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 

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 

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

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. 

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 

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. 

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? 

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! 

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. 

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. 

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 

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