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Teaching Time Savers: Grading Quickly and Consistently Using Equivalence Classes

By Susan E. Martonosi

Grading consistently is perhaps the most time-consuming aspect of grading for me. I can go through the papers and correct them easily and quickly enough, but I am often bogged down by the task of deciding how many points to award to a particular combination of errors and insights, especially when I can?t remember how I graded similar solutions earlier in the stack. Moreover, the grade I think a solution might be worth when I start grading is not necessarily the grade I think it?s worth after I?ve examined every paper, so students making similar mistakes don?t always receive similar grades.

The end result is probably 15-30 seconds of hemming-and-hawing about the grade on each paper per problem, as well as the occasional confrontations by pairs of students wondering why they received different scores for similar solutions. Even when the students don?t confront me, I often worry that I haven?t graded the papers consistently.

Grading rubrics can help, but only to a limited extent. For papers with multiple right answers or when a student makes a quirky combination of errors, rubrics don?t often provide enough guidance. However, I?ve found a trick that saves time and yields more consistent grades.

For each problem on an assignment or exam, I sort the students? papers into equivalence classes: rather than assigning a grade upon the first pass through the stack of papers, I treat the first pass as a chance to read each solution, mark it up and then put it into a pile corresponding to the grade that I think it merits based on the mistakes made. This way, whenever I come across a particular type of mistake or combination of mistakes, I can put the paper into a pile of similar papers. I usually end up with approximately ten piles. At the end, I then go through the papers a second time by pile, usually starting with the best pile. I assign grades to the piles, occasionally bumping individual papers up or down if it?s clear that my grading scale shifted over time.

This second pass does add some additional time but the benefits outweigh the costs. The second pass applies only to the ten or so equivalence classes, rather than to the n individual papers, so I hem-and-haw about grades only ten, rather than n, times per problem. Furthermore, I no longer worry that I have penalized one student more than another for a similar type of mistake; my grades are consistent. Another perk: by sorting papers based on similar errors, I have been able to identify cases of academic dishonesty, even in a large class.

Time spent: 15-30 seconds to assign a grade to each equivalence class, per problem.

Time saved: 15-30 seconds to assign a grade to each student, per problem; and fewer meetings with students about grade inconsistencies.

Susan E. Martonosi teaches at Harvey Mudd College.

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