E.P.S., If not a soft spot for burlesque, certainly an appreciation for Burl Ives.
MidasKnight, it isn't grades which encourage students. They are markers for a level of mastery occasionally, but they also are a way to put students into a rough ranking...winners and (ahem) losers. For some, the C, D or F is encouragement to try harder. For vastly more, it is a harsh judgement of the individual as often as it is a judgement of the work. A students may be considered worthy of getting into Harvard...of course, only if they are from a "good" school.
As to math, consider this question: What is the sum of 10 + 1?
It is a trick question, of course. I'm expecting you to think in terms of our common number base so you will say 11 and mean eleven. In fact I'm being nasty and using the binary base-2 where the same answer 11 is three. A lot of math boils down to the use of canned recipes for getting the right answer. Those who memorize the recipe do well. Those who understand a math concept, but struggle with the recipe from time to time may not do so well. In my youth, a measure of math proficiency was being able to rapidly go through the multiplication table, the faster the better, then to do similar "calculation" randomly. Was speed a measure of calculation skill or merely a good memory for 7 x 8 or 12 x 5? Were the slower to respond actually less math fluent? I remember feeling very inadequate for a long time. Even before the digital calculator (much less spreadsheets) made such skill of dubious value, I just never saw the point.
Math is assumed to have "right" answers and getting 7 of 10 correct on a quiz is a passing grade of C- or D in most schools. Even with that, compare a baseball player whose batting average is 700. That's the same level of performance, but we would effusively praise such a player while probably shaking our heads at the performance of the student with the 70 (after he/she turned and walked out the classroom door).
You might argue that comparing a C- or D with a 700 average hitter is comparing apples to oranges. Well, maybe so, but to go back to math one last time. 6 apples plus 6 oranges still equals 12, no matter that the units are now called "fruit."
Now, don't "
burl" over from too much heated argument...

Words are a game. Sometimes I play alone, but I encourage YOU to play, too.