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.
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]
Twitter: @danaernst & @IBLMath
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
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
Data to support
Intro to Proof, Number Theory, Abstract Algebra, & Real
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
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.
Keep us on track
Mr. Super Positive
Cross my arms and say, “hmmm”
Students may request mini-lectures or screencasts.
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
I take notes during presentation & add to spreadsheet:
Who & what problem
Exercise or proof
4 Completely correct and clear proof or solution. Yay!
Solution/Proof has minor technical flaws, some unclear language, or
lacking some details. Essentially correct.
A partial explanation or proof is provided but a significant gap still exists
to reach a full solution or proof.
Minimal progress has been made that includes relevant information &
could lead to a proof or solution.
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
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
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
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
Students love the felt tip pen approach. Numerous positive
comments about how useful this is.
Grading of the Daily Homework is fast!
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.
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):
4 This is correct and well-written mathematics!
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.
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
Students share project
with me; I can help
Would be nice if
students could submit
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
Does the audience have any other ideas?