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

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

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. 46-48

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

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.

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

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.

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.

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.

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

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.

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!

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

Typical class period Students sign up to present problems.

Sign-up for presentation of problems

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

Announcements, answering questions

Announcements, answering questions

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

Queries

Queries

Queries

Queries

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

Presentations

Presentations

Presentations

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

More queries

More queries

More queries

More queries

More queries

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

Wrapping up

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.

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.

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

http://citadel.sjfc.edu/faculty/rgantner/ibl/

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

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

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

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.

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

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

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.

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