This talk was given on January 15, 2014 as part of the Project NExT Panel Discussion on Tried & True Practices for IBL & Active Learning at the 2014 Joint Mathematics Meetings in Baltimore, MD.
Tried & True Practices for IBL & Active Learning ! Project NExT Panel, JMM 2014 Dana C. Ernst Northern Arizona University Email: [email protected] 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 a student: 0 • First exposed to IBL/Moore Method during a Project NExT workshop run by Carol Schumacher. • By most metrics, I was an excellent instructor. But: • Taught 1st full-blown IBL class in Fall 2009. • Attended IBL Workshop during Summer 2010. • IBL Courses: Intro to Proofs, Number Theory, Real Analysis, Abstract Algebra, undergrad research. • IBL-Lite Courses: calculus sequence, Linear Algebra “Things my students claim that I taught them masterfully, they don’t know.” -- Dylan Retsek
What is IBL? • Instructor provides well-crafted problems/tasks requiring students to solve problems, conjecture, experiment, explore, create, & communicate. • Key ingredients: Students are responsible for ‣ guiding acquisition of knowledge, & ‣ validating ideas/arguments that are presented. • Example: Modified Moore Method, after R.L. Moore. Twin Pillars 1. Deep engagement in rich mathematics. 2. Opportunities to collaborate. See current research by Laursen, et al.
Obstacles • The elephant in the room: coverage! • “That’s how I learned, & it worked for me...” ‣ But you are peculiar! • “I like inspiring lectures.” ‣ Inspiration is necessary, but not sufficient. • “I’m afraid the students won’t like it.” ‣ I bet if you are passionate, having fun, & willing to adapt, it’ll be amazing. • Control! ‣ 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. • Doubt from colleagues & administration. ‣ You are in Project NExT, they paid for you to be here!
1. Student presentations. 2. Small group work. Two Typical Approaches to IBL IBL vs Presentations/Group Work • Student presentations & group work act as vehicles for IBL. • Yet student presentations & group do not imply IBL. • What matters is what is happening during these activities.
• Proof-based courses. • 5-10 “tasks” are assigned each class meeting (Daily Homework). Due at beginning of next class. • Students are responsible for digesting new material outside of class (readings and screencasts). • Nearly all class time devoted to students presenting or discussing proposed solutions/proofs to assigned tasks. • Students may request mini-lectures or screencasts. My Approach to IBL • Students use felt tip pens to annotate work in light of discussion and presentations. • Daily Homework graded on ✔ system. What did they have done before class?
Problem Sequence • Notes consist of definitions & very few examples mixed together with exercises, problems, & theorems to prove. • As opposed to typical course, students responsible for proving the key (& interesting!) theorems of the course. • Source of my notes available on GitHub: http://github.com/dcernst 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.
• 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. • HW worth 15% of overall grade. • 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 felt-tip pens. • Presenters are not graded, but 5-8% of grade is for participation. My Approach to IBL-Lite
Keys to Success • Marketing! ‣ Students have had 12+ years of direct instruction. Even if they don’t like it, it’s what they are used to. ‣ Students need to understand student & instructor roles. ‣ Students need to know that it is ok to be stuck & that you will support them in this endeavor. • Adjust problems/tasks appropriately. • Patience, trust, & community. Build on positive experiences. • Pick a style that you are comfortable with.
• The evidence in favor of IBL is compelling. • If I spend 50 minutes talking, it’s unlikely I’ve done any assessment. • During a typical day in an IBL course, the whole class session is spent on assessment. • When I used to predominately lecture, I was really just guessing at how effective I was being. Students lulled into thinking they understood. • Students presenting, discussing, & collaborating provides me & them with immediate feedback about how things are going. Keeping My Mouth Shut...and Assessing
Resources • Academy of Inquiry Based Learning ‣ http://www.inquirybasedlearning.org ‣ Small Grants available for developing IBL materials ‣ Mentoring • The IBL Workshop ‣ MAA Prep Workshop ‣ http://iblworkshop.org • Journal of Inquiry-Based Learning in Mathematics ‣ http://jiblm.org ‣ Refereed IBL materials • Legacy of R.L. Moore Conference ‣ http://legacyrlmoore.org ‣ Conference devoted to IBL and the Moore Method
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