These slides accompanied a plenary talk I gave as part of the 2014 IBL Workshop that took place in Portland, OR. The slides are meant to be a summary to my approach to IBL.
Soup to Nuts: My
Approach to IBL
IBL Workshop 2014
Dana C. Ernst
Northern Arizona University
• 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 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.
• 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.
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
‣ Desire for feedback to be useful
• After some trial and error, I’ve settled on an approach that
works great for me.
• Produce examples/counterexamples
• Validate arguments
• Make conjectures
• Produce valid proofs
• Learn to write
• Develop perseverance
• Develop independence
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
• Started by using others’ notes/book, but now prefer to
write my own.
• Source of 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.
• 5-10 “tasks” assigned each class meeting (Daily HW). Due
• Students responsible for digesting new material out of
• Nearly all class time devoted to students presenting
proposed solutions/proofs to Daily HW.
• My job:
‣ William Wallace meets Robin Williams
‣ Mr. Super Positive
• Students may request mini-lectures or screencasts.
• Students type up subset of problems from previous week
• 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
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.
• 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
‣ No penalty for use of pen.
• Graded on ✔-system. What did they have done before
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
• Grading of the Daily HW is fast!
Mode of engagement is different when listening to expert vs.
• 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):
4 This is correct and well-written mathematics!
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.
Data to support
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
My Approach to IBL-Lite
• Effective marketing
• Return to your guiding principle
• Adjusting problems/tasks appropriately
• Patience & trust!
• Build on positive experiences
• Pick a style that you are comfortable with
• Adapt, overcome, & improvise
Keys to Success