1. Inquiry-Based Learning: A Rookie’s Perspective
Jonathan Cox
Sigma Xi
May 1, 2015

2. FEEDBACK ENCOURAGED!

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

4. Scenario 1: K-12 education
“Over the past twenty years many educational theorists have claimed that if children are allowed to play with concrete material … and to explore ideas with the right kind of guidance from a teacher, they can turn themselves into experts in mathematics. According to this view, effective teachers can create conditions in their classrooms that will allow their students to construct knowledge and make discoveries. … A famous saying in education … captures this philosophy: ‘The teacher should be the guide on the side, not the sage on the stage.’ This approach to teaching, which usually goes by the name of discovery-based learning or inquiry-based learning, is now mandated in one form or another in curricula across Canada and the United States. … A teacher can’t simply hand out base-ten blocks and expect the students to discover efficient means for adding and subtracting large numbers.” – John Mighton, The End of Ignorance, pp

5. Scenario 2: Graduate school
Oklahoma State University
Point set topology course taught using “the Moore method”
Instructor sat in the back of the room, never saying anything.
Students had a textbook and were left entirely to their own devices to learn the subject.
Typical results

6. Scenario 3: Undergraduate course
University of Louisiana – Monroe
A colleague tried to teach the introduction to proofs course using IBL.
Result: most of the students were scared away from taking any further math classes.

7. The problem There are many great teaching ideas in education.
But anyone can pick up a good idea, twist it into something ineffective or even harmful, and still keep the same name on it.
Causes:
Making changes too fast
Taking the easy way

8. What Inquiry-Based Learning actually is
Cite defining features identified by others,
Highlight key principles common to IBL practitioners, and
Describe what my own IBL course is like
“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 class, etc.

9. 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. Good aspiration We need to go deeper.

10. 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.

11. 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

12. The Role of the “audience”
Peer review presenters’ work
Critique, ask questions, pay complements
Make observations and contribute ideas
Assist presenters in filling gaps or fixing errors
Students evaluate the mathematics of others for themselves.

13. The Role of the instructor
Little or no direct instruction
Guides and monitors
Facilitates student progress and class discussions
Ensures the class moves to increasingly sophisticated ways of thinking
Coach, mentor, collaborator, and guide, as well as a source of positive reinforcement
Provides the problems!

14. A concrete example Spring 2015 MATH 341 (Geometry)
Reading assignments from the course notes
Plainer and briefer than a textbook
Only one proof!
In the place of proofs, it has problems interspersed.
Major effort involved!
vital preparation for the next class meeting

15. Typical class period
Students sign up to present problems.

16. Sign-up for presentation of problems

17. Typical class period Students sign up to present problems.
I make announcements and answer questions.

18. Announcements, answering questions

19. Announcements, answering questions

20. Typical class period Students sign up to present problems.
I make announcements and answer questions.
Queries

21. Queries

22. Queries

23. Queries

24. Queries

25. Typical class period Students sign up to present problems.
I make announcements and answer questions.
Queries
Presentations

26. Presentations

27. Presentations

28. Presentations

29. Typical class period Students sign up to present problems.
I make announcements and answer questions.
Queries
Presentations
Activities

30. More queries

31. More queries

32. More queries

33. More queries

34. More queries

35. Typical class period Students sign up to present problems.
I make announcements and answer questions.
Queries
Presentations
Activities
Wrapping up, assignments

36. Wrapping up

37. My journey
Geometry has been my first full-fledged IBL course. I’ve been incorporating some active learning elements into my courses for years but have been slow to embrace the full implementation of IBL.

38. Fears I would do it wrong and harm students.
I would take an impossible amount of time to prepare.
I wouldn’t cover the needed material.

39. Upstate New York Inquiry-Based Learning Consortium
Encouragement from Patrick Rault
Spring 2014 text: Euclidean and Transformational Geometry: A Deductive Inquiry by Shlomo Libeskind

41. Upstate New York Inquiry-Based Learning Consortium
Encouragement from Patrick Rault
Spring 2014 text: Euclidean and Transformational Geometry: A Deductive Inquiry by Shlomo Libeskind
Invitations
Persistence
Funding

42. June 23-26, 2014
Inquiry-Based Learning Workshop at Kenyon College, Ohio
Funding:
Upstate NY Inquiry-Based Learning Consortium
Dean of the College of Arts and Sciences

43. Benefits from the workshop/consortium
Preparatory articles and videos
Practical sessions at the workshop
listserve
IBL mentor – Jane Cushman
UNYIBL workshops at math meetings
IITG grant application: course release to work on Geometry course notes

44. Soundbites/Insights
Fredonia’s vision: A Transformative Learning Experience for All What does that mean? “Information is not transformation.” - Shaun Achor Transmission of knowledge up through Middle Ages We live in the Google age! It is no longer necessary to transmit information in this way.

45. The BIG QUESTION
What is the goal of education? Independence. And how can that be accomplished? A “developing sense of feeling capable in the context of our guidance is what helps children develop confidence, which is the beginning of independence.” – Dr. Laura Markham, Peaceful Parent, Happy Kids} “The primary goal of [an IBL] course is to address the content in such a way as to develop in students the ability to investigate problems independently.” – Ted Mahavier, The Moore Method

46. Lecture method & student attitudes
Talking about Leaving by Seymour and Hewitt
Why students leave Science, Math, and Engineering (SME) majors:
lack of/loss of interest in SME
non-SME major offers better education/more interest
poor teaching by SME faculty
curriculum overload, fast pace overwhelming

47. Critical mass Evidence!
MOST students learn little to nothing from sitting there watching a professor do math.
Lecturing may actually harm students in the “attitude toward mathematics” aspects.

48. Other topics
The challenge of this ideal: “What is critical is that the instructor never provides the students with the actual proof of a proposition. All proofs are generated by the students themselves.” - Keith Weber
Issues in my IBL classroom
The coaching/practice analogy
Incremental changes in other courses
Changes in student thought patterns
Eg. A more straightforward way of doing induction proofs