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Topic: Concrete to abstract in dividing fractions?
Replies: 8   Last Post: Aug 24, 2014 12:26 PM

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kirby urner

Posts: 3,690
Registered: 11/29/05
Re: Concrete to abstract in dividing fractions?
Posted: Aug 24, 2014 10:59 AM
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On Sat, Aug 23, 2014 at 3:26 PM, Robert Hansen <> wrote:

> On Aug 23, 2014, at 5:49 PM, kirby urner <> wrote:

> > A lot of us believe in spiraling. I often cite John Saxon as a master
> spiral-er and promulgator of the concept.
> >
> > So early on, the grand scheme of N < Z < Q < R < C should be unveiled.

> See the staircase before you climb all the stairs. Preview. Heads up.
> >
> > This is versus "heads down" curricula which just say: trust us, you'll

> see a bigger picture someday, in the meantime just listen to us and focus
> on that next step.
> The way I see it, and I am in a position to see it, the reason our
> graduates are having so much difficulty competing against foreign graduates
> in the STEM space is that they cannot do the work. After three decades of
> making math more interesting, the result is, our students aren?t even in
> the game anymore.

I recall that professor at Willamette University (Salam, Oregon) saying
"Intel can find only 19% of its qualified people from Oregon and
Washington". That might be a misquote actually, as maybe she just said
Oregon. I doubt she said "Cascadia" although that's common enough to say
and show the flag of out here. Portland has a flag too. I suppose most
cities do? Where's the visual database for that one then? Here we go: in
the US: (you'll find pages
for cities grouped by country on other pages too)

Anyway, my point is the same as yours: a lot of well paying techie jobs go
vacant out here, and no one really qualifies. Either they rewrite the job
description or someone finally gets it from far away and moves here,
swelling the population with techies and their kids.

However, next time a vacancy goes up, it may get filled more quickly by a
local techie. She was from India the first time, but having moved here
with her family, she counts as a local when she power-shifts to a startup
or whatever.

Hey, did you know some of those pulling up stakes in Afghanistan (I'm
talking about "the troops" that are coming home) are choosing Portland as
their next destination. They count as "not from around here" but do have
American citizenship already, for the most part. I've gotten to know some
of them.

> There is no ?versus heads down?. Even if injecting future notions is a good
> thing, and done correctly it is, in order to capitalize on any of it, you
> have to have heads down. You have to do the work. There is no easy button
> to play an instrument, nor is there an easy button for mathematics.

It's not either / or. I'm not advocating for "only heads up" or "only
heads down" but a combination of both -- it's a spectrum.

Right now, we're into dumb little exercises with mostly silly math with
superficial STEM layers.

We've farmed out the curriculum to mass publishing and have this 1900s
concept of "textbook" that's just silly, is all I can say -- maybe not to
start, but how we still cling to it. Our farcical "schoolish habits" are
worthy of parody for sure (but it's hard to tell sometimes where the parody
leaves off the the reality begins).

> It has become far too acceptable for teachers to shy away from the heads
> down work and the tests that goes with that and instead spend their time
> making mathematics interesting. It has also become far too acceptable to
> have so many kids in classes that they have no business being in. You
> shouldn?t be in algebra if you can?t do arithmetic and you shouldn?t be in
> calculus if you can?t add two fractions.
> You are just very late to an experiment in math education that has been
> going on for 30 years.

I think I'm not making the same proposals as many in the "math reform
biz". I'm not just adding my voice to the chorus. My Buckminster Fuller
focus, for example, my underlining of polyhedrons so much: that's not in most
of the journalism I see. I'm too esoteric for the NYT if not the
Washington Post (I was actually written up in the Oregonian a couple times,
as a local area "futurist").

I talk about how 'Sesame Street' was a big step in the right direction, as
was 'Donald Duck Visits Magic Math Land' (another Donald). My "teachers"
tend to be characters like Big Bird, who won't share anything about complex
numbers with the little dears. No one on the street ever talks about Phi.
But then the Muppets have a large adult following so go figure.

Speaking of 'The Muppets', they were on the marquee yesterday, where I saw
'To Be Takei' (about the guy behind Sulu on Star Trek).

> Make math more interesting and less hard.
> The results were horrible.

I don't think they succeeded in making it more interesting.

That Time-Life book, Mathematics, now that was pretty interesting. A lot
of trade books are interesting.

But textbooks tend to be boring by their very nature, unless you stock the
classroom with hundreds and routinely grab one to mock its treatment of
something. Ridiculing textbooks is lots of fun, have the kids see how
poorly it communicates concepts, speak extensively of the idiocy of the
adults in that era of history. Show lots of 'fails' like on Youtube,
featuring silly adults and their antics (e.g. their sloppy handling of
radio-toxins). And now lets laugh at how they taught math! ROTFLOL! *Of
course* they behaved like bozos, with textbooks like *that*!

> And I am not sure at this point there is a way out of this mess for public
> schools. Even if your idea of doing coding in school was good, you and I
> know that they would do it stupidly. They were strip of all talent and do
> it as a rote hands on activity so that everyone can do it and then claim to
> be against rote.

> And what you suggest is not spiraling, but you know that.

I think developing a "type sense" as one moves into numbers, as well as
retaining a sense of "the string type" (such as the paragraphs of whatever
they're reading) and its being formatted into a "document" (segue to DOM,
XML, CSS, HTML) is appropriate for elementary school kids.

Start marking up with HTML as soon as you've learned some typing. How
early to teach touch typing, that is the question. All drag and drop
visual programming needs to go lexical at some point. All graphical and no
lexical is no better than all lexical and no graphical.

True, a lot of CS-unfriendly teachers have no clue what the DOM is, and
school is a lot more about employing adults than teaching children, I think
we all know that.

That's why I'm not only focused on "school" as an institution, as distinct
from the broader cultural process of transmitting skills and information,
what we call "the education process".

However I am focused on schools too. They're important and need remodeling
as a concept, along with physical upgrades and liberation from the


> Bob Hansen

Message was edited by: kirby urner

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