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Inquiry-Based Learning: What, Why, and How?

Dana Ernst
October 02, 2012

Inquiry-Based Learning: What, Why, and How?

What is inquiry-based learning (IBL)? Why use IBL? How can you incorporate more IBL into the classes that you teach? In this talk, we will address all of these questions, as well as discuss a few different examples of what an IBL classroom might look like in practice.

This talk was given at the Mathematics Instructional Colloquium at the University of Arizona.

Dana Ernst

October 02, 2012
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Transcript

  1. Inquiry-Based Learning:
    What, Why, & How?
    Mathematics Instructional Colloquium
    University of Arizona
    Dana C. Ernst
    Northern Arizona University
    Email: [email protected]
    Web: http://danaernst.com
    Twitter: @danaernst & @IBLMath
    Thanks to Stan Yoshinobu for providing some of the content.
    1

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  2. About me
    • Ph.D. from University of Colorado.
    • Areas of research:
    ‣ Combinatorics of Coxeter groups and diagram algebras,
    ‣ A little math education.
    • Currently an assistant professor at NAU (dream job!).
    • Spent 4 years at Plymouth State University prior to NAU.
    • Number of IBL classes I had as a student: 0
    • Taught first IBL class in Fall of 2009.
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  3. What?
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  4. What is inquiry-based learning (IBL)?
    • 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.
    • Students are responsible for guiding acquisition of
    knowledge.
    • Often involves very little lecturing, and typically involves
    student presentations.
    • Sometimes called Modified Moore Method, after R.L.
    Moore.
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  5. Continually ask yourself the following question:
    Guiding Principle of IBL
    Where do I draw the line
    between content I must impart
    to my students versus content
    they can produce independently?
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  6. Our main objective
    How do we get here?
    Students answering
    questions
    Students asking
    questions
    6

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  7. Why?
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  8. One minute version of why IBL
    • Our system needs an upgrade.
    • Unintended negative outcomes via traditional methods.
    • Research suggests IBL outcomes are better.
    8

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  9. • When I started teaching, I mimicked the experiences I had
    as a student (i.e., I lectured).
    • By most metrics, I was a successful teacher (e.g., high
    evaluations, several awards). Why change?
    • Inspired by a Project NExT Workshop run by Carol
    Schumacher (Kenyon College), I decided to give IBL a try.
    • For 3 consecutive semesters, I taught an intro to proof
    course at Plymouth State University.
    • 1st two iterations taught via lecture-based approach.
    • 3rd time taught using IBL with emphasis on collaboration.
    • When I taught an abstract algebra course containing
    students from both styles, anecdotal evidence suggested
    students taught via IBL were stronger proof-writers & more
    independent as learners.
    My first IBL class
    9

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  10. Some data
    • 4-5 million freshmen in HS.
    • 75% HS graduation rate.
    • 1.2 million bachelors degrees annually.
    • Less than 1% of BA/BS are in math.
    • Only 400-500 U.S. citizens/residents earn a Ph.D. annually.
    • Education is a self-populating institution!
    Conclusion?
    You are peculiar!!!
    We need to renormalize.
    10

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  11. 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)
    11

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  12. • About half of STEM majors
    switch to non-STEM.
    • Top 4 reasons for switching
    are teaching related.
    • Good ones leave, too.
    • Loss of interest.
    • Non-STEM majors offer
    better education/more
    interest.
    • Curriculum overload.
    • Poor teaching.
    • Weed-out culture.
    Talking About Leaving
    12

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  13. 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, etc.)
    13

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  14. The Colorado study
    • Sandra Laursen, CU Boulder.
    • Statistically significant advantages for students in IBL vs
    traditional courses.
    Interview SALG
    Pre-post
    tests
    Transcript
    Data
    Gender
    IBL
    Non-IBL
    Class
    Observation
    14

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  15. Force Concept
    Inventory
    (Posttest -Pretest)/(Max
    Possible Gain)
    Hake, Am. Journal Physics, 1998
    15

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  16. Twin Pillars
    1. Deep engagement in rich mathematics
    2. Opportunities to collaborate.
    16

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  17. How?
    17

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  18. Instructor Obstacles
    • “That’s how I learned, and 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.”
    ‣ My kids like Gummi Bears, but that doesn’t mean they
    are good for them.
    • 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.
    18

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  19. Student Obstacles
    The main obstacle:
    Most students do not enjoy direct
    instruction, but it is what they are used to.
    They expect to be passive, & they have had
    14+ years of experience to develop deep-
    rooted beliefs about how STEM classes
    should operate & what is expected of them.
    It is vital that student expectations & roles are clearly
    established. To help reset these expectations students need
    to have a clear understanding of what IBL is & why they
    should care.
    19

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  20. Marketing!
    • Most students do not come equipped with the skills and
    interests that we have.
    • What are the secondary goals of the course? How are these
    skills acquired?
    • Students need to know what their role is.
    Students are asked to solve problems
    they do not know the answers to, to take
    risks, to make mistakes, and to engage in
    "fruitful struggle." These are all very
    different from normal expectations.
    20

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  21. Marketing! (Continued)
    • Students need to know what the instructor’s role is.
    • Expectations & goals need to be reiterated throughout the
    course.
    • Students need to know that it is ok to be stuck and that
    you will support them in this endeavor.
    • Use analogies: learning to play an instrument, learning to
    ride a bike, etc.
    • Tip: Get the students to tell you what the best way is to
    acquire the skills necessary for effective thinking!
    21

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  22. Content delivery & knowledge
    acquisition
    • For content that is to be imparted to students, how will it
    be delivered?
    ‣ Assigned readings?
    ‣ Lectures? Pre-planned vs. by request?
    ‣ Worksheets?
    ‣ Screencasts (Flipped Classroom)?
    • For content that students produce, how & when will it be
    acquired?
    ‣ Task/problem sequences?
    ‣ In-class vs. homework?
    ‣ Worksheets?
    ‣ Collaboration vs. independence?
    22

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  23. 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.
    23

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  24. Examples
    Let’s take a look at two examples.
    24

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  25. Proof-based classes
    A Moore method approach with collaboration
    25

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  26. • My experience:
    ‣ Intro to Proof, Number Theory, Abstract Algebra, & Real
    Analysis.
    ‣ 10-30 students.
    • Encourage collaboration.
    • Typical grade determination:
    The big picture
    Category Weight Notes
    Homework 25% Mix of Daily & Weekly Homework
    Presentations & Participation 30% Students present problems from Daily Homework
    3 Exams 45% Typically take-home exams
    26

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  27. Optimization problem!
    Useful feedback
    for students
    Data to support
    grades
    Time required
    27

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  28. • 5-10 “tasks” (e.g., exercises, proofs of theorems) are
    assigned each class meeting (Daily Homework). Due at
    beginning of next class.
    • Students are responsible for digesting new material
    outside of class.
    • Nearly all class time devoted to students presenting
    proposed solutions/proofs to assigned exercises.
    • Students (usually) volunteer to present.
    • My job:
    ‣ Facilitate discussion
    ‣ Keep us on track
    ‣ Mr. Super Positive
    ‣ Cross my arms and say, “hmmm”
    • Students may request mini-lectures or screencasts.
    Day-to-day operation
    28

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  29. More on student presentations
    • Must present at least 2x prior to each exam in order to
    receive a passing grade for Presentation category. (Is this
    working?)
    • I take notes during presentation & add to spreadsheet:
    ‣ Who & what problem
    ‣ Exercise or proof
    ‣ Miscellaneous notes
    ‣ Score 1-4
    Grade Criteria
    4 Completely correct and clear proof or solution. Yay!
    3 Solution/Proof has minor technical flaws or is lacking some details.
    2 A partial explanation or proof is provided but a significant gap still exists.
    1 Minimal progress has been made.
    29

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  30. Daily Homework
    • These problems form the backbone of the class.
    • Problems from task sequence are assigned based on where
    we ended previous class.
    • Felt tip pens!!!
    ‣ Credit: Clark Dollard (Metro State
    in Denver)
    ‣ Each student grabs a felt tip pen
    on way into class
    ‣ Students use pens to annotate
    homework in light of presentation
    & related discussion
    ‣ No penalty for use of pen
    • Graded on ✔-system. What did they have done before
    class?
    30

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  31. Advantages of the felt tip pens
    • I know what happened before class versus during class.
    • Students mark up their work in ways they never did
    before.
    • Students have (mostly) correct work by the end of class
    (pedantic details & logical structure).
    • Students have a record of what happened in class together
    with their homework.
    • When students look back at their notes they see their
    comments about what they were thinking & they see
    corrected mistakes.
    • Students love the felt tip pen approach. Numerous positive
    comments about how useful this is.
    • Grading of the Daily Homework is fast!
    31

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  32. Weekly Homework
    • On week n+1, students choose 2 *-problems (subset of
    proofs) from Daily Homework from week n.
    • Proofs must be typed (LaTeX preferred) & well-written.
    • Email PDF using my naming convention.
    • Files stored on Dropbox. Use iPad to annotate PDFs &
    then email back to student.
    32

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  33. Weekly Homework (continued)
    • Submitted on a non-class day.
    • Students forced to reflect on previous week’s work by
    reviewing their notes from Daily Homework.
    • Incorporates multiple rounds of revision.
    • Graded harshly on 1-4 scale (credit: Ted Mahavier):
    Grade Criteria
    4 This is correct and well-written mathematics!
    3
    This is a good piece of work, yet there are some mathematical errors or
    some writing errors that need addressing.
    2 There is some good intuition here, but there is at least one serious flaw.
    1 I don't understand this, but I see that you have worked on it.
    33

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  34. Calculus sequence
    An IBL-lite approach
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  35. • 20-50 students (NAU has larger class sizes than PSU).
    • Class meets 4 days per week.
    • 4 midterm exams and a cumulative final.
    • 3-4 Daily Homework assignments per week (WeBWorK).
    • Homework worth 15% of overall grade.
    • 1 Weekly Homework assignment per week. Covers main
    topics from the previous week. More challenging than Daily
    Homework.
    • 3 class meetings are devoted to introducing new material,
    either via lecture or IBL-style worksheets.
    • 1 class meeting devoted to students presenting problems
    from Weekly Homework. Students annotate with felt-tip
    pens.
    • Presenters are not graded, but 5% of grade is for
    participation.
    The big picture
    35

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  36. • Academy of Inquiry-Based Learning
    (www.inquirybasedlearning.org)
    • Journal of Inquiry-Based Learning in Mathematics
    (www.jiblm.org)
    • Small grants from AIBL
    • IBL Workshop at JMM 2012
    Resources
    Thank you!
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