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Tried & True Practices for IBL & Active Learning

Dana Ernst
January 15, 2014

Tried & True Practices for IBL & Active Learning

This talk was given on January 15, 2014 as part of the Project NExT Panel Discussion on Tried & True Practices for IBL & Active Learning at the 2014 Joint Mathematics Meetings in Baltimore, MD.

Dana Ernst

January 15, 2014
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  1. Tried & True Practices
    for IBL & Active Learning
    !
    Project NExT Panel, JMM 2014
    Dana C. Ernst
    Northern Arizona University
    Email: [email protected]
    Web: http://danaernst.com

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  2. About Me
    • Assistant professor at Northern Arizona
    University
    • PhD from University of Colorado (2008)
    • Project NExT Red08
    • Special Projects Coordinator for
    Academy of Inquiry-Based Learning
    • MAA blogger at Math Ed Matters with
    Angie Hodge
    • Spent 4 years at Plymouth State
    University prior to NAU
    It may be the most recent addition
    to MAA’s blog offerings, but Math
    Ed Matters already has a varied
    backlog of informative, entertain-
    ing, and inspiring posts—and a
    lively comments section. Launched
    on April 10, 2013, Math Ed Matters
    showcases the irregular but more-
    than-monthly musings of Angie
    Hodge (University of Nebraska,
    Omaha) and Dana Ernst (Northern
    Arizona University) on topics and
    current events related to undergrad-
    uate mathematics and mathematics
    education.
    Hodge and Ernst have a lot in
    common. They’re both Project
    NExT fellows. (They met at a Project
    NExT ice cream social in 2008.)
    They both regularly undertake feats
    of physicality the less fit among us
    cannot begin to fathom: They run
    ultramarathons and scale sheer rock
    faces and accomplish thousands of
    feet of elevation gain under their
    own power. The pair also shares
    interest in and engagement with
    inquiry-based learning (IBL), and
    their belief in the efficacy of IBL
    colors the content of their blog.
    Within its first few months, Math
    Ed Matters treated readers to a
    video of Angie’s students doing
    a calculus version of the Korean
    pop hit “Gangnam Style”; Dana’s
    meditations on how instructors’
    personalities influence their choice
    of teaching methods; and reflections
    on MAA MathFest 2013 and the
    16th Annual Legacy of R. L. Moore
    Conference. Hodge and Ernst also
    provided, for the uninitiated, an
    inquiry-based learning primer titled
    “What the Heck Is IBL?”
    An Eager Audience
    Even as it spreads the word about
    IBL, Math Ed Matters has found a
    ready-made following in the com-
    munity of mathematics educators
    already implementing the student-
    centered pedagogy in their class-
    rooms. An August post about Ernst’s
    success giving his students colored
    pens to annotate their homework
    as classmates present solutions at
    the board spurred a discussion in
    the comments section. As read-
    ers requested clarification, voiced
    concerns, and offered suggestions
    of their own, Ernst periodically
    interjected.
    Ernst and Hodge have big plans
    for Math Ed Matters. In the coming
    months they expect to tackle online
    LaTeX editors, the University of Ne-
    braska, Omaha’s Calculus Bee, and a
    University of Colorado study of IBL
    effectiveness. They’ll also offer their
    perspectives on how to choose stu-
    dent presenters and secure student
    buy-in.
    “We are thrilled to be part of the
    discussion about improving teach-
    ing and the importance of math-
    ematics in education,” says Ernst.
    “Come on over [to the blog] and
    share your thoughts.”
    Angie Hodge (left) and Dana Ernst.
    http://maamathedmatters.
    blogspot.com/
    0$$)2&86v'HFHPEHU-DQXDU\vPDDRUJSXEVIRFXVKWPO
    Nice socks!

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  3. My IBL History
    • Number of IBL classes as a student: 0
    • First exposed to IBL/Moore Method during a Project NExT
    workshop run by Carol Schumacher.
    • By most metrics, I was an excellent instructor. But:
    • Taught 1st full-blown IBL class in Fall 2009.
    • Attended IBL Workshop during Summer 2010.
    • IBL Courses: Intro to Proofs, Number Theory, Real Analysis,
    Abstract Algebra, undergrad research.
    • IBL-Lite Courses: calculus sequence, Linear Algebra
    “Things my students claim that I taught them
    masterfully, they don’t know.” -- Dylan Retsek

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  4. What is IBL?
    • Instructor provides well-crafted problems/tasks requiring
    students to solve problems, conjecture, experiment,
    explore, create, & communicate.
    • Key ingredients: Students are responsible for
    ‣ guiding acquisition of knowledge, &
    ‣ validating ideas/arguments that are presented.
    • Example: Modified Moore Method, after R.L. Moore.
    Twin Pillars
    1. Deep engagement in rich mathematics.
    2. Opportunities to collaborate.
    See current research by Laursen, et al.

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  5. Obstacles
    • The elephant in the room: coverage!
    • “That’s how I learned, & it worked for me...”
    ‣ But you are peculiar!
    • “I like inspiring lectures.”
    ‣ Inspiration is necessary, but not sufficient.
    • “I’m afraid the students won’t like it.”
    ‣ I bet if you are passionate, having fun, & willing to
    adapt, it’ll be amazing.
    • Control!
    ‣ If I lecture, then I dictate pace.
    ‣ If I write something on the board, then there is a good
    chance that it will be done correctly.
    • Doubt from colleagues & administration.
    ‣ You are in Project NExT, they paid for you to be here!

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  6. 1. Student presentations.
    2. Small group work.
    Two Typical Approaches to IBL
    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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  7. • Proof-based courses.
    • 5-10 “tasks” are assigned each class meeting (Daily
    Homework). Due at beginning of next class.
    • Students are responsible for digesting new material
    outside of class (readings and screencasts).
    • Nearly all class time devoted to students presenting or
    discussing proposed solutions/proofs to assigned tasks.
    • Students may request mini-lectures or screencasts.
    My Approach to IBL
    • Students use felt tip pens to
    annotate work in light of discussion
    and presentations.
    • Daily Homework graded on ✔
    system. What did they have done
    before class?

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  8. Problem Sequence
    • Notes consist of definitions & very few examples mixed
    together with exercises, problems, & theorems to prove.
    • As opposed to typical course, students responsible for
    proving the key (& interesting!) theorems of the course.
    • Source of my notes available on GitHub:
    http://github.com/dcernst
    Rules of the Game
    • Students should not look to outside resources
    • Internet, other texts, other faculty, math major cousins,
    etc. are forbidden.
    • On the other hand, students are encouraged to collaborate
    on homework & even take-home exams.

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  9. • Calculus sequence. A work in progress for me.
    • 30-45 students.
    • 4 midterm exams & a cumulative final.
    • 3-4 Daily HW assignments per week (WeBWorK).
    • 1 Weekly HW assignment per week. Covers main topics
    from previous week. More challenging than Daily HW.
    • HW worth 15% of overall grade.
    • 3 class meetings devoted to introducing new material,
    either via lecture or exploratory group work.
    • 1 class meeting devoted to students presenting problems
    from Weekly HW. Students annotate with felt-tip pens.
    • Presenters are not graded, but 5-8% of grade is for
    participation.
    My Approach to IBL-Lite

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  10. Keys to Success
    • Marketing!
    ‣ Students have had 12+ years of direct instruction. Even
    if they don’t like it, it’s what they are used to.
    ‣ Students need to understand student & instructor roles.
    ‣ Students need to know that it is ok to be stuck & that
    you will support them in this endeavor.
    • Adjust problems/tasks appropriately.
    • Patience, trust, & community. Build on positive
    experiences.
    • Pick a style that you are comfortable with.

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  11. • The evidence in favor of IBL is compelling.
    • 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.
    Keeping My Mouth Shut...and Assessing

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  12. Resources
    • Academy of Inquiry Based Learning
    ‣ http://www.inquirybasedlearning.org
    ‣ Small Grants available for developing IBL materials
    ‣ Mentoring
    • The IBL Workshop
    ‣ MAA Prep Workshop
    ‣ http://iblworkshop.org
    • Journal of Inquiry-Based Learning in Mathematics
    ‣ http://jiblm.org
    ‣ Refereed IBL materials
    • Legacy of R.L. Moore Conference
    ‣ http://legacyrlmoore.org
    ‣ Conference devoted to IBL and the Moore Method

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