A discussion about inquiry-based learning (part 1)

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 Wednesday, November 19, 2014.

Transcript

1. a discussion about inquiry-based learning
   NAU Mathematics & Statistics Teaching Showcase
   Dana C. Ernst
   Northern Arizona University
   November 19, 2014
   

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2. setting the stage
   

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3. Directions
   ∙ Get in groups of size 3–4.
   ∙ Group members should introduce themselves.
   ∙ For each of the questions that follow, I will ask you to:
   1. Think about a possible answer on your own.
   2. Discuss your answers with the rest of your group.
   3. Share a summary of each group’s discussion.
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4. question one
   What are the goals of a university education?
   What are the goals of a university education?
   What are the goals of a university education?
   3
   

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5. question two
   How does a person learn something new?
   How does a person learn something new?
   How does a person learn something new?
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6. question three
   What do you reasonably expect your students to
   remember from your courses in 20 years?
   What do you reasonably expect your students to
   remember from your courses in 20 years?
   What do you reasonably expect your students to
   remember from your courses in 20 years?
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7. question four
   What is the value of making mistakes in the
   learning process?
   What is the value of making mistakes in the
   learning process?
   What is the value of making mistakes in the
   learning process?
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8. productive failure #pf
   “Any creative endeavor is built on the ash heap
   of failure.” — Michael Starbird
   “Any creative endeavor is built on the ash heap
   of failure.” — Michael Starbird
   “Any creative endeavor is built on the ash heap
   of failure.” — Michael Starbird
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9. 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.
   Lofty Goals
   ∙ Transition students from consumers to producers!
   ∙ I want to provide the opportunity for a transformative experience.
   ∙ I want to change my students’ lives!
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10. what is ibl?
    

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11. 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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12. what is ibl?
    Guiding Principle of IBL
    Continually ask yourself the following question:
    Where do I draw the line between content I must impart to my stu-
    dents versus content they can produce independently?
    Where do I draw the line between content I must impart to my stu-
    dents versus content they can produce independently?
    Two Typical Approaches/Modes to IBL
    ∙ Student presentations.
    ∙ Small group work.
    Most IBL instructors implement some combination.
    Where do I draw the line between content I must impart to my stu-
    dents versus content they can produce independently?
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13. what is ibl?
    Important Role Changes
    ∙ Instructor becomes a mentor, cheerleader, and coach. Focus on
    teaching process.
    ∙ Student becomes the mathematician.
    IBL vs Presentations/Group Work
    ∙ Student presentations & group work act as vehicles for IBL.
    ∙ Yet student presentations & group do not imply IBL.
    ∙ What matters is what is happening during these activities.
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14. 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.
    ∙ My job:
    ∙ Facilitate/manage
    ∙ Mr. Super Positive
    ∙ William Wallace meets Robin Williams
    ∙ 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.
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15. 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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16. why ibl?
    

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17. why ibl?
    My IBL origins
    ∙ Number of IBL classes as student: 0
    ∙ When I started teaching, I mimicked experiences I had as a
    student (I lectured).
    ∙ By most metrics, I was an excellent instructor. But:
    “Things my students claim that I taught them masterfully, they don’t
    know.” — Dylan Retsek
    “Things my students claim that I taught them masterfully, they don’t
    know.” — Dylan Retsek
    ∙ First exposed to IBL/Moore Method during a Project NExT
    workshop run by Carol Schumacher (Kenyon College).
    ∙ Taught 1st full-blown IBL class in Fall 2009.
    ∙ To date taught using various forms of IBL over a dozen times.
    ∙ Currently Special Projects Coordinator for AIBL & mentor for new
    IBL practitioners.
    “Things my students claim that I taught them masterfully, they don’t
    know.” — Dylan Retsek
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18. why ibl?
    Some Data
    ∙ 4-5 million freshmen in HS.
    ∙ 75% HS graduation rate.
    ∙ 1.2 million bachelors degrees annually (< 1% of BA/BS are in
    math).
    ∙ 48,000 doctoral degrees annually (400–500 PhDs in math).
    Conclusion?
    Education is a self-populating institution!
    You are peculiar!
    You are peculiar!
    We need to renormalize.
    You are peculiar!
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19. why ibl?
    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
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20. why ibl?
    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. 2011/2013/2014, etc.
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21. 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.
    ∙ Statistically significant advantages for students in IBL vs
    traditional courses.
    The Twin Pillars
    ∙ Deep engagement in rich mathematics,
    ∙ Opportunities to collaborate.
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22. 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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23. personal reflections
    

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24. 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 is a lot of work, but to me it is worth it.
    ∙ Implementing IBL requires patience, flexibility, and 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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25. personal reflections
    Personal Obstacles
    ∙ If I lecture, then I dictate pace.
    ∙ I enjoy lecturing!
    ∙ If I write something on the board, then there is a good chance that
    it will be done correctly.
    ∙ Keeping my mouth shut is hard.
    CONTROL!
    CONTROL!
    Personal Concerns
    ∙ I think it would be a shame if students never had the opportunity
    to meditate on some of the classic mathematics texts (e.g., Rudin,
    Gallian).
    ∙ There is such a thing as too much collaboration.
    CONTROL!
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26. 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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27. 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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28. personal reflections
    Reflections on current courses
    ∙ MAT 136: Calculus 1
    ∙ MAT 320: Foundations of Mathematics
    ∙ MAT 411: Abstract Algebra
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29. 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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30. 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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31. personal reflections
    “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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