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.

Transcript

1. a discussion about ibl
   Part 2
   NAU Mathematics & Statistics Teaching Showcase
   Dana C. Ernst
   Northern Arizona University
   January 21, 2015
   

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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.
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3. what is ibl?
   

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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).
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5. what is ibl?
   Two Typical Approaches/Modes to IBL
   ∙ Student presentations.
   ∙ Small group work.
   Most IBL instructors implement some combination.
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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?
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7. what is ibl?
   Important Role Changes
   ∙ Instructor becomes a mentor, cheerleader, & coach. Focus on
   teaching process.
   ∙ Student becomes the mathematician.
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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?
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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
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10. why ibl?
    

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

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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.
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16. personal reflections
    

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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.)
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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.
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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!
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20. personal reflections
    Keys to Success
    ∙ Effective marketing
    ∙ Return to your guiding principle
    ∙ Adjusting problems/tasks appropriately
    ∙ Patience & trust!
    ∙ Community
    ∙ Build on positive experiences
    ∙ Pick a style that you are comfortable with
    ∙ Adapt, overcome, & improvise
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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.
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22. closing
    

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23. closing
    IBL Resources
    ∙ Academy of Inquiry-Based Learning
    ∙ Helpful resources
    ∙ Mini-grants
    ∙ IBL Workshops
    ∙ Discovering the Art of Mathematics
    ∙ Journal of Inquiry-Based Learning in Mathematics
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24. closing
    “We’re in the business of changing lives.” — Michael Starbird
    “We’re in the business of changing lives.” — Michael Starbird
    “We’re in the business of changing lives.” — Michael Starbird
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