers are there? Numbers are hard to come by, but I doubt there are even one million scientists and engineers in the U.S. World-wide, 10 million is a pretty comfortable upper bound, I bet. The other 6.5 BBBillion people in the world have, as their highest mathematical aspiration, to be left alone by people like you. > > Haim > Keep The Change >
I think we're all aware of your particular psychology and what makes you tick.
You wish to speak for the worlds billions, have them say "leave me alone, we don't want any of your math education".
That's a self appointed position.
It's just as easy for me to step in and speak for them too: "give us the luxury of being able to study some of this stuff as any lifestyle that makes room for such study is likely not a life of pure toil and drudgery, which is what so many of us experience today -- and we're all the more exploitable given we don't get clued in (and our exploiters would just as soon keep it that way)."
I would take the opposite view of yours for debating purposes: there is only mathematics and nothing but, as every breath, step, utterance, blink of an eye, is a mathematical phenomenon in a mathematical terrain. Those who play lots of computer games (e.g. Sims) already have this sensibility: it's ALL math. Or if you wanna break it into two subjects: Geometry + Geography. The former is everything abstract (including algebra) and the latter is everything physical (including astronomical and subatomic phenomena).
That being said, I'm sympathetic to Duddley's idea that a lot of math learning occurs "on the job". If you look at Spaceship Earth as one Global University (easy to do), then sure, life-long learning is the name of the game (or call it "world game").
We're all perpetually engaged in work / study, no matter what our walk of life. If there's less sitting in rows and columns day in and day out, less of the standard pattern we call "school", that might be a good thing. Less passive staring at screens.
I've been urging an "off your duff" kind of math, with slogans like "math is an outdoor sport" and such.
You could see where I might even sound like a military or para-military recruiter in that respect (National Guard?), as these services are always advertising the technological skills you might get if you sign up with 'em (cryptography etc.).
Again though, I'm concerned about over-specialization and over-emphasis on mass murder as a way of life, especially where North Americans are concerned (it's getting harder to go overseas without receiving stern lectures about so-called "American" corporations). I'd prefer to be seen as a recruiter for the health professions, likewise math intensive (cite Andy McKay's talk about using Python to sort through SMS messages from field clinicians in Kenya).