Last Update: 17 December 2012
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"When the American painter, sculptor and installation artist Paul Thek
(1933–88) taught art classes at Cooper Union in the late 1970s,
he wrote and then gave to his students a long, provocative and now famous list of questions and marching orders he titled ‘Teaching Notes.’ …‘Teaching Notes’ closed with this statement, which professors (and critics) everywhere should etch onto the bottom rims of their reading glasses, facing outward: ‘Remember, I'm going to mark you, it's my great pleasure to reward real effort, it's my great pleasure to punish stupidity, laziness and insincerity.’"

An essay elaborating on the theory presented on this website is:
Rapaport, William J. (2011), "A Triage Theory of Grading: The Good, the Bad, and the Middling", Teaching Philosophy 34(4) (December): 347–372.
"Grading homework is teachers' neverending homework. Compared to that, Sysyphus lucked out."

0 = assignment not done
1 = assignment done, but clearly incorrect
2 = assignment done, but only partially correct
3 = assignment done, and clearly correct
Presumably, 0s, 1s, and 3s are clearly identifiable; anything not clearly identifiable is a 2.
For multiplepart items, each part can be graded on this scale, so, e.g., a programming project that requires a problem definition, a topdown design, documented code, and annotated output might be graded as follows:
problem definition  0 1 2 3 
topdown design  0 1 2 3 
documented code:  
code:  0 1 2 3 
documentation:  0 1 2 3 
annotated output:  
output:  0 1 2 3 
annotations:  0 1 2 3 
Total possible points  18 
Or, e.g., a HW assignment with 10 problems could have each problem graded on the 0 1 2 3 scale, for a total of 30 points.
Or, e.g., a HW assignment one of whose problems has 2 parts: Each part could be graded on the 0 1 2 3 scale.
If the instructor wants to weight some part more than another, multiply by some factor; e.g., in the programming project example above, if the instructor feels that documented code is far more important than anything else, the instructor might use this:
problem definition  0 1 2 3 
topdown design  0 1 2 3 
documented code:  
code:  0 5 10 15 
documentation:  0 5 10 15 
annotated output:  
output:  0 1 2 3 
annotations:  0 1 2 3 
Total possible points  42 
And so on. The main principle is to grade in quantum units.
The main advantage, besides ease of grading, is that the instructor doesn't have to argue with students over an extra point for a missed semicolon. (In general, a handwritten program whose only fault is a missed semicolon probably deserves full credit, unless the instructor is a real stickler for detail.)
It also tells the student more than some arbitrary number of points does: A 3 says "you got it right (for all practical purposes)", a 2 says "almost, but not quite", a 1 says "nope", a 0 says "you didn't even try"; various weightings indicate relative importance.
Other variations: The instructor can always add a "fudge factor" to express an overall impression of a student's work. And so on.
0 = assignment not done
1 = assignment done, but clearly incorrect
2 = assignment done, but only partially correct
3 = assignment done, and clearly correct
I take:
0 = F
1 = D
2 = C
3 = A
since C is supposed to be "average".
What about B, you ask? Well, if enough assignments during a semester are given using this lettergrade scheme, Bs will appear when things get averaged. They will also appear, as will + and  grades, if the total number of points for a given assignment is large enough, using the following mapping:
3 pts  correct  A 
2 pts  partial credit  C (average) 
1 pt  incorrect  D 
0 pts  work not done  F 
factor  grade  range  T = 100%  width 

3n  A  (17T/18 + 1)  T  95  100  T/18 
17n/6  A  (8T/9 + 1)  17T/18  90  94  T/18 
8n/3  B+  (5T/6 + 1)  8T/9  84  89  T/18 
5n/2  B  (7T/9 + 1)  5T/6  79  83  T/18 
7n/3  B  (13T/18 + 1)  7T/9  73  78  T/18 
13n/6  C+  (2T/3 + 1)  13T/18  68  72  T/18 
2n  C  (5T/9 + 1)  2T/3  57  67  T/9 
5n/3  C  (4T/9 + 1)  5T/9  45  56  T/9 
4n/3  D+  (T/3 + 1)  4T/9  34  44  T/9 
n  D  (T/6 + 1)  T/3  18  33  T/6 
0  F  0  T/6  0  17  (T/6 + 1) 
For example, to take the 42point programming project above, I would use the following lettergrade equivalents (T = 42):
A  41  42 
A  38  40 
B+  36  37 
B  34  35 
B  31  33 
C+  29  30 
C  24  28 
C  20  23 
D+  15  19 
D  8  14 
F  0  7 
factor  grade  range  T=100%  width 

3n  A  (17T/18 + 1)  T  95  100  T/18 
17n/6  A  (8T/9 + 1)  17T/18  90  94  T/18 
8n/3  B+  (5T/6 + 1)  8T/9  84  89  T/18 
5n/2  B  (7T/9 + 1)  5T/6  79  83  T/18 
7n/3  B  (13T/18 + 1)  7T/9  73  78  T/18 
13n/6  C+  (2T/3 + 1)  13T/18  68  72  T/18 
2n  C  (T/3 + 1)  2T/3  34  67  T/3 
n  D  (T/6 + 1)  T/3  18  33  T/6 
0  F  0  T/6  0  17  (T/6 + 1) 
0 = assignment not done
1 = assignment done, but clearly incorrect
2 = assignment done, but only partially correct
3 = assignment done, and clearly correct
Presumably, 0s, 1s, and 3s are clearly identifiable; anything not clearly identifiable is a 2.
For multiplepart items, each part can be graded on this scale, so, e.g., a programming project that requires a problem definition, a topdown design, documented code, and annotated output might be graded as follows:
problem definition  0 1 2 3 
topdown design  0 1 2 3 
documented code:  
code:  0 1 2 3 
documentation:  0 1 2 3 
annotated output:  
output:  0 1 2 3 
annotations:  0 1 2 3 
Total possible points  18 
Or, e.g., a HW assignment with 10 problems could have each problem graded on the 0 1 2 3 scale, for a total of 30 points.
Or, e.g., a HW assignment one of whose problems has 2 parts: Each part could be graded on the 0 1 2 3 scale.
If the instructor wants to weight some part more than another, multiply by some factor; e.g., in the programming project example above, if the instructor feels that documented code is far more important than anything else, the instructor might use this:
problem definition  0 1 2 3 
topdown design  0 1 2 3 
documented code:  
code:  0 5 10 15 
documentation:  0 5 10 15 
annotated output:  
output:  0 1 2 3 
annotations:  0 1 2 3 
Total possible points  42 
And so on. The main principle is to grade in quantum units.
The main advantage, besides ease of grading, is that the instructor doesn't have to argue with students over an extra point for a missed semicolon. (In general, a handwritten program whose only fault is a missed semicolon probably deserves full credit, unless the instructor is a real stickler for detail.)
It also tells the student more than some arbitrary number of points does: A 3 says "you got it right (for all practical purposes)", a 2 says "almost, but not quite", a 1 says "nope", a 0 says "you didn't even try"; various weightings indicate relative importance.
Other variations: The instructor can always add a "fudge factor" to express an overall impression of a student's work. And so on.
0 = assignment not done
1 = assignment done, but clearly incorrect
2 = assignment done, but only partially correct
3 = assignment done, and clearly correct
I take:
0 = F
1 = D
2 = C
3 = A
since C is supposed to be "average".
What about B, you ask? Well, if enough assignments during a semester are given using this lettergrade scheme, Bs will appear when things get averaged. They will also appear, as will + and  grades, if the total number of points for a given assignment is large enough, using the following mapping:
3 pts  correct  A 
2 pts  partial credit  C (average) 
1 pt  incorrect  D 
0 pts  work not done  F 
factor  grade  range  T = 100%  width 

3n  A  (17T/18 + 1)  T  95  100  T/18 
17n/6  A  (8T/9 + 1)  17T/18  90  94  T/18 
8n/3  B+  (5T/6 + 1)  8T/9  84  89  T/18 
5n/2  B  (7T/9 + 1)  5T/6  79  83  T/18 
7n/3  B  (13T/18 + 1)  7T/9  73  78  T/18 
13n/6  C+  (2T/3 + 1)  13T/18  68  72  T/18 
2n  C  (5T/9 + 1)  2T/3  57  67  T/9 
5n/3  C  (4T/9 + 1)  5T/9  45  56  T/9 
4n/3  D+  (T/3 + 1)  4T/9  34  44  T/9 
n  D  (T/6 + 1)  T/3  18  33  T/6 
0  F  0  T/6  0  17  (T/6 + 1) 
For example, to take the 42point programming project above, I would use the following lettergrade equivalents (T = 42):
A  41  42 
A  38  40 
B+  36  37 
B  34  35 
B  31  33 
C+  29  30 
C  24  28 
C  20  23 
D+  15  19 
D  8  14 
F  0  7 
factor  grade  range  T=100%  width 

3n  A  (17T/18 + 1)  T  95  100  T/18 
17n/6  A  (8T/9 + 1)  17T/18  90  94  T/18 
8n/3  B+  (5T/6 + 1)  8T/9  84  89  T/18 
5n/2  B  (7T/9 + 1)  5T/6  79  83  T/18 
7n/3  B  (13T/18 + 1)  7T/9  73  78  T/18 
13n/6  C+  (2T/3 + 1)  13T/18  68  72  T/18 
2n  C  (T/3 + 1)  2T/3  34  67  T/3 
n  D  (T/6 + 1)  T/3  18  33  T/6 
0  F  0  T/6  0  17  (T/6 + 1) 