About Grades


About Feedback

The Uses of Grades

What Grades Mean

Concluding Thoughts

Sometimes it seems as if the purpose of going to school is to get good grades. That is how we tell ``good'' students from not-so-``good'' students. It has gotten to the point that many people assume that there is a contract of sorts: if a student works hard, the student earns a good grade. Moreover, people take grades personally, as if getting an A means that one is an A person --- and getting a C means that one is a C person (or at least, that the professor takes that person for a C person). The result of these half-baked half-spoken notions is that some students spend enormous amounts of time and energy obsessing aboutgrades, some teachers worry that they are damaging their students by giving them grades that are ``too high'' or ``too low'', and some newsmedia pundits pontificate about grade inflation, grade deflation, and other grade flations. All the while, vast arrays of letters are assigned to young people every term, and no one quite knows what, if anything, these letters mean.

What are grades good for anyway? If you listen to the newsmedia pundits, you might get the impression that grading is a device for providing parents, employers, insurers, and statesmen a compact method for evaluating people. Thus the ``grade inflation'' debate: if everyone gets As, how will we know who is ``really'' good? Notice the underlying assumption: there is a minority that is ``better'' than everyone else, and should get the As; it is to protect this worthy minority that we must keep the riff-raff relegated to their Cs. If, by some calamity, all students started performing at traditional ``A'' level, the result would be chaos, with no one knowing who should defer to whom. Thank heavens for mediocrity!

Umm, but grades should have some purpose besides making a few people feel superior to everyone else. And there is ...

About Feedback

It is extremely difficult to learn without getting feedback. Until you've learned to provide yourself with your own feedback (i.e., you no longer need answers at the back of the book), it helps to have an arrangement like the following:

  • You put what you learn into a compact performance, like the answer to an exercise.
  • You present this performance to a professional evaluator, who tells you how well you did -- and hopefully, what you did right and what you did wrong.
By going through this cycle repeatedly, you gradually learn how to do performances well. Hopefully, in the process, you learn how to master whatever it is you are trying to learn. Various studies confirm that this method works well, especially if the feedback is unambiguous and occurs soon after the performance.

The classical model is Ivan Pavlov's conditioned reflex, in which one is repeatedly exposed to a stimulus (e.g., a box of chocolate), and one responds subconsciously (e.g., by salivating). The Classical school of Behaviorism held that all animal and human behavior was constructed out of such learned components, much as all ordinary matter is made of atoms. And indeed, much animal training is based on this approach: break the desired behavior into small bits, teach an animal each bit (rewarding animals for each bit done right), assemble the bits, and you have a learned behavior.

Of course, there are problems with this theory, but it ``works'' often enough that many are willing to swallow the indignity and philosophical difficulties and apply the methodology, at least in education. There are a few basic principles:

  • Break the thing to be learned into very small pieces, and then gradually assemble the pieces. For example, in teaching reading, one might begin with assembling words in a system like Phonics, and then learn how to use words as basic building blocks of sentences, thus looking and saying the words in a Whole Language approach. (Funnily enough, there is a Language War between the advocates of these two approaches.) This hierarchical approach seems to fit how people learn things, first learning little pieces and then bigger ones: this is certainly the approach suggested by the work of Adriaan de Groot in chess.
  • Positive reinforcement appears to be more effective than negative reinforcement. This is certainly true in animal training (no one ever taught a dog to stand up by swatting it whenever it failed), and seems to be true in teaching people as well. Of course, it is impossible to separate the strands of reward from punishment: simply failing to get a reward is disappointing, while simply escaping punishment is relieving.
But if the question is how should the subject being reinforced (negatively or positively) deal with feedback?

The Uses of Grades

There are several things to observe about the feedback rationale for grades.

The first thing to observe is that the grade is not an personal evaluation, nor a reward. It is merely an evaluation of a performance. It is very difficult to look at a grade objectively, but that is the best way to approach a grade. If you get a grade, that grade is not a reward or a punishment or a judgement on your moral worth, but merely a datum for analysis:

``There is no success or failure, only more data.''
By looking at an evaluation, you can see what you do understand, and how well and at what level one understands it (this is good practice for mathematics education majors: your students will be going through this some day). And hopefully, you can use the evaluation to find out what you are doing well, and what you are doing not-so-well, so that you can adjust your strategies and do better in the future. Grades are imperfect things, and you must interpret them carefully.

The second thing to observe is that the student is the intended audience. This is a problem, since grades, boiled down to A, B, C, D, or worse, appear on a transcript that can then be demanded by parents, insurers, graduate schools, employers, and so forth. (One of the explanations for the current bout of grade inflation is that during Vietnam, a draftee could stay on ``deferred status'' as long as he was at school, and to stay at school, the draftee needed decent grades, and professors knew this and thus felt guilty about giving students low grades.) The audience-of-transcript problem can have odd effects. Some professors may give high grades because they don't want to damage students' prospects. Others may worry about the bridges that their students may build or the patients that they may treat, and tend to give lower grades. And during the last century, our society has become obsessed with evaluations, and grades are only a foretaste of what is to come in employed life. Here at USF, professors themselves are graded each year on ``research'', ``teaching'', and ``service'', on a scale suspiciously similar to the A, B, C, D, F scale. Virtually all institutions, public and private, have similar evaluation schemes of employees. The time to learn to take these things dispassionately is now.

What Grades Mean

The grading game is complicated by the problem that no one is quite sure what A, B, C, D, and F mean. As different professors have different standards and use different methods for getting different grades, one ``B'' might mean something quite different from another ``B''. One thing to be kept in mind is the difficulty of the performance: getting a 90/100 for an easy exam may be easier than getting a 70/100 from a more difficult one.

Here are some popular grading schemes:

  • ``Grading by the curve.'' This means that the professor decides ahead of time what percentage of the class gets As, what percentage gets Bs, and so on. Obviously, if the class was unusually strong or unusually weak, the grades would be inappropriate. Furthermore, if the class is small (smaller than 50, say), the results are usually skewed.
  • Preset cutoffs. This is the most popularized method. You must get some percentage of the points possible for an A, some lesser for a B, and so on. This method is very neat, but has definite `missed it by that much' problems. It is also misunderstood: as many teachers use 90 % as the A cutoff, silly people (politicians, pundits, etc.) then assume that a 94 % cutoff for As means ``higher standards''. In fact, for reasons I discuss in my test page, that is not at all true.
  • Winging it. This is how most graduate courses, and many small undergraduate classes, are graded. This works only if the professor has some coherent idea about what ``A work'', ``B work'', etc., are.
  • Some mixture of the above, e.g., using preset cutoffs (based on historical positions of the curve) modified by moderate winging.
You can see the problem: except for those professors who (competently) wing it, there is a weak connection between the grade-generating process and the ultimate grade, unless the performance itself has been designed to produce an appropriate grade. So either: you were graded on a well-designed performance, or you were graded by a discerning professor winging it, or you were graded somehow on something-or-other, and what does that grade mean?

There is no consensus about what grades mean. Some professors hand out As like candy, while others are proud of their misanthropy. Some institutions (some ivy leaguers in particular) give lots of high grades; others, either because of higher standards or pretensions, give out lower ones (I know that professors, not institutions, give grades, but the institutional culture affects what grades those professors give). If you asked a professor what a grade means, he may or may not be able to give an intelligible response. The lack of consensus about grades has led to grade inflation, attempts to establish criteria for grades (even Legislatures have been known to try this, with predictable results), and condemnation of the entire grading system. The defenders of the status quo usually rationalize that over many courses, students tend to get the GPAs that reflect their performance. (In my experience, this is true, but notice the use of the verb ``tend.'') So you one should not put all that weight in a single grade.

Concluding Thoughts

A grade is only a measure. What you want (hopefully) is an education, and the grade only measures how well you were able to display your mastery of whatever subjects you wanted to learn.

  • If an education is what you wanted, and what you got, then you have succeeded in your effort. Conversely, if all you got were good grades, but no education, then you did not succeed.
  • Be aware that some people are simply better at displaying their abilities than others (there is a story that when Stephen Binet developed the very first IQ test, he took it down the hall to the mathematician Henri Poincare, the world's preeminent genius and notorious test-phobe, who flubbed it); this problem is especially severe because of our inflexible test structure. See my my tests page for more on this.
Even if you have been taking courses because you had to, because ``they'' won't let you do what you want unless you get good grades in these yucky courses, these courses are usually required because you need to master the material in them in order to accomplish what you do want to do. And if you don't master that material, then you will not succeed in the end.

One bit of advice from Confucious. It is more effective to learn how to perform in a position than to get a position, for if one gets a position and does not perform, the consequences are serious and last a long time. And all grades in themselves do is help you to get the position: it is your mastery that helps you keep it.

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