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Effective and efficient grading for an IBL course

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.

Dana Ernst

June 18, 2012
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  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: [email protected]
    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
    [email protected]
    Does the audience have any other ideas?
    Other ideas

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