Again, Stan, I find myself disagreeing respectfully with part of what
you have written.
I do agree with your statement, "Math should support all applications to
help learners in real life." In fact, historically, that is what math
education did in this country. I've just discovered, by the way, that
Ferdinand Hassler wrote a popular textbook on practical arithmetic that
saw some wide use in public schools and colleges (including West Point's
USMA).
But that traditional approach was based on practical math, not modern
topics such as number theory, generalization of units, and so forth.
Children grow from concrete reasoning to abstract reasoning. The
development of an ability to reason abstractly requires the
underpinnings of concrete knowledge, which then serves as the model and
the framework for that abstraction.
Today, many of our ninth graders (perhaps a fourth of them) fail to
reach high school graduation. Those who do graduate often require
remedial education upon reaching college or direct entrance into the
workforce. The areas of education include science, English, and math --
but especially the latter.
At one time, elementary and middle school math classes mostly taught
practical arithmetic. Students learned to use math operations to balance
check books, to calculate percentages, to weigh and measure, to
calculate areas and volumes, to deal with rates, and to do proportions.
Some (such as I) learned even how to take square roots and cube roots by
pencil-and-paper methods. Or casting out nines to check arithmetical
calculations. All high school graduates entered their work lives able to
do the practical math required of them. They could deal with mortgages,
buying paint to paint a room, planting gardens, handling family
finances, shopping intelligently, make change, scaling recipes in the
kitchen, buying cloth for sewing projects or wood for construction
projects, and so forth. Their numerical word problems were the concrete
predecessors to the abstract word problems of algebra courses available
to them in their high school years.
Then came the "new math". Students were taught to use arbitrary units
(beans, paper clips, etc.) in weighing and measuring. They were taught
number theory topics once reserved for upper high school and college
courses. Later, Euclidean geometry gave way to "discovery" geometry,
thus doing away with training in a concrete logic system. High school
courses stopped teaching logarithms (it fell into the "if time remains
at the end of the year" bin) once calculators (with log buttons)
replaced slide rules. This left chemistry teachers the chore of teaching
it in order to explain the use of pH or physics teachers in order to
teach decibel scaling.
I have seen college students (and a few faculty members) struggle with
the simple concepts of the quantity calculus. (See the latest edition of
the SI brochure on this.) One can teach a parrot to repeat phrases but
that parrot's understanding of their meanings is shallow at best. That's
the situation one would be in when teaching measurements in elementary
and middle schools (the main focus of the NMAP) using "any" units. Let's
give them a sound, concrete, and practical math education before trying
to turn our K-8 students into abstractionists.
One of those "new math" graduates, undoubtedly more familiar with beans
or paper clips as units, standing in line ahead of my wife in a fabric
store, asked the clerk, "How many feet in a yard? Four?" And you want
her to have been taught how to convert yards into meters?
Jim
STANLEY DOORE wrote:
The SI should be taught and used in science and other classes where
applications are taught and used. It would be more meaningful. Pure
math should use any units so unit symbols can be factored into
computations, including conversions. Math should support all
applications to help learners in real life. It would have been nice for
the NMP to include something about the SI The SI simplicity since
that's what the NMP panel tried to do in its math education
recommendations.
Stan Doore
----- Original Message -----
*From:* Bill Hooper <mailto:[EMAIL PROTECTED]>
*To:* U.S. Metric Association <mailto:[email protected]>
*Sent:* Saturday, March 15, 2008 2:45 PM
*Subject:* [USMA:40585] Re:
On 2008 Mar 14 , at 5:32 AM, Pat Naughtin wrote:
The NMAP final report did not mention:
the metric system
the International System of Units
metres (or meters)
grams
litres (or liters)
I found litres (spelled "liters") mentioned several times in
examples such as the following one:
For example, the reasoning that “if five people need 12.5 liters of
water for a camping trip, then eight people need 20 liters” would be
accepted as a sensible rule-of-thumb in everyday life.
It almost seems like they are ASSUMING metric will be used so they
don't bother STATING that metric should be used.
Bill Hooper
72 kg body mass*
Fernandina Beach, Florida, USA
* plus or minus a kilogram or so.
--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
(H) 931.657.3107
(C) 931.212.0267
