An Introduction to Inquiry-Based Learning NAU Mathematics & Statistics Teaching Showcase August 22, 2013 Dana C. Ernst Northern Arizona University Email: [email protected] Web: http://danaernst.com 

“Things my students claim that I taught them masterfully, they don’t know.” -- Dylan Retsek How did I get here? 

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. 

Some data • 4-5 million freshmen in HS. • 75% HS graduation rate. • 1.2 million bachelors degrees annually (<1% of BA/BS are in math). • 48,000 doctoral degrees annually (400-500 PhDs in math). • Education is a self-populating institution! Conclusion? You are peculiar!!! We need to renormalize. (NCES & NSF) 

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. 

The Colorado study • Comparing IBL vs non-IBL university mathematics courses. • Sandra Laursen, CU Boulder. • Statistically significant advantages for students in IBL vs traditional courses. Interview SALG Pre/post tests Transcript Data Gender IBL Non-IBL Class Observation 

Recent Laursen paper “Our study indicates that the benefits of active learning experiences may be lasting and significant for some student groups, with no harm done to others. Importantly, ‘covering’ less material in inquiry-based sections had no negative effect on students’ later performance in the major.” Kogan, M., & Laursen, S. L. (2013). Assessing long-term effects of inquiry-based learning: A case study from college mathematics. Innovative Higher Education, 39(3). 

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. 

• 5-10 “tasks” are assigned each class meeting (Daily HW) • Students are responsible for digesting new material outside of class (readings & screencasts). • Nearly all class time devoted to students presenting proposed solutions/proofs to assigned tasks. • My job: ‣ Facilitate discussion & keep us on track ‣ Cross my arms and say, “hmmm” • Students may request mini-lectures or screencasts. My approach in proof-based courses 

• 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 ‣ I am a Special Projects Coordinator for AIBL ‣ Mentoring ‣ Small Grants available for developing IBL materials • 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