I have taught kindergartners to measure the length, etc. of objects in
centimeters (an appropriate scale for their age) using a meter stick
marked down to the centimeter scale level (no millimeter marks). I also
taught them to measure the area of squares and rectangles on
centimeter-gridded paper by counting the squares. They knew and could
verify that the edge of each grid square was 1 cm. I also taught them to
properly record their measurements: 8 cm, 12 cm2 [raised 2], etc. But in
no sense did I teach them exponents, nor **why** we called those "square
centimeters" apart from the obvious fact that they were counting
squares. One class asked why we used "2" instead of another number and I
replied that we measured those squares in two directions: up and across.
There is a technique in education called spiraling. One teaches a bit of
something (often empirically) before the main topic comes up (spiraling
forwards). The main topic then is not entirely "new" when presented. And
after the main topic is taught, one goes back to previously learned
material to tie it together (spiraling backwards). So, what I did with
kindergartners was some spiraling forward. Hey! They can't multiply! How
are you going to teach exponents until after they've mastered that?
Writing cm2 is an accepted shorthand in plaintext emails, John. I
despise HTML formatted email. The more idiotic the messages are that
come into my inbox, the more HTML kerflooies the writers use. I go the
opposite direction. Also, HTML email takes roughly 3 times the bandwidth
that plaintext email takes.
Jim
On 2011-01-02 1341, John M. Steele wrote:
I think second or third grade is too early for a "thorough grounding."
You can probably teach squared and cubed (and symbols for it) for area
and volume. I don't think you can teach higher powers, scientific
notation, etc. at that age. As "zero counting" is stupid, you can't
teach "very large" and "very small" numbers until you teach scientific
notation -- maybe sixth grade, or 7th?
Based on questions at a conversion website, Americans obviously have a
very poor grasp on area and volume (maybe only those with a poor grasp
come to a conversion site with questions).
On the matter of square meters or meters squared, the SI Brochure,
section 5.2, specifies the exponent after the unit, but it specifically
permits (does not require) an exception for area and volume. So meters
squared, meters cubed, seconds squared, etc are preferred, but square
meters and cubic meters are specifically allowed as an alternative.
I noticed you had a real superscript on m², but as other people replied,
it was stripped and became m2. Is that an html superscript? It may have
been stripped to plaintext. I use Alt-0178 to get the small superscript
2 from CharMap.
------------------------------------------------------------------------
*From:* Paul Trusten <[email protected]>
*To:* U.S. Metric Association <[email protected]>
*Cc:* [email protected]; [email protected]; "Gentry, Elizabeth"
<[email protected]>
*Sent:* Sun, January 2, 2011 11:40:24 AM
*Subject:* [USMA:49395] powers of ten--becoming an exponent proponent
The previous discussion of Zimbabwe currency in the article in question
(http://news.yahoo.com/s/ap/20110102/ap_on_re_af/af_zimbabwe_numbers_game )
reminded me that part of our problem in accepting metrication in the
U.S. is that we Americans are not yet proponents of exponents. We tend
to limit the teaching of exponents to a small part of our mathematics
education and don't apply that education to the practical subject of
measurement. When I stop to consider the metric system, I sense that I
am returning to eighth-grade algebra, when I should have learned
something about exponents /much/ earlier than that. At least to me,
facility in exponential notation makes the meanings of the SI prefixes
easier to understand and manipulate.
I don't know what it's like in metric countries, but, here in the land
of the foot and the mile, even the simplest application of exponents in
connection with SI falls on innumerate ears. For example, in pharmacy I
have yet to hear one of my colleagues look at the symbol m^2 and
pronounce it "square meter." They will pronounce it "meters squared,"
which may be good as an exponential statement but, I think, bad as a
measurement unit. Some (usually outside of pharmacy) can't even get that
far, and will state a dose of 50 mg/m^2 as "50 milligrams emm two,"
reading it out to me with difficulty, not knowing what it means.
Pharmacists use common sense and can interpret, based on the drug being
ordered, that 50 milligrams per square meter is what was meant, but if
two people are communicating purely on the basis of the expression being
used, with nothing else to refer to, who knows? From the resulting
confusion, we may get a medical Gimli Glider.
I remember, in the fourth grade (which, for me, was 50 years ago),
learning "decimal places," and learning the "millions place" and the
"thousands place," but at that time, those places were never connected
to the concept of bases and exponential notation. Had that been done for
us,I think we could have adapted to the metric system the very next day
and become metric citizens.
As I mentioned, I haven't been in the fourth grade for 50 years, and the
timing of the study of exponents may have changed since then (big grin).
I'd be interested in what the teachers on this list think of the above.
So, my question is:: to what extent do you think a thorough grounding in
exponential notation in the early years of mathematics education (2nd,
3rd grade?) would improve the ability of the U.S. to go metric?
Paul T.
--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
(C) 931.212.0267
(H) 931.657.3107
(F) 931.657.3108
