Effective and efficient grading for an IBL course

In this talk, we relay one possible approach to grading for an IBL course.  In particular, we will focus on the grading of written homework for undergraduate proof‐based courses such as Introduction to Proof, Abstract Algebra, Number Theory, and Real Analysis.

Transcript

1. Effective and efficient grading
   for an IBL course
   Legacy of R.L. Moore Conference
   Austin, TX, June 14, 2012
   Dana C. Ernst
   Northern Arizona University
   Email: dana@danaernst.com
   Web: http://danaernst.com
   Twitter: @danaernst & @IBLMath
   

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2. When I first started using IBL, grading/assessing students
   caused me the most anxiety.
   Desire for data to justify letter grade
   Grading written work is extremely time-consuming (for
   me)
   Desire for feedback to be useful
   After some trial and error, I’ve settled on an approach that
   works great for me.
   Not discussing anything ground-breaking.
   Motivation & some disclaimers
   

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3. Optimization problem!
   Useful feedback
   for students
   Data to support
   grades
   Time required
   

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4. Intro to Proof, Number Theory, Abstract Algebra, & Real
   Analysis.
   10-30 students.
   Encourage collaboration.
   Typical grade determination:
   The big picture
   Category Weight Notes
   Homework 25% Mix of Daily & Weekly Homework
   Presentations & Participation 30% Students present problems from Daily Homework
   3 Exams 45% Typically take-home exams
   (Currently) Highly modified for calculus sequence & Linear
   Algebra.
   

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5. 5-10 “tasks” (e.g., exercises, proofs of theorems) are
   assigned each class meeting (Daily Homework). Due at
   beginning of next class.
   Students are responsible for digesting new material
   outside of class.
   Nearly all class time devoted to students presenting
   proposed solutions/proofs to assigned exercises.
   Students (usually) volunteer to present.
   My job:
   Facilitate discussion
   Keep us on track
   Mr. Super Positive
   Cross my arms and say, “hmmm”
   Students may request mini-lectures or screencasts.
   Day-to-day operation
   

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6. More on student presentations
   Must present at least 2x prior to each exam in order to
   receive a passing grade for Presentation category. (Is this
   working?)
   I take notes during presentation & add to spreadsheet:
   Who & what problem
   Exercise or proof
   Miscellaneous notes
   Score 1-4
   Grade Criteria
   4 Completely correct and clear proof or solution. Yay!
   3
   Solution/Proof has minor technical flaws, some unclear language, or
   lacking some details. Essentially correct.
   2
   A partial explanation or proof is provided but a significant gap still exists
   to reach a full solution or proof.
   1
   Minimal progress has been made that includes relevant information &
   could lead to a proof or solution.
   

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7. Daily Homework
   These problems form the backbone of the class.
   Problems from task sequence are assigned based on where
   we ended previous class.
   Felt tip pens!!!
   Credit: Clark Dollard (Metro State
   in Denver)
   Each student grabs a felt tip pen
   on way into class
   Students use pens to annotate
   homework in light of presentation
   & related discussion
   No penalty for use of pen
   Graded on ✔-system. What did they have done before
   class?
   

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8. Advantages of the felt tip pens
   I know what happened before class versus during class.
   Students mark up their work in ways they never did
   before.
   Students have (mostly) correct work by the end of class
   (pedantic details & logical structure).
   Students have a record of what happened in class together
   with their homework.
   When students look back at their notes they see their
   comments about what they were thinking & they see
   corrected mistakes.
   Students love the felt tip pen approach. Numerous positive
   comments about how useful this is.
   Grading of the Daily Homework is fast!
   

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9. Weekly Homework
   On week n+1, students choose 2 *-problems (subset of
   proofs) from Daily Homework from week n.
   Proofs must be typed (LaTeX preferred) & well-written.
   Email PDF using my naming convention.
   Files stored on Dropbox. Use iPad (GoodReader) to
   annotate PDFs & then email back to student.
   

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10. Weekly Homework (continued)
    Submitted on a non-class day.
    Students forced to reflect on previous week’s work by
    reviewing their notes from Daily Homework.
    Incorporates multiple rounds of revision.
    Graded harshly on 1-4 scale (credit: Ted Mahavier):
    Grade Criteria
    4 This is correct and well-written mathematics!
    3
    This is a good piece of work, yet there are some mathematical errors or
    some writing errors that need addressing.
    2 There is some good intuition here, but there is at least one serious flaw.
    1 I don't understand this, but I see that you have worked on it.
    

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11. More on students using LaTeX
    Students highly encouraged, but not required to use LaTeX
    to write up Weekly Homework.
    By end of the semester, all but 1 or 2 are using LaTeX.
    Students create free accounts on ScribTeX (ShareLaTeX
    might be a better choice):
    LaTeX in web browser;
    nothing to install
    Students use my
    homework template
    Students share project
    with me; I can help
    debug
    Would be nice if
    students could submit
    from here
    

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12. Categorize presentations (exercise versus proof)?
    Modify requirement for minimum number of presentations?
    Put exercises online & provide immediate feedback (like
    WeBWorK, Coursera, Udacity, etc.)?
    Eliminate emailing back of Weekly Homework using LMS?
    Ideas for improvement
    Thank you! Please contact me if
    you have questions or suggestions
    dana@danaernst.com
    Does the audience have any other ideas?
    Other ideas
    

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