Pedagogy, Technology, & Course Redesign VIIIVera CherepinskyMACS DepartmentJune 5, 2008Getting Students to Learn from Their Mistakes:Self-Reflective Grading
Setting & MotivationFairfield UniversityJesuit university in Fairfield, CTFounded in 1942Offers several Masters degrees (including math)Undergraduate enrollment: about 3200 students
In introductory math courses, students rarely use graded exams to study
SourceArticle in Conversations on Jesuit Higher Education, No.27, pp1720, 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 Sp06 and MA125/126/227 in 06-07 AY)
Logistics: General IdeaExams first returned without comments or gradesEach problem marked with or X, if completely correctX, if there is some error in the solutionMay be a serious mistake, or something very minor in the correct solutionStudents get detailed directions on what to do to get points backThey have a week to go over their exams and must resubmit original exam with a set of corrections
Logistics: Corrections RulesFor each problem marked with X, Find all errors made (may be more than one!)For each errorDecide whether it was major or minor and explain why, andShow 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 DirectionsMA126 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 ExamExplain grading method Make very clear: over-relying on fixing it later is a bad strategyExtreme 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 SideMarking original exam Keep track of how far each student got on each problem (to distinguish original vs. corrections work)Grading correctionsIf all conditions are satisfied, half lost points are returnedTotal gradeShow both grades for each problem
Marking Exam (First-Pass)
Results: Survey FormNumerical questions 1 (disagree strongly) to7 (agree strongly)Free-form questionsWould you use it again? Y/N/No preference
ResultsTimingMeasures student perceptions, hence givenright after exams + corrections are handed in, butbefore a grade is assigned
Numerical Data Summary
Free-form Questions: Themes#6 (what did you like?) top responsesCan earn back points/improve gradeNext theme varied by class/semesterMA126, MA125, and MA122 E1: able to go over work & correct mistakesMA122 E2: understand material betterQuotesNot only does it give me a chance to get a better grade, it also ensured that I had a decent grasp of the materialI 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 (contd)#7 (how to improve?) top responsesMA126good as isshow how much got wrong (how serious?)MA125good as isshow / go over areas of common mistakesMA122 show how much got wrong (how serious?)good as isgive a hint on where errors are (esp in multi-part probs)
Trends & Modifications MadeTrendsStudents who originally do poorly love thisStudents who were almost right like this less
Modifications madeFirst, a typo or notation error got a problem an XBased on student comments, since then, a correct solution with a typo gets a with a small slash
ConclusionExperience of using it over the past 4 semesters and student survey data convinced me that self-reflective gradingbenefits student learninghelps develop their self-error-correcting skillsThus, despite the extra time spent on grading, I believe it is an investment well worth its while.
AcknowledgementsChris Petersen Black (Central Washington University Lynnwood)Original idea from her article in Conversations
Larry Miners, Economics Dept. and CAE (Fairfield U.)Helped design the survey formUsed self-reflective grading in his small upper-level economics classes
Questions?__________________________________Dr. Vera CherepinskyAssistant Professor of MathematicsFairfield UniversityPhone: 203-254-4000 x3089Email: firstname.lastname@example.org__________________________________
10 mins total: 1 min on setting/motivation/source; 5 min on logistics; 3 min on results; 1 min conclusion/acknowledgement. Remaining 5 mins for questions.