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]
• Assistant professor at Northern Arizona
• 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
• 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
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
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
“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.
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.
1. Deep engagement in rich mathematics.
2. Opportunities to collaborate.
See current research by Laursen, et al.
• 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.
• 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
• Daily Homework graded on ✔
system. What did they have done
• 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:
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
My Approach to IBL-Lite
Keys to Success
‣ 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
• 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
• 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
‣ Small Grants available for developing IBL materials
• The IBL Workshop
‣ MAA Prep Workshop
• Journal of Inquiry-Based Learning in Mathematics
‣ Refereed IBL materials
• Legacy of R.L. Moore Conference
‣ Conference devoted to IBL and the Moore Method