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.

Transcript

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

   View Slide

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.
   2
   

   View Slide

3. What?
   3
   

   View Slide

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.
   4
   

   View Slide

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?
   5
   

   View Slide

6. Our main objective
   How do we get here?
   Students answering
   questions
   Students asking
   questions
   6
   

   View Slide

7. Why?
   7
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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

    View Slide

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

    View Slide

17. How?
    17
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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

    View Slide

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

    View Slide

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
    

    View Slide

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

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

34. Calculus sequence
    An IBL-lite approach
    34
    

    View Slide

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
    

    View Slide

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!
    36
    

    View Slide