This talk is meant to be a "high altitude" introduction to inquiry-based learning (IBL). The intention is to whet the audience's appetite and inspire dialogue.
This talk was given on August 22, 2013 as part of the Department of Mathematics and Statistics Teaching Showcase at Northern Arizona University.
An Introduction to
NAU Mathematics & Statistics Teaching Showcase
August 22, 2013
Dana C. Ernst
Northern Arizona University
Email: [email protected]
“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.
1. Deep engagement in rich mathematics.
2. Opportunities to collaborate.
• 4-5 million freshmen in HS.
• 75% HS graduation rate.
• 1.2 million bachelors degrees annually (<1% of BA/BS are
• 48,000 doctoral degrees annually (400-500 PhDs in math).
• Education is a self-populating institution!
You are peculiar!!!
We need to renormalize.
(NCES & NSF)
• 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.
‣ 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
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
• 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
Keeping my mouth shut...and assessing
• Academy of Inquiry Based Learning
‣ I am a Special Projects Coordinator for AIBL
‣ Small Grants available for developing IBL materials
• Journal of Inquiry-Based Learning in Mathematics
‣ Refereed IBL materials
• Legacy of R.L. Moore Conference
‣ Conference devoted to IBL and the Moore Method