A discussion about inquiry-based learning (part 2)

77d59004fef10003e155461c4c47e037?s=47 Dana Ernst
January 21, 2015

A discussion about inquiry-based learning (part 2)

In many mathematics classrooms, "doing mathematics" means following the rules dictated by the teacher, and "knowing mathematics" means remembering and applying these rules. However, an inquiry-based-learning (IBL) approach challenges students to create/discover mathematics. Boiled down to its essence, IBL is a method of teaching that engages students in sense-making activities. Rather than showing facts or a clear, smooth path to a solution, the instructor guides students via well-crafted problems through an adventure in mathematical discovery. In this talk, we will address the following questions: What is IBL? Why use IBL? What are some of the challenges of IBL? How can you incorporate more IBL into the classes that you teach? In addition, I will relay my personal experience and discuss how I came to IBL and where I plan to go with it. Time permitting, we will also discuss a few different examples of what an IBL classroom might look like in practice.

This talk was given at the NAU Department of Mathematics and Statistics Teaching Showcase on January 21, 2015.


Dana Ernst

January 21, 2015


  1. a discussion about ibl Part 2 NAU Mathematics & Statistics

    Teaching Showcase Dana C. Ernst Northern Arizona University January 21, 2015
  2. the big picture Claims ∙ An education must prepare a

    student to ask and explore questions in contexts that do not yet exist. That is, we need individuals capable of tackling problems they have never encountered and to ask questions no one has yet thought of. ∙ If we really want students to be independent, inquisitive, & persistent, then we need to provide them with the means to acquire these skills. 1
  3. what is ibl?

  4. what is inquiry-based learning? ∙ 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: Moore Method, after R.L. Moore. ∙ Students should as much as possible be responsible for: ∙ Guiding the acquisition of knowledge, ∙ Validating the ideas presented (i.e., students should not be looking to the instructor as the sole authority). 3
  5. what is ibl? Two Typical Approaches/Modes to IBL ∙ Student

    presentations. ∙ Small group work. Most IBL instructors implement some combination. 4
  6. what is ibl? Video and Discussion It’s helpful to see

    what IBL might look like in practice. ∙ Clip 1: Mike Starbird, number theory at UT, small class, their introduction to proof class, week 1 of semester. ∙ Clip 2: Mike Starbird, discrete structures at UT, small class, middle of semester. ∙ Clip 3: Discovering the Art of Mathematics video, liberal arts mathematics at Westfield State University. (part 1, part 2, part 3) Questions ∙ What is presenter doing? ∙ What is teacher doing? ∙ What is the audience doing? ∙ What would you do differently? 5
  7. what is ibl? Important Role Changes ∙ Instructor becomes a

    mentor, cheerleader, & coach. Focus on teaching process. ∙ Student becomes the mathematician. 6
  8. what is ibl? Are you doing IBL? ∙ Who develops

    the mathematics that is discussed? ∙ Who presents the mathematics? ∙ Who critiques the mathematics that is presented? ∙ Who decides what is correct mathematics? ∙ Who asks the questions that drive further work? 7
  9. what is ibl? My version of IBL ∙ 5-10 “tasks”

    assigned each class meeting (Daily HW). Due next class. ∙ Students responsible for digesting new material out of class. ∙ Nearly all class time devoted to students presenting proposed solutions/proofs to Daily HW. ∙ Students may request mini-lectures. ← Hang on every word! ∙ Each week, students submit a subset of problems similar or identical to problems from the previous week (Weekly HW). Graded harshly ∙ My job: ∙ Facilitate/manage ∙ Mr. Super Positive ∙ William Wallace meets Robin Williams 8
  10. why ibl?

  11. why ibl? The Colorado Study by Sandra Laursen et al.

    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. IBL Interviews SALG Pre/Post Tests Transcripts Gender Observations Non-IBL 10
  12. why ibl? The Twin Pillars ∙ Deep engagement in rich

    mathematics, ∙ Opportunities to collaborate. 11
  13. why ibl? 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.” 12
  14. obstacles

  15. obstacles Potential Obstacles to Implementing IBL In small groups, discuss

    what you feel are potential obstacles to implementing IBL. Be prepared to share your thoughts. Solutions Now, let’s come up with some solutions to the obstacles that were discussed. 14
  16. personal reflections

  17. personal reflections My overall point of view ∙ I’m hooked.

    For most students, the net overall gain beats out lecturing. ∙ IBL is not a magic bullet. ∙ IBL can be a lot of work, but to me it is worth it. ∙ Implementing IBL requires patience, flexibility, & regular refinements. ∙ One reason IBL works: Mode of engagement is different when listening to expert vs novice. ∙ With the right set of materials, content coverage is not really an issue (my IBL notes for Abstract Algebra need some work in regards to coverage.) 16
  18. personal reflections Keeping my mouth shut…and assessing ∙ 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. 17
  19. personal reflections IBL is messy (and that’s ok) ∙ In

    an IBL class there are lots of issues that bubble to the surface that we blissfully ignore when lecturing. ∙ More day-to-day differences between IBL classes. I usually have no idea what will happen each day! ∙ We are responding to what the students are doing & thinking, & there are natural & necessary ups & downs. ∙ 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! 18
  20. personal reflections 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 19
  21. personal reflections Marketing! ∙ Students are asked to solve problems

    they do not know the answers to, to take risks, to make mistakes, & to engage in #PF. ∙ Students need to know that it is ok to be stuck & that you will support them in this endeavor. ∙ Students need to know what their role is & what the instructor’s role is. ∙ Expectations & goals need to be reiterated throughout the course. 20
  22. closing

  23. closing IBL Resources ∙ Academy of Inquiry-Based Learning ∙ Helpful

    resources ∙ Mini-grants ∙ IBL Workshops ∙ Discovering the Art of Mathematics ∙ Journal of Inquiry-Based Learning in Mathematics 22
  24. closing “We’re in the business of changing lives.” — Michael

    Starbird “We’re in the business of changing lives.” — Michael Starbird “We’re in the business of changing lives.” — Michael Starbird 23