Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Education » math-teach

Topic: Math Wars Philosophizing in the NY Times
Replies: 67   Last Post: Jun 28, 2013 11:06 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
kirby urner

Posts: 1,704
Registered: 11/29/05
Re: Math Wars Philosophizing in the NY Times
Posted: Jun 20, 2013 1:00 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
att1.html (6.6 K)

On Thu, Jun 20, 2013 at 6:51 AM, Robert Hansen <bob@rsccore.com> wrote:

>
> Devlin's argument isn't against teaching any particular arithmetic
> algorithm. He is against all of them. Sure, introduce an algorithm,
> whatever it is, but dare not teach it long enough that the student develops
> a personal fluency with arithmetic. Heavens no. That would be a total waste
> of time because we have machines that can add and subtract.
>


When Devlin came to Oregon for our ISEPP-organized "math summit" in 1997,
his schtick was not against teaching basic arithmetic but against
compartmentalizing the teaching of arithmetical algorithms such that only
"math teachers" or "math classes" bore the brunt, while none of the other
subject teachers had to spend much time on it, and just assumed "the math
teachers" were doing their job. [1]

In point of fact, elementary schools are largely taught by all-subjects
teachers which gives students more continuity. Or maybe they have "home
room" teachers yet go from room to room more like in high school.
Compartmentalization is in the architecture, but there's still lip service
around inter-disciplinary integration (in some schools -- I'm sure that's a
dead end in others).

But when it comes to basic arithmetic, Devlin's contention was basic
numeric literacy is something all teachers should gang together and diffuse
through the entire curriculum, not concentrate in one corner under the
heading of "math" in particular, as if "math" were no more than
"arithmetic" (that still confuses people).

Part of the point was to drive home that these are basic skills common to
all adults and NOT stereotypically relegated to one walk of life or
another. Arithmetic is our common heritage. Airline pilots, chefs,
accountants, doctors, nurses, pharmacologists, bus and taxi cab drivers,
farmers, business managers, disaster relief workers, environmental
monitoring workers, zookeepers... all need to add, subtract, multiply,
divide, and sometimes take a log, raise to powers.

Geography / geodesy should come with plenty of trig (doesn't have to be
spherical -- when you zoom in enough it's locally planar, with triangles =
180 degrees). Geography includes demographics, ecology, rates of change.
Geology includes exponential rates of decay, the concepts of half life etc.

My core heuristic (on MathFuture mostly), some may remember, is Geometry +
Geography as the two basic subjects. Under Geometry comes all mathematics
irrespective of empirical concepts and measures and under Geography comes
all physical phenomena, from subatomic to astronomic, humans somewhere in
the middle (scale-wise).

History could be taught with great attention to numbers systems and
engineering. UCSC's Ralph Abraham (mathematician) was of the same mind
(also at said summit).

For example, back to the "cooking / following a recipe" meme: if you're
doing problems around home economics and budgeting, talking about how much
rice to buy or the average rate of bean consumption, then you've got
(a) units of measure
(b) prices
(c) time and rates of change.

Why not take this opportunity to dive into all the operations necessary to
(a) compute the monetary cost of serving 30 people X, Y and Z
(b) compute the calories, proteins etc.
(c) develop a budget for the next six months, in terms of stores needed
(d) compute the energy costs in terms of joules through the meter

(in South Africa, food energy values on the labels are in joules as well,
not calories, which helps students make the connection between the energy
they burn in their bodies from food, and the energy the import through the
wall sockets).

You can do a lot with computer games and simulations at this point.

'Oregon Trail' is / was popular, because you needed to buy and sell stores,
negotiate for supplies.

But this could just as well be "history" or "economics" as "math".

Fast forward: I think we're closer to Devlin's vision today, in that STEM
is about countering over-specialization and over-compartmentalization. My
own contention is once within the purview of STEAM (adding anthropology)
it's not so important to decide "exactly which" subject is being studied at
any given moment. Is this technology or mathematics? Is this engineering
or science? These need not be considered useful questions.

I would be happy to see "math class" and "math teachers" disappear all
together in some experimental curricula, in favor of STEM as a holistic
network of topics and skills. The idea of "math class" as a completely
divorced subject may be convenient for administrators, but it churns out
adults with less integrated thinking and a weaker grasp on academic
subjects in general (this would be my contention).

Of course in my overview synoptic comments here, I'm embracing more than
just elementary school, during which the basics should be learned.

I was doing multi-digit addition in 3rd grade at Junior English (Rome) and
having Narnia by C.S. Lewis read to me by the same teacher.

In Manila, our Introduction to Physical Sciences teacher did a lot with
scientific notation and decimal points, logs and exponents. Looking back,
I see that's how it should be: science teachers teaching math.

Physics needs vectors and should teach vectors.

In the smarter / better curricula of tomorrow, I'm guessing we'll see
far less artificial fragmenting into "different subjects". We'll be
content that it's STEM and not worry about the subcategory.
Over-specialization was taken way too far in the 1900s and we paid an
enormous price. Devlin's vision is not out of line with my own in this
respect.

Kirby

[1] http://www.grunch.net/synergetics/mathsummit.html
(Oregon Math Summit,
1997)


Message was edited by: kirby urner


Date Subject Author
6/17/13
Read Math Wars Philosophizing in the NY Times
Joe Niederberger
6/17/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/17/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/17/13
Read Re: Math Wars Philosophizing in the NY Times
Clyde Greeno @ MALEI
6/17/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/17/13
Read Re: Math Wars Philosophizing in the NY Times
Domenico Rosa
6/18/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/18/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/18/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/18/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/18/13
Read Re: Math Wars Philosophizing in the NY Times > K-calculus
Clyde Greeno
6/18/13
Read Re: Math Wars Philosophizing in the NY Times
Joe Niederberger
6/19/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/19/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/18/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/19/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/19/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/19/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/19/13
Read Re: Math Wars Philosophizing in the NY Times
Dave L. Renfro
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
Richard Strausz
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
W. Stephen Wilson
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/22/13
Read Re: Math Wars Philosophizing in the NY Times
W. Stephen Wilson
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
Joe Niederberger
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
Joe Niederberger
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
Joe Niederberger
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
Joe Niederberger
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/20/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Joe Niederberger
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Joe Niederberger
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Robert Hansen
6/22/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
Joe Niederberger
6/22/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/23/13
Read Re: Math Wars Philosophizing in the NY Times
kirby urner
6/21/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/24/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/24/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/24/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/24/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/25/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/26/13
Read Re: Math Wars Philosophizing in the NY Times
Wayne Bishop
6/26/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy
6/28/13
Read Re: Math Wars Philosophizing in the NY Times
GS Chandy

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.