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Re: "Proper" scientific notation





On Mon, 9 Mar 1998, Daniel L. MacIsaac wrote:

My students also think 10e3 is the same as 10^3; they do this all the time.
They also think sin^(-1) is the same as ArcSin of a number. Since they
only rarely invert the sine function (except possibly for critical angle
calculations in Total Internal Reflection) in my course.

I think all we can do is teach the difference explicitly; the
calculators have all standardized on misleading terminology and we have
to cope with the fallout.


You can see why. On many calculators the way you enter 4x10^3 is to key

4 (key labeled E or worse, EXP) 3

So the students aren't thinking beyond the keystrokes.

There's the crux of your problem. If you want to address student
difficulties, first find out what students are *doing*, which may tell you
what they are *thinking* (or not thinking) then find a way to encourage
effective thinking and block the ineffective habits.

If left to their own devices, students will rely on rote memorization,
blind procedures, plug-and-chug, ill-formed concepts, and inadequate
visual models. Students will go to incredible lengths to avoid thinking.
And if we, as teachers, give homework problems and exam questions which
can be "successfully" done by these methods, we will not encourage
physical thinking. We must exercise great ingenuity to structure our
measures of accomplishment so that all of these "crutches" are blocked
completely, so that a student simply cannot pass the course by using them.
Students *are* capable of the kind of thought we want to encourage, but it
isn't natural to most human beings. So distasteful is it to many that if
we insist upon it, many students will change to "easier" majors. That's
probably why few profs have the courage to insist upon it.

I recall back in slide rule days many physics profs didn't allow slide
rules in exams in introductory courses. The exams were constructed so that
all the math required could be done in one's head or with
"two-significant-figure" calculations. Many of the questions required
algebra or calculus only. Many were mathematical proofs. Perhaps a return
to this policy is in order.

Believe it or not, I've had junior and senior students who've had the
full sequence of calculus ask me "What's a 'proof'?" I recall my student
days in which over half the questions on any calculus exam were proofs. We
now have a population of students who blindly use equations and
procedures, but when asked "What's the proof of this, or what experimental
evidence is it based upon?" they don't know. They don't know where
*anything* comes from, or how one thing relates to another. We need to ask
such questions more often.

It's obvious that even if a good textbook is used, students will skip
anything that looks like a mathematical development, and will skip most of
the supporting verbal explanations to get the the bottom line: the boxed
or highlighted equation. When pressed, you find out they cannot grasp the
supporting math development, or even the verbal supporting material.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Professor of Physics FAX: 717-893-2048
Lock Haven University, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu http://www.lhup.edu/~dsimanek
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