Grading Details

David W. Lyons
Fall 2009

This document describes details of the procedure used to determine cumulative average and letter grades. Grading policies and procedures are subject to adjustment at any time at the discretion of the instructor.

Grading Criteria

Your semester grade is determined by two components: one is quantitative and the other qualitative. The quantitative component is the cumulative weighted average of graded work items (such as homework, in-class work, and exams) that have numerical scores. The qualitative component is determined by participation and engagement.

Each item of graded work receives a raw point score. The numerical grade, or simply the score, for an item of graded work is the raw point score divided by the total number of possible points for that item. 

               raw point score
   score =  ---------------------
            total possible points
For example, if Joe Student has a raw point score of 18 on a quiz that has 20 total possible points, then Joe's grade for that quiz is 18/20 = .9 = 90%. Most of the remainder of this document is devoted to the procedure used to compute an overall cumulative average from the individual graded items.

The way in which class participation and attendance affect your semester grade is described in the final section below.

Weighted Averages

The weighted average of a list of numbers 
   x1, x2, x3, ..., xn
with weights given by the list of nonnegative numbers 
   w1, w2, w3, ..., wn
not all of which are zero, is the quantity 
   x1w1 + x2w2 + x3w3 + ... + xnwn 
   ------------------------------ .
      w1 + w2 + w3 + ... + wn

Example

Joe Student has test scores of 79%, 86%, and 73%. The tests have weights 25/100, 40/100, and 35/100, respectively. The weighted average of the three test scores is 
   (.79)(25/100) + (.86)(40/100) + (.73)(35/100)
   ---------------------------------------------  = .797 = 79.7%.
            25/100 + 40/100 + 35/100
If the weights are changed to 1, 3, and 2, the new weighted average becomes 
   (.79)(1) + (.86)(3) + (.73)(2)
   ------------------------------  = .805 = 80.5%.
             1 + 3 + 2

Weights used in grading

The course syllabus gives a list of weights used for groups of scores. Here is an example. 
   Graded Exercises   20% total
   Midterm Exams      50% total
   Final Exam         30%
The total Graded Exercise weight of 20% is divided equally among the individual graded exercises. For example, if there were 20 graded exercises, each gets a weight of 1%. Likewise, the total Midterm Exam weight of 50% is divided equally among the midterm exams. If there are 2 midterm exams, each gets a weight of 25%.

Possible forgiveness of a low grade

Resetting a weight to zero and recalculating a cumulative grade average may produce a higher cumulative average. For example, suppose we have three tests with grades 80/100, 90/100 and 10/100, with weights 1/3, 1/3 and 1/3. The cumulative average of these three tests is 
   (80/100)(1/3) + (90/100)(1/3) + (10/100)(1/3)
   ---------------------------------------------  = .6 = 60%.
                 1/3 + 1/3 + 1/3
If we reset the third weight to zero, the new cumulative average is 
   (80/100)(1/3) + (90/100)(1/3) + (10/100)(0)
   ---------------------------------------------  = .85 = 85%.
                 1/3 + 1/3 + 0
From the student's point of view, the second cumulative average is a dramatic improvement. The act of recalculating a cumulative average after resetting a weight to zero is called dropping a grade.

Of all your nonzero grades lower than your final exam grade, one may be dropped. After the final exam is given, the computer grading program will automatically determine the highest possible cumulative average that can be obtained by dropping one nonzero grade (which must be lower than your final exam grade). This is your final cumulative average. Note that this dropping procedure can only increase your cumulative average.

Note: grade dropping is only applied in courses that have a final exam.

Meaning of letter grades

According to the College Catalog, letter grades have the following meanings. 
   Letter Grade     Meaning
   ------------     ------
        A           excellent
        B           good
        C           satisfactory
        D           requirements and standards met at a minimum level
        F           course requirements not met
Standards for ``excellent'' and ``good'' (letter grades A and B) are high. In this course, your grade reflects your mastery of the material. A good grade is not guaranteed by class attendance and performing the motions of homework; to earn an A or a B, you must demonstrate understanding that transcends mere rote familiarity.

Determination of letter grade

At the end of the semester, your final cumulative average is used to assign a letter grade. The scale used to convert cumulative averages to letter grades is based on the ``standard 10 point scale'' (A for 90% and above, B for 80% and above, C for 70% and above, etc.), but the scale may be adjusted, at the discretion of the instructor, so that the meanings of the letter grades fit the descriptions given in the previous section.

Pluses and minuses are used to distinguish between the low, middle and high achievers within each letter grade category. This is where the qualitative assessment of participation and engagement has an effect. For example, there may be a group of students with final cumulative averages in the high 80s. A student in this group who showed consistent effort in class and during office hours might receive a B+, while a student never came to office hours, did not say much during class discussions, and had several unexcused absences might earn a B.