I assume John your 3x5 card is - cm (a bit small), mm (way too small), meters (way too big)? You wouldn't be using any other measurement units, would you?
John F-L ----- Original Message ----- From: John M. Steele To: U.S. Metric Association Sent: Sunday, January 02, 2011 8:24 PM Subject: [USMA:49402] Re: powers of ten--becoming an exponent proponent Interesting. I am not advocating html and I agree it often has problems. I do use what symbols I can from CharacterMap (I have a 3x5 card full of alt-codes for the ones I use). I reluctantly accept cm2, only because the number applies to a unit symbol and can't be mistaken. In the absence of real superscripts, I think caret (^) notation is better, cm^2. It is certainly better for powers of 10; 10^80 is clear, 1080 is meaningless. ------------------------------------------------------------------------------ From: James R. Frysinger <j...@metricmethods.com> To: U.S. Metric Association <usma@colostate.edu> Sent: Sun, January 2, 2011 3:04:44 PM Subject: [USMA:49401] Re: powers of ten--becoming an exponent proponent 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 <trus...@grandecom.net> > *To:* U.S. Metric Association <usma@colostate.edu> > *Cc:* usma@colostate.edu; si...@listserv.ieee.org; "Gentry, Elizabeth" > <elizabeth.gen...@nist.gov> > *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
