Last night I was in a conversation with someone that somehow turned to the topic of school in general, and grading specifically.  I don’t have an exact recall for conversation (unlike Carol Jordan in Val McDermid’s series of novels), but at one point I was talking about teachers (generally pre-college in this case) who felt threatened when students asked questions, or just by smart students overall.  I mentioned my 9th grade biology teacher (the deplorable Mrs. Hood), who hated it if students asked any questions, because (I assume this is why, anyway) they almost inevitably revealed her lack of knowledge of the subject.  (I should mention that this woman wasn’t a substitute teacher, or a gym teacher pressed into service, or anything like that — she had at least an undergraduate biology degree)  Anyway, I then commented that my questions probably pissed off some of my fellow students, since I was asking abut stuff over which we wouldn’t be tested.  I do understand how classmates could be legitimately upset if a side conversation completely derailed the class, but I’m not talking about that sort of questioning.

ANYWAY!  We moved on from pre-college teachers to teachers in general.  I forget exactly how we got there, but eventually I made some comment that a teacher, especially at the university level, should not have to spoon feed everything to their students.  It would be okay if, GASP, something wasn’t covered in lecture and the students had to read it on their own.  The teachers all hold offices hours, so of course you would always have the opportunity to ask questions about what you had read, if you didn’t understand something.

From there I went on to observe that most students seemed to feel not only entitled to the teacher spoon-feeding them all of the material, but also that nothing could be on the test which wasn’t explicitly covered in class.  And I don’t feel that such entitlement is justified or good for our educational system.  Now I’m not advocating that teachers put material on their tests which is wholly unrelated to the course at hand (although one of my all-time favorite math teachers, David Santos, often had extra-credit questions on his exams which had nothing to do with math, such as seeing how much of Don Quixote we could memorize in the original Spanish — but I disgress).  I’m just saying that the point of a class (to my mind) isn’t simply to be presented with a list of facts by the teacher, you memorize said list, and then you are tested to prove that it has been memorized.  Or even presented with a list of procedures, and then tested that you can execute those procedures (like doing math problems, say).  I DO think that this should be part of it, but a student who can demonstrate mastery at that level deserve, in my opinion, a C.  MAYBE a B.  I feel like to get an A you should really demonstrate COMPREHENSION of the material.  The best test questions, I think, are ones which force you to apply the knowledge you’ve learned in a way that you didn’t have to do during class.  Something which you should be able to do if you really understand the MEANING of what you learned, rather than just its superficial content.

<I just took a break to take a shower, so forgive me if there is a bump in the stream-of-consciousness road that is my blog>

An example of this could be something along these lines…  In Calculus you learn that an integral is a way of measuring the area under a curve, and you learn how to solve and calculate integrals.  To test for just basic knowledge of the subject, the student should be able to tell you that the integral can be used to measure the area under a curve, and the student should be able to solve and calculate integrals which are given to them (within reason — not crazily complex ones).  And if a student can do that, I’d say that is C or C+ knowledge.  They know the basics, the MINIMUM you should know to be able to say that you are familiar with Calculus.  To get a B maybe the test would have a word problem that describes the shape of some real-world object (perhaps a swimming pool), and ask the student to calculate the volume of the pool.  They’d need to realize that they’d have to figure out the equation which governs the shape of the bottom of the pool, solve that integral, and the multiple it by the width of the pool (assuming we’re dealing with a rectangular pool whose only non-standard feature is the slope of the bottom).  A student who could put that together is getting toward B- or B knowledge.  For A or A+ knowledge I’d want it to be something perhaps even a step beyond that.  Something that would demonstrate that to the student, Calculus has become a tool they can use to solve real problems, and, just as important, they can recognize when and how it is appropriate to bring that tool to bear.

I should mention that I’m not saying the class should just cover basic knowledge for the entire semester, and then all of a sudden add these more complex questions on the exams.  The homework should include questions like this, and some things of this kind should be discussed in class.  But the point being, the exam shouldn’t be an exercise in demonstrating the student’s ability to memorize — it should also measure the ability to apply that knowledge, both to obvious situations and to non-obvious ones.

In the conversation last night, we didn’t discuss it in too much length.  But my friend’s reaction was “But if a student wants to get into college or into graduate school, they need good grades.  They can’t be happy with a C.”  My response to that was twofold.  First, if you’re applying to graduate school for, say, computer science, then I’m assuming the admissions department will give more weight to your grades in CS-related classes than in, say, foreign language classes.  And presumably if you want to study computer science at the graduate level, then you should have been able to demonstrate A-level mastery in your CS classes.  Someone who only has minimum basic CS knowledge probably should NOT be the top choice for graduate admissions.  And second (since she objected that they look at all of your grades, not just those in relevant coursework), if two candidates both got all A’s in their CS classes, but one of them also got A’s in the rest of their stuff, and one did not, then I think the graduate department probably SHOULD favor the student who excelled all around.  I do not think this is an injustice to the other student.  That said, I suspect that if one student had a 3.6 GPA overall, but a 3.4 GPA in CS-specific coursework, and another student had a 3.4 GPA overall, but 3.6 GPA in CS-related stuff, then the graduate school would probably take the student with the lower overall GPA, but the higher CS GPA.  This is speculation on my part, of course, and I’m sure that at some point this would no longer be true — a 2.0 GPA overall is probably going to be in trouble, no matter how well they did in their CS coursework.

Anyway, that line of thinking got me thinking — what is the point of grading anyway?  It almost sounded like she was saying something like “You need good grades to get a job or to get into higher education, and it’s not fair to deny someone the ability to do those things, so a student who can demonstrate basic knowledge should not be discriminated against.”  As I said, we didn’t discuss this at length, so that is likely not her position at all — that’s just how it felt to me on reflection.  But in that system, you may as well just do pass/fail, if you don’t want to differentiate between levels of success.  In that world, a C may as well be a failing grade, if you are expected to need As to get anywhere.

Personally, I see grading has having two somewhat-related purposes.  First, it is to measure a student’s mastery of a given subject (and within that, we set some line which we consider to be the minimum level of mastery necessary — ie a passing grade).  This spans from no knowledge at all, to some knowledge, to knowing the basics, to knowing the basics and being able to apply them in basic situations, etc, all the way up to having in-depth knowledge and being able to apply it in non-obvious situations.  And why do we want to measure the level of mastery, rather than just do pass/fail?  Because most jobs want the most qualified applicant, not to pick randomly among all applicants with the minimum possible knowledge.  Grades are ONE tool which can help determine this.  And same thing for graduate schools or other advanced education — they are looking for students who excel in the subject matter, not someone who has a limited understanding of it.  Okay, so we have grades to measure mastery.  Why else?  Well, second, I think it’s so the student has some idea of how well they really know a subject.  It’s very difficult to self-evaluate your knowledge of a subject, since you can’t really do a good evaluation unless you know a lot about the subject, and can thus see what parts you don’t really know.  Kind of a chicken and egg thing.  Anyway, so teachers, in addition to imparting the knowledge, are also best able to evaluate how well we’ve internalized it.  And grading is a concrete way to communicate this.  And along these same lines, this can serve to motivate students to excel — aim for A’s.

Is this elitist?  I don’t know.  A quick Google search says elitism is defined as “The belief that certain persons or members of certain classes or groups deserve favored treatment by virtue of their perceived superiority, as in intellect, social status, or financial resources.”  Well, I guess I *am* arguing that the group of people who have superior grades in a subject deserve, all other things being equal, favored treatment when it comes to job applications or school admissions.  And I guess by extension, since in general intelligence often makes school easier, this could be extended to imply that more intelligent people deserve to be favored in those things.  People have a knee-jerk reaction to accusations of intellectual elitism — obviously it’s a terrible, unjust thing, right?  Well, yes, if you’re talking about euthanizing children below a certain intelligence level, or only guaranteeing public education based on intelligence level, or something like that.  But when it comes to hiring?  It depends on the job, of course, but for many jobs, being more intelligent or more educated will allow someone to do a better job.  I mean, don’t we want hospitals to hire the smartest and most educated doctors without worrying about accusations of intellectual elitism?

It’s not that simple, though, I suppose.  Education is too often tied to socio-economic status, meaning that if we favor the more educated, then we are in some way favoring the wealthy.  But I’m not sure the solution to that is to just give out grades undeservedly, or to ignore grades when hiring.  It’s a complex problem.

Okay, so that aside, I mentioned that grades can also serve to motivate students.  If all you need to do to get an A is memorize a list, then we’re not exactly motivating students to excel beyond that point.  Kind of like they talk about in industry — once you start measuring something by certain criteria, then people will make achieving those criteria their mission.  They become a slave to the numbers, rather than trying to do the best job possible.  So if we train kids that they just need to learn the minimum to excel, then a lot of them will content themselves with that.

The motivation issue brings two things to mind for me.  First is David Santos, the math teacher I mentioned earlier who gave us extra credit for memorizing Don Quixote.  He taught me my first couple of semesters of Calculus at the college level.  You know my definition of what you should need to do in order to earn an A?  Well, I’d say in his class, if you had that level of mastery, you could expect maybe a 40 or 50 on one of his tests.  If not lower.  I forget the exact numbers now, but for one of the finals I remember having something like the third best grade in the class, and it was 36 or thereabouts.  The next highest was not too far above mine, and the highest was in the 70s — but the guy who got that score is probably the most brilliant person I’ve ever met.  Anyway, it’s kind of hard for me to describe David’s teaching strategy, but the best I can do is to say that he kind of acted like he was teaching us a class several semesters beyond where we were.  A class in which basic Calculus knowledge as already assumed, even though we were in a basic Calculus class.  This is not to say that he didn’t go over the basic Calculus concepts in the class, but we’d go way beyond them.  And the homework would go much further beyond that.  I remember we would, as a class, get together to work on the homework, and I don’t recall that we were ever able to fully finish an assignment.  Often we wouldn’t fully answer more than a handful of questions.  We’d pore over our book and our notes, discuss the problems with each other, try to think of how we could approach various problems, etc.  It’s really hard to talk about it and not sound like I am exaggerating, but I can tell you that a LOT of students dropped the class within the first month.  And the grades I’m talking about were AFTER those folks dropped.

Okay, so that sounds awful, right?  I mean, I can tell you that I honestly loved working on the homework assignments, because it was the opposite of busywork homework.  We worked together as a team, had interesting discussions, had the thrill of coming up with new insights, etc.  But despite that, we’d turn it in and get a 25 or whatever.  There were some people in the class, perhaps most of them, who thought this meant that we’d all fail and we were screwed.  Even then, with my limited college experience, I knew that wouldn’t be the case.  I realized that teachers really weren’t able to just fail entire classes of students.  So while I was definitely not used to receiving grades so shockingly low, I wasn’t actually worried about what my ultimate grade would be.  I sure didn’t know if it would be an A or a B or a C, but I knew that I was never among the lowest scoring on the tests, so I didn’t worry that I would pass after a curve.  And I don’t remember for sure now, but I think I ended up getting an A both semesters.

Okay, so why was that my favorite experience?  Well, at the time I just knew that it was one of the most intellectually enjoyable experiences I’d had in school.  I felt like someone who was actually LEARNING something and figuring it out, not being spoon fed the stuff.  And I’ll tell you, when you learn it that way, it stays with you a lot longer and gets internalized a lot more.  Anyway, at the time it was just something that I enjoyed and joked about with other students — laughing about the impossible question on the latest homework or exam, or showing off my 28 test score, or whatever.  But after I finished those two semesters and went on to the next math class in the series, this one taught by some other teacher, I came to realize that we had learned not only everything we were supposed to learn in those two classes (per the school-published syllabus), but we knew most or all of the material from the next several math classes.  It was at least a year or two later before I would take a math class and NOT think to myself “Wow, we learned a bit about this in Dr. Santos’ class.”

So what’s my point?  Well, Dr. Santos took kind of the opposite view of students being entitled to good grades.  His philosophy almost was that NO student should reasonably be able to score above a 90 (or 80, or 70) unless they were truly brilliant AND willing to put in the work and time.  As I noted, he didn’t carry this over into the letter grade realm — he still gave out As, Bs, etc.  But the point is, instead of motivating students to learn the minimum, or even motivating us to master the basics, he essentially motivated us to give 100% mental effort.  Because none of us ever realized something like “Oh, I can just give 80% effort and ace this class”.  I feel like there is some trite motivational saying about aiming really high because even if you fall short, you’ll still end up going further than people who set realistic goals.  If there isn’t, someone should make one. Looking back, I wish I had more teachers who had Dr. Santos’ teaching philosophy.  He isn’t the only great teacher I ever had, but I without question learned more from his classes than I did from any other classes I’ve ever taken.

Now, I will readily admit that this sort of motivation doesn’t seem to work for everyone.  Some people found it overwhelming or depressing.  They hated that they could never get that magic 90 (or, hell, 60), even if they realized it would have to be curved later.  They hated not being able to finish the homework.  For them, it made them want to give up rather than just give it their best.  Part of that could be because they were raised in this culture where you expect to always get good grades if you put in a certain amount of effort, so it’s jarring to be in a situation where that isn’t the case (even though we DID end up with good letter grades, we just had really low number grades on the way).  I’m no psychologist and I don’t know why his class was extremely motivating for some of us and not others (although I WILL say that some folks stuck with his class who were not thrilled with the methods I have described, but despite that, they ended up knowing a fuck of a lot more Calculus than students in the “regular” classes – so maybe it’s not required that you like the methods, just that you don’t give up).

So anyway, approximately 9000 paragraphs earlier I mentioned that the idea of grades as a motivation tool brought two things to my mind.  The first was Dr. Santos’ class, as evidence that the higher you require students to aim, the more they will end up learning.  Okay, so what’s the other thing?  For several years, up until I was 9, I went to a, well, hippie school in Maine.  The folks who founded it and worked there were pretty much all former hippies, and their educational philosophies kind of reflected that.  The school was not broken up into grades (ie no 1st grade, 2nd grade, etc) — we were just all lumped together.  And there were ALSO no grades given out.  And the curriculum was kind of fluid — each kid learned at their own pace, was encouraged to pursue things which interested them, etc.  It is a long time ago now, so I don’t know what techniques they used to ensure that everyone ended up learning the necessary basics in all subjects, even if they weren’t interested in them.  I do know this must have happened, since most kids from that school seemed to do well in school even after they left and went to a conventional school.  Anyway (wow, I use the word anyway a lot.  ANYWAY…), because this was so long ago, I don’t have the same kind of concrete recollections like I did for Dr. Santos’ classes.  But it is my impression that I learned more there than I would have in a conventional school.  And this despite the fact that grades were obviously not used for motivation.  So obviously grades are not the ONLY way to motivate students, lest anyone think I am trying to make that claim based on my length diatribe above.

However, even if grades weren’t needed for motivation in that case, I’m not sure how colleges, for example, could get an idea about the student’s levels of subject mastery.  Sure, there is the SAT, but that measures a pretty narrow set of things.  And there are teacher recommendations, essays, etc.  But students from conventional schools have all of those things, PLUS grades to either bolster or hurt their case.  After I left that school I was put in a 3rd grade class at a regular school (the reason for leaving the school was that we moved from Maine to Texas, not due to any dissatisfaction with the school), so I never had to find out how the grade thing would have worked out.

That last point (about how colleges would deal with the lack of GPA) brings one last thing to mind.  For 11th and 12th grade I attended the Texas Academy of Math and Science (TAMS), which is a program run at the University of North Texas in Denton.  It was designed to promote math and science education in Texas.  The short version is that students from across Texas can apply to go there following their 10th grade year.  If you’re accepted, you go stay in a dorm on the college campus, take two years of college classes (mostly freshman level stuff like english, history, chemistry, biology, physics, math, etc), and graduate with a high school diploma plus around 60 hours of college credit.  It was an experience that I treasure for many reasons (and is also where I took the classes from Dr. Santos), but that’s a story for another time.  The reason I bring it up here is that the GPA issue was a sticky one for a couple of reasons.  First, the schools all around Texas were upset that their best math and science students would go to TAMS and take their (presumably higher) GPAs with them.  And second, TAMS students were concerned that when they applied to college, they would possibly have lower GPAs than their peers from standard high schools, under the premise that it was harder to earn good grades in the college classes we were taking, and thus the TAMS students figured they’d have had a higher GPA had they remained in a standard high school.  I forget how TAMS solved the problem with the Texas schools — I seem to remember that maybe the GPAs we earned at TAMS were actually credited to the school from which we came, so they could include us in their calculations (which seems pretty dubious to me, but whatever).  I DO remember how they handled the student concern though.  We were given a letter to include with our college applications that explained all about TAMS and then said something like “Because of this, their GPA should not be directly compared to students from other high schools.  Graduates of TAMS are in the top 2% of Texas students, and so you should consider their GPA to be in that range as well.”  I forget the exact wording.  Of course, along with that letter we still sent them a copy of our North Texas college transcript, which included our GPA for those classes, so it’s not like it was hidden from the places we applied.  This TAMS/grade discussion really doesn’t have any bearing on the rest of this post — it just came to mind, and since I just type what I think as I think it, well, you get what you get.

So, conclusions?  I don’t have any.  Well, that’s a lie.  I strongly disagree with the idea that students are entitled to As.  An A should be something that is a real accomplishment, not a default expectation.  Isn’t C defined as “average” somewhere?  Or did I dream that?  Anyway, I think C *should* be an acceptable grade that indicates the student knows the basic subject matter.  A student can choose to be unhappy with a C grade, but the response shouldn’t be that the teacher had exam questions which were not explicitly discussed in class — the response should be to work harder, ask more questions, etc.

I’ve often said that I would hate to be a teacher unless I only had to teach motivated students.  Or, I guess, if I would be allowed to fail students who truly didn’t deserve to pass.  Or give Cs to students who expected As for demonstrating a basic grasp of the subject.  Needless to say, I’d probably be fired, because I know for sure that I wouldn’t be willing to give out a grade that I didn’t think a student deserved.  Even though my taking a principled stand on that issue would accomplish very little unless the system and society itself changed.

Ok, I have written a novel.  Blog post over!