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Friday, 8 July 2011

MATH EDUCATION Grades (part 2)

Grades (part 2)


When students learn their grade for a given course, what they are learning is how they compare with their peers, which is one indicator of "how they are doing". (See Grades, part 1). Grade or no grade, many students know exactly where they fit in the classroom hierarchy, though some may not admit it to their parents or even to themselves. It is true that some (often boys) overestimate themselves, and others (often girls) underestimate themselves. For those students, knowing the grade may be a helpful corrective. But is it a good idea, educationally, to dwell on comparisons between students?
Teachers are reluctant to make comparisons between students, which they see as unfair and unproductive. Unfair, because students come from many different family and educational backgrounds. Comparisons between students end up being largely about that. Unproductive, because it is not realistic, in most cases, to expect major changes in the short run. A hard-working C student often will need years, not weeks, to become a hard-working B, or even A student. We can point them in the right direction, offer them intellectual tools, help them to improve their work habits, and over the course of their high school career we can see spectacular changes. And we often do -- this is one of the most satisfying parts of working at a good school.

But paradoxically, the way to get there is not to dwell on the grades. (It's a bit like searching for happiness -- you're more likely to find it if you don't dwell on that as a goal.) At most schools, the conversation is about "what do I need to do to get an A?" (or a B), and of course, that is the subtext of many conversations at any school. The teacher's responsibility is to deflect that conversation towards the specifics of this particular student's needs at this stage. Perhaps the A is already guaranteed, but the student needs to focus on their ability to communicate their ideas better. Perhaps the A is just not going to happen this term, but the student needs to work on developing their symbolic manipulation skills. There is always work to do, (and a time to stop working,) irrespective of where the student stands in the grades distribution at this particular time.
A grades-focused conversation means that in these very common situations (the A is guaranteed, or the A is unattainable at this point) there is little to discuss. It can also lead to grade inflation in a variety of ways: in order to motivate students with the grade, we might make it easier to attain. Or in order to not be hassled, we might make A's more plentiful. Grade inflation is not the end of the world, but if we want to inflate grades, we ought to do it deliberately and not as an unexpected consequence of uncomfortable conversations.
If a student's place on the academic ladder is constantly harped on by the school culture, students can internalize the label and stop striving. Skillful teaching is largely about bringing out students' different strengths and different intelligences to the table, whether or not those lead to a better grade in the short run. For example, a strongly visual student can contribute a lot to a discussion, even if he or she is not yet ready to translate that talent into points-earning write-ups.
Bottom line: intrinsic motivators (such as interest in the subject matter) are a lot more powerful, a lot longer-lasting, and a lot more meaningful than extrinsic motivators (such as grades.) Our task, as teachers, is to move students from the latter to the former. It is a challenging enterprise, but we must try to keep the focus on the discipline we teach rather than on the lines separating our students into A, B, and C. Teaching students to be self-motivated learners is a vastly more useful contribution to them as future college students and lifelong learners than (say) the Pythagorean Theorem.

MATH EDUCATION


Grades (part 1)


Grades have no intrinsic, absolute meaning. An A at an elite private school does not mean the same thing as an A at a public school that serves a poor neighborhood. An A at my own school today does not mean the same thing as an A meant 20 years ago. An A in Science does not mean the same thing as an A in History. And on it goes. The one feature of grades that is quite reliable is that an A in a given department at a given school is better than a B, which in turn is better than a C. In other words, the meaning of grades is relative. They are how we compare students to each other.

Almost all teachers will fix how they compute their grades if the outcome does not sort the students correctly. If a student deserves an A, and your calculation yields a B, you will find a way to tweak the percents, or the scores, or the participation points, or the extra credit, or something, to make sure the student does not get cheated by a pseudo-objective algorithm. (Admittedly, if the calculations yield an A, rather than the B we expected for a given student, most of us would let it be.) This makes sense, because teaching is as much an art as a science. Given a small enough class and enough of the right sort of contact with the students, a competent teacher knows better how to sort the students than any formula. (Yes, better assessments yield more accurate grades — that’s what I meant by “the right sort of contact”.)

In the rare case of the teacher who delivers worse grades than expected by their school, they will be taken aside by an administrator, and told that their practice is out of line. This does not require looking at the students’ work — more evidence that grades are strictly a relative measure.

In short, grades compare students to each other. They have no other meaning. This is why colleges are interested in grades. If grades were not about sorting students, they would be useless. (Just to be clear: grades do not compare students only to others in the same section of the same class, but with the somewhat broader group of students in the same cohort at the same school.)

One might argue that grades are a measurement of how well a student meets the standards of a given class. This is true enough, but the standards in question only exist in relation to the specific students currently enrolled at the school. If almost every student met a given set of standards, no matter how valid those are, it could not and would not be used as a way to assess achievement in the class and determine the grade. In fact, such a set of standards would make for a course that is too easy for the given population. Conversely, a set of standards that is met by almost no one makes for too difficult a course. The only standards worth having are precisely the ones that help us sort students into A, B, C bins.

This is an argument against a system with no grades at all. Without grades, it would be easier to set your expectations too high or too low, or to have a bimodal distribution, with some students doing very well, others clueless, and little in between. Giving grades helps us calibrate challenge and access in the classes we teach. (Courses should be designed so that most students get B’s, with the strongest getting A’s and the weakest getting C’s. At least that is a reasonable recipe given societal expectations.) In other words, giving grades is not per se wrong. In fact, it can be useful.