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Tactics and Strategy for Tests and Examinations
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by Professor Tom Jenkyns,
Department of Mathematics,
Brock University
A portion of this appeared in "The Teaching Professor" in January 1995
Prologue
I teach a number of freshman service courses in Mathematics:
Statistics to Social Science students, Calculus to Business students, and
Discrete Math to Computer Science and Education students. For many of
these students, taking a mathematics course means engaging in a sort of
battle with all the accompanying anxiety, risk of humiliation, fear and
loathing. I use this military analogy to give them advice on how to write
and how to prepare for tests and exams, partly to amuse them, partly to
authenticate their feelings, but mainly to provide a context in which
they may deliberately act to control their fate. What follows is the
lecture I give after returning their first test papers.
Tactics
My dictionary defines 'tactics' as that part of generalship
related to deploying one's forces when in actual contact with the enemy.
What I describe here is what to do when actually writing a test. But I
point out that the enemy is the questions and the clock. Not me, I'm more
like a sympathetic arms supplier. I want them to win and buy more
munitions from me. My job is to empower them to defeat the enemy.
For tactics I use the mnemonic
SAW ARMS, I (the general)
and ask them to imagine that they are like Napoleon, astride a huge white
horse overlooking the battlefield and directing their troops. I then
divide the mnemonic as S-AW AR-MS I, and give five specific tactics.
- The first tactic: S for SURVEY THE ENEMY
ie., view the whole battle site, see what forces are arrayed against you,
examine the order in which they are arrayed, evaluate the potential of
each regiment opposing you.
What I really mean is:
- Read the whole paper first.
I tell them they will likely have to read each question more than
once so this time is not wasted, and reading all of them now can produce
substantial rewards as I'll explain later.
- Write, on the question paper, a preliminary estimate of the
difficulty of each question.
Put E if the question looks easy; VE if the question looks very easy;
put
ARITH if the question looks easy but requires some arithmetic to solve;
put H if the question looks hard; VH if the question looks very hard; and
put NBI if you have no bloody idea how to solve it.
- The second tactic: AW for ATTACK the WEAKEST point
ie., if there is Prussian cavalry on the right, British artillery in the
center, and a band of peasants with pointed sticks on the left, you know
where to focus your attack.
What I really mean is:
- Answer the easiest question first.
This will probably be done quickly, so allow relatively more time for
the hardest ones (remember the clock is also the enemy). You will feel
better, and more confident having done a question and therefore more
capable of doing others. But even more important you will be able to
utilize what I believe is a capability of your mind akin to 'parallel
processing' in computer science.
I then ask "Do you find that you actually CAN think of other
things while I am lecturing about math?, ... and that you can do this
quite easily?, ... and that your mind sometimes wanders during exams?".
You do seem to be able to think of two things at the same time. And you
might be able to do this in a test to your advantage if you give your
mind something else to think about. While you do an easy question, a part
of your mind may also be considering hard questions, or the one about
which you had no idea. But you can only exploit this hypothetical
capacity of your mind if you have read all questions first.
- The third tactic: AR for ADVANCE and RETREAT
ie., if the battle is going against you, retreat to fight on other ground.
What I really mean is:
- When a problem is not working out as you expected or you're
simply stuck, leave it for a time, work on something else, and plan to
return to it later.
If you persist on a particular problem your mind will tend to
repeat exactly what it did before. Twenty more minutes on that same
problem may earn a few additional marks but twenty minutes spent on new
problems will earn far more.
Even though it is hard to leave a problem when its almost done or
when you have already invested so much time on it, working on a new
problem will earn more marks. In addition, there is the possibility that
some part of your mind is now free to attempt the earlier problem from
another or perhaps many other approaches. This unstructured sneak-attack
on the old problem may be more successful than continuing under conscious
control in a direct assault.
- The fourth tactic: MS for MAKE SURE
ie., make sure the enemy is really dead, if it's safe to do so.
What I really mean is:
- Check your answers, if you have time, and make sure
you've answered the questions that were asked.
- The fifth tactic: I for IMPRESS (the general)
ie., impress the general with your valour, skill and resourcefulness.
What I really mean is:
- Impress the Marker with your knowledge and competence.
- Neatness counts: a marker expects perfect answers to look
perfect, and poor answers to look messy, tentative, and disorganized. If
she has to search through lines of hieroglyphics to find a certain
number, she will become frustrated, irritated and may give up entirely.
Remember "A happy marker is like money in the bank".
- Write more than enough. Display the process you used to get
your answer; for me and my evaluation of your work, the process is more
important than the arithmetic. Also, if you cannot decide whether the
answer is a formula or a value, write both, like "n(n-1)=110". If the
marker is looking for either of these she will find it. Why gamble on one
or the other?
- If a question is ambiguous, give your interpretation and
answer that. Show the marker what you know. No answer at all is worth no
marks at all, and you are likely right that the question does have
several interpretations.
- If you can see your answer is wrong tell the marker what you
know - say its wrong but you can't find your arithmetic mistake or you
don't have time to re-do the calculations. (Of course it would be much
better to re-do it correctly if you can.)
- Don't erase anything, cross out your mistake so the marker
can still see it. It might be right even though you rejected it and if it
is wrong the marker sees that you knew it was wrong. No answer at all
guarantees zero, and does it show what you know?
- Finally, since no answer guarantees a mark of zero, make
guesses. You may be right, and in any case a reasonable guess will
impress the marker, and will show what you know. Good ideas always
impress me, and probably other instructors.
Strategy
My dictionary defines 'strategy' as that part of generalship
related to preparing one's forces so as to impose upon the enemy the
place, time and condition of combat most favourable to oneself. Students
can't impose the time or place of the exams but I describe here what to
do when not actually writing the test but when they are preparing for
tests.
For strategies I use the mnemonic
S-E-X
- The first stratagem: S for SPYING
ie., gather intelligence about what forces might be arrayed against you,
evaluate the potential of each division opposing you and your potential
of vanquishing them. In general, know the enemy and anticipate the
enemy's action.
What I really mean is:
- Listen carefully to the lectures, I will tell you (one way or
another) the most important ideas in the course, the ones I want you to
learn, the ones I will pay for with marks, the ones I will give you an
opportunity (a test) to show you have learned.
- Find old exams, copies are kept in the library at Brock.
These will show what I thought was important enough in previous years to
be put on an exam and these most important ideas don't change much from
year to year.
- The second stratagem: E for EXERCISE your troops
ie., hold field manoeuvres, mock battles and war games to assess and
improve the effectiveness of your forces.
What I really mean is:
- Practise the new methods I teach you in assigned exercises
immediately after I present the material. This practical reinforcement of
the theory adds many more "hooks" on which the material can hang inside
your mind. It also creates more pathways for retrieval of information.
The connection to my presentation is very much weakened and the sketch of
my presentation in your mind faded by the passage of time.
- Do the questions on old exams under battlefield conditions:
alone, at a small table, on a hard chair, under harsh lights, with no
music. And time yourself.
Our minds seem to attach body-cues to information. You can well
imagine a person who has studied in a comfortable chair, listening to
their
favourite group, who "blanks out" at certain critical points in the exam
when placed under comparatively severe conditions and subjected to
the stress of an exam. Then when the exam is over that person is very
relieved, relaxes, gets into the car, sits in a soft seat, turns on the tape
deck and suddenly their mind is flooded with all sorts of answers
that couldn't be retrieved when most needed.
- The third stratagem: X for eXperimental weapons
ie., procure new weapons systems, like smart bombs that seek out targets
automatically and are carried by computer-guided missiles for miles over
hostile terrain, joyfully.
What I really mean is:
- Integrate new ideas into your belief-system with joy and
excitement as new ways of solving old problems or new problems solvable
in old ways. Don't reject new ideas as foreign bodies invading your
brain. New knowledge makes you bigger, better, stronger, more beautiful.
Tests and exams are opportunities to show how wonderful you
are by allowing you to show what you have learned.
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