Dana Ernst
January 21, 2015
200

# A discussion about inquiry-based learning (part 2)

In many mathematics classrooms, "doing mathematics" means following the rules dictated by the teacher, and "knowing mathematics" means remembering and applying these rules. However, an inquiry-based-learning (IBL) approach challenges students to create/discover mathematics. Boiled down to its essence, IBL is a method of teaching that engages students in sense-making activities. Rather than showing facts or a clear, smooth path to a solution, the instructor guides students via well-crafted problems through an adventure in mathematical discovery. In this talk, we will address the following questions: What is IBL? Why use IBL? What are some of the challenges of IBL? How can you incorporate more IBL into the classes that you teach? In addition, I will relay my personal experience and discuss how I came to IBL and where I plan to go with it. Time permitting, we will also discuss a few different examples of what an IBL classroom might look like in practice.

This talk was given at the NAU Department of Mathematics and Statistics Teaching Showcase on January 21, 2015.

January 21, 2015

## Transcript

Part 2
NAU Mathematics & Statistics Teaching Showcase
Dana C. Ernst
Northern Arizona University
January 21, 2015

2. the big picture
Claims
∙ An education must prepare a student to ask and explore
questions in contexts that do not yet exist. That is, we need
individuals capable of tackling problems they have never
encountered and to ask questions no one has yet thought of.
∙ If we really want students to be independent, inquisitive, &
persistent, then we need to provide them with the means to
acquire these skills.
1

3. what is ibl?

4. what is inquiry-based learning?
∙ According to the Academy of Inquiry-Based Learning:
∙ IBL is a teaching method that engages students in sense-making
activities.
∙ Students are given tasks requiring them to solve problems,
conjecture, experiment, explore, create, & communicate.
∙ Rather than showing facts and/or algorithms, the instructor
guides students via well-crafted problems.
∙ Often involves very little lecturing, and typically involves student
presentations.
∙ Example: Moore Method, after R.L. Moore.
∙ Students should as much as possible be responsible for:
∙ Guiding the acquisition of knowledge,
∙ Validating the ideas presented (i.e., students should not be
looking to the instructor as the sole authority).
3

5. what is ibl?
Two Typical Approaches/Modes to IBL
∙ Student presentations.
∙ Small group work.
Most IBL instructors implement some combination.
4

6. what is ibl?
Video and Discussion
It’s helpful to see what IBL might look like in practice.
∙ Clip 1: Mike Starbird, number theory at UT, small class, their
introduction to proof class, week 1 of semester.
∙ Clip 2: Mike Starbird, discrete structures at UT, small class, middle
of semester.
∙ Clip 3: Discovering the Art of Mathematics video, liberal arts
mathematics at Westﬁeld State University. (part 1, part 2, part 3)
Questions
∙ What is presenter doing?
∙ What is teacher doing?
∙ What is the audience doing?
∙ What would you do differently?
5

7. what is ibl?
Important Role Changes
∙ Instructor becomes a mentor, cheerleader, & coach. Focus on
teaching process.
∙ Student becomes the mathematician.
6

8. what is ibl?
Are you doing IBL?
∙ Who develops the mathematics that is discussed?
∙ Who presents the mathematics?
∙ Who critiques the mathematics that is presented?
∙ Who decides what is correct mathematics?
∙ Who asks the questions that drive further work?
7

9. what is ibl?
My version of IBL
∙ 5-10 “tasks” assigned each class meeting (Daily HW). Due next
class.
∙ Students responsible for digesting new material out of class.
∙ Nearly all class time devoted to students presenting proposed
solutions/proofs to Daily HW.
∙ Students may request mini-lectures. ← Hang on every word!
∙ Each week, students submit a subset of problems similar or
identical to problems from the previous week (Weekly HW). Graded
harshly
∙ My job:
∙ Facilitate/manage
∙ Mr. Super Positive
∙ William Wallace meets Robin Williams
8

10. why ibl?

11. why ibl?
The Colorado Study by Sandra Laursen et al.
300 hours of classroom observation, 1100 surveys, 110 interviews, 220
tests, and 3200 academic transcripts, gathered from > 100 course
sections at 4 campuses over 2 years.
IBL
Interviews SALG
Pre/Post
Tests
Transcripts Gender Observations
Non-IBL
10

12. why ibl?
The Twin Pillars
∙ Deep engagement in rich mathematics,
∙ Opportunities to collaborate.
11

13. why ibl?
Laursen et al. 2013
“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.”
Laursen et al. 2014
“Despite variation in how IBL was implemented, student outcomes
are improved in IBL courses relative to traditionally taught courses,
as assessed by general measures that apply across course types.
Particularly striking, the use of IBL eliminates a sizable gender gap
that disfavors women students in lecture-based courses.”
12

14. obstacles

15. obstacles
Potential Obstacles to Implementing IBL
In small groups, discuss what you feel are potential obstacles to
implementing IBL. Be prepared to share your thoughts.
Solutions
Now, let’s come up with some solutions to the obstacles that were
discussed.
14

16. personal reflections

17. personal reflections
My overall point of view
∙ I’m hooked. For most students, the net overall gain beats out
lecturing.
∙ IBL is not a magic bullet.
∙ IBL can be a lot of work, but to me it is worth it.
∙ Implementing IBL requires patience, ﬂexibility, & regular
reﬁnements.
∙ One reason IBL works: Mode of engagement is different when
listening to expert vs novice.
∙ With the right set of materials, content coverage is not really an
issue (my IBL notes for Abstract Algebra need some work in
regards to coverage.)
16

18. personal reflections
Keeping my mouth shut…and assessing
∙ 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.
17

19. personal reflections
IBL is messy (and that’s ok)
∙ In an IBL class there are lots of issues that bubble to the surface
that we blissfully ignore when lecturing.
∙ More day-to-day differences between IBL classes. I usually have
no idea what will happen each day!
∙ We are responding to what the students are doing & thinking, &
there are natural & necessary ups & downs.
∙ Some IBL class sessions look rougher than others because
students are in the process of learning difﬁcult things. #PF
∙ In contrast, in a lecture class, we control everything that happens
at every instant. This can look lovely to an observer but buries
most of the messiness. IBL is jazz!
18

20. personal reflections
Keys to Success
∙ Effective marketing
∙ Patience & trust!
∙ Community
∙ Build on positive experiences
∙ Pick a style that you are comfortable with
19

21. personal reflections
Marketing!
∙ Students are asked to solve problems they do not know the
answers to, to take risks, to make mistakes, & to engage in #PF.
∙ Students need to know that it is ok to be stuck & that you will
support them in this endeavor.
∙ Students need to know what their role is & what the instructor’s
role is.
∙ Expectations & goals need to be reiterated throughout the course.
20

22. closing

23. closing
IBL Resources