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Andrew W. (drew) Smith, Phd
02-02-1999, 05:04 PM
Dear All,

I guess this issue is another one of those "you say 'toe-may-toe', I say
'toe-mah-toe'" kind of things. The discussion so far has offered many
insights.

However, there is one important aspect of either way of dealing with
equations and problem-solving in a subject area like biomechanics that I
always try to stress. And, that is the very important final step (Step 6 in
the method I teach - if any of my students/former students remember) called:
Interpret your answer (or "Does it make any sense?").

Even the brightest student or the one with the best memory for equations can
still solve a problem, make a simple calculation error and then tell you at
the end of it all, "the runner's velocity was 198.6 m/s!"

The key is to get both sides of the brain speaking to each other, I guess.

Cheers
Drew
__________________________________________________ ____________

Andrew W. (Drew) Smith, PhD
Assistant Professor
Department of Rehabilitation Sciences
The Hong Kong Polytechnic University
Hung Hom, Kowloon
Hong Kong
Special Administrative Region of the People's Republic of China

Voice: +852 2766 7094
FAX: +852 2764 1435
Mobile: +852 9689 7094
Email Address: rsdrew@polyu.edu.hk
WWW: http://www.polyu.edu.hk/~rs
ICQ: 6164882 Nickname: Daddio
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-----Original Message-----
From: Biomechanics and Movement Science listserver
[mailto:BIOMCH-L@NIC.SURFNET.NL] On Behalf Of Young-Hoo Kwon, Ph.D.
Sent: Wednesday, 3 February, 1999 2:41 PM
To: BIOMCH-L@NIC.SURFNET.NL
Subject: Re: Memorizing Equations

Dear Jared and colleagues:

I've read Prof. Jared Coburn's summary regarding the memorization of
equations issue with interest. It is not a surprise to see that the majority
of people who responded to his posting do not require students to memorize
the equations. I guess it is the trend at least in the US.

I certainly don't intend to argue with others on this matter, but I guess I
can still tell others my side of story once again. Here are some of my
observations in the classroom and my thoughts:

1. From time to time, I see students who simply memorize, from the examples,
the problem solving steps without really understanding the ideas behind.
Even some of the top students do this. In spite of my twisting the situation
a bit in the quizzes, they will still attempt what they have memorized and
eventually screw things up somewhere.

2. I think the concepts and equations are two faces of a coin in many cases.
I don't really see how I can separate them. Equations provide the technical
definitions of concepts, and they really help students to understand things
better. The advantage of an equation over a lengthy definition is that it is
very concise and shows several different aspects quite efficiently. For
example, Newton's second law says "F = ma". This can be rewritten as "a =
F/m". Or "F = 0 --> a = 0" (Newton's first law of motion). One equation
shows three different ideas quite nicely. It is hard to imagine the
situation in which students try to understand the three concepts without
having the common "F = ma" in memory. If students really understand the
basic mechanical concepts, they don't have to consciously try to memorize
equations. Because they already have it. If students should always rely on
the equation sheet for the relationship bewteen "a" and "v", they may not be
able to easily relate "a = 0" with "v = constant" shown in the Newton's
first law above.

3. From time to time, I also observe students using the equations without
knowing the concepts. But they perfectly understand what each symbol in the
equation stands for. Then plug the numbers in the equation to compute the
answer. Hoooo, what kind of problem solving is this? Isn't the real reason
for memorizing the equations to be free from the equations? Relying on the
equations written on a piece of paper each time you try to solve something
must be quite painful. Besides, they are all in the textbook.

4. One more interesting observation. I noticed that my students, without any
exception, always plug the numbers in the equation up front without first
manipulating the equation to obtain a more useful form. I presume this is
the general trend of math education in the US. I was trained to always
pre-treat the equation in such a way that later you get direct answer from
the final form of equation. [ This is partially because of the tough
university-entering exam in my country.] This approach gives a tremendous
advantage. You will be able to learn different properties of the same
equation in this process. It certainly has positive impacts on the student's
learning process.

Anyway, based on my belief I require my students (sophomore to senior in PE
& ExSci) to memorize the equations directly related to the definitions of
the basic concepts while providing them the equations of more secondary
nature. Naturally, I spend a lot of time to explain the equations in
relation to the concepts to encourage them to see both sides of the coin in
the process of understanding the mechanical aspects of human body and its
motion. Frankly speaking, this process is quite exhausting. Does anybody
have a nice and efficient way to ease the burden without sacrificing
students' learning? I would appreciate any philosophical awakening or
suggestions/tips from your experience. Peace!

Young-Hoo Kwon
-------------------------------------------------------------------
- Young-Hoo Kwon, Ph.D.
- The Human Performance/Biomechanics Lab
- Ball State University
-
- Phone: +1 (765) 285-5126
- Fax: +1 (765) 285-9066
- E-mail: ykwon@bsu-cs.bsu.edu
- Homepage: http://www.cs.bsu.edu/~ykwon/
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