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Pedagogy, Technology,


Title: Recombinant DNA class Guest Lecture Author: vcherepinsky Last modified by: vcherepinsky Created Date: 4/18/2006 3:39:18 AM Document presentation format – PowerPoint PPT presentation

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Title: Pedagogy, Technology,

Pedagogy, Technology, Course Redesign VIII
Getting Students to Learn from Their
Mistakes Self-Reflective Grading
  • Vera Cherepinsky
  • MACS Department
  • June 5, 2008

  • Setting
  • Motivation
  • Source
  • Logistics
  • Results
  • Conclusion

Setting Motivation
  • Fairfield University
  • 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

  • Article 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
  • 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 Idea
  • Exams first returned without comments or grades
  • Each problem marked with ? or X
  • ?, if completely correct
  • X, if there is some error in the solution
  • 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
  • For each problem marked with X,
  • Find all errors made (may be more than one!)
  • For each error
  • 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
  • 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
  • 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
  • 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
  • Marking original exam
  • Keep track of how far each student got on each
    problem (to distinguish original vs. corrections
  • Grading corrections
  • If all conditions are satisfied, half lost points
    are returned
  • Total grade
  • Show both grades for each problem

Marking Exam (First-Pass)
Grading Sample
Total Grade
Results Survey Form
  • Numerical questions
  • 1 (disagree strongly) to
  • 7 (agree strongly)
  • Free-form questions
  • Would you use it again?
  • Y/N/No preference

  • Timing
  • Measures student perceptions, hence given
  • right after exams corrections are handed in,
  • before a grade is assigned

Numerical Data Summary
MA227 Fa07 (15) MA126 Sp07 (22) MA125 Fa06 (28) MA122 E2 Sp06 (41) MA122 E1 Sp06 (36) Avg
1 (more time) 6.4 6.4 6.4 6.2 6.5 6.4
2 (easy to find) 4.4 4.0 4.1 3.5 3.4 3.8
3 (get it better) 6.3 5.8 5.6 5.4 5.3 5.6
4 (enjoyed) 4.8 4.6 4.7 3.3 3.8 4.1
5 (higher grade) 6.4 6.9 6.2 5.8 5.7 6.1
Y 100 95.5 92.9 73.2 55.6
N 0 0 3.6 2.4 0
No preference 0 4.5 3.6 22.0 36.1
Free-form Questions Themes
  • 6 (what did you like?) top responses
  • Can earn back points/improve grade
  • Next theme varied by class/semester
  • MA126, MA125, and MA122 E1
  • able to go over work correct mistakes
  • MA122 E2 understand material better
  • Quotes
  • 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 (contd)
  • 7 (how to improve?) top responses
  • MA126
  • good as is
  • show how much got wrong (how serious?)
  • MA125
  • good as is
  • show / go over areas of common mistakes
  • MA122
  • 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
  • Trends
  • Students who originally do poorly love this
  • Students who were almost right like this less
  • Modifications made
  • First, a typo or notation error got a problem an
  • Based on student comments, since then, a correct
    solution with a typo gets a ? with a small

  • Experience of using it over the past 4 semesters
    and student survey data convinced me that
    self-reflective grading
  • 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.

  • Chris Petersen Black (Central Washington
    University Lynnwood)
  • Original idea from her article in Conversations
  • Larry Miners, Economics Dept. and CAE (Fairfield
  • Helped design the survey form
  • Used self-reflective grading in his small
    upper-level economics classes

  • __________________________________
  • Dr. Vera Cherepinsky
  • Assistant Professor of Mathematics
  • Fairfield University
  • Phone 203-254-4000 x3089
  • Email
  • __________________________________