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Student presentations in calculus: A vehicle for getting students to talk about mathematics

Dana Ernst
January 08, 2016

Student presentations in calculus: A vehicle for getting students to talk about mathematics

This talk was given on January 8, 2016 as part of the "Increasing Student Engagement & Understanding through Active Learning Strategies in Calculus I" minicourse at the 2016 Joint Mathematics Meeting in Seattle, WA.

Dana Ernst

January 08, 2016
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  1. student presentations in calculus
    A vehicle for getting students to talk about mathematics
    Increasing Student Engagement & Understanding through Active Learning
    Strategies in Calculus I
    Dana C. Ernst
    Northern Arizona University
    January 8, 2016

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  2. claims
    1. An education must prepare a student to ask & explore questions
    in contexts that do not yet exist. That is, we need individuals
    capable of tackling problems they have never encountered & to
    ask questions no one has yet thought of.
    2. If we really want students to be independent, inquisitive, &
    persistent, then we need to provide them with the means to
    acquire these skills.
    1

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  3. what is ibl?
    ∙ Often involves very little lecturing & typically student
    presentations focused.
    ∙ Example: Moore Method, after R.L. Moore.
    ∙ Students should as much as possible be responsible for:
    2. Guiding the acquisition of knowledge,
    2. Validating the ideas presented (i.e., students should not be
    looking to the instructor as the sole authority).
    ∙ Two Typical Approaches/Modes to IBL
    1. Student presentations.
    2. Small group work.
    ∙ Most IBL instructors implement some combination.
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  4. my version of ibl in calculus
    ∙ Students responsible for digesting most new material out of class
    by working on a sequence of problems.
    ∙ Nearly all class time devoted to students presenting proposed
    solutions/proofs.
    ∙ Each batch of problems are meant to do some subset of the
    following:
    ∙ Introduce a new topic
    ∙ Develop intuition about a concept
    ∙ Synthesize ideas from a few concepts
    ∙ Prove a theorem
    ∙ Get practice doing routine or non-routine problems
    ∙ My students prove most of the theorems.
    ∙ Large-ish WeBWorK assignments due weekly.
    3

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  5. my version of ibl in calculus
    ∙ Presentations typically take one of 3 forms.
    1. An individual presenting their proposed solution to whole class.
    2. An individual presenting their proposed solution to a small
    group.
    3. An individual acts as a spokesperson for his/her small group &
    presents the group’s proposed solution to whole class.
    ∙ Instructor’s role: guide discussion & nudge students to ask the
    right questions.
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  6. my version of ibl in calculus
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  7. my version of ibl in calculus
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  8. my version of ibl in calculus
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  9. my version of ibl in calculus
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  10. my version of ibl in calculus
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  11. my version of ibl in calculus
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  12. more on student presentations
    ∙ Presentations are meant to drive classroom discussion, not to
    prove to you that Sally knows how to do Exercise 15.
    ∙ The perfect presentation is one that is interestingly wrong.
    “You will become clever through your mistakes.” — German proverb
    “You will become clever through your mistakes.” — German proverb
    ∙ One reason IBL works: Mode of engagement is different when
    listening to expert vs novice. “Student as skeptic.”
    ∙ Asking students to prove theorems, make conjectures, come up
    with examples/counterexamples, and come up with definitions
    generally make productive conversations.
    “You will become clever through your mistakes.” — German proverb
    11

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  13. questions to ponder
    ∙ How much scaffolding will you provide on the problems?
    ∙ Mode of student presentations?
    ∙ How will you choose presenters?
    ∙ How will you assess presenters?
    ∙ Are students expected to generate proofs of theorems? Will proofs
    be assessed on exams?
    ∙ What constraints do you have on physical space?
    ∙ What’s your plan for obtaining student buy-in?
    12

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  14. why ibl?
    The Colorado Study by Sandra Laursen et al.
    300 hours of classroom observation, 1100 surveys, 110 interviews, 220
    tests, & 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
    13

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  15. why ibl?
    Laursen et al. 2013
    “Our study indicates that the benefits of active learning experiences
    may be lasting & 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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  16. personal reflections
    ∙ In an IBL class there are lots of issues that bubble to the surface
    that we blissfully ignore when lecturing. Feature not a bug!
    ∙ We are responding in real time to what the students are doing &
    thinking.
    ∙ 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!
    15

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  17. personal reflections
    ∙ With the right set of materials, content coverage is not really an
    issue. Pace accelerates.
    ∙ Keeping my mouth shut…and assessing
    ∙ If I spend 50 minutes talking, it’s unlikely I’ve done any
    assessment.
    ∙ In an IBL course, nearly whole class session is spent on
    assessment.
    ∙ Students presenting, discussing, & collaborating provides me &
    them with immediate feedback about how things are going.
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  18. examples
    Suppose a function f has the following graph. Assume that the graph
    is made up of parts of lines and parts of circles.
    −3 −2 −1 1 2 3
    2
    If F is an antiderivative of f such that F(−4) = 42, find F(−1).
    17

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  19. examples
    As a preparation for the long bright summer days, Dr. Acula plans to
    store plasma in closed tin cans that have the shape of a cylinder. As
    an environmentally conscious member of the community, eh wants
    to use as little metal as possible. What should be the relationship
    between the radius and the height of his cans?
    18

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  20. examples
    “Are we there yet?”, asked Kelly. This was not the first time this
    question came up and the odometer in the family Dodge was
    broken, so he did not know how far they had traveled. Luckily, Kelly’s
    brother Bud traveled with them and he diligently check the
    speedometer every 10 minutes. He had the following measurements
    in this notebook: 30 40, 35, 40, 20. What distance did they cover so
    far approximately?
    19

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  21. ibl resources
    ∙ Academy of IBL (inquirybasedlearning.org)
    ∙ IBL mentoring
    ∙ Mini-grants
    ∙ IBL Workshops (iblworkshop.org)
    ∙ Discovering the Art of Mathematics (artofmathematics.org)
    ∙ Journal of Inquiry-Based Learning in Mathematics (jiblm.org)
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