About Tests


What is tested?

Tests as Teaching Devices

Preparing for a Test

During the Exam

Test Grades

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 auguries. In the more mundane world, engineers test the strength of alloys, artisans test the soundness of wood, and astronomers test the accuracy of clocks. 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 following him. 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 watching. 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 single student.
  • 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 anticipates.
  • It leaves a limited record. Unless the exam is minuted (or taped), one cannot tell what really went on 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.

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 schoolchildren.

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 to test. 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 examiners tested. 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 student, respectively. 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 favor. 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 Gawain's strength. 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 skills? 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 frequent tests. (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 study. 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:

  1. To find out how the student is doing on the material.
  2. To find out what kind of person the student is.
  3. To make the student keep up with his/her studies.
  4. To do something to the student.
  5. To teach the student something.
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.

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. Hmmm. 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 drunkenness. It also figures in plane crashes, train wrecks, industrial accidents, and other disasters.
  • 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.
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.)

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 the exam. 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 Homework page.
  • 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.
  • 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).
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.

This leads to an important point. In High School, there is a tendency for exams to consist of many easy regurgitation-type problems. 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 strategy. 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 give up.
  • A test consisting of 20-60 % hard problems will have a different grading scale. 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 stupid mistakes. In such exams, much of the credit students get is partial credit, so students should aim at accumulating as much partial credit as possible.
There are many kinds of exams, ranging all the way up to the four-week take-home exam. 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.

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.

Test Grades

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 out. 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:

  • 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.
Of course, not all of the course grade comes from the tests.

When you get your test back, go over it carefully. There are two reasons for this.

  • 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 is something you do not understand, see the professor.
  • 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 professor. Professors are always happy to see students who want to improve their work (or at least, they should be).
  • 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.
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

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