Pedagogy, Technology,
& Course Redesign VIII
Getting Students to Learn
from Their Mistakes:
Self-Reflective Grading
Vera Cherepinsky
MACS Department
June 5, 2008
Outline
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Setting
Motivation
Source
Logistics
Results
Conclusion
Setting & Motivation
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Fairfield University
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Jesuit university in Fairfield, CT
Founded in 1942
Offers several Masters degrees (including math)
Undergraduate enrollment: about 3200 students
In introductory math courses, students rarely
use graded exams to study
Source
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Article in Conversations on Jesuit Higher
Education, No.27, pp17–20, 2005.
Incorporating Reflection – one of the Ignatian
pedagogy principles – into the math classroom.
Intriguing idea: a method of grading requiring
students to “review their graded exams, get help on
what went wrong and re-submit their corrections.”
After thinking through logistics, I decided to
implement this idea in my intro calculus classes
(MA122 in Sp’06 and MA125/126/227 in ’06-’07 AY)
Logistics: General Idea
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Exams first returned without comments or grades
Each problem marked with  or X
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, if completely correct
X, if there is some error in the solution
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May be a serious mistake, or
something very minor in the correct solution
Students get detailed directions on what to do to
“get points back”
They have a week to go over their exams and must
resubmit original exam with a set of corrections
Logistics: Corrections Rules
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For each problem marked with X,
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Find all errors made (may be more than one!)
For each error
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Decide whether it was major or minor and explain why, and
Show how to fix it.
On due date, both original exam and corrections are
collected from each student and graded together.
Each problem on original is assigned a grade (with
partial credit).
For each error correctly identified, classified, and
fixed, the student gets back half the points lost on it.
Logistics: Sample Directions
MA126 Exam 2 Corrections: Due Wednesday, 4-25
Marked exams were returned in class on Wednesday. An "X" next to a problem indicates there was
some error in the solution. It may be a serious mistake, a question left unanswered, an unjustified claim,
or something very minor in the mostly-correct solution, such as a typo in the explanation. (If the only
thing wrong was clearly a typo or an incorrect notation, this was indicated with a check-mark with a small
slash through it; otherwise, something else is wrong as well.) Note also that there may be more than one
error per problem, so check your ENTIRE solution to make sure you found them all. Also, don't be
discouraged if you didn't get any of the problems completely right: it may just mean you made a minor
error in each one.
CORRECTIONS (on separate sheets of paper -- DO NOT write on the original set of exam solutions!):
For each problem marked with an "X", you must
1) find the error(s); and for each error,
2) decide whether it is major or minor (and EXPLAIN WHY); and
3) explain how to fix it (for example, you may do this by writing out a correct solution and indicating where
you went wrong).
Your corrections AND the original exams will be collected back on WEDNESDAY, 4-25. BOTH of these
will be graded; for each error you correctly identify, classify, and fix, you will get back up to half the points
lost due to making it in the first place.
You are welcome to work together, use your books and notes, and come ask me for help if you can't
figure out what you did wrong. Note, however, that each of you must hand in INDIVIDUAL corrections to
your exam.
Logistics: Prior to Exam
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Explain grading method
Make very clear: over-relying on “fixing it
later” is a bad strategy
Extreme case: originally leaving exam blank
and then solving everything perfectly to hand
in as “corrections” earns at most 50% (an ‘F’)
Other extreme: not doing any corrections at
all (just returning original) is equivalent to
traditional grading
Logistics: Instructor Side
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Marking original exam
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Grading corrections
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Keep track of how far each student got on each
problem (to distinguish original vs. corrections
work)
If all conditions are satisfied, half lost points are
returned
Total grade
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Show both grades for each problem
Marking Exam (First-Pass)
Grading Sample
Total Grade
Results: Survey Form
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Numerical questions
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1 (disagree strongly)
to
7 (agree strongly)
Free-form questions
Would you use it
again?
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Y/N/No preference
Results
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Timing
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Measures student perceptions, hence given
right after exams + corrections are handed in, but
before a grade is assigned
Numerical Data Summary
MA227 MA126
Fa’07
Sp’07
(15)
(22)
1 (more time)
2 (easy to find)
3 (get it better)
4 (enjoyed)
5 (higher grade)
%Y
%N
%No preference
6.4
4.4
6.3
4.8
6.4
100
0
0
6.4
4.0
5.8
4.6
6.9
95.5
0
4.5
MA125
Fa’06
(28)
6.4
4.1
5.6
4.7
6.2
92.9
3.6
3.6
MA122 E2 MA122 E1
Sp’06 (41) Sp’06 (36)
6.2
3.5
5.4
3.3
5.8
73.2
2.4
22.0
6.5
3.4
5.3
3.8
5.7
55.6
0
36.1
Avg
6.4
3.8
5.6
4.1
6.1
Free-form Questions: Themes
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#6 (what did you like?) – top responses
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“Can earn back points/improve grade”
Next theme varied by class/semester
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MA126, MA125, and MA122 E1:
“able to go over work & correct mistakes”
MA122 E2: “understand material better”
Quotes
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“Not only does it give me a chance to get a better grade, it
also ensured that I had a decent grasp of the material”
“I like that I had a chance to improve my grade. I also like
that this assignment forced me to understand the material.”
Free-form Questions: Themes (cont’d)
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#7 (how to improve?) – top responses
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MA126
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MA125
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“good as is”
“show how much got wrong (how serious?)”
“good as is”
“show / go over areas of common mistakes”
MA122
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“show how much got wrong (how serious?)”
“good as is”
“give a hint on where errors are (esp in multi-part probs)”
Trends & Modifications Made
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Trends
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Students who originally do poorly love this
Students who were almost right like this less
Modifications made
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First, a typo or notation error got a problem an “X”
Based on student comments, since then, a correct
solution with a typo gets a “” with a small slash
Conclusion
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Experience of using it over the past 4
semesters and student survey data
convinced me that “self-reflective grading”
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benefits student learning
helps develop their self-error-correcting skills
Thus, despite the extra time spent on
grading, I believe it is an investment well
worth its while.
Acknowledgements
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Chris Petersen Black (Central Washington
University – Lynnwood)
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Original idea from her article in Conversations
Larry Miners, Economics Dept. and CAE
(Fairfield U.)
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Helped design the survey form
Used self-reflective grading in his small upperlevel economics classes
Questions?
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Dr. Vera Cherepinsky
Assistant Professor of Mathematics
Fairfield University
Phone: 203-254-4000 x3089
Email: vcherepinsky@mail.fairfield.edu
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