1. Jonathan Cox Fredonia Teaching and Learning Conference August 17, 2015
Inquiry-Based Learning: Ultimate Engagement in the Mathematics Classroom
Jonathan Cox
Fredonia Teaching and Learning Conference
August 17, 2015

2. Introductory activity
In groups of 3-4 with people around you,
introduce yourselves (if you haven’t already).
Then take turns on the following two tasks:
Describe something you are really good at.
Finish the following sentence. “I learn mathematics best when…”
Make lists on the boards

4. Swimming analogy

5. Swimming analogy
Doing mathematics, or other subjects, can be scary as well. “Get in the water. I promise I won’t let you drown!” My role: Coach vs. Performer/referee

6. Status quo: How did we get here?
From ancient times, the transmission of knowledge has been vital to society.
Before the invention of the printing press, this was most effectively accomplished by transcribing.
Origin of the traditional lecture method of instruction
We live in the Google age!

7. The (Modified) Moore Method
IBL
Inquiry-Based Learning
Discovery-Based Learning
Active Learning
The (Modified) Moore Method

8. What is IBL?
Initial definition: Inquiry-Based Learning is a problem-based approach to teaching mathematics which aims to develop in students the ability to investigate problems independently. We need to go deeper. “There are as many instantiations of the MMM as there are proponents of it” – J. C. Smith Remarkably consistent philosophy and set of core practices Beyond mathematics: POGIL, flipped classroom, etc.

9. Broad themes
Students actively participate in forming and contributing ideas.
Student ideas and explanations drive progress in the course.
Students presenting solutions is the primary classroom activity.
Students are engaged in apprenticeship into the practice of mathematics.

10. The material Based on a carefully constructed sequence of tasks
These tasks are problems to be solved—often propositions to be proved (or disproved).
Provided in the form of course notes that often also contain axioms, definitions, and perhaps a few motivating examples and some background explanation.
No textbook (or a textbook designed for IBL)

11. IBL classroom mini-experience
Joe counts 48 heads and 134 legs among the chickens and dogs on his farm. How many dogs and how many chickens does he have? Any method is fair game! * * Except looking up on the internet—the point is to construct a solution yourself!

12. Another way to get a flavor: Video
Look inside an IBL classroom in action
We’ll watch a video if we have time at the end. (Unlikely!)
Never fear, you can watch the video yourself later.
My IBL page, with information and links related to this talk:
Previous talk - Inquiry-Based Learning: A Rookie’s Perspective

13. Philosophy
What is the goal of education? My answer: Independence Second, how can the goal be accomplished? (postpone)

14. Evidence on the lecture method
Claim: Whatever your goal for education is, the lecture method fails to accomplish it effectively.
Eric Mazur (physics) – video Confessions of a converted lecturer
Yoshinobu and Jones – article The coverage issue
cite Talking about Leaving by Seymour and Hewitt, who studied why students leave Science, Math, and Engineering majors.

15. Why students leave STEM majors
Lack of/loss of interest in STEM
Non-STEM major offers better education/more interest
Poor teaching by STEM faculty
Curriculum overload, fast pace overwhelming
Yoshinobu and Jones connect these reasons to the typical STEM teaching environment, particularly the lecture method.

16. Affective outcomes
Various other studies have also found that the lecture method has a negative effect on students’ attitudes toward mathematics, … as well as on their ways of thinking about mathematics, and their persistence in taking more math classes. Together, these types of perception changes are called affective outcomes of a course or way of teaching.

17. My conclusion based on this evidence
MOST students learn little to nothing from sitting there watching a professor do math.
Lecturing actually harms students in the affective aspects.
Conclusion: I could stop lecturing and do almost anything else, and it would still be an improvement for students.
There are many forms of active learning.
Why IBL?

18. Why IBL?
Goal: intellectual independence of students An IBL class is tailored precisely toward achieving this goal by facilitating maximum possible independence of students. This is really highlighted by the description of Theron Hitchman, a prominent advocate for IBL: How many of the following questions can be answered with “the students” rather than “the professor”?

19. “The students” or “The professor”?
Who presents the mathematics?
Who develops the mathematics to be presented?
Who has the responsibility for critiquing the mathematics which is presented?
Who has the final say on whether a bit of mathematics is judged “correct”?
Who is responsible for asking questions which drive further work?

20. Evidence for effectiveness of IBL
The most comprehensive study so far has been undertaken by the Ethnography and Evaluation Research unit at the University of Colorado at Boulder. The results showed greater cognitive and affective gains for students in IBL courses at statistically significant levels. Subsequent courses: As many or more courses, with grades as good or better

21. What causes these differences?
The portion of class spent on student-centered, rather than instructor-centered, activities
The “twin pillars of IBL”:
Deep engagement with the mathematics
Collaboration—broadly defined as working with peers, whether in small groups or critiquing solutions as a class.
These are the uses of class time to strive for.

22. One last appeal for action
“We are not put into this world to sit still and know; we are put into it to act.”
— Woodrow Wilson, Presidential Inaugural Address, Princeton, October 25, 1902
(Quoted by James D. Douglas, J.D., in 2015 Fredonia Commencement Address)
Resources for this talk are located at .

23. Bonus!
If there is extra time, we can watch this video from the media library at Discovering the Art of Mathematics. Notice how the IBL classroom environment seems messy, chaotic, and slow to gain direction. This is typical. This is how real learning occurs! The pace picks up as students take charge of their learning.