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Re: [Phys-l] Unit Conversions (was Mass and Energy)



There are several problems here. The first one is that students are told
incorrectly that the SI or metric system deals in powers of 10. This is
only true for a few select units. All the others are in powers of 1000 so
the units line up with the way we write number grouped by 3 digits. So
perhaps also grouping digits to the right of the decimal place could help
students. This would also provide a visual cue.

The second problem is that the mix of students you have has a large number
of students who do not understand proportional reasoning. The big symptom
here is getting conversions upside-down. Although this can happen with
students who test positive for proportional reasoning, it is a lot less
likely. One tactic might be to ask a question such as which is bigger micro
or pico, then ask when you convert 10 microxxx to picoxxx will you have
more pico, less pico or the same. If you have a classtalk system, you can
give this as a quick quiz in class. The concept of which is bigger or
smaller should really come before the mechanics of conversion. Only 20% of
HS graduates test OK for proportional reasoning.

Finally you may have some students who do not really understand how numbers
work. I have seen this in HS graduates. They literally can not divide an
interval into 10ths properly and will create phony digits by methods that
show nonunderstanding of numbers. I gave a test on which students had to
read a scale with 20 divisions from 0 to 1.0. Only the ticks for 0, .5 and
1.0 are labeled. The correct answer was .67. Some students put down .533
!!!! Then there are the ones who put down 6.7. Obviously they are treating
numbers as abstract objects which have no meaning. They do not understand
the connection between adjacent digits.

And of course learning units is like learning vocabulary. Unless it becomes
a part of the active vocabulary it will not be remembered. Students need
connections such as measurements and mental pictures.

Metric might be helpful because then the metric units would also be used in
"real" life and would not be as disconnected to reality. At one time
studies found that US students had a better understanding of fractions
because they were taught how to read fractions of an inch and had to measure
things correctly using this technique. But they found that European
students had a better gasp of decimal numbers. Now the better US
understanding of fractions has gone away. I would propose that students
should be required to take a good shop course in HS. This would prepare
them much better for physics than the usual physics course. It is too bad
that Philip Sadler did not ask about shop courses in his survey that showed
that HS physics courses had only a small effect on college physics outcomes.

John M. Clement
Houston, TX



Anthony Lapinski and Bernard Cleyet have commented on the failure of the
USA to go metric, thereby forcing students to spend time on unit
conversions and distracting them from the physics. Ludwik Kowalski
commented that he considers units consisting of an SI unit prefaced with
a multiplier such as centi-, kilo-, milli- are still SI units.

The "metric system" does not solve the problem, and centimeters,
picofarads, kilometers are not SI.

It was implicit in my original post that students have difficulty
converting from milliseconds to seconds. They find this every bit as
difficult as converting from inches to meters. You may say, yes but at
least the ms-to-s conversion doesn't require the students to look up a
conversion factor. I wish that were true. There are two problems. (1)
Even though I tell students to memorize the power-of-ten prefixes from
pico to tera, and I tell them the names, abbreviations, and numbers will
be on the first exam, over half the class will miss some of these on the
exam. One or two weeks after the exam it is almost as if I never told
the students to learn these. (2) Even if the student remembers that
milli is one-thousandth rather than one-millionth, they still have
difficulty in a conversion as to whether they divide by 1000 or multiply
by 1000. Moving the decimal point is no more easy than multiplying or
dividing by 2.54 cm/in.

I am sad and embarrassed to tell you that I mostly deal with college
sophomores taking calculus-based physics. These are biology, chemistry,
physics, computer science, pre-med, pre-science-teacher students. They
absolutely cannot do metric-to-SI conversions any more readily than
USA-to-SI.

Here is an example...

Using a movable-plate parallel-plate air-dielectric capacitor they
measure capacitance in picofarads as a function of plate separation in
millimeters. They plot capacitance as a function of inverse-separation
to get a straight-line plot with slope of [plate-area times
permittivity-of-air]. Of course in SI units the permittivity of air is
about 8.85E-12 farads-per-meter. The slope of their graphs, if they
keep their data units, has units of picofarad-millimeters. They measure
the plate diameter with a calipers reading centimeters, so their plate
area is in units of square-centimeters. The permittivity is slope
divided by area, and their result comes out in units of
[picofarad-millimeter per square-centimeter]. How many students can
convert this to farads-per-meter without my help? In the second
semester of their sophomore year, fewer than half of my students can do
this without a trip into my office to help them find out why they are
off by several orders of magnitude. It is truly sad.

What's the problem? (a) forgetting that pico is 10^-12, milli is 10^-3
(rather than 10^-6), centi is 10^-2 (rather than 10^+2), centimeters^2
would be 10^-4 meters^2 rather than 10^-2. (b) mixing up division and
multiplication; that is, multiplying by an upside-down conversion
factor.

Perhaps worse (more comical?) is the student who has poor data, does the
unit conversions correctly, gets a permittivity of 1.02E-11 F/m, and
wants to know why they are off by a factor of ten.

Anyway, "going metric" won't help this kind of problem.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu


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