Soup to Nuts: My Approach to IBL IBL Workshop 2014 Portland, OR Dana C. Ernst Northern Arizona University Web: http://danaernst.com

About Me • Assistant professor at Northern Arizona University • PhD from University of Colorado (2008) • Project NExT Red08 • Special Projects Coordinator for Academy of Inquiry-Based Learning • MAA blogger at Math Ed Matters with Angie Hodge • Spent 4 years at Plymouth State University prior to NAU It may be the most recent addition to MAA’s blog offerings, but Math Ed Matters already has a varied backlog of informative, entertain- ing, and inspiring posts—and a lively comments section. Launched on April 10, 2013, Math Ed Matters showcases the irregular but more- than-monthly musings of Angie Hodge (University of Nebraska, Omaha) and Dana Ernst (Northern Arizona University) on topics and current events related to undergrad- uate mathematics and mathematics education. Hodge and Ernst have a lot in common. They’re both Project NExT fellows. (They met at a Project NExT ice cream social in 2008.) They both regularly undertake feats of physicality the less fit among us cannot begin to fathom: They run ultramarathons and scale sheer rock faces and accomplish thousands of feet of elevation gain under their own power. The pair also shares interest in and engagement with inquiry-based learning (IBL), and their belief in the efficacy of IBL colors the content of their blog. Within its first few months, Math Ed Matters treated readers to a video of Angie’s students doing a calculus version of the Korean pop hit “Gangnam Style”; Dana’s meditations on how instructors’ personalities influence their choice of teaching methods; and reflections on MAA MathFest 2013 and the 16th Annual Legacy of R. L. Moore Conference. Hodge and Ernst also provided, for the uninitiated, an inquiry-based learning primer titled “What the Heck Is IBL?” An Eager Audience Even as it spreads the word about IBL, Math Ed Matters has found a ready-made following in the com- munity of mathematics educators already implementing the student- centered pedagogy in their class- rooms. An August post about Ernst’s success giving his students colored pens to annotate their homework as classmates present solutions at the board spurred a discussion in the comments section. As read- ers requested clarification, voiced concerns, and offered suggestions of their own, Ernst periodically interjected. Ernst and Hodge have big plans for Math Ed Matters. In the coming months they expect to tackle online LaTeX editors, the University of Ne- braska, Omaha’s Calculus Bee, and a University of Colorado study of IBL effectiveness. They’ll also offer their perspectives on how to choose stu- dent presenters and secure student buy-in. “We are thrilled to be part of the discussion about improving teach- ing and the importance of math- ematics in education,” says Ernst. “Come on over [to the blog] and share your thoughts.” Angie Hodge (left) and Dana Ernst. http://maamathedmatters. blogspot.com/ 0$$)2&86v'HFHPEHU-DQXDU\vPDDRUJSXEVIRFXVKWPO Nice socks!

My IBL History • Number of IBL classes as student: 0 • When I started teaching, I mimicked experiences I had as a student (I lectured). • By most metrics, I was an excellent instructor. But: • First exposed to IBL/Moore Method during a Project NExT workshop run by Carol Schumacher. • Taught 1st full-blown IBL class in Fall 2009. • Attended IBL Workshop during Summer 2010. “Things my students claim that I taught them masterfully, they don’t know.” -- Dylan Retsek

• For 3 consecutive semesters, I taught an intro to proof course at Plymouth State University. • 1st two iterations taught via lecture-based approach. • 3rd time taught using IBL. • When I taught an abstract algebra course containing students from both styles, I was convinced that students taught via IBL were stronger proof-writers & more independent as learners. • And finally I saw the potential for transformative change. My First IBL Class “We’re in the business of changing lives.” -- Mike Starbird

What is IBL? • Key ingredients: Students are responsible for ‣ guiding acquisition of knowledge, & ‣ validating ideas/arguments that are presented. • Student presentations and group work do not imply IBL. Personal Obstacles • If I lecture, then I dictate pace. • If I write something on the board, then there is a good chance that it will be done correctly. • Keeping my mouth shut is hard. Control!

Continually ask yourself the following question: Guiding Principle of IBL Where do I draw the line between content I must impart to my students versus content they can produce independently?

A Modified-Moore Method

• 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. Comments

• Produce examples/counterexamples • Validate arguments • Make conjectures • Produce valid proofs • Learn to write • Develop perseverance • Develop independence Goals Category Weight Notes Homework 25% Mix of Daily & Weekly Homework Presentations & Participation 30% Students present problems from Daily Homework 3 Exams 45% Mix of take-home and in-class exams Grade Determination

Problem Sequence • Started by using others’ notes/book, but now prefer to write my own. • Source of notes available on GitHub: http://github.com/dcernst/IBL-IntroToProof Rules of the Game • Students should not look to outside resources • Internet, other texts, other faculty, math major cousins, etc. are forbidden. • On the other hand, students are encouraged to collaborate on homework & even take-home exams.

• 5-10 “tasks” assigned each class meeting (Daily HW). Due next class. • Students responsible for digesting new material out of class. • Nearly all class time devoted to students presenting proposed solutions/proofs to Daily HW. • My job: ‣ William Wallace meets Robin Williams ‣ Facilitate/manage ‣ Mr. Super Positive • Students may request mini-lectures or screencasts. • Students type up subset of problems from previous week (Weekly HW). Day-to-Day Operation Hang on every word.

Student Presentations • One student at a time talking & writing. • Must present at least 2x prior to each exam in order to receive a passing grade for Presentation category. • I take notes during presentation & add to spreadsheet. • Presentations are serious business, not meant to be formal Grade Criteria 4 Completely correct and clear proof or solution. Yay! 3 Solution/Proof has minor technical flaws or is lacking some details. 2 A partial explanation or proof is provided but a significant gap still exists. 1 Minimal progress has been made.

Daily Homework • Problems from task sequence are assigned based on where we ended previous class. • Colored pens!!! ‣ Each student grabs a colored pen on way into class. ‣ Students use pens to annotate HW in light of presentation & related discussion. ‣ No penalty for use of pen. • Graded on ✔-system. What did they have done before class?

Advantages of Colored Pens • I know what happened before class versus during class. • 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 HW. • When students look back at their notes they see their comments about what they were thinking & they see corrected mistakes. • Grading of the Daily HW is fast! Important! Mode of engagement is different when listening to expert vs. novice.

Weekly Homework • On week n+1, students choose 2 *-problems from Daily HW from week n. • Proofs typed (LaTeX, check out writeLaTeX). • Submit PDF on non-class (Canvas). • Students forced to reflect on previous week’s work by reviewing their notes from Daily HW. • Graded harshly on 1-4 scale (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.

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

An IBL Lite Approach

• Calculus sequence. A work in progress for me. • 30-45 students. • 4 midterm exams & a cumulative final. • 3-4 Daily HW assignments per week (WeBWorK). • 1 Weekly HW assignment per week. Covers main topics from previous week. More challenging than Daily HW. • 3 class meetings devoted to introducing new material, either via lecture or exploratory group work. • 1 class meeting devoted to students presenting problems from Weekly HW. Students annotate with colored pens. • Presentation day looks like last Starbird video. • Presenters are not graded, but 5-10% of grade is for participation. My Approach to IBL-Lite

• Effective marketing • Return to your guiding principle • Adjusting problems/tasks appropriately • Patience & trust! • Community • Build on positive experiences • Pick a style that you are comfortable with • Adapt, overcome, & improvise Keys to Success