>In some ways the wrong people are writing textbooks. The way=20
>the game is played now, a math professor writes a textbook based=20
>upon what they know and how they have been trained.
Right, which means what you learn from this textbook may be=20
most useful to you only if you plan to become a math professor=20
in the same tradition. Students shouldn't necessarily be=20
switched to a vocational or trade school track so early in=20
their careers.
>If you want a book of practical applications, go out to business and
>industry people, actuaries, engineers, architects and so forth and ask =
them
>"What math do you actually use and what problems have you had to try to
>solve?"
>
>Then ask them "Can I use this material in a textbook?"
Yes, something closer to this would be a better approach.
=46or example, I use Standard Query Language (SQL) almost daily.
It has elements of boolean algebra, depends on knowing stuff
about Venn diagrams, understanding unions and intersections.
Databases are a huge part of modern life. Banking, ticketing
and reservations, medical records, insurance, geographic=20
information systems (GIS) -- all databases behind the scenes.
So here we have a golden opportunity to make some links. =20
Here's Johnny, learning all that truth table stuff (if p
then q), Venn diagrams, unions and intersections. So=20
lets show him how to write at least some simple SQL e.g.:=20
SELECT last,first ;
FROM students ;
WHERE gradelevel =3D 6 ;
ORDER BY last,first
Then we should go on to explain (perhaps in a video --=20
I'm a big believer in using multimedia, even for homework)
what databases are, how SQL is used in the real world. =20
Even if you don't do lots of kill and drill, you should=20
have at least "for your information" exposure to concepts=20
like: record, field, primary key, rules of normalization.
You could cover the above topics in a day or two at the=20
junior high level. Keep it light. No flogging.
Like, a 10th grader should be able to read an article=20
such as the one cited below (re databases etc.):
http://www.fcw.com/pubs/fcw/1999/1018/fcw-agdia-10-18-99.html
and at least semi-comprehend it -- because in math class she=20
or he learned a little about XML, what it's all about (how
it relates to HTML, SGML and so on).
One might say "oh no, this is all too slanted towards high
tech and computer stuff, isn't 'traditional mathematics'
the way we understand it at all".
To which my response is "precisely so, and K-12 is about=20
absorbing a lot of generic numeracy/literacy about how the=20
world works, the way symbolic processing, both numeric and=20
alphanumeric, supports our shared infrastructure. Math is=20
a skeleton key that unlocks many doors, 'makes the invisible=20
visible' as Keith Devlin likes to say. A math teacher's=20
job should be to make sense of that big world out there,=20
using mathematically-informed concepts. You're a story-
teller, an explainer, not just some drill master, and not=20
too proud of your 'abstract thinking abilities' to ever=20
bother with the 'real world' in any substantial way=20
(phoney applications don't count)."
Here are some paragraphs from my article in the March 1999
issue of FoxPro Advisor (Advisor Communications, Inc), which
well summarize where I'm coming from (I've probably posted
them to this list before -- apologies):
=3D=3D=3D
Math makeover in the Silicon Forest
I live in Greater Portland, the Silicon Forest. Intel,
Tektronics, Hewlett-Packard, and Symantec all nest in this
area, and Microsoft, near Seattle, isn't far away.
The high tech sector is now Oregon's biggest employer.
Oregon is like an oil-rich state on the Persian Gulf,
except our wealth, being know-how, is more invisible --
and more renewable.
I bring up matters economic to give some background as=20
to why a "math makeoever" might be taking hold here out
of necessity. Our employers need computer literate,=20
fast learners who aren't math phobic. But then, what=20
is mathematics exactly? Judging from your average=20
textbook, it's pretty much what we remember from our
own K-12 careers (arithmetic, geometry, algebra, and=20
calculus). But open a VFP manual and you see operators=20
like DTOT(), ASORT() and PACK. More than just number=20
crunching or even algebraic manipulation, our business=20
world needs full-fledged symbolic processing.
Business rules pertain to alphanumeric, not just numeric
content, and our character sets are becoming increasinginly
international. Nor is it just businesses that need large
data tables, relational structures, and class hierarchies.
Scientists and engineers work with the same tools. So
why postpone much significant exposure to all of this=20
content until college? Why aren't we teaching VRML,
XML, and SQL in eight grade? Certainly, many students
are ravenous to learn this stuff, but when do their
teachers have time to learn it all themselves?
=20
=3D=3D=3D
=46rom: Success Story: Teaching Object-Oriented=20
Programming with Visual FoxPro, FoxPro Advisor,
March, 1999 pg. 53.
>> ----------
>> From: urner@alumni.Princeton.EDU[SMTP:urner@alumni.Princeton.EDU]
>> Reply To: urner@alumni.Princeton.EDU
>> Sent: Wednesday, October 27, 1999 2:15 PM
>> To: mathedcc@archives.math.utk.edu
>> Subject: Re: [MATHEDCC] Why Johnny can't do math
>>=20
>>=20
>> "Cohen, Deborah" <dcohen@jt.cc.va.us> wrote:
>> >separate somehow from the calculations). Also, have you looked =
lately at
>> >the majority of these word problems - they are contrived, dull =
problems=20
>> >that
>>=20
>> Indeed. Contrived. Dull. That's it in a nutshell.
>>=20
>> >it is stupid!! If we can't come up with more realistic problems to=20
>> >justify some of the skills we're teaching, we have to begin to ask=20
>> >ourselves if these skills are necessary). After being fed a steady=20
>> >diet of this kind of=20
>>
>> Agreed. Too much of the math we teach is just the math you need to
>> be a math teacher. That's a very specialized approach. =20
>>=20
>> Curriculum writers need to do a better job of working backwards from
>> the actual challenges facing people in different walks of life, where
>> math applies.
>>=20
>> >them to think that word problems that involve calculation are =
frequently
>> >stupid, so they don't recognize a real-life sort of reasonable =
problem
>> >when they finally see one. =20
>>=20
>> Good point.
>>=20
>> >important as others - one quick example - when I started teaching 10
>> >years ago, teaching interpolation for trig and logarithmic functions=20
>> >was thought to be sacred - fortunately, $5 calculators finally made=20
>> >folks realize that interpolation is no longer a necessary skill to=20
>> >teach). =20
>>=20
>> Exactly. Lots of material is dead weight, carried forward in time
>> only because the teacher knows how to do it, and so thinks this=20
>> must be critical knowledge to pass along. But teachers need to be
>> students forever. Always say to yourself: "there's some very=20
>> critical, important mathematics out there which my students=20
>> really need today -- and I don't yet know it myself, but I plan to
>> learn it and share it, because that's my job, and I'm good at my
>> job."
>>=20
>> Kirby
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