What is tested?
Tests as Teaching Devices
Preparing for a Test
During the Exam
There is something obnoxious about tests.
Testing the trueness, integrity, virtue, and miscellaneous of people is
an ancient practice.
In the Bible, Abraham, Job, and Christ are tested by God, the Adversary,
and Satan respectively, and are found pious.
Lesser examiners test the faithfulness of their wives, the loyalty of their
children, the integrity of their citizenry, and the accuracy of their
In the more mundane world, engineers test the strength of alloys,
artisans test the soundness of wood, and astronomers test the accuracy of
All this testing is done to make sure that whoever, whatever, is being
tested measures up.
Who got the bright idea of testing students?
The oldest form of teaching is the tutorial, with a wise old sage and
suitably awed youngsters (all the really old-fashioned pedagogues agree
that students should ``worship'' their teachers).
The sage would frequently test the students to find out if they were
The test consisted of asking the student to say or do something, which
the student would say or do, right then, with teacher watching.
This is a very effective technique, used by music teachers and athletic
coaches to this very day: if students know that they will be so tested,
they will practice, practice, practice.
So here comes the most famous surreptitious motive for having tests: a
threat of a test makes a good whip.
The ad hoc tests in tutorials probably led to the oldest kind of formal
exam: the oral exam.
The student is led into the August Presence of various sages, usually
including his own teacher.
The sages would ask the student questions, which the student would answer.
The sages would ask the student to demonstrate his skill by doing various
things, which the student would immediately do, with the committee
All very intimidating.
The oral examination may be the best kind of exam because of its flexibility,
and the impossibility of cheating.
(It also means that thinking on one's feet is a skill the teacher will
have to teach.)
There are many disadvantages:
It is very labor intensive.
For at least an hour, the time of several sages is monopolized by a
It requires a lot of skill to be an examiner.
While an examiner does prepare by writing out questions in advance,
the examiner has to be flexible, to be able to follow the course of
the exam as it takes a course which, sometimes, no one in the room
If there were too few competent examiners, or or too many students,
there would have to have a different kind of exam.
It leaves a limited record.
Unless the exam is minuted (or taped), one cannot tell what really went
on in the room.
In Medieval China, posts in the bureaucracy were theoretically open to
everyone with a sufficient education, and the educational system was
theoretically a meritocracy that any student could get into.
(In practice, China was a somewhat ossified society with a rather rigid
class structure, but never mind that.)
There were many students coming in, but few were called to serve.
Thus there were many written exams.
These were very stylized things, like the terminal exam that consisted of
writing, in eight paragraphs, in a preset form, an essay on a topic that
would be announced at the test.
This may seem to be an odd exam, for it tests only the ability to write
extemporaneously in a particular artificial format: the irrelevance of
such exams --- and the credentials that they generated --- inspired the
phrase `Mandarin requirement'.
But what the exam really did was test if the student had been sufficiently
indoctrinated in the world view of the bureaucracy, and this the exam did
very well, for a student would have to spend a lot of time immersing
himself (and these students were male) in neo-Confucian philosophy and
court esthetics and fashion to make an even half-decent performance.
During the last two centuries, written tests have become the most popular
kind of test.
The bellweather was Stephen Binet's IQ test, which was designed to test the
ability of students to answer, in writing, vast numbers of silly little
questions rapidly and reliably; to test, in other words, how well the
French children taking the test had been made into successful French
What is tested?
There is a problem.
What the test appears to be testing may not be what the exam actually
is supposed to test.
(For example, the IQ test is not testing the examinee's knowledge of
miscellaneous subjects; it is testing the examinee's ability to answer
silly little questions rapidly and reliably.)
Most psychometricians claim that there is a mysterious capacity, often called
g, that IQ-type tests measure; more sophisticated psychologists claim
that there are several capacities (g1, g2,
g2, ...) that various different kinds of tests measure.
There is ample reason to be suspicious of these claims (ladies and gentlemen,
let me offer you Dr. S. Nake Oyl's Techno-Intellometer, guaranteed to measure
all otherwise undetectable g's known to or suspected by Modern Science;
and for a modest grant ...), but there does seem to be some kind of difference
between people who have an IQ of 100 and people who have an IQ of 180.
But it is not entirely clear what.
There is a difficulty in studying for a test if one is not sure what (if
anything) is being tested.
One consequence is that if one prepares for the test by preparing for what
the test appears to test, one might not do as well as if one had been
developing whatever mysterious capacity that the test actually is supposed
Many tests are like this.
The most famous is the SAT, which is supposed to test aptitudes for
college --- the SAT is testing something similar to what the Medieval Chinese
Notice that this kind of aptitude testing is not so much testing what the
student knows as whether or not the student's education has made the student
into the kind of person that the examiner is interested in: the kind of
person who would make a good Chinese bureaucrat, or a good American college
Such suspicions about SAT-type exams is encouraging some universities to
downgrade or even eliminated them in considering admissions.
Let's look at a very famous test.
According to an anonymous poet, a Green Knight arrived in Camelot one day,
and challenged any knight to chop off his head.
All the Green Knight asked in return is that whatever knight took the challenge
had to come to the Green Knight's lair and let the Green Knight return the
Ho, ho, says Sir Gawain, who chops off the Green Knight's head --- whereupon
the Green Knight picks up his head, reminds Sir Gawain of his appointment,
and rides off.
So there is this most Medieval test.
Sir Gawain's honor is tested: will he keep his word?
Then Sir Gawain must travel to the the Green Knight's castle, through blasted
moors, ragged mountains, fiery dragons, and howling storms, a test of of Sir
Then he comes to a castle, where the charming lady of the castle launches a
test of Sir Gawain's chastity.
Finally, he must kneel before the Green Knight himself and let his head be
chopped off, a test of Sir Gawain's courage.
(Oh yes, the Green Knight lets Sir Gawain off with a knick to remember him by.)
This is the sort of test that is supposed to matter, a test of what kind of
person one is.
This is what the Chinese Examiners (is the candidate a good bureaucrat?),
the psychometers (is this a programmable student?) and the Educational
Testing Service (has the student been programmed?) are really interested in.
It helps to know what is being tested: character? native talent? learned
Once one knows what is being tested, one has a better idea of what to prepare
for ... and how to prepare.
But some tests are not meant to collect information.
Some tests are meant to do something to the examinee.
Tests as Teaching Devices
Let's follow this ancient (but currently disturbing) notion of an
education as something that transforms the student, rather than someting
that teaches the student something.
Consider a famous test from Buddhist mythology: a particularly troubled
student asks a guru to fix his messed up life.
The guru tells the student to build a house.
When the student builds the house, the guru tells him to tear it down and
build a tower.
When the student builds the tower, the guru tells him to tear it down and
build a house.
And so on.
The guru was not interested in architecture; he was interested in
... um ... stripping his student of his personae.
In essence, the test was not being used to find out how the student was
doing; the test was in itself a pedagogical device, which was used
to make the student more tractable.
The most obvious use of a test is as a whip: rehearse, practice, do the
homework, or else you'll be sorry.
This use of exams is probably not very effective.
Most pedagical research suggests that feedback is most effective if it is
rapid and unambiguous: this means that using tests as a whip requires
(Well, some classes to have weekly quizzes, or even numerous pop quizzes.
Its not clear what these mini-exams measure, but they don't seem to be
the obvious method for measuring what a student has learned after sustained
But the mini-exams make great whips.
And we all know how to deal with them: keep up and memorize major facts.)
So much for tests as combination of carrot and stick.
But tests can have other purposes: one can introduce ideas and get students
to play with them in exams.
Since tests are emotionally charged periods, what the student encounters
during a test is likely to be remembered better, so a test can be used
to reinforce memory.
(On the other hand, since tests are stressful times, novel ideas are not
handled as well as they would be handled as homework.)
So the basic kinds of motives for giving students tests are:
Notice that in this era, where students are regarded as customers and
professors are regarded as service personnel, only the first motive is
regarded as entirely respectable (although everyone knows that the third
is used an awful lot).
But all five motives appear prominently in the history of education, and
since the service industry model of education has been producing some
dubious results, the other three motives will certainly remain around, and
perhaps make a comeback.
To find out how the student is doing on the material.
To find out what kind of person the student is.
To make the student keep up with his/her studies.
To do something to the student.
To teach the student something.
Notice that the five motives listed above all feature a wise sage treating
the student as a dependent.
The teacher (or board of examiners) want information about the student, or
they want to do something to the student.
But it does not have to be that way.
Many people test themselves, to find out what they know or can do, what
kind of people they are, and/ or to transform themselves.
In fact, it may be advisable to approach every test this way, to try to
fit it into one's own agenda, to find out what you know or can do, to
find out what kind of person you are, and to use the test to try to make
yourself into the kind of person you want to be.
This includes tests in classes and tests in `real life'.
With all this in mind, let's look at how to do tests in class.
Preparing for a Test
First of all, since the primary respectable motive for a test is to test
how much the student knows, the most effective way to prepare for a test
is to study.
This means reading the texts carefully, taking and reviewing notes, doing
homework problems, and generally familiarizing yourself with the material.
This may seem a waste of time to people used to preparing for tests by
cramming for a few days before the exam, but cramming does not seem to
work as well.
The reason has to do with how memory works.
Long-term memories are created by changing the brain's hardware.
Long-term memories are created when new connections between the axon
of one neuron connects to dendrites of another.
Long-term memories are accessed by sending a signal through the first
neuron, and then receiving the message from the second.
So two things are involved in creating long-term memory that you can use:
building the initial connection, and then reinforcing it by building
many connections to that initial connection, and/or many copies of
that initial connection.
Remember trying to recall a word that you knew you knew?
What is happening is that the word is indeed in your head, but you cannot
access it: the connections to that memory are momentarily out of reach,
out to lunch, or whatever.
This failure to recall occurs especially under stress, e.g., during exams.
When you studies regularly, you builds neural connections as you learns
and get involves (mentally and emotionally) with the subject, and then you
reinforce those connections by revisiting them regularly, while building
additional paths by doing exercises with varying approaches to the issue.
Consider the popular practice of cramming at the last minute.
Cramming builds many connections, but they are more tentative and do not
last long (we are all familiar with the phenomenon of cramming for an
exam, and then forgetting all the material a few days after the test).
Since the memories from cramming are more tentative and less organized,
they are not very helpful in dealing with ``think-type'' questions:
cramming is useful primarily in preparing for memorization exams in which
you merely regurgitates memorized data.
And even then, cramming does not work as well: as you have not built many
connections to the tentative memory, you are more likely to fail to access
the memory during the exam.
Assuming that the object of taking the course is to develop long-term memories
containing the material, regular homework is more effective than cramming.
(See the Homework
page for more information about homework.)
But as the exam approaches ... .
One form of test preparation that is recommended is to practice dry runs.
Get a stack of problems, and try to do them all in fifty minutes, without
peeking at your book or your notes.
This may give you an idea of how you are doing.
One book (How to Study Mathematics, Chemistry, Statistics, Physics,
by Jason Frand) recommends finding an empty classroom to do the dry run
in: the real exam is in a classroom, and the classroom itself seems to
do something to your mind, so it may help to be used to that, too.
Many tests are tests of skills, so prepare by practicing skills.
Second, try to be in good physical and psychological condition for the exam.
Many times, I have had students who did well in their homework, who seemed
to know the material, who bomb in their exams.
And they don't understand how they could have bombed because, after all,
they were up studying until 4 am the night before.
Irritated professors have been doing studies on sleep deprivation during
the last few years, and we have found that:
Drowsiness is the second highest cause of car ``accidents'', after
It also figures in plane crashes, train wrecks, industrial accidents,
and other disasters.
The advantage that you will get by additional hours studying is more than
cancelled by the disadvantage of coming to the exam half-asleep.
(Comment: many people have difficulty falling asleep before exams.
This is a sleep disorder, and you may want to consult a sleep disorder
book, a counselor, or a doctor, if it is a recurrent problem.)
Students and employees who do not get eight hours of sleep regularly
build up ``sleep deficits''; someone with a sleep deficit has a limited
attention span, lower energy (physical and mental), and performs poorly
in standard `tests' of intelligence and creativity.
In addition, overstudying may create may make you so fatigued or depressed that
you are not able to do well on the exam.
It is wise to find out (by experiment) what is the optimal time that you should
spend studying for an exam, and then not study more than that.
Remember, exam preparation is review: exam performance ultimately depends
on the time and energy spent on homework.
One other thing: the brain runs on glucose.
If your blood sugar is low, then your brain will not function very well.
So have a meal before the test: if the test is in the morning, have breakfast
(and I don't mean just a glass of orange juice: get several hundred calories).
And of course, relax.
Many students wind themselves up very tight, and then freeze or go blank during
Of course, test anxiety is a common problem, and if you have it, you should
seek assistance --- from professors, counselors, etc.
(Don't be afraid of seeking assistance: your tuition and tax dollars are
paying for it.)
In general, try not to obsess over an exam.
Some students have the wise practice of not studying during the day of the
exam: the benefits of last minute studying are cancelled by the psychic
cost of worrying about the exam just before taking it.
One thing to remember is this: when you are thinking about a problem, you are
making progress, but when you are thinking about thinking about a problem, you
may merely be obsessing to no good purpose.
During the Exam
During the exam itself, pace yourself.
Test strategies vary depending on the exam, but unless the exam is so easy
that everyone is supposed to get near-perfect grades (this is the kind of exam
a single stupid mistake can wreck), you should prioritize.
First, read the entire exam, so that you know what you are facing, and so
you can start your Unconscious mind chewing on the harder problems.
For more on how the Unconscious behaves, see the
Then get the easy problems out of the way: this will get as much time for
you to deal with the hard problems safely, while assuring that you at least
get a passing grade for dealing with the easy problems.
And do not obsess over how you are doing, and whether you are going to pass,
and what you can do if you don't, etc., etc.: these obsessions are
distracting demons, up to no good, and it may help to try to just displace
them with mathematical thoughts.
If you get tense, try relaxing with yoga exercises (the two best are yawning
--- which relaxes the face, neck, and shoulder muscles --- and stretching
--- which relaxes the large limb and torso muscles).
This leads to an important point.
In High School, there is a tendency for exams to consist of many easy
These are the exams in which 90 % and above is an A, 80 % and above is a B,
and so on.
In College, one sees more and more exams with problems that take up to fifteen
(or more) minutes to solve --- out of a 50-minute test period.
These are the exams that test a student's ability to think on his/her feet.
But tests with such hard problems have two properties:
One can't figure out how to do hard problems within the first minute.
So giving up on a problem after a minute or two is a very unsuccessful
Instead, after reading all the problems of the exam (to find out
which ones are easy and which ones are hard --- and to give your
Unconscious a head start on the hard ones), you should get the easy
problems out of the way first.
That should not take much time.
In the left over time, you should work on the hard problems, and don't
There are many kinds of exams, ranging all the way up to the four-week
Different exams require different strategies, so you should know what kind
of exam you are facing before walking into the room, so you can
prepare for it.
If you don't know what kind of exam you are facing, ask.
A test consisting of 20-60 % hard problems will have a different grading
Some tests are so hard that the A line is at 50 %.
These tests are actually harder to get an A in, but some of us old
fogeys think that they are more fair: they test a student's ability to
use concepts under pressure, rather than a student's ability to avoid
In such exams, much of the credit students get is partial credit, so students
should aim at accumulating as much partial credit as possible.
One other thing.
Over the years, I have noticed that people who have better organized
answers tend to get higher grades.
Of course, partly this is human nature: a happy grader is a lenient grader.
But mostly this is because students who organize their thoughts more carefully,
and on paper so that they can see it, tend to develop a better understanding
of the problem as they are working on the problem.
Either way, clarity, organization, and even penmanship helps.
Then you turn it in.
It rarely is a good idea to turn tests in early: you simply miss the chance to
solve problems whose solutions you could have found, or to catch errors you
could have caught.
Remember, a 50-minute test is testing your ability to do the problems in 50
minutes, not your ability to do them in 35 minutes.
And then it gets graded.
Evil professors, when they die, go to Hell and spend eternity grading papers.
Most people hate grading (this is why opaque, muddled, or hashed answers are
unwelcome: they take a long time to grade).
Most tests are graded by what is on the paper, not on what might be or is sort
of there, but what actually is there, and most tests are graded by as
consistent a manner as possible.
When consistency and fairness come into conflict, it is consistency that wins
Since grading is time-consuming (hours and hours and ...), most comments on
exams are negative; there is not enough time to write all the praise that
should or could be written.
The result is that the best test papers tend to be the ones with the least
amount of red ink on them.
Anyway, after being graded, each paper is boiled down to a number.
(And now, a word to my colleagues: pedagogical research says that tests are
most effective if they are returned in a timely manner, with as unequivocal
an evaluation as possible.)
And the following can happen:
Of course, not all of the course grade comes from the tests.
The test could come back with a letter grade.
That tells the student immediately how he or she did.
The test could come back with a number.
The professor could say that such-and-such a range is Aish, such-and-such a
range is Bish, and so on.
What that means is that when the course grades are computed at the end
of the semester, they are computed by adding the test grades, and then
letter grades are assigned according to what the test grade sums are:
if a student got Bish grades all the way through, he will probably get
a B at the end.
What happens if a student gets a variety of test grades is less clear,
and depends on what formulas the professor uses.
When you get your test back, go over it carefully.
There are two reasons for this.
If there is something you do not understand, see the professor.
You want to find out how you did, what you apparently knew and didn't know.
Graders are only human, and there might be a mistake in the grading.
If there was a problem you that did not know how to do, or a type of
problem that you just don't get, or if you did not understand some material,
see the professor.
Sometimes you can go over this in class, but don't be afraid to see the
Professors are always happy to see students who want to improve their work
(or at least, they should be).
And then, try to figure out where you stand, and where to go from there.
If you get a high grade, do not rest on your laurels, and if you get a low
one, do not weep over spilt milk.
It was just one of many tests to find out where you are, to help you assess
your progress towards where you want to go.
For more about grades, go to the Grades Page
If there was something you don't understand about the grading, or if you
think a mistake was made, see the professor.
Some professors have policies to discourage cheating, but no
professor should be unwilling to look at a paper.