Dana Ernst
October 12, 2012
1.2k

# Inquiry-Based Learning: What, Why, and How?

What is inquiry-based learning (IBL)? Why use IBL? How can you incorporate more IBL into the classes that you teach? In this talk, we will address all of these questions, as well as discuss a few different examples of what an IBL classroom might look like in practice.

This talk was given at the 2012 ArizMATYC conference, which took place at Yavapai College in Prescott, AZ.

October 12, 2012

## Transcript

1. Inquiry-Based Learning:
What, Why, & How?
2012 ArizMATYC
Yavapai College
Dana C. Ernst
Northern Arizona University
Email: [email protected]
Web: http://danaernst.com
Thanks to Stan Yoshinobu for providing some of the content.
1

• Ph.D. from University of Colorado.
• Areas of research:
‣ Combinatorics of Coxeter groups and diagram algebras,
‣ A little math education.
• Currently an assistant professor at NAU (dream job!).
• Spent 4 years at Plymouth State University prior to NAU.
• Number of IBL classes I had as a student: 0
• Taught first IBL class in Fall of 2009.
2

3. What?
3

4. What is inquiry-based learning (IBL)?
• 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.
• Students are responsible for guiding acquisition of
knowledge.
• Often involves very little lecturing, and typically involves
student presentations.
• Example: Modified Moore Method, after R.L. Moore.
4

5. 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?
5

6. Our main objective
How do we get here?
questions
questions
6

7. Why?
7

8. One minute version of why IBL
• Our system needs an upgrade.
• Unintended negative outcomes via traditional methods.
• Research suggests IBL outcomes are better.
8

9. • When I started teaching, I mimicked the experiences I had
as a student (i.e., I lectured).
• By most metrics, I was a successful teacher (e.g., high
evaluations, several awards). Why change?
• Inspired by a Project NExT Workshop run by Carol
Schumacher (Kenyon College), I decided to give IBL a try.
• 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 with emphasis on collaboration.
• When I taught an abstract algebra course containing
students from both styles, anecdotal evidence suggested
students taught via IBL were stronger proof-writers & more
independent as learners.
My first IBL class
9

10. Some data
• 4-5 million freshmen in HS.
• 1.2 million bachelors degrees annually.
• Less than 1% of BA/BS are in math.
• Only 400-500 U.S. citizens/residents earn a Ph.D. annually.
• Education is a self-populating institution!
Conclusion?
You are peculiar!!!
We need to renormalize.
10

11. What is happening in STEM education?
• There exists a growing body of evidence suggesting
students are dissatisfied with learning experiences in
STEM.
• Math Education Research suggests that college students
have difficulty with:
‣ Solving non-routine problems,
‣ Packing/Unpacking mathematical statements,
‣ Proof.
(Schoenfeld 1988, Muis 2004, Selden and Selden 1995,
1999, 2003, Dreyfus 2001, Sowder and Harel 2003,
Weber 2001, 2003, Weber and Alcock 2004, Tall 1994)
11

12. • About half of STEM majors
switch to non-STEM.
• Top 4 reasons for switching
are teaching related.
• Good ones leave, too.
• Loss of interest.
• Students dissatisfied with
teaching of STEM classes
and less so with non-STEM.
• Weed-out culture.
12

13. The good news
Evidence from the math ed literature suggests that active,
learner-centered instruction leads to improved conceptual
understanding, problem solving, proof writing, retention,
habits of mind, and attitudes about math.
(Boaler 1998, Kwon et al 2005, Rassmussen et al 2006,
Smith 2006, Chappell 2006, Larsen et al 2011, etc.)
13

• Sandra Laursen, CU Boulder.
• Statistically significant advantages for students in IBL vs
Interview SALG
Pre-post
tests
Transcript
Data
Gender
IBL
Non-IBL
Class
Observation
14

15. Force Concept
Inventory
(Posttest -Pretest)/(Max
Possible Gain)
Hake, Am. Journal Physics, 1998
15

16. How?
16

17. Instructor Obstacles
• “That’s how I learned, and 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.”
‣ My kids like Gummi Bears, but that doesn’t mean they
are good for them.
• 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.
17

18. Student Obstacles
The main obstacle:
Most students do not enjoy direct
instruction, but it is what they are used to.
They expect to be passive, & they have had
14+ years of experience to develop deep-
rooted beliefs about how STEM classes
should operate & what is expected of them.
It is vital that student expectations & roles are clearly
established. To help reset these expectations students need
to have a clear understanding of what IBL is & why they
should care.
18

19. Marketing!
• Most students do not come equipped with the skills and
interests that we have.
• What are the secondary goals of the course? How are these
skills acquired?
• Students need to know what their role is.
Students are asked to solve problems
they do not know the answers to, to take
risks, to make mistakes, and to engage in
"fruitful struggle." These are all very
different from normal expectations.
19

20. Marketing! (Continued)
• Students need to know what the instructor’s role is.
• Expectations & goals need to be reiterated throughout the
course.
• Students need to know that it is ok to be stuck and that
you will support them in this endeavor.
• Use analogies: learning to play an instrument, learning to
ride a bike, etc.
• Tip: Get the students to tell you what the best way is to
acquire the skills necessary for effective thinking!
20

21. Content delivery & knowledge
acquisition
• For content that is to be imparted to students, how will it
be delivered?
‣ Lectures? Pre-planned vs. by request?
‣ Worksheets?
‣ Screencasts (Flipped Classroom)?
• For content that students produce, how & when will it be
acquired?
‣ In-class vs. homework?
‣ Worksheets?
‣ Collaboration vs. independence?
21

22. Examples
Let’s take a look at two examples.
22

23. A Modified Moore Method
Approach
23

24. • My experience: Linear Algebra, Intro to Proof, Number
Theory, Abstract Algebra, & Real Analysis. 10-30 students.
• Would likely work well for Calculus 3 and Differential
Equations.
• Encourage collaboration.
The big picture
Category Weight Notes
Homework 25% Mix of Daily & Weekly Homework
Presentations & Participation 30% Students present problems from Daily Homework
3 Exams 45% Typically take-home exams
24

25. Optimization problem!
Useful feedback
for students
Data to support
Time required
25

26. • 5-10 “tasks” (e.g., exercises, proofs of theorems) are
assigned each class meeting (Daily Homework). Due at
beginning of next class.
• Students are responsible for digesting new material
outside of class.
• Nearly all class time devoted to students presenting
proposed solutions/proofs to assigned exercises.
• Students (usually) volunteer to present.
• My job:
‣ Facilitate discussion
‣ Keep us on track
‣ Mr. Super Positive
‣ Cross my arms and say, “hmmm”
• Students may request mini-lectures or screencasts.
Day-to-day operation
26

27. More on student presentations
• Must present at least 2x prior to each exam in order to
working?)
‣ Who & what problem
‣ Exercise or proof
‣ Miscellaneous notes
‣ Score 1-4
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.
27

28. Daily Homework
• These problems form the backbone of the class.
• Problems from task sequence are assigned based on where
we ended previous class.
• Felt tip pens!!!
‣ Credit: Clark Dollard (Metro State
in Denver)
‣ Each student grabs a felt tip pen
on way into class
‣ Students use pens to annotate
homework in light of presentation
& related discussion
‣ No penalty for use of pen
• Graded on ✔-system. What did they have done before
class?
28

29. Advantages of the felt tip pens
• I know what happened before class versus during class.
• Students mark up their work in ways they never did
before.
• 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 homework.
• When students look back at their notes they see their
corrected mistakes.
• Students love the felt tip pen approach. Numerous positive
• Grading of the Daily Homework is fast!
29

30. Weekly Homework
• On week n+1, students choose 2 *-problems (subset of
proofs) from Daily Homework from week n.
• Proofs/solutions must be typed (LaTeX or Word).
• Email PDF using my naming convention.
• Use iPad to annotate PDFs & then email back to student.
30

31. Weekly Homework (continued)
• Submitted on a non-class day.
• Students forced to reflect on previous week’s work by
reviewing their notes from Daily Homework.
• Incorporates multiple rounds of revision.
• Graded harshly on 1-4 scale (credit: Ted Mahavier):
4 This is correct and well-written mathematics!
3
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.
31

32. An IBL-Lite Approach
32

33. • My experience: Precalculus and Calculus 1, 2, & 3.
• 20-50 students (NAU has larger class sizes than PSU).
• 3-4 midterm exams and a cumulative final.
• 3-4 Daily Homework assignments per week (WeBWorK).
• Homework worth 15% of overall grade.
• 1 Weekly Homework assignment per week. Covers main
topics from the previous week. More challenging than Daily
Homework.
• 2-3 class meetings are devoted to introducing new
material, either via lecture or IBL-style worksheets.
• 1 class meeting devoted to students presenting problems
from Weekly Homework. Students annotate with felt-tip
pens.