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What proportion of course material mastery should we consider is "passing?"

In the US a typical grading rubric is A = 90%-100% B = 80%-89% C = 70%-79% D = 60%-69% F = below 59%

As a professor I often curve the numerical range of grades in my course, and depending on the class, the raw score for a passing grade might end up being even lower than 50%. My question is, at what point does this stop?

A professor could decide that mastery of only 15% of the course material is "passing" because a curve can make 15% into any number. If the professor writes and grades the test he or she could also just decide to only teach and test over 15% of the actual syllabus. In each case students are happy, administrators are happy, etc. because of the "nice grade distribution." But it seems a bit disingenuous to say that a student who learned only 15% of the course material actually passed.

I've heard that accreditation boards have various requirements for a university to maintain its accreditation. For instance, students have to pass enough courses or their major. But is there any accountability for the students to actually learn a minimum amount of material? It seems that everyone in a university could agree that the only requirement to pass a class and graduate is that the student pays tuition. Obviously this is would be big disservice to society. But what incentives do professors have (other than moral ones) not just teach less, and pass more students?

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    You're assuming that a grad of 15% represents a mastery of only 15% of the material. In my experience, the two are often not that related.
    – Ric
    Dec 2 '15 at 17:39
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    Elaboration of previous comment: At one extreme, you could have your exam consist purely of Putnam (NB: a national math contest on which the median score is 1/120) style questions based on the material in your class. Someone who manages a grade of 5% has probably (though not certainly) mastered 95% of the class material. At the other extreme, your exam questions might only ask students to recall the simplest facts in the subject, and 100% on the exam might only reflect mastery of the easiest 5% of the material. Dec 2 '15 at 18:28
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    The relationship between grades and mastery is really much, much weaker than the one you're assuming. And, as odd as it seems, even professors, in most --if not all -- cases, don't have a 100% mastery of what they're teaching.
    – Massimo Ortolano
    Dec 2 '15 at 18:37
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    As an undergrad I had a 30% average for an honors physics course. That was an A - the professor intentionally set very hard problems, since the value was in seeing how students wrestled with them rather than getting a correct final answer.
    – Jon Custer
    Dec 2 '15 at 21:32
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    My PhD supervisor always liked to quip that the best way to learn a subject was to teach it.
    – Bill Barth
    Dec 2 '15 at 22:06
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TL;DR: As much as a student would need to know in order to succeed in their career.

I think part of this answer will be subjective - does a student even need to master course material to pass, or do they need to be familiar enough with it to know how to re-learn it later in their career? I come from a STEM background - I know how to do calculus, but if you asked me to come up with a Taylor polynomial right now off the top of my head, I'd give you a blank stare.

In my opinion, the goal of any class is to teach familiarity with the subject at hand. No student will ever use 100% of what is taught in a given class - their career will dictate what they need to know. As they spend more and more time working in a particular field, the knowledge that is important will stay with them, and the knowledge that isn't important will be set aside - not entirely forgotten, but not readily accessible without review. The point is - they still know how to re-learn the material; they just don't know it off the top of their head.

With that in mind, I argue that the proportion of course material mastery that we should consider as "passing" is however much is needed to ensure that a student could, given a reasonable amount of preparation, re-learn the material at any point later in their career. That amount will vary from class to class, and it's worth remembering that some skills will carry over and be reinforced from class to class. To my mind, this means that fundamental skills - calculus, introductory classes, writing courses - need to be held to a higher standard.

As for incentives for professors - there's a variety. For one, if you want to work at a high-caliber institution, you're going to want high-caliber students. This means pushing them to learn and master more of the material than perhaps a professor at a not-so-high-caliber institution might care. For another, there's an element of peer pressure involved: if I teach my students poorly, and don't require them to learn enough of the material, then my peers will have to pick up the slack in later courses. That reflects poorly on my teaching, and it means that I may have to do the same thing with these students in later courses that I teach.

So what proportion of course material mastery should we consider is "passing?" Whatever is necessary for a student to (1) be able to relearn the material in a reasonable amount of time and (2) be able to retain the core concepts for use in later courses.

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