View Full Version : Summary of Replies: Memorizing Equations

Jared Coburn
02-02-1999, 06:28 AM
Hello Biomch-L-ers

Several days ago I posted a message to the list regarding the
memorization of equations for an undergraduate biomechanics course in
human movement. The responses have been very thought provoking and I
would like to share them with the list.

It is interesting to note the differences of opinion on this issue, and
although I have not been totally swayed one way or the other, I am happy
to see that others are also giving the matter careful consideration.

Here is my original post, followed by responses received to date. I will
follow-up with another post if more responses come in.

Original Post:

On Fri, 29 Jan 1999, Jared Coburn wrote:

Hello Group,
I'm hoping some of you can offer some insight into your philosophy
regarding memorization of equations for undergraduate biomechanics of
human movement courses. Specifically, I'm interested in knowing whether
or not you require your students to memorize equations for velocity,
acceleration, angular velocity and acceleration, Newton's Laws of
Motion, moment of inertia, etc., for exams.
Thank you in advance for any insight.

Jared Coburn
Assistant Professor
Department of Kinesiology
California Baptist University
Riverside, CA 92504
(909) 343-4298



From: Joann Johnson
To: Jared Coburn

After doing this for forty five years now, I have come up with what has
worked best for me for undergraduate human biomechanics applied physics.
I let them make a "cheat sheet"....they can write anything they want to
one 8 1/2 by 11 sheet of paper. Anything. This always includes
formulaes. It motivates each student to make one of these cheat sheets,
and in writing almost everything down in the most miniscule writing or
smallest fonts imaginable, requires them several hours of
time....well-spent.... getting ready for the test.

Another thing I have tried recently, is to allow them to work in pairs
they prepare for the testing and actually take the test in pairs. I
thought I would do something like this, but test scores have risen
dramatically and I see a lot of good things happening because of this,
too. No one wants to be "carried" or be a "carrier"...lots of pressure
each student to be an equal partner. This is optional, of course. Some
just do better by themselves.

Good luck in teaching this fascinating discipline!


Joann Johnson, PhD Phone: 1.218.726.8530
Professor of Physical Education 1.218.724.7256
SPHC 107 UMD Fax 1.218.726.6243
Duluth, MN 55812-2496 email:jjohnso6@d.umn.edu


From: John Chow [j-chow1@uiuc.edu]
To: Jared Coburn
Re: Equations for Undergrad Course

Students in my biomechanics class do not need to memorize equations.
they are required to know how to apply equations to solve problems. I
Hay's book (The Biomechanics of Sports Techniques) for my class and
students are allowed to bring a xerox copy of Appendix B (Equations) to
exams. I even let them bring a copy of Appendix A (Elementary
Trigonometry) if they find it helpful during the exams.

John Chow tel:(217)244-3987
Department of Kinesiology fax:(217)244-7322
241D Louise Freer Hall e-mail:j-chow1@uiuc.edu
960 S. Goodwin Ave., MC-052 http://www.kines.uiuc.edu/
Univ. of Illinois at Urbana-Champaign
Urbana, IL 61801


From: N.FOWLER [N.Fowler@mmu.ac.uk]
Re: Equations for Undergrad Course

I took a philosophical decision a number of years ago that memorizing
equations was unimportant in the context of the learning environment.
What you need to question is what are you trying to achieve through
your courses - If remembering the equations is central to the
achieving your learning outcomes then I guess that you need to assess
this in the exam. However, I suspect that your intended learning
outcomes are more directed towards the understanding of the
principles and the ability of the student to solve problems - The
equations afterall are only tools for solving problems !!!!!

Therefore I teach my students about what the principles are and how
to go about applying these principles and laws to understanding the
context in which they are working. If you like a problem or
application driven approach. When I examine the students I allow them
to bring in any equations they which because what I want to know is
can they use them to answer questions. Those who have remembered them
can work quicker by not having to look things up.

What I have found is that students gain a greater understanding of
the biomechanics with this approach. They concentrate on what the
equations mean and how the laws can be applied rather than focussing
upon learning equations by rote, leaving no time to learn the
important stuff.

Dr Neil Fowler
Senior Lecturer in Sports Biomechanics

Dr Neil Fowler
Dept Exercise and Sport Science
Manchester Metropolitan University
Hassall Road

Tel 0161 247 5466
Fax 0161 247 6375
email N.Fowler@mmu.ac.uk


From: James Dowling SMTP:dowlingj@mcmail.cis.McMaster.CA]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 2/1/99 12:10 PM

Hello Jared,
I require my undergraduate students of biomechanics to memorize several
formulae of mechanics like the ones you mentioned in your posting. My
reasons for requiring this is my belief that this makes them much better
kinesiologists even when they are not making calculations. For instance,
knowing that kinetic energy is one half mass times velocity squared
allows intelligent decisions to be made about work and energy. Without
making any calculations, it is obvious that the amount of work required
to produce a movement is proportional to the mass of the object and very
sensitive to the velocity since that term is squared. My students would
know that a modest increase in velocity will require a large amount of
work and could advise a client of such a fact without having to look it
up. Mechanics is not very intuitive by nature and what seems to be
common sense is often mechanically incorrect. The best defence against
saying something wrong is to have a firm grasp of the fundamental laws
and this means having them with you at all times (i.e. memorized). I was
a delegate at a biomechanics teaching symposium in Texas a couple of
years ago and some of the American delegates were advocating a strategy
that tried to avoid as much mathematics as possible in the teaching of
undergraduate biomechanics. There were various reasons stated ranging
from math not being necessary for understanding mechanical principles to
inadequate backgrounds to deal with mechanics in a mathematical sense.
One delegate thought that teaching math only confused the students and
actually prevented a good understanding of the principles. My position
was opposite and I tried to present a method that would allow
instructors to go straight at the mathematics and present it as a hurdle
that can be cleared by all students regardless of background. In the
business world there is a very fine line between sounding like you know
what you are talking about and actually knowing what you are talking
about. However, as soon as decisions have to be made and consequences
have to be paid for being wrong, it is not long before those who
actually know what they are talking about reap the benefits from their
correct decisions or avoid the consequences of poor decisions. If your
students are going to be involved with exercise or rehabilitation
devices or making clinical decisions about human movement, it will not
be long before they are discovered to be "talkers" or a "knowers".

Jim :-)

__________________________________________________ _________

\ /| Jim Dowling, Ph.D. |\
| , , |
| / |_ . Associate Professor . _| \ |
|/ |_ Department of Kinesiology _| \|
/ McMaster University \
/ Hamilton, Ontario L8S 4K1 \
/ (905) 525-9140 Ext.23572 \
\ Fax: (905) 523-6011 /
| Ask an inappropriate question to get an appropriate
answer. |

|_________________________________________________ ______________________


From: Juan C. Garbalosa [SMTP:garbalosa@uhavax.hartford.edu]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 2/1/99 12:46 PM


I do not in my course.


Juan C. Garbalosa, PhD, PT
Assistant Professor
Physical Therapy Program
University of Hartford
200 Bloomfield Avenue
West Hartford, CT 06117
Phone: (860) 768 -5371
Fax: (860) 768 - 5244
email: garbalosa@uhavax.hartford.edu


From: Butcher, Monique [SMTP:mbutcher@mail.barry.edu]
To: 'Jared Coburn '
RE: Equations for Undergrad Course
Sent: 2/1/99 8:48 AM

Jared -

I teach an undergraduate kinesiology/biomechanics course of juniors and
seniors. There is also a laboratory section with the course. I do have
them memorize those formulas you mentioned - we work with them so much
in homework assignments and laboratory sessions that I suppose I'm
hoping that it's not just a measure of memorization. Plus, on the exam
they need them to solve problems. One thing I have done with some of
the more complex equations (not those that you listed) is have 5 or so
points of matching, where the equations are on the left and the
variables are on the right (I do not make up any mock equations to throw
them off). Then, only those equations will be used for the next 5 or so

Hope this helps.

G. Monique Butcher PhD ATC
Assistant Professor
Sport and Exercise Sciences
Barry University
11300 NE 2nd Ave.
Miami Shores, FL 33161


From: Knudson, Duane [SMTP:DKNUDSON@csuchico.edu]
To: 'Jared Coburn'
RE: Equations for Undergrad Course
Sent: 2/1/99 8:41 AM


I do not require my students to memorize the basic physics formulas that
form the foundation for biomechanics. I teaching the basic algebraic
definitions of these formulas and put them (often more than needed or
relevant) on the chalk board for examinations. I believe that the
conceptual understanding of these laws of physics as applied to humans
in motion is the more important that memorizing formulas.

Most of our students, even the ones that go on to PT, PA, medicine,
dental or other professional schools do not become biomechanical number
crunchers. They may use math in dealing with functional tests (strength,
range of motion, etc.) but will not likely be calculating center of
gravity, net joint moments, or segmental energy. For this reason the
Biomechanics Academy of NASPE has had guidelines and standards (G&S)
for undergraduate kinesiology/biomechanics that say the empahsis of the
introductory course sould empahsize qualitative application of
biomechanical principles/laws. The G&S is currently under revision, but
I would be glad to send you a copy of the 1992 G&S.
A couple weeks ago I announced on BIOMCH-L the biomechanics academy
program for the AAHPERD convention in Boston. It included a 2 hour
session on teaching biomechanics. I hope you and many others can attend
to listen and contribute to the discussion to follow.

Duane Knudson, Ph.D.
Chair, Biomechanics Academy

Duane Knudson, Ph.D.
Department of Physical Education and Exercise Science
California State University, Chico
Chico, CA 95929-0330
530-898-4932 Fax


From: chalmers@cc.wwu.edu [SMTP:chalmers@cc.wwu.edu]
Subject: equations
Sent: 2/1/99 8:30 AM

I provide equations. My goal is not to evaluate if students can learn
and reproduce equations from memory. Rather, I am interested in having
the students focus their learning time and efforts on developing problem
solving and critical thinking skills. I am interested in having my
evaluations reflect those latter higher levels thinking skills.


************************************************** ***********
Gordon Chalmers, Ph.D.
Dept. of Physical Education, Health and Recreation
Western Washington University, MS-9067
Bellingham WA

Phone: (360) 650-3113
FAX: (360) 650-7447


From: Larry Abraham [SMTP:l.abraham@mail.utexas.edu]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 2/1/99 7:04 AM


In my undergraduate class I do not require students to memorize
equations. In fact I provide all equations used in class on a separate
sheet for each exam. However I give students enough practice problems
that most end up memorizing the equations anyway. My goal is for
students to be able to select the necessary equations from a set or
list, given any problem.

Lawrence D. Abraham, EdD
Associate Dean
College of Education
SZB 216
The University of Texas at Austin
Austin, TX 78712

FAX: (512)475-8159



From: Stephen Page [SMTP:spage@kmrrec.org]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 2/1/99 5:05 AM

I don't know if this will help or not, but I always felt it absurd to
make students memorize any sort of equation or formula. It will be
available to them in "real-world" scenarios, and the real application
lies in whether they can apply it when needed. Often our tests are open
book and I still have students fail because they don't know the

Steve Page, Ph.D.


From: Ross Anderson * [SMTP:ross.anderson@ul.ie]
To: Jared Coburn
RE: Equations for Undergrad Course
Sent: 2/1/99 2:27 AM

I am responsible for 2nd and 3rd year biomechanics here at the
university of limerick. I would expect my students to memorise the
basic equations in biomechanics, ie the ones you mentioned. I would
supply, in an exam situation, more complex equations for example the
butterworth filter formulae. The understanding of these basic equations
needs to be thorough. A biomechanist should, in my view, know the basic
equations of motion off by heart. By the third year students can carry
out FBD analysis, jCoR analysis, angular momentum calculatio etc etc
within an exam situation with no given formulae.

Hope this helps
__________________________________________________ _______________
Ross Anderson Tel - +353 (0)61 202820
P1007 Sports Building Fax - +353 (0)61 330431
PESS Mobile - +353 (0)86 8388064

University of Limerick ICQ - 8679473

IRELANDe-Mail - ross.anderson@ul.ie


From: Richard Hinrichs [SMTP:hinrichs@asu.edu]
To: 'Jared Coburn'
RE: Equations for Undergrad Course
Sent: 1/31/99 9:51 PM


For students in the core biomechanics course (EPE 335), I give the
students a list of equations for them to use on exams. I require them
to memorize the equations in all of the advanced (400 level)
biomechanics courses (we have three: biomechanics of the skeletal
system, qualitative analysis in sport biomechanics, and
electromyographic kinesiology).


Richard N. Hinrichs, Ph.D.
Dept. of Exercise Science
Arizona State University
Box 870404
Tempe, AZ 85287-0404 USA
(1) 602-965-1624 (phone)
(1) 602-965-8108 (fax)
Hinrichs@asu.edu (email)
www.asu.edu/clas/espe (Dept. web page)


From: Young-Hoo Kwon, Ph.D. [SMTP:ykwon@bsu-cs.bsu.edu]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 1/31/99 7:45 PM

Dear Jared:

I read your message with interest.

I strictly require my students to memorize all the equations related to
the basic mechanical concepts such as velocity, acceleration, Newton's
law. I believe it is important to let students know that concepts and
equations are indeed the same thing and it is impossible to separate
them. Equations must be helpful for them to understand the concepts
well. But I provide some secondary equations which are not really
related to the basic mechanical concepts such as projectile motion

As far as my goal of teaching is to have students understand the amazing
mechanical principles of human body structure and human motion, I would
rather teach them the concepts than how to plug numbers into the
equations. I may be wrong. I may be in wrong place at wrong time.

One more thing! Since I am a Korean and my undergraduate major was
astronomy, it is kind of interesting to learn more and more about the
American way of teaching college students. And more and more about how
students would typically react to my teaching style and approach. It is
also quite interesting to note in most of the institutions with
well-established graduate biomechanics programs in Kinesiology or
Exercise Science that faculties generally go easy with their
undergraduate students and recruit graduate students from other areas
such mechanical engineering, etc. It seems there is a huge gap between
the undergraduate program and graduate program.

Hope to hear the views of others!

- Young-Hoo Kwon, Ph.D.
- The Human Performance/Biomechanics Lab, PL 202
- 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/


From: jamal wakeem [SMTP:jw229@umail.umd.edu]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 1/31/99 11:55 AM

Memorizing the equations or knowing their application is the question.
I stress on the application of these equations. Usually, I give the
equations out during the exam. It changes the student's mood and do

Jamal Wakeem
Dept. of Kinesiology
University of Maryland College Park


From: Nancy.Hamilton@uni.edu [SMTP:Nancy.Hamilton@uni.edu]
Re: Equations for Undergrad Course
Sent: 1/31/99 10:17 AM

Hi Jared -
Your concern about undergrads and equations is a valid one. Before you
have these students memorizing equations, look at the applications they
will likely make of the education they are getting. If the majority of
your students are going to be teachers or coaches, it is much more
important for them to understand the concepts of mechanics in practical
terms. I have my undergrads learn equations as shorthand for concepts.
In other words, F=ma is just shorthand for the idea that there is a
definite and logical relationship between the amount of force applied
and the acceleration that will occur in any mass. Students who will be
teaching students of there own must be able to think and speak in
practical, applied terms rather than equations. If the long range goals
of your students include MA and PhD programs, then a sound grounding in
the equations and their use and meaning might be more appropriate. Hope
this helps.

Nancy Hamilton, PhD
University of Northern Iowa


From: Peter Stothart [SMTP:stothart@uottawa.ca]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 1/31/99 6:57 AM

Hi Jared,

I always provide a formula sheet with all the necessary formula plus
extra so that students must at least be able to recognize the
appropriate one for a given application.



From: Donald H Sussman [SMTP:dhs15@juno.com]
Re: Equations for Undergrad Course
Sent: 1/31/99 6:03 AM


For all those quantities mentioned, I require my students to memorize
the equations, basically the equations are another way of stating the
definitions. I do not require students to memorize equations for
calculation of range including the equations of constant acceleration.
But I warn my students that if they do not know those equations by the
time an exam is written; they have not practiced enough problems.

Donald H Sussman
dsussman@odu.edu (Office)


From: Patrick Castagno [SMTP:chestnut@UDel.Edu]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 1/30/99 8:23 PM


I teach senior level undergraduate biomechanics at the University of
Delaware. I do not have my students memorize equations or conversion
factors. I feel that these equations will always be available to them
if they need them in the future in some reference. They use the
equations so much during the semester that most of them end up knowing
them anyway. It is my feeling that if they learn and understand which
equation to choose for a given problem and how to manipulate it to get
the answer, this indicates to me that they know the material. I always
put equations on board each day and for exams.

Patrick Castagno
Manager/Biomechanist duPont Hospital for Children
Wilmington, DE


From: D. Gordon E. Robertson, Ph.D. [SMTP:dger@uottawa.ca]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 1/30/99 10:17 AM

I don't require my students to memorize equations. They are allowed to
bring as many equations as they can fit on a single sheet of paper to
midterm and final exams. The text that I use even provides a list of
all equations of interest (approx. 100). I want them to know how and
when to apply the equations to solve questions about human motion.

D. Gordon E. Robertson, Ph.D.
Associate Professor of Biomechanics
School of Human Kinetics, University of Ottawa
Ottawa, ON, Canada K1N 6N5
+1-613-562-5800 Off. ext. 4253 Lab. ext. 4246 Fax: +1-613-562-5149


From: Kathryne J Hirsch [SMTP:kjhst31+@pitt.edu]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 1/30/99 10:13 AM


I am not a teacher of these subjects but a grad. student with an
undergrad in Mech Eng. from my experience the standard equations of
motion were material that had to be memorized. fo the equations you
mentioned only moment of inertia was not memorized. It was no great
task esp. since after so many problems they were memorized anyway. I
may be biased since i have seen some of the equations since high school
physics. I guess it depends if you are putting them all on one test or
spreading it out a bit.

I hope I have given some help.

Kitty Stabile
Department of Bioengineering, Univ. Of Pittsburgh
email: kjhst31+@pitt.edu


From: Stephen J. Kinzey, PhD [SMTP:skinzey@olemiss.edu]
To: Jared Coburn
RE: Equations for Undergrad Course
Sent: 1/30/99 9:28 AM


To answer your question about memorization...Absolutely not! I don't
memorize formulae so why should / would I expect them to either. For
exams I allow them a single 8.5 x 11 sheet for formulae. I inspect each
sheet for notes because only formulae are allowed no text.

Hope this helps you out, Good luck.


Stephen J. Kinzey, Ph.D.
Assistant Professor / Director Applied Biomechanics and Motor
Performance Laboratory
The University of Mississippi
Department of Exercise Science & Leisure Management
Turner Center
University, MS 38677
Phone: 601-232-5540
Fax: 601-232-5525
Lab: 601-232-5570
Email: skinzey@olemiss.edu
WWW: www.olemiss.edu/~skinzey/biomch.htm


From: Wynne Lee [SMTP:wlee@casbah.acns.nwu.edu]
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 1/30/99 8:40 AM

Memorization -- the process of committing information to memory,
preferably long-term memory -- can be invaluable, especially when
coupled with understanding. Just imagine if we didn't memorize the
shapes of letters, the sound and meaning of words and grammar. How would
we speak, read write? Or what if you didn't "memorize" motor skills like
starting up a car, driving around curves, parking? Is it truly enough
to say, "Oh, I can look that up when I need it." (Incidentally, these
and numerous other examples show that memorization can sometimes be very
useful even without understanding.)

Same is true for knowledge about the physical world that is expressed
mathematically, including Newtonian principles, equations of motion,
etc. Knowing something well enough to easily retrieve it from memory,
when needed, is an important, practical skill. If the students lack a
solid, reliable understanding of mechanics (kinetics as well as
kinematics, incidentally), how can they become competent in evaluating
movement patterns, or in using and interpreting motion analysis, force
plate, kincom, etc information? Unfortunately, many in our culture have
a math phobia. Coupled with the (trendy but peculiar) notion that being
able to "look it up" is always enough, the math phobia insists that its
OK to let students remain basically illiterate re: math, physics, and
biomechanics. But how can people claim to be specialists re: human
movement, when they lack competence in physics and biomechanics, which
are the basic language of describing movement? While this perspective
has deep historical precedents and adherents, is that perspective really
justified? (And just because some students don't see the relevance of
some specific knowledge, like biomechanics which include equations of
motion, doesn't mean it *is* irrelevent.)

The phrase "memorization for exams" is a bit worrisome, though. It might
be interpreted to suggest that transient performance on exams per se
are what's important, not knowledge that can be applied in the future.
If that's *all* that's going on, memorization probably is pointless for
most people. So it depends on what you want the students to be able to
do, now and in the future.
Wynne A. Lee, Ph.D.
Associate Professor
Programs in Physical Therapy, and the Neuroscience Institute
Northwestern University Medical School
645 N. Michigan Avenue (Suite 1100)
Chicago IL 60611-2814
voice: (01) 312-908-6795
fax: (01) 312-908-0741
email: wlee@casbah.acns.nwu.edu


From: Anthony G Moreno [SMTP:morenoan@pilot.msu.edu]
To: jcoburn@calbaptist.edu
Subject: Kinesiology for undergrads
Sent: 1/30/99 8:25 AM


I was teaching undergrad biomechanics at Nevada, Reno for a year now I'm
at Michigan State getting my Ph.D. I don't make them memorize formulas
I'm more interested in them getting the concepts. If its an upper
division course with physics prerequisite they MUST know all formulas,
especially if they plan on going to PT or grad school.



From: Nick_Stergiou/COE/UNO/UNEBR@unomail.unomaha.edu
To: Jared Coburn
Re: Equations for Undergrad Course
Sent: 1/30/99 7:02 AM

yes I do require the student to memorize equations as the ones that you
mentioned because they are what I call "essential" equations. I also use
some 'matching' questions for my exams to make sure that the students
learn the equations.


From: Bing Yu [SMTP:Bing.Yu@css.unc.edu]
To: Jared Coburn
re: Equations for Undergrad Course
Sent: 1/30/99 5:10 AM


I am not teaching undergraduate courses but I don't think memorizing
equations is very important for undergraduate students. The most
important thing in biomechanics as well as in mathematics, physics, and
mechanics is to have correct basic concepts. With correct basic
concepts, it is easy to write the equations out. Without correct basic
concepts, memorizing equations does not mean anything. Students can
always find equations they need after your course but they can't apply
them correctly if they don't have correct basic concepts. I apply this
phiolosiphy to my graduate courses. I provide a equation list in my
exams and let students choose the correct equations.

Bing Yu, Ph.D.
Assistant Professor
Division of Physical Therapy
The University of North Carolina at Chapel Hill


From: William L. Siler, Ph.D. [SMTP:silerwl@SLU.EDU]
Subject: memorizing equations
Sent: 1/29/99 8:02 PM

Dear Jared:

I don't make my students memorize equations in what I believe to be the
traditional sense. Rather, I take a very Aristotelian approach in which
I present the equations as paragraphs summarizing the relationships
between parameters in the physical world. I want my students to be able
to anticipate the change caused in one parameter by another and to
understand the relative significance of one parameter to another. In
short, I encouage my students to focus on the concepts summarized by
number sentences rather than on the equation. I hope I'm making sense -
I've had excellent success with this approach, receiving really positive
feedback from students who despised physics because it was reduced to a
math class where story problems reign supreme and concepts are glossed
over without explanation.


William (Bill) Siler, Ph.D.
Department of Physical Therapy
Saint Louis University


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