Inquiry-Based Education in Mathematics: Models, Methods, and Effectiveness for Higher Education

Inquiry-based learning (IBL) is a paradigm for education that puts primary responsibility for sense-making on the learner. The instructor takes on the roles of coach, cheerleader, and mentor, and manages the learning environment through careful questioning and task setting. An IBL approach may manifest itself in a variety of ways depending on the context, but the common theme is that students are engaged in doing mathematics the way professionals do: conjecturing, experimenting, solving problems, and making arguments. The presenters shall share the philosophy behind this approach, a variety of classroom implementations of the ideas, and evidence for the effectiveness of IBL. Participants will engage in activities aimed at preparing for an IBL class in their setting, see some classroom video of IBL in action, and discuss the opportunities for and challenges of using IBL methods.

These slides were used as part of a two-day IBL workshop that was facilitated by Dana C. Ernst and Theron Hitchman as part of the Workshop on Innovations in Higher Education Mathematics Teaching that took place at Cardiff University on July 8-9, 2014.

Transcript

1. Inquiry-Based Education in Mathematics: Models,
   Methods, & Effectiveness for Higher Education
   Dana C. Ernst, Northern Arizona University
   Theron J. Hitchman, University of Northern Iowa
   http://danaernst.com
   http://www.uni.edu/theron/
   Workshop on Innovations in Higher
   Education Mathematics Teaching
   Cardiff University, 7–9 July 2014
   D.C. Ernst and TJ Hitchman Inquiry-Based Education in Mathematics 1 / 27
   

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2. Introductory Questions
   Introductory Questions
   Introductory Questions
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3. Question One
   Why are we here?
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4. Question One: Sharper Version
   From a learner’s perspective,
   what is the purpose of
   continuing to study past
   secondary school?
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5. Question Two
   What are the goals of a
   university education?
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6. Question Three
   Information is very free and
   open these days. Given that
   one can read and study on
   one’s own, what is the point of
   going to university?
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7. Question Four
   What do you reasonably expect
   that your students will
   remember from your courses
   20 years later?
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8. Question Five
   How does a person learn
   something new?
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9. Question Six
   How should a course of study
   be structured to facilitate
   learning?
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10. Question Seven
    What are the potential pitfalls? What challenges do
    we face in building a community where we all
    engage in collaborative inquiry?
    Specifically:
    What barriers would a
    newcomer encounter that
    might make them leave such a
    group?
    D.C. Ernst and TJ Hitchman Inquiry-Based Education in Mathematics 10 / 27
    

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11. Question Eight
    How do we create a safe space,
    so that we can all engage in
    the process with minimum
    psychological damage?
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12. What is IBL?
    What is IBL?
    What is IBL?
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13. The Big Picture
    If we really want students to be independent, inquisitive,
    & persistent, then we need to provide them with the
    means to acquire these skills.
    If we really want students to be independent, inquisitive,
    & persistent, then we need to provide them with the
    means to acquire these skills.
    If we really want students to be independent, inquisitive,
    & persistent, then we need to provide them with the
    means to acquire these skills.
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14. 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.
    • Often involves very little lecturing, and typically involves student
    presentations.
    • Example: Modified Moore Method, after R.L. Moore.
    • Students should as much as possible be responsible for:
    • guiding the acquisition of knowledge and,
    • validating the ideas presented. (Students should not be looking
    to the instructor as the sole authority.)
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15. Guiding Principle of IBL
    Continually ask yourself the following question:
    Where do I draw the line between content I must impart
    to my students versus content they can produce
    independently?
    Where do I draw the line between content I must impart
    to my students versus content they can produce
    independently?
    Our Main Objective
    How do we get here?
    Students
    answering
    questions
    Students
    asking
    questions
    Where do I draw the line between content I must impart
    to my students versus content they can produce
    independently?
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16. Two Typical Approaches/Modes to IBL
    1. Student presentations.
    2. Small group work.
    Most IBL instructors implement some combination.
    Important Role Changes
    • Instructor becomes a mentor, cheerleader, and coach. Focus on
    teaching process.
    • Student becomes the mathematician.
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17. 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.
    IBL vs Inverted/Flipped Pedagogy
    • IBL/Moore Method is an instructional practice.
    • The flipped classroom is:
    • A platform, not an instructional practice.
    • Centered around the idea of removing some/all of the
    information transfer tasks outside of class & replacing the time
    that’s freed up with whatever instructor feels is appropriate.
    • IBL and flipped learning (see R. Talbert’s talk) are compatible.
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18. Are you doing IBL?
    • Who develops the mathematics which is discussed?
    • Who presents the mathematics?
    • Who critiques the mathematics once presented?
    • Who decides what is correct mathematics?
    • Who asks the questions that drive further work?
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19. Why IBL?
    Why IBL?
    Why IBL?
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20. One minute version of why IBL
    • Our system needs an upgrade.
    • Unintended negative outcomes via traditional methods.
    • Research suggests IBL outcomes are better.
    “Things my students claim that I taught them
    masterfully, they dont know.” – Dylan Retsek
    “Things my students claim that I taught them
    masterfully, they dont know.” – Dylan Retsek
    “Things my students claim that I taught them
    masterfully, they dont know.” – Dylan Retsek
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21. My IBL origins
    • 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.
    • I was sold from that moment on.
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22. Some Data
    • 2010: 3.7 million students in secondary school.
    • 2010: 52% of those go to University.
    • 2013: 38% of the UK population had a degree.
    • 2010: 16,000 people started a PhD.
    Conclusion?
    Education is a self-populating institution!
    You are peculiar!
    You are peculiar!
    We need to renormalize.
    You are peculiar!
    D.C. Ernst and TJ Hitchman Inquiry-Based Education in Mathematics 22 / 27
    

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23. 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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24. Talking About Leaving
    • About half of STEM majors switch to
    non-STEM.
    • Top 4 reasons for switching are
    teaching related.
    • Good ones leave, too.
    • Loss of interest.
    • Curriculum overload.
    • Students dissatisfied with teaching of
    STEM classes and less so with
    non-STEM.
    • Weed-out culture.
    E. Seymour, N.M. Hewitt. Talking about leaving: Why undergraduates
    leave the sciences. Westview Press, 1997.
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25. 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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26. The Colorado Study by Sandra Laursen et al.
    • Quasi-experimental study: Data include 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.
    IBL
    Interviews SALG
    Pre/Post
    Tests
    Transcripts Gender Observations
    Non-IBL
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27. The Twin Pillars
    1. Deep engagement in rich mathematics,
    2. Opportunities to collaborate.
    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.”
    D.C. Ernst and TJ Hitchman Inquiry-Based Education in Mathematics 27 / 27
    

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