I go back to school — yet again!

In all the mathematics and science courses that I ever took in high school, or as an undergraduate at the University of Toronto, or as a graduate student at Stanford, I almost never had any idea of what the teacher or professor was talking about.  In all those years, I did not blame my lack of comprehension on the educational system — I blamed it on my own lack of preparation.  My conclusion was that I did not understand what was being said because I was not keeping up with the work.  I felt responsible.  I felt guilty.  I thought that the school and the teacher were in the right, and that I was in the wrong.  I thought that nobody was to blame but myself.

But recently, I have been enrolled in mathematics and science courses at the University of British Columbia (UBC) under different circumstances and with a different attitude.  I was now in my 50s, I had a Ph.D. in experimental psychology from Stanford, I had myself taught for 11 years in the Department of Psychology at the University of Western Ontario.  And now I found myself taking a broad range of undergraduate courses, mainly in mathematics and science — that is, Calculus, Physics, Chemistry, Computer Science; but also Ukrainian and French.  Why?  I was educating my young son, Marko, and when he was nine years old, we began taking courses together at UBC, with me enrolled formally, and him being granted permission to attend lectures and write examinations but without having formal standing.  We continued doing this when he was ten, and even for a time after he was formally admitted — upon invitation, on the strength of his unofficial performance — into the faculty of science at the age of 11.

So, now I was mature, disciplined, and motivated.  Now I not only did my homework, but I did it several times, and did more than was assigned.  Now I read ahead.  As I explained all the material to Marko, and summarized it for him, and simplified it, and discovered mnemonics, and read supplementary materials for clarification and depth, I often saw that I could have done a better job delivering the day's lecture to the class than the course instructor himself was doing.  Now I was getting high marks.  And so now what did I find?  Several things.

In the first place, when I had learned a topic beforehand, then yes, I could follow the lecture — usually, and only if I strained.  Also, now that I was reading ahead, I could see how often the material must be incomprehensible to anyone who was hearing it for the first time — the instructor might fail to stress some critical point, or he might word something poorly, or he might be unaware of some simplification that was possible or some mnemonic that made the whole easier to remember.  Or, when as the lecture progressed and each new point depended on the ones that had gone before, the instructor's assumption that the student was able to remember all those earlier points seemed unjustified.

Professors make mistakes

And now that I was following the lectures closely, I noticed something else — professors made mistakes.  Even the most competent ones made one or two per lecture; in other cases, a dozen mistakes per lecture might not be unusual.  Mistakes were inevitable because mathematics or science lectures often involved the continuous writing of proofs or else the solution of complex problems, so that over the course of a fifty-minute class, the lecturer might cover several blackboards with densely-packed symbols over and over again.  So the fact that there were mistakes was not significant, but what happened after each mistake was significant — I would look around for some reaction from the other students, and I wouldn't see any.  As many as fifty or a hundred, perhaps even a hundred and fifty, students might be sitting in the classroom or lecture hall, and not one had raised his hand, and not one was frowning or shaking his head or looking to his classmates for clarification.  Many were looking right at the blackboard, many appeared to be copying into their notebooks, but nobody was objecting.  Often the mistake was far from trivial; rather, it was often so gross that anyone who was following the lecture must immediately have been struck by it.  Seeing that nobody else was going to say anything, I would then raise my hand and point out the error, and the instructor would acknowledge the error and would correct it, and then all the other students would docilely revise their notes.  But a while later, the same thing would happen all over again.

The zombie hypothesis

As this failure of students to catch errors repeated itself, I began at first to entertain, and later to be entirely convinced of the truth of, the zombie hypothesis.  The zombie hypothesis is that in a typical mathematics or science lecture, between zero and five percent of the students are following what is being said.  These are the non-zombies.  Therefore, from 95 to 100 percent of the students are not following what is being said.  These are the zombies.

My regression to zombiism

There is something else that happened that has a bearing on the zombie hypothesis — and that is that sometimes I would not have read ahead and mastered the upcoming material.  Perhaps I had not had time, perhaps the professor was not following any predictable path through the textbook, perhaps it was a lecture course and there was no textbook that I could read ahead in.  In all such cases, I usually reverted to having no idea of what the professor was talking about.  I had joined the ranks of the zombies — no, I had rejoined the ranks of the zombies, for a zombie is what I had been throughout my youth.  And so now again among the zombies, I sat and copied without understanding.  Now I was catching no errors, and when there should happen to be some rare non-zombie in the class who caught an error, it seemed like a miracle to me that he was able to do it, and my having copied down the error without objection stood as a just accusation of my total lack of comprehension.  I was still getting high marks, but I was learning everything after each incomprehensible lecture, and nothing before and nothing during.

Teachers are aware that students are unaware

Are mathematics and science lecturers aware that almost nobody — and sometimes absolutely nobody — is following them?  Well, their behavior suggests that they are aware, for they studiously avoid taking any action which might provoke a confirmation of the zombie hypothesis.  For example, I never saw a UBC professor in mathematics or science address a question to a random student.  An instructor might ask a rhetorical question, but this he would immediately answer himself.  More rarely, he would put a question to the entire class, and here he might be saved by one of the few non-zombies providing an answer; or if no answer was forthcoming, the instructor would provide it himself, an outcome which was non-diagnostic in that it was possible to ascribe the students' silence not to universal catatonia, but rather to a universal shyness which the instructor tactfully chose not to encroach upon.  More rarely still, the instructor might put a question to some obvious, card-carrying non-zombie.  In Mathematics 140, Dr. Astaneh asked exactly one question during the entire course, and this he addressed to me, fully aware that I more than almost anybody else in the room was likely to know the answer.  But what no instructor ever did was address a question to a random student — and the reason was that he knew that almost every time he would get no answer and the zombie hypothesis would be confirmed.  Let sleeping zombies lie is a rule that avoids much unpleasantness.

The zombie hypothesis is easy to verify

But the zombie hypothesis is not something any lecturer should believe on the basis of someone else's observations — he has it within his power to put it to an empirical test in his very next lecture.  All he needs to do is to ask every once in a while, "Would all the people who understand everything I have said so far please raise their hands?"  What would he observe if he did ask this question?  He would observe that almost nobody raises his hand.  Better than that, he can intentionally introduce several subtle, and yet fatal, errors into each lecture, and a line or two later, pick the name of a student out of a hat and ask him whether he sees anything wrong.  Yes, the name-out-of-a-hat is a little cumbersome, but if the instructor doesn't institute some measure to guarantee randomness, then of course he will tend to pick some helpful non-zombie that he is aware of.  And what would he observe as being the result of this test?  He would observe that the student he has addressed is unable to detect anything wrong.  Or, the instructor can erase the last line or two of a solution or proof, and ask a random student to come up to the board and reconstruct what has been erased, something that should be easy for any student who had been following the lecture.  And what will he observe?  He will observe that the randomly-picked student is unable to reproduce the erased lines.

The best thing that he can do is to deliver a lecture on an unannounced topic, and right after the lecture give an unannounced quiz on the material covered in that lecture.  And what will he observe?  He will observe massive failure on the quiz, and howls of protests from the students.  Even an announced quiz at the end of a lecture covering that day's material is not to be thought of.  Such things are never done in mathematics and science, and for good reason — the lecture hall is not where learning takes place, and disaster threatens anyone who assumes the opposite.  An interval between a lecture and a test on the materials covered in that lecture is always allowed, and it is during that interval that the student learns the material for the first time, without the assistance of the lecturer.

The zombie hypothesis applies only to lectures in mathematics and science

I am talking mainly about mathematics and science courses.  There are other courses to which my comments do not apply, courses like English, History, or Law, in which it might be entirely possible for students to follow a lecture from beginning to end.  When I was a graduate student in experimental psychology at Stanford, for example, I took my exercise with the Stanford Karate Club, and one day the karate instructor recommended our attending an upcoming lecture in a law course that would be relevant to the question of when violence could be employed legally.  I attended this law lecture, and even though I was not a law student, I understood every word.  Today, more than thirty years later, I still remember two situations discussed in that lecture.  In one situation, we imagine that a film crew is staging a scene in which one actor grabs another, shoves a gun in his face, and shouts "I'm going to kill you!"  However, suppose some pedestrian walking down the street happens on to this movie set, is mistakenly grabbed, has a gun shoved into his face, and hears "I am going to kill you!"  Our pedestrian pulls out his own real gun, and shoots the actor who is pointing the fake gun in his face.  Is our pedestrian liable?  No, not if it truly appeared to him that he was in imminent danger.  The situation described is a tragic accident, but the pedestrian incurs no blame.  The second situation that I remember from the lecture is that under Texas law, someone under attack is under no obligation to avoid the attack by yielding his ground, even if he is readily able to do so.  Suppose, for example, that a man in a wheel chair is coming at you with a knife.  You could easily avoid the attack.  Instead, you stand your ground and kill the wheel-chair attacker.  Are you at fault?  Not in Texas, you're not.

Thus, I fully acknowledge that my discussion of the zombie hypothesis does not apply to lectures that avoid the manipulation of symbols and the solution of problems.  The zombie hypothesis applies to mathematics, chemistry, physics, computer science, symbolic logic, and courses like that.  Although I have never taken courses in engineering or medicine, I assume that many of these would fall into the same category.  The characteristics of this latter sort of lecture are entirely different from the sort in which anecdotes are related, stories are told, and everyday English is the chief vehicle of communication.  If I had to write an examination on the contents of that one law lecture that I heard more than three decades ago (but that I never studied), I might today stand some chance of passing it.  In contrast, if I had to write an examination on any of the mathematical-scientific lectures that I heard at UBC just a few years ago, (and that I studied assiduously), I would today score exactly zero on every one of them.  It is one of the grand mistakes of our educational bureaucracy to assume that all subjects are similar enough that they can be taught using the same methodology, and more specifically that they can rely equally on the lecture method, when it is obvious that this assumption is false.  The result of this erroneous assumption is vast inefficiency in teaching a very significant category of subjects — the mathematical-scientific subjects.

And I must qualify as well that occasionally, even in a mathematics or science lecture, something that is generally comprehensible may take place.  The instructor may relate some interesting anecdote, or he may give some memorable demonstration.  He may use balloons to show electron configurations, or he may use ping-pong balls to show molecular stacking, or he may produce striking color changes by mixing liquids, or produce violent bubbling or a loud bang.  In other words, he may put on a show resembling the shows that one can catch at a local science center.  I do not deny that this is valuable, but I do suggest that it occupies a very small proportion of lecture time, and that it goes a very small distance toward preparing the student for his examinations.  Thus, I do not take the position that it is every last minute of a student's time that is wasted in science-mathematics lectures, it is only most of his time.  And I do suggest as well that the difficult core of the curriculum cannot be taught with anecdotes and demonstrations, and it cannot be taught in lectures at all — the student must learn it mostly on his own.  Learning in mathematics and science consists largely in writing strings of numbers and symbols, and this is accomplished largely by doing, and little by watching, just as one learns to play tennis largely by hitting the ball, and little by watching someone else hit the ball, and just as one learns to play piano largely by striking the keys, and little by watching someone else strike the keys.  I can sit beside a tennis court for a thousand hours watching tournament play in tennis, and at the end of that time find myself unable to beat a good eight-year-old at the game.  I can sit beside the greatest pianist in the world closely watching his hands for a thousand hours, and at the end of that time find myself unable to play chopsticks.  I can sit through an entire calculus course watching the symbols unfold on the blackboard in front of me, and at the end of the course score zero on the examination.  Passive viewing is not how calculus or piano is learned.  Active practice is the only way it can be done.

Bogus verification

Although genuine verifications of student incomprehension are available but unused, bogus checks are commonplace.  A lecturer might say something like, "Any questions so far?" and take the ensuing silence as indicative of perfect understanding, not troubling himself with the possibility that it may also be indicative of a perfect lack of understanding.  I recollect Vince Manis of Computer Science 124 inviting anyone in the class to request from him a repetition of the last portion of the lecture, saying, "If even one student says he didn't understand it and wants to hear it again, I will repeat it."  Nobody raised his hand.  I hadn't understood him, and I didn't raise my hand.  I didn't want him to repeat anything.  He had been incomprehensible when he had presented the material the first time, and he would have been just as incomprehensible the second time.  The material was too complex to be grasped by means of passive viewing — I needed to work through it by myself.  If Vince Manis had not been shamming, he could have begun to get a rough idea of the level of student comprehension by employing any of the checks outlined above, but as this might have proved embarrassing, he preferred his bogus check which gave such complimentary results.

The students misbehave

But if the zombie hypothesis is true, if almost nobody understands what is going on, then what are all those students doing there?  Well, in the first place, they're not all there.  At UBC, full attendance is not the rule, it is the exception.  So rare is full attendance, or anything close to full attendance, that it is simpler to explain it than the opposite.  Full attendance usually means one of four things: (1) a test is being given, during which one is amazed at the contrast between the large number of students who suddenly make their appearance in comparison to the small number that one observes during lectures; (2) it's a lecture course without a textbook; (3) it's a small class and attendance contributes toward final grades, or at least non-attendance will be noticed; (4) it's not a mathematics or science course, and so comprehension is possible.

In a typical first-year mathematics or science lecture, however, attendance is likely to be closer to half of enrolment than to total enrolment.  Then on top of that, of the students who are in attendance, large numbers are paying no attention: some chat with their neighbors throughout the lecture, some read newspapers or work on unrelated material, some come for a few minutes and then walk out, some doodle and gaze around without taking notes, some sleep.  I do not exaggerate.  In practically every lecture, some students can be seen to be sleeping.  To take an extreme case of inattention to the lecturer, I vividly recall at one point sitting between two students who were talking to each other, and they talked loudly enough that they carried on their conversation without turning their heads toward each other, both looking straight ahead toward the blackboard, while separated by me.  Occasionally, a lecturer will complain of student noise, and sometimes even a student will burst out with a demand for quiet — but the effect is only a brief stilling of the tumult, and it soon resumes, as irrepressible as the roaring of the sea.

So then, what is going on?  If the amount of learning that takes place in a lecture is really negligible, then why are any students coming at all, and why do so many of the ones who come behave so badly?

Big textbooks, many problems

From the point of view of the student, the chief role of the lecture is to provide curriculum definition.  That is, when the course begins, the student does not know what material is examinable.  He typically has a textbook, but it may be some 800 to 1,200 pages long, and may contain anywhere from 2,000 to 10,000 problems — which is far more than he will be expected to master.  In a typical half-course (that goes from September through December or January through April, with the last month in each four-month segment being given over largely to examinations), he might only have to read a quarter that number of pages, and might only have to solve one-twentieth that number of problems, and so he has to come to class to find out which pages and which problems these are.  He also comes to class to learn the dates of tests and what these tests will cover, to find out what homework is assigned and to hand in homework, and to obtain other procedural information — all of which I include under the heading of curriculum definition.

Curriculum definition is dispensed only in class

Obviously, this curriculum-definition information could all be made available on the first day of class.  It could even be made available a month before classes start.  It could even be available on the Internet continuously.  But it is not — it is released in dribbles over the duration of the course.  Oh yes, there is sometimes a course outline indicating what pages are to be read, but in my experience, this is skimpy and unreliable.  It is skimpy chiefly in that while it may indicate what pages should be read, it will not indicate what problems are to be solved.  And it is unreliable.  For example, from our experience taking Physics 110 at UBC, Marko and I learned the Wheatstone Bridge, Young's modulus, shearing and compression, and Hall's method of distinguishing p-type from n-type semiconductors because these topics were on pages assigned in the course outline.  However, none of these topics turned out to be on the course.  So, given that the student will have his hands full if he does no more than the necessary work, he will want to avoid doing unnecessary work.  And for this reason, he will quickly realize that the advisable thing to do is come to class and listen for curriculum-definition information, and the inadvisable thing to do is to follow the course outline.  The super-astute student will continually verify with teaching assistants and faculty members exactly what it is that he should be studying, which Marko and I neglected to do, catching on only belatedly on the high importance of precise curriculum definition.

Supplementary materials

On top of that, some of the course will turn out not to be in the textbook at all — every instructor offers new material orally and by writing it on the board and by distributing it on handouts, and of this material too, only a fraction might turn out to be examinable, and it is up to the student to obtain this material which is made available only in class, and then to eventually discover what fraction of it is examinable.

The curriculum shifts

The students have to listen attentively because the curriculum is constantly being shifted on them.  For example, the students are given a handout, it is discussed, they invest time learning it — but then later they are told that they don't have to know it.  They are given problems for homework, they complete them and hand them in — and they are then informed that two of the problems won't be graded because they involve concepts that are not required for the course.  They copy down proofs of theorems in class, later find out that they needn't have bothered because these proofs are in the book — and as test after test fails to ask for any proof, they eventually realize that proofs are not examinable.

Here is a representative experience demonstrating the student's confusion — my confusion in this case — as to what it was that I was supposed to study and to know.  In Vince Manis's Computer Science 124 featuring the language Scheme, the main text along with supplementary texts were recommended and stocked at the bookstore, in which I found on page 16 or one text, page 17 of another, and page 35 of a third, a description of the cond expression.  The latter text described cond as "Scheme's most general and powerful tool for making choices.  In fact, once you have read this section, you don't ever have to use if again, since any if expression can easily be rewritten in cond form" (Eisenberg & Abelson, Programming in Scheme, 1988, p. 35).  And so on one of my lab assignments, I did use this general and powerful cond instead of the more limited and awkward if.  But Vince Manis had not as yet lectured on cond, and the marking key that he had provided the teaching assistant who was grading the labs used the more elementary and more awkward if.  This teaching assistant had had no previous exposure to the Scheme language, and so he did not recognize the cond in my lab report, and the teaching assistant complained to Vince Manis about the unfairness to him of not being able to simply compare each student's lab against the marking key.  As a result, Vince Manis announced to the class that the use of any expressions not covered in lectures would be penalized.  But how was I supposed to know that?  Every one of the three books that were either assigned or recommended for the course discussed cond early on, and recommended its use above if.  We were supposed to be reading these books, and presumably benefitting form them.  This incident is unusual in that it demonstrates not only the failure to provide curriculum definition, but the threatened penalization of students for knowing more than they had been authorized to know to date.  The course instructor having a choice between asking his teaching assistant to read ahead a few pages and learn something that he hadn't known before, or penalizing students in his course for doing so, preferred to keep his students back rather than moving his teaching assistant forward.

In other words, course instructors are in a continuous process of defining and redefining the curriculum as they go, of recommending material that they will penalize the student for using, of presenting material that they later decide they will not test, and of skimming cursorily over material that they will end up testing in depth.  The student is obligated to keep a vigilant eye on the instructors as they struggle to make up their minds, and as they release hints and clues and revisions.  One of the hardest tasks put before the student is to construct an accurate picture of the examinable curriculum.  Students who acquire skills in curriculum inference will find that such skills make a substantial contribution in smoothing their path toward earning a degree.

A second look at the lecture hall

Now let's get back to the students in a typical mathematics or science lecture hall.  Why do they act the way they do?  Here is my guess.

As curriculum-definition announcements tend to be made at the beginning of the class, that is why some of them come for the first few minutes and then leave.  When homework is due, students who have not done it come to class to copy it from someone else.  I made a point of handing mine in upon arriving in the lecture hall so that I would not be pestered with requests to borrow it by students who hadn't done it and wanted to copy mine.  After a student has copied someone else's homework, he has several options, the most brazen that I saw being to walk up to the front of the class while the lecture was in progress, arrogantly slap his paper down on the pile already on the table, and walk out of the lecture hall.  As for the students who don't come at all — they have trusty friends from whom they can get the curriculum information, or with whom they share the burden of coming to a fifty-minute class in order to extract two minutes' worth of curriculum information.  The somnambulists sleep during the portion of the lecture that is incomprehensible anyway, but were awake during the critical first few minutes, and at the end of the lecture will be in a position to have some wakeful fellow-student inform them of any curriculum-relevant announcements they may have missed while asleep; and will be awakened to receive any handouts that are being passed around.  The chatterers, the newspaper readers, the doodlers, and the crossword-puzzle solvers have given up trying to follow the lecture, and find that even while chatting or whatever, they can still pay enough attention to catch any curriculum-definition information that may be tossed their way.  In a no-textbook lecture course where students are forced to take notes, they find that conversation does not interfere appreciably with the mindless transcription of meaningless symbols, and so they enliven their copying with chatting.  And so maybe that's who the zombies are and that's why they come to class.

Zombiism not the fault of the student

Now I don't mean the word "zombie" derogatorily.  Fundamentally, there is nothing wrong with these students.  Outside the lecture hall, they are overall a decent, considerate, attentive, and responsible lot — at least as much as can be expected given their age.  But in the lecture hall, they understand the game in which they are being forced to play the pawns, and they participate on their own terms — grudgingly, perfunctorily, rudely.  But their negligence and irresponsibility are superficial and situation specific — if one looks not at their classroom behavior but at their accomplishments, then one gets a very different impression, for where society credits them with mastering a year's academic work in an academic year's time, and only with the help of their teachers, they in fact accomplish most of their learning in a small number of cramming sessions and largely on their own.  Under more optimal learning conditions, students with such demonstrable powers could accomplish miracles.  I started out calling them "zombies" because they had as much idea of what a lecture was about as if they were in a coma — but this it turns out is no sin, for it is almost impossible for anyone to know what the lecture is about.  If students are guilty of any sin for which they deserve the label "zombie" in a derogatory sense, it is the sin of failing to grasp that they are being victimized and that their victimization is escapable, and of failing to demand their own emancipation.

Now on the one hand, the confirmation of the zombie hypothesis is very bad news — it tells us that mathematics and science students have the bulk of their lecture time wasted.  But on the other hand, it is very good news because the situation is easily remedied by adopting an open curriculum, and the remedy brings with it several astonishing benefits.  The remedy, furthermore, is not totally unprecedented — it is merely an extension of something that is already being done in the occasional course with great success.

The student must be given the core curriculum

Imagine, now, that for a calculus half-course lasting three months, the student purchases at the book store a booklet containing 500 core problems, and is told that learning to solve these 500 problems constitutes the course.  I pick the number 500 because Marko and I did take an integration half-course from Professor Charles Swanson at UBC — Mathematics 101 — in which approximately 500 problems did constitute the core curriculum.  For other courses a smaller number of problems will be appropriate, and perhaps for other courses a larger number.

On any examination, the student will be asked to solve some sample of these 500 core problems, and of course the problems on that examination will be altered by transforming the core problems.  Sometimes the transformation will be superficial, as by changing the coefficients and the variable names, so that for example where within a core problem there is a 2X + 3 which yields a final correct answer of 31, the transformed problem might instead contain in the same place a 5Y - 9 which yields a final correct answer of 14.  Such changes will make it unprofitable to memorize the correct answers to the 500 core problems, and will make it impossible to be reminded of the nature of the required solution by seeing a particular pattern of numbers and letters in a question.

But the transformation of a core problem into one that is actually given on an examination need not be as superficial as merely changing the numerical coefficients and the symbols.  For example, I recollect that in integration, one learns general techniques for computing a certain class of volumes, and that these techniques apply to an indefinitely large number of shapes.  For example, one may imagine outlining a volume as follows: one draws on the ground a given circle, then using wire one builds an equilateral triangle sticking straight up into the air, where the base of the equilateral triangle is a diameter of the circle.  Then, parallel to the first wire triangle, one constructs a whole bunch of equilateral triangles, all sticking straight up into the air, and all having as their base a chord of the circle, such that the triangles become smaller and smaller the farther they lie from the original diameter that provided the base for the first and tallest triangle.  The computation of the volume of the form that is being outlined by this construction is straightforward, and the technique applies no matter what shape is initially drawn on the ground, and no matter what wire shape is built up into the air using the shape on the ground as a foundation.  For example, if one can compute the volume in the first problem, then one can also compute the volume in a problem where a given ellipse is drawn on the ground, and with wire squares built on the ellipse so that they stick straight up into the air with their bases parallel to the minor axis of the ellipse.  Thus, perhaps if the first problem is specified in the core curriculum, the second problem may appear on an examination because the second is merely a variation of the first.

The student must be given solutions to the core curriculum

Now it is important that every problem also come accompanied by a complete and optimal solution, or with several alternative solutions where more than one is possible.  Without complete solutions, the student will often get stuck and find himself unable to continue — and in such a case, what is he to do?  I will tell you what he is to do, because either Marko or I have often had to do it, and I hope you will be as astounded at my answer as I am, and as indignant at the educational bureaucracy as well.  The student is to wait until the professor's office hours, which may be several days removed.  Already, we see a travesty — a student with a question having to wait several days before he can hope to have it answered.  The examination that the student is studying for may be only a week away, and yet he may be required to wait several days before he gets to ask his question.  The examination may be tomorrow, and yet the student cannot ask his question until the professor has his office hours, which may not be until the day after tomorrow.

In any case, let us assume that the blessed day containing the office hours arrives — what then?  Then the student stands in line cooling his heels, because with the examination coming up, a line of students has formed outside this professor's office.  In standing in this line, any student who is in the habit of conceptualizing better worlds may feel his impatience mounting.  He has better things to do than to stand in this line; there are better ways to deliver information to him than this procedure which is no improvement over what might have been the practice in the Middle Ages.  Here the student feels himself the victim of the contempt of the university toward efficiency and toward saving the student time.

Well, and eventually the student is admitted into the professor's office, puts his question, scribbles down something that the professor says or writes on his own board, and then take it away with him to his own desk where he can begin to ponder it.  That's what the student has to do when he has a question.  Mind you, this may be examination time, and he has other courses, and so he might have a hundred more such problems which he urgently needs to solve after the one that just stumped him, and so this waiting for office hours and getting into line to obtain each piece of information may strike him as cumbersome and inconsiderate of his time — but that's what the university deems best for him, and that's what he's stuck with.  And if, as often happens, he finds that what he scribbled down in the professor's office still has not helped him, then what?  Then it's rush back to the professor's office before his office hour or hours for that day have expired, else the student will have to wait for another day to continue the clarification of the point on which he is having trouble.

And that's not the worst case.  A worse case is an instructor — Vince Manis teaching Computer Science 124 at UBC, for example — who refuses to announce office hours.  A worse case is Vince Manis who refuses to announce office hours and who on top of that does not answer his door when a student knocks, pretending he's not in, cowering silently in his unlit office waiting for the student to go away, and opening his door only when his teaching assistant knocks and whispers, "Vince!  It's me!"  That is worse, and that does happen at UBC, and similar travesties happen everywhere.

But surely any of this sort of inconvenience and delay in obtaining information is insufferable and indefensible.  Surely there is a better way of delivering information.  And surely that way is to give students complete solutions to all problems on the curriculum so that when they get stuck, they can unstick themselves without delay.  Surely to restrict the flow of information is totalitarian in intent and in effect — totalitarian in intent in that it increases the power of those controlling the information, and totalitarian in effect in that it increases the dependency of those to whom the information is denied.  I have been in situations in which I have had full access to all solutions, and the only effect of this was to expedite my learning, and I have been in situations in which full access to solutions was denied me, and the only effect was to put an obstacle in the path of my learning.

The student must be given lecture notes

And there is a third thing that the student must be given — lecture notes.  Not just any lecture notes, but a really good set, an optimal set, a superb set.  Such lecture notes would differ from a textbook in that they would be both necessary and sufficient, which a textbook is not.  Necessary in that everything in the lecture notes would be needed and would be examinable — which is not the case of a textbook, in which a lot of material is not examinable.  Sufficient in that nothing more would be needed in order to write a perfect final examination — which is not the case of most courses which add material that is not in the textbook.  Students would still have mammoth textbooks recommended to which they could turn for greater depth on topics that they found interesting, or for a more detailed explanation on topics that they found difficult, or for color and richness and anecdote and pretty pictures — but the existence of the official lecture notes would banish the possibility of confusing or misleading students as to exactly what was examinable in this textbook and what was not.

Copying these lecture notes off a blackboard day after day — the way that it is done now — is not an acceptable alternative to being handed the whole batch of them at the beginning of the course.  There can be no justification for making students come to class to copy things that they aren't going to understand at the time of copying, and when the resulting notes are sure to be defective.  How might they be defective?

(1) As the lecturer is writing on the board, he is bound to make a mistake or two (which may or may not be caught by someone).  (2) As the student is copying off the board, he is bound to make a mistake or two more.  (3) The student may have terrible handwriting, and so produce notes that are in places illegible.  (4) The student may be too rushed to get down everything that the instructor is saying.  (5) The student may be sitting toward the back of the class, and thus find it hard to read some small or indistinct or faint writing on the board.  (6) The student may have his view obstructed by a projector, or by the body of the lecturer.  (7) The student may be unable to hear clearly what the instructor is saying because the instructor has his back turned, or because he is mumbling, or because he has a strong foreign accent, or because there is commotion in the room.  (8) The student may be late coming to class, or may miss a class.  Still other reasons can be found for notes being defective.  Marko described a case to me in which he was sitting toward the right in the front row of a lecture theater, and the instructor was writing at the leftmost of three boards, and Marko was unable to see what the instructor was writing, and so was forced to copy from the notes of the student to his left, but that student was copying from the notes of the student to his left, and that student was copying from the notes of the student to his left.  Although any one of the impediments to good note taking mentioned above may have only a small probability of occurring during any particular lecture, the probability of one or more occurring during every lecture is high.  The result is defective notes.  And on top of all that, any notes copied in class that are intended to cover the entire course are likely to be defective because the amount of material in an optimal set of lecture notes will probably exceed what the student has time to write down during the available lectures.

Examination construction must be computerized

So, we start with a student who has been given his 500 core questions, complete with solutions, and accompanied by superb lecture notes — and this is what I mean by an "open curriculum," and already it is a vast improvement which by itself guarantees that such a course will be popular and that the students in such a course will turn in superior performances.  As I said above, Charles Swanson did something close to that at UBC, and his course was swamped with students trying to get in, and student performance was high.

But that is not all — here comes the really good part.  Imagine that these 500 questions are put on computer, and then a program is written which selects questions that will appear on a final examination — a program that picks say one question from the first section, two questions from the second section, and so on.  Imagine, furthermore, that the computer introduces random changes both in the coefficients within each problem and into the variable names, and introduces all the variations which have been specified as being permissible, as discussed above, and so is able to print out sample examinations — as many as the student wants — and also solutions to each sample examination.  The real examinations administered by the university, furthermore, are printed out by the same program, so that the students' sample examinations are indistinguishable from the real ones.  At the same time, students who are not ready for any final examination but who want to test themselves on what they have learned so far can ask for tests on individual topics, or on several topics at one time.  And imagine, finally, that this program is put on diskette or on CD-ROM and sold in the university bookstore for some nominal sum.  What would be the result? The result would be a revolution in education!

Benefits of an open curriculum

First of all, the students would have an unprecedented level of curriculum definition.  They would have the 500 core problems with solutions, and they would be told the rules by which the computer selected problems for a final examination, and the rules by which the computer altered the questions, and they would have access to an unlimited supply of sample examinations, every question accompanied by an optimal solution, of course.

Now this resembles what already happens.  Today, it is commonplace for students to purchase past years' examinations with solutions.  But doing it on computer as part of an open curriculum would be better for two reasons:  (1) As things are now, the curriculum shifts from year to year, so that previous examinations cover different material.  (2) The solutions presently being provided tend to be prepared by senior students and are error-ridden.  Forever etched in my memory was the anxiety on the face of a fellow student when I informed her — as we were about to enter a final-examination hall — that several of the previous-examination solutions that we had all purchased from mathematics students and had studied from and trusted were wrong.  Marko and I had come to this realization during our study, and Marko had taken our information concerning defects in the solutions to the senior mathematics students who had acknowledge their errors, but there was no way of getting corrections to the students who had purchased the solutions and were relying on them — no one had a record of who these students were, and there was no time.

The computer-generated sample examinations, in contrast, would remove both of these shortcomings — every sample examination would be highly similar to the upcoming examination, and the accompanying solutions would be error-free.

No more examination by ambush

And as a result, forever abolished from the face of the earth would be examination by ambush — the examination to which the student goes not knowing what to expect, or the examination to which the student goes with reasonable expectations, but which asks such bizarre questions that it seems to be from some other course.

No more fluctuations in examination difficulty

A computer-based open curriculum would also prevent the frequent miscalculation on the part of the instructors of the difficulty of an examination, and so would prevent the ludicrous outcome of seventy percent of a class being failed, which has happened at UBC, and which reflects not at all on the students, but only on the immaturity and inexperience of their instructors.

No more failure

Indeed, under a computerized open-curriculum system, failure might become a rare phenomenon, as students would now be able to pre-evaluate themselves as often as they wished, and according to the same criterion that the university would be using to evaluate them, and so if their own pre-evaluations told them they were going to fail, then they might be convinced that they needed to do more work before examination day.  And even if a student did take an official examination and did fail it — there is no reason why this should become a permanent part of his record.  Let this failure be re-defined as a practice examination.  Let the student's loss be no greater than a $20, say, administration fee.  Let the student take as many examinations as he wants, with only his highest grade being recorded on his transcript, and all the others being considered to be exercises under conditions of official invigilation.

No more cheating

A computer-based open curriculum brings other unlooked-for benefits.  Today, cheating is a serious problem.  On term tests in particular, in a large crowded lecture theater, the students may sit elbow to elbow, with the answers being written by the student to the left of them almost as close as their own, and only more difficult to scan because of that neighbor's hand being in the way, and only when that student is right-handed.  But with computer-generated examinations, cheating can be prevented by having the computer generate a different examination, or a different variation of the same examination, for each student.  Having many alternative versions of an examination within one classroom would slow grading, but only trivially — each examination would come with its own code number, and punching that code number into the computer would produce a printout of that paper's solutions, and that printout could be stapled to the students' answers.  The markers would then consult the attached printout when marking, and the students could later use the same attached printout of solutions to review their performance.  The computer programming required to achieve this result strikes me as modest, such that I could readily see myself writing such a program for introductory calculus, even though I am not a professional programmer.

Still on the topic of cheating — at the University of Western Ontario where I once taught, my secretary was propositioned by a cleaning lady to steal examination papers for money.  My office seemed under constant assault by students trying my door when they thought I wasn't in, usually at night.  A student was once left alone in my secretary's office when she stepped out for a moment, and he immediately opened a side door between her office and my own, and stepped into my office, but was unable to account for why he had done so.  A coed invited me to help her study at her apartment on the evening before one of my examinations.  Thus, a professor's having curriculum-definition information, or examination information, that is denied to students makes him the object of theft and of corruption.  A computer-based open curriculum circumvents all such perils by equating teacher and student on their knowledge of any upcoming examination.  The roles of teacher and evaluator become separated — the teacher prepares the student to write an examination, but his information as to exactly what questions will be asked is no better than the student's information and in preparing the student, the teacher freely divulges everything he knows, and so there is nothing to be gained from breaking into his office, and nothing to be gained by offering him bribes.  It is the evaluators that the student must satisfy, and these consist of a small staff with whom he has no contact, and who rely on the same computer program available to him.

No more unfair advantage

And there are other things that would be prevented that may not qualify as outright cheating, but that constitute the granting of unfair advantages.  As things are done today, one professor may give away more of an upcoming examination to his class than another, or a given professor may happen to drop more hints to a few of his students than he does to others.  The professor is subjected to incessant pressure from students who use every means at their disposal — the chief two being their personal attractiveness and their stories of the handicaps under which they have to labor — to extract from the professor information as to the nature of an upcoming examination.  The system, then, is one that invites corruption, and where corruption is invited, it necessarily occurs.

Teaching assistants, too, may know things about a professor's examination policies and preferences, or they may have seen the final examination, or may have helped to prepare it, and so be in a position to pass along pertinent information to favorite students.

Some professors give similar — sometimes almost identical — examinations from year to year, and students who learn this and discover that these examinations are on file and available for inspection and photocopy can benefit enormously.  Some professors attempt to keep all their past examinations from students and refuse to put them on file, but as these examinations have passed through hundreds of hands, a few students are able to obtain copies, and these few benefit enormously.

With a secret curriculum, a teacher must hold back and measure how much in clear conscience he can tell any particular student about an upcoming examination.  With a computer-based open curriculum, he is not only permitted to tell everything he can, but is also obligated to.  He is thus transformed from an antagonist of the student to an ally.  The role of teacher and evaluator are sundered, such that the teacher is no longer the evaluator, and thus he can concentrate all his energies upon the role of preparing the student for the evaluation that will be conducted independently.

No more errors

The preparation of a final examination is often more hectic than it should be, so that sometimes a question turns out to be devastatingly hard, or unsolvable, or entirely meaningless.  Or, sometimes after a final examination has been graded and the grades officially released, it is discovered that the solution that the graders had assumed was correct was in fact incorrect, so that some students who had wrong answers were given credit, and all students who had the right answer were given no credit, and since re-marking that question on thousands of examinations and then revising all the grades would be costly and embarrassing, the error is hushed up.  Problems such as these the computerized open curriculum would also sweep away.  All questions would make sense; all solutions would be correct.

No more simultaneous testing

The extra labor of devising make-up examinations for students who excusably missed an examination is now replaced by the touch of a button.  In fact, there need no longer be any such thing as a missed examination because there would no longer be any reason to herd students into large halls so that they could write their examinations simultaneously.  If a particular student felt that he had mastered a three-month course in one month, he could just walk over to a testing center, and if it was booked for the day, he could reserve a time on the next day, or the day after, but if there was an empty desk available right then, then the attendants could just punch a few buttons, and out would come his examination questions which he could answer on the spot.  Graders would be continuously available, and as the optimal solutions could at any time be printed out, the examination could be graded within minutes after being completed.  When the student walked out of the examination hall, he could be clutching in his hand not only his question paper, but also a photocopy of his own answers, a copy of the correct solutions, and his grade.  If he failed, or if he received a grade he was unhappy with, he could resume study for a few more hours, or a few more days, or a few more weeks, and retake the examination at any time.  No need to keep a record of the inferior performance — why not consider it merely a practice examination?  Students can take practice examinations as often as they want — for free, of course, if they do it with their own software on their own computers, and for an administrative fee if they want to take the practice exam in a formal examination hall.  A student would fail, or be credited with a low grade, only in the case where he simply did not care to make the effort to upgrade a poor performance.  Or, a failure to meet a minimal standard need not be recorded, the school measuring a student by what he has been able to do in a given space of time, and not by what he hasn't.

Perhaps all this is a little optimistic.  Perhaps, for example, it would be impractical to have graders competent in all subjects always available, so that a student taking an examination would typically have to wait a day or two to receive an examination grade.  But it certainly wouldn't take anything like the unconscionable six weeks to receive a final examination grade that it takes today.  And even if his official grade might not be available for a day or two, the student could still walk out of the examination hall clutching a copy of the question sheet, a copy of his answers, and a copy of the correct solutions.

No more unverified grades

Anyone with experience taking mathematics and science examinations, and who still remembers these experiences accurately, will agree that the nature of the experience is entirely different from what someone who has never lived through it might imagine.  The naive person without experience taking mathematics and science examinations imagines that the student learns the material as it is delivered to him, and having learned it knows it in some permanent sense — retains it until the time of the examination, and knows it almost as well a month later or a year later.  But that impression is in error.

The reality is that the material that will be examined in a typical mathematics or science examination at a good university like UBC is so voluminous and so complicated, that even a very good student brings his mastery of the entire course to a high level only in the final hour or two before the examination.  If the student had been suddenly commanded to take the examination one day earlier, he would have scored dramatically lower, and two days earlier, catastrophically lower.  And just as learning mounts to a peak just before the examination, so too does it evaporate rapidly afterward.  Following the examination, forgetting is precipitous.  A few of the most difficult topics, the ones that were crammed in the last hour or two before the examination, will be forgotten within a few hours afterward.  A student who was suddenly commanded to retake a comparable exam just a day or two later, would perform much worse.  A student who received a very high mark on an examination, but a month later was without warning commanded to retake a comparable examination could easily fail it.

This rapid learning, and more particularly the rapid forgetting, is relevant to the topic of a student demanding to inspect his final examination answers, which he does have the right to do today at UBC.  More specifically, suppose that a student thinks that he wrote an excellent examination, but finds he gets a disappointing grade.  Suppose, furthermore, that the course instructor has demonstrated that he is negligent and irresponsible and incompetent.  The combination of a disappointing mark together with an untrustworthy instructor happened only once at UBC to Marko and me, in a computer science course — yes, it was Vince Manis from Computer Science 124.  Marko and I requested to see our final examinations, the only occasion on which we had ever requested to do so — which I point out only to dispel the notion that we were malcontents always griping in an effort to raise our grades, when the reality was that we uniformly got high grades and uniformly found no reason for dissatisfaction with examination grading.  But such was not the case on this one occasion, and so we arranged a time on which we could examine our examination answers and view the marks that had been assigned to them.

And so we met in a small room, Vince Manis handed us our examinations, and then waited for us to complete our perusal.  But what good did this do?  None whatever!  The final marks had been released some six weeks after the examination, and arranging to see the examinations took another week or two — I don't remember exactly how long.  Thus, we were looking at our examinations almost two months after having written them.  By that time, our forgetting had been severe.  Had we been able to verify our examinations within minutes of taking them, or at most in the day or two after taking them, we would have remembered enough to make the verification meaningful.  But almost two months later! — We weren't able to remember enough to follow our own solutions, or to tell whether the mark that had been assigned was justified or not.  But even at that late time, had we been able to photocopy our examinations and take the photocopies with us, and had we been supplied with what the instructor thought were the correct solutions, then we would have been able to review the course enough to compare our answers with the instructor's answers, and decide whether we had been fairly graded or not.  But such a review on our parts would have taken time — hours at the very least, and possibly days.  But we were not allowed to photocopy our answers, and we were not allowed to see the instructors answers, and we were not allowed days — we were allowed minutes.  This permitted us to accomplished exactly nothing.  After a quick and uninformative look, we left, having gotten no nearer to understanding whether we had been fairly graded or not.

My point is that all this is bad, and all this is easily avoided in a computer-based open curriculum.  A computer-based open curriculum permits a student to compare his answers to what the university holds to be the correct answers immediately, at a time when his knowledge of the course still permits him to understand the two.  A computer-based open curriculum makes it possible for the student to be convinced that the mark he received was fair, and not the result of some prejudice or error.  A computer-based open curriculum permits an examination to become not only a means of evaluating the student, but also a learning experience for the student.  As things stand now, there is effectively no way for a student to verify his grade.  A few minutes' scanning of his examination paper two months after he writes the examination brings him no benefit, and is incapable of correcting any injustice, other than the simple one of correcting an instructor's adding up the marks incorrectly.  Thus, given that the student would immediately be able to compare his answer to the correct answer, and would very quickly be told what mark he had been given for his answer, he would no longer be left with the nagging suspicion that the markers may have misunderstood his unconventional answer and given him no credit for it, or the nagging suspicion that a certain question really had no correct solution at all, or that there may have been a mistake in adding up his final grade — now it would all be open and above-board and verifiable.

No more timetable clashes

And no more examination time-table conflicts where a student has two of his examinations scheduled at the same time, or examination pile-ups where several tough examinations have to be written with insufficient breathing time in between, or examination spread-outs where some simple examination has to be written weeks after all the others, and perhaps delays the student's departure for home of for a job in a distant city.

And similar things can be said about course scheduling.  As things now stand, students must sometimes select only one of two courses that they would like to take because the lectures for these two courses have been scheduled for the same times, or for overlapping times — but this would be less of a problem if an open curriculum released students from attending lectures for purposes of curriculum definition.  Or, as things now stand, students are often prevented from registering in a course because of limitations on the capacity of the lecture hall in which it is taught — but this ceiling could be raised if it turned out that fewer students attended because attending in order to obtain curriculum definition had been removed as a motive.

The student can start sooner

The freedom that a computer-based open curriculum brings is truly radical, because now there would be no need for a student to waste time waiting for a course to begin.  Imagine a student in April who finds himself unable to get a summer job, or who preferred to make progress toward his degree rather than taking a summer job.  As things stand now, there is not much that he can do.  Many of the heavy courses that he wants to take are not offered in the summer, so that the next time that he can resume his studies is in September, more than four months away.  So, for four months, he marks time as far as academic progress goes.  He loafs through the summer, or he does land a job flipping burgers.  The world cries out for better physicists, better computer engineers, but tells physics students and computer engineering students who are itching to get on with their studies that they have to kill four months awaiting the convenience of the university to begin teaching.  But why this enforced passivity?  Why does the educational bureaucracy demand such large gaps in the time he spends learning?  By what right does the university deny students speedy progress toward their degrees?  What is the rationale for granting a university a monopoly on information, and then allowing the university to strangle the flow of information?

A computer-based open curriculum permits the student to start a course whenever he wants.  If he has nothing to do in May, and wants to begin studying Japanese in May, then he can start his studying the very same day — at the very moment when the urge seizes him.  He does not have to wait until after Labor Day in September.  How can anybody object to that?  How can anybody see any virtue in discouraging a student from beginning any course of studies for four months?  What educational theorist has advocated the enforcement of four months of intellectual idleness during a summer, even when a student would prefer to continue advancing toward his degree starting in May?  How does it come to pass that this peremptory and wasteful strangulation of education is accepted as inevitable?

And delay can be much more onerous than that.  Imagine a young man who has a checkered academic record, and following some interruptions, decides he would like to become a lawyer.  Excellent choice, in his case.  He has the brains, and he has the personality, and he has learned lessons on the importance of dedication toward a career goal.  But think of the obstacles that stand in his way!

First, he has to take the LSAT, and that may be months away, enough months that he will miss the application deadline for admission the coming autumn.  The nearest it will be too late for him to apply to law school the coming autumn.  But that next autumn may be a year and a half away!  It is discouraging enough to foresee that one can become a lawyer after maybe three years of law school and one year of articaling--but that one can't start this process for another year and a half is very discouraging.  And the dealy is entirely unnecessary.  In the ideal society, and one that it not unrealistically Utopian, but rather is realizable today, and will be realized in the near future is that anyone who wants to study, say, criminal law today, will be able to begin his study just as quickly as he logs on to a computer.  Not a year and a half should it take to begin studying law, but a minute and a half.  And not three years of law school, when if the wasted time is eliminated, the whole thing can be done in two years and during those two years a much higher level of mastery can be achieved.  That is what is available today.

And one sees in the description the reason that it is not available today.  In order to reduce competition for lawyer slots in our society, existing lawyers oppose and prevent the removal of obstacles to the study of law.  They don't want people knowing law, because that weakens their career tenure.  They strangle education, they obstruct learning, practices which are damaging to the society, and should be not only discouraged, but criminalized.  Yes, obstructing learning should be a criminal offense, and should win jail time.

The student can start later

But the computer-based open curriculum is not merely a system allowing some students to shoot ahead.  It is, rather, a system which accomodates all needs.  And so, some students will want to go slower.  Perhaps they have other obligations and other distractions which do not permit them to progress at an accelerated pace or even at the standard pace.  Perhaps their personalities are such that they prefer to linger over on each topic, that they prefer to reach the peak of enjoyment that accompanies a peak of mastery of each topic before moving on to the next.  Why, then, should they be forced to complete a half-course in three months when they might prefer to complete it in four, or five, or six months. for such reasons, as I say, that they have other obligations, or perhaps because they particularly enjoy the subject and wish to delve into it more deeply than is required?

Or, instead of starting a course earlier than in September, why should they not be allowed to start it in October, or November, or December?  Perhaps they can't start at the traditional date after Labor Day in September because their polar expedition is not quite finished yet, or their solo crossing of the Atlantic in a kayak happens to be in progress, or they have not yet finished writing their novel, or they are about to give birth, whatever.  Why should the educational bureaucracy be empowered to tell a student that wants to start a month later, in October, that his only option is to start in September of the following year?  This answer is unsatisfactory.  The educational bureaucracy is being peremptory, inconsiderate, and destructive.  The advent of computers has made it possible for students to learn at their convenience, and to be released from the burden of being forced to learn only at the convenience of the school.

Less wasted faculty time

The open curriculum would save a vast amount of faculty time.  Right now all over North America, thousands of faculty members are all busy trying to figure out which pages to ask the students to read, which problems to assign, what questions to ask on examinations, what might be the correct answers to these questions, and so on.  And the question must arise as to why these thousands should all be duplicating each other's efforts, when it needs to be done only once on the computer, and from then on the computer program can be improved and refined , but with a far smaller investment of time, and with an increasingly superb product available all over the continent, all over the world, with each revision.

No more rejection of qualified students

In those lectures whose chief benefit to the student is curriculum definition, an open curriculum will lead to a drop in attendance.  If any students should remain who value the lectures either as the primary conduit of course material or as an adjunct to their private study of an open curriculum, then they can continue to attend lectures — but these students will constitute a minority.  Such a drop in attendance can be viewed as still another benefit of a computer-based open curriculum.  It will benefit, among others, students like the 3,300 qualified applicants who were denied admission to UBC in the fall of 1992.  These students were denied admission because there was no room for them in the lecture halls, but if they could have found seats in these lecture halls, then in most cases they would not have understood what was being said in them anyway, so in fact there was no need to deny them admission.  Far better to have admitted them and to have given them adequate curriculum-definition so that they were not forced to come to these lecture halls for the sole purpose of obtaining curriculum-definition.  And from the university's point of view, far better to have pocketed their fees too.  No news should be met with greater joy by cash-strapped universities than that student morale can be boosted and student learning can be facilitated while cutting costs at the same time.  From a financial point of view, the recipe of the open curriculum is irresistible.  Of course some of the savings would have to be passed along to the students and to the taxpayers.

Why must students be qualified, anyway?

But the revolutionary impact of a computer-based open curriculum seems to know no bounds.  Having implemented such a computer-based open curriculum, it would become immediately apparent that meeting admission requirements would play a greatly reduced role.  Thus, if someone who has studied calculus on his own wishes to come to the university and pay the fee for taking a calculus examination, why should he be prevented from doing so, and from being given official credit for his performance?  In a society which values learning, which promotes academic achievement, which prizes intellectual accomplishment, which needs the mastery of difficult skills in order merely to survive, how can the university be given a monopoly on dispensing higher learning, and how can it justify granting credit for mastery of any subject on criteria other than a demonstration of competence?  Just as it is sometimes said that God is everywhere and hears your prayers as well whether you are in a formal place of worship or sitting on a bus, so is it too with learning — learning can take place everywhere, and learning that takes place on a bus can be just as effective as learning that takes place on a campus.  If it is learning that is important, and not the preservation of the university's monopoly on learning, then learning must be recognized as being ubiquitous, and every demonstration of that learning must be admitted onto one's academic record.

Lower tuition costs

And here is suggested an argument that students who periodically protest fee hikes should be using — that much of their tuition goes for things that fail to benefit them — indeed, that injure them; specifically, lecture halls in which they do not enjoy being confined, and lecturers that they do not understand.  Their time is wasted, their morale sapped, and to defray the cost of this they are handed an ever-increasing bill.

Answering unprecedented questions

To the objection that the open curriculum would teach students how to answer the core questions, but that what the university should be teaching them is how to answer new questions, several replies come to mind:  (1) When one becomes aware of how little the average student actually learns, and that in first-year calculus, something like a quarter to a third of all the students fail, the idea that the secret-curriculum system teaches the creative solution of unprecedented questions does not seem credible — it seems laughable.  (2) Whatever questions are asked on an examination must inevitably be drawn from some pool, and so the only issue remaining is whether the student is to be allowed to see this pool or not.  If he can see it, he knows what to study; if he can't, he doesn't.  (3) The best way to learn how to solve unprecedented problems may be to acquire experience in solving a diverse selection of given problems — and so that students coming out of an open-curriculum course may be able to outperform students coming out of a secret-curriculum course on any examination, whether it contains unprecedented questions or not.  (4) One wonders whether there are any truly unprecedented questions being asked on examinations today, or whether these are merely variations on problems that have been studied.  (5) If truly unprecedented questions are being asked, can this be justified?  Surely, an examination legitimately tests what a course has taught, and not what some rare genius among the students may be able to answer.  (6) That rare genius may be merely a student whose love of the subject has exposed him to a broader range of problems, so that the problem which for most students seems unprecedented, for him falls within a familiar pool, and so that if that question had been included in the core of an open curriculum, then prior exposure would have been equated for all students.  (7) If difficult and unfamiliar questions are indeed being asked, then one may enquire how many students are answering them correctly.  If the purpose of any question is to distinguish the more able students from the less able, then a question that no student answers correctly is a totally wasted question, and a question that almost no student answers correctly is an almost totally wasted question.  A totally wasted examination is one which assigns the same grade to all students; the best examination is one on which the overall grade varies the most.  In the case of questions whose answer is either right or wrong, the greatest variance in grades on the whole examination will be achieved when the probability of a student answering each question correctly is 0.5 (which is to say, when half the students answer each question correctly, and which is to say, when all questions are of moderate difficulty).  The more that the probability of answering a question deviates from 0.5, the more wasted a question is.  In the extreme case, a question that every student gets right is totally wasted because it fails to distinguish the better students from the worse, and fails to increase the variance of the overall grades, and the same is true of a question that every student gets wrong.

A look back at the secret-curriculum system

For the secret-curriculum system that is presently in place, it is difficult to muster any defense.  It is a system in which the student learns what a course requires of him only by spending many weary hours picking the information out of a stream of unintelligible verbiage.  It is a system which pretends that course content is transmitted from teacher to pupil, but where in reality the pupil often understands only the curriculum information that defines for him what he will eventually have to cram on his own.  It is a system which places obstacles in the path of learning, and then blames the student when he doesn't learn.  It is a system by which the faculty establishes a monopoly on curriculum-definition information, and dispenses this information to students in small pieces as a reward for attending lectures and thus for bestowing an air of legitimacy on the lecture method.

The abolition of lectures?

Advocating an open curriculum is not at all advocating the abolition of lectures, it is only advocating the removal of a single reason for attending lectures — the bad reason of curriculum definition.  Upon the removal of this reason, attendance will indeed drop in lectures dealing with topics that because of their complexity are not amenable to being taught by the lecture method.  In some cases, that attendance will approach zero.  In consequence, the role of the faculty in certain disciplines will change.  As things are done now, mathematics and science students put the faculty to greatest use before examinations when the students have begun their cramming, and when for the first time they have learned enough to be able to ask questions — that is when the lines start to form outside the professors' offices.  If the result of an open curriculum, and the self-pacing that computerization permits, is that students engage in a more even and sustained effort, and if the result is also that they take their examinations staggered over time, the chief effect on the faculty might be that students begin appearing at the professors' doors in a less overwhelming but steadier stream throughout the year, such that in certain disciplines, voluntary individual consultations might replace lectures as the primary mode of faculty-student interaction.  Thus, there is no reason to think that with fewer lectures to deliver, the faculty will have less to do, or that a smaller number of faculty members will be required.  All that will be changed is how the faculty spends its time.

The student's many gains

From the point of view of the student, the benefits of a computer-based open curriculum are so numerous and so weighty as to make the option irresistible.  The student's time is no longer wasted travelling to and from, and sitting in, a class where he learns nothing.  He is relieved of the guilt and demoralization that result from being made to feel stupid many hours each week listening to incomprehensible lectures.  He gains the security of knowing exactly what it is that he is responsible for learning, and he does not spend time learning things that are not examinable or neglecting to learn other things that are examinable.  He is able at every stage to pre-evaluate himself so that he knows where he stands; to pre-test himself on every examination so that he can estimate how well he is going to do.  He is freed of the fear of examination by ambush.  Following every problem that he works out, and following every examination that he takes, he is given immediate and error-free feedback.  He is not plagued by errors in his notes and in exercise problems and examination questions.  He is not corrupted by seeking unfair advantage, nor does he have his class standing lowered by other students who succeed in gaining unfair advantage.  He is able to pick up where he left off following some interruption to his studies, and able to move through a curriculum either faster or slower than is typical.  Because he no longer pays for lecture halls and lecturers which do not benefit him, his tuition fees drop.  Because the university's costs fall too, it is able to provide the student with finer libraries and better-equipped laboratories.  By the elimination of scheduling conflicts, he is given a wider selection of courses, and by scheduling his own examinations, he avoids examination timetable clashes and inconveniences.  Perhaps most important of all, he is relieved of the nightmare of every day having to participate in the charade of pretending that learning takes place in the classroom, when it does not.

True of elementary school, high school, and university

Although most of the comments above apply to my experiences at university, they obviously apply equally to high school, and to elementary school as well.  All of education, from the first day to the last, is hurt by a closed curriculum, and all education is helped by the adoption of an open curriculum.

Educational crimes

A revolution in education is imminent and unstoppable, and will take place just as soon as the public begins to recognize that placing impediments in the path of learning is a crime.  It is a crime to hold a monopoly on education, and to exercise that monopoly so as to perpetuate archaic and inefficient bureaucracies.  It is a crime to take many times the money from the public purse than is needed to achieve a given end.  It is a crime to subordinate individual needs to institutional needs at a time when advances in information technology make such subordination no longer necessary.  It is a crime to support a system which demoralizes students while wasting their time.  It is a crime to teach students to submit in silent resignation to practices for whose failure they are asked to shoulder the blame.