## (The Triage Theory of Grading)

### William J. Rapaport

#### Department of Computer Science and Engineering, Department of Philosophy, and Center for Cognitive ScienceState University of New York at Buffalo, Buffalo, NY14260-2000

 Last Update: 7 March 2006 Note: or material is highlighted

Here are my theories about grading. Please feel free to send me comments or to discuss this on the newsgroup. I owe the basic idea here to my former teacher, Paul Vincent Spade, but he is in no way responsible for my elaboration of it.

1. Fundamental Assumption: Any item to be graded can best be graded on a 4-point scale:

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 multiple-part items, each part can be graded on this scale, so, e.g., a programming project that requires a problem definition, a top-down design, documented code, and annotated output might be graded as follows:

 problem definition 0 1 2 3 top-down 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 top-down 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.

So much for points. How do I convert this to letter grades? Here's my principle, which is independent of the above point-grading scheme. Since

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 letter-grade 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:

#### General principle:

 3 pts correct A 2 pts partial credit C (average) 1 pt incorrect D 0 pts work not done F

#### Then:

Each assignment is worth a multiple of 3 points, and this is mapped into letter grades as follows, where n = the multiple of 3 and T = the total number of points (so: n = T/3). Note that 3n maps to A, 2n maps to C, n maps to D, 0 maps to F; others are interpolated in an evenly-spaced fashion (see tables below).

3nA(17T/18 + 1) - T95 - 100T/18
17n/6A-(8T/9 + 1) - 17T/1890 - 94T/18
8n/3B+(5T/6 + 1) - 8T/984 - 89T/18
5n/2B(7T/9 + 1) - 5T/679 - 83T/18
7n/3B-(13T/18 + 1) - 7T/973 - 78T/18
13n/6C+(2T/3 + 1) - 13T/1868 - 72T/18
2nC(5T/9 + 1) - 2T/357 - 67T/9
5n/3C-(4T/9 + 1) - 5T/945 - 56T/9
4n/3D+(T/3 + 1) - 4T/934 - 44T/9
nD(T/6 + 1) - T/318 - 33T/6
0F0 - T/60 - 17(T/6 + 1)

For example, to take the 42-point programming project above, I would use the following letter-grade 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

Where n = T/3:

3nA(17T/18 + 1) - T95 - 100T/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)

#### Miscellaneous:

For a humorous essay on the "joys" of grading, see Clio 2003, 2004.

#### Bibliography and References:

1. Anonymous (2006, January 3),
"When Did the A to F Grading System Start? And What Happened to E?" Ask Yahoo!.

2. Clio, Max (2003, November 21), "Grading on My Nerves", Chronicle of Higher Education.

3. Clio, Max (2004, June 25), "On Your Marks", Chronicle of Higher Education.

4. Cohen, Randy (2005, April 3), "The Art of Grading", The New York Times Magazine.

5. Georgia State University Senate (1998, April 15), "Admissions and Standards Committee Resolution Concerning Plus/Minus Grading"

6. Krumholtz, John D., & Yeh, Christine J. (1997, February 7), "Competitive Grading Sabotages Good Teaching" Phi Delta Kappan

7. Matthews, Jay (2005, October 18), "A to F Scale Gets Poor Marks but Is Likely to Stay" Washington Post.

8. Wolff, Robert Paul (1969), The Ideal of the University (Boston: Beacon Press), Part Two, Ch. 1 ("A Discourse on Grading"), pp. 58-68.