Letter Grade Mapping

When instructors choose to assign letter grades to individual
assignments and roll these scores up into a course grade, the MyUCDavis
course grades tool strategy has been to store these "letter grades" as a
numeric score. Sakai's new gradebook tool has adopted this same strategy.

MyUCDavis is currently using the following table to map letter grades
directly to a number when assigned:

A+      99
A       96
A-      92
B+      89
B       86
B-      82
C+      79
C       76
C-      72
D+      69
D       66
D-      62
F       59
0       0

In mapping these letter grades to numeric scores, the goal is basically
to choose numbers that are evenly distributed across the score range, so
that averaging between different scores produces roughly intelligible
results. That is, a student who receives an A and a C on equally
weighted assignments will receive a B for the overall grade.

But as you will notice from the table above, in MyUCDavis, due to the
constraint of storing integer values, the differences between scores are
not precisely equivalent. So the different between 99 and 96 is 3,
between 96 and 92 is 4, and between 92 and 89 is 3 again. And generally
this is true down the entire scale, with the following pattern: 3, 4, 3,
3, 4, 3, 3, 4, 3, 3, 4 . . . The effect of this uneven distribution is
to introduce a degree of inconsistency and arbitrariness to the overall
scoring in MyUCDavis gradebooks that use letter grades for grade entry.

This can be demonstrated by imagining the impact of a grading decision
where the instructor "marks down" students by one-half grade for some
identical error. That is, if there is one student with a B+ before the
mark-down and another with a B, and both have their grades reduced by a
half-grade, then the first student loses 3 points by receiving a B
instead of a B+, and the second student loses 4 points by receiving a B-
instead of a B.

The new Sakai gradebook tool allows us to store much higher precision
numbers for individual grades. We have chosen to store these values to
10 decimal places. The result of this is that we can eliminate the
inconsistency of the gaps between values in our gradebook. So our
mapping table is the following:

A+      98.3333333333
A       95.0000000000
A-      91.6666666666
B+      88.3333333333
B       85.0000000000
B-      81.6666666666
C+      78.3333333333
C       75.0000000000
C-      71.6666666666
D+      68.3333333333
D       65.0000000000
D-      61.6666666666
F       58.3333333333
0       0

The effect of this change is that course grades will vary slightly for
identically configured gradebooks that use letter grades for grade entry
between the MyUCDavis and Sakai Gradebook.
 
Although it is obviously not desirable to have the two tools diverge,
still we believe that it is preferable to use the extended decimal
values and to distribute scores more evenly across the range in the
newer tool, since this will produce fairer and more consistent course
grades between individuals.