Transitioning students from consumers to producers

The world is changing faster and faster. We need individuals capable of tackling problems they have never encountered and to ask questions no one has yet thought of. In addition to helping students develop procedural fluency and conceptual understanding, as educators, we must prepare them to ask and explore questions after they leave our classrooms, potentially in contexts that do not yet exist. If we truly want students to be independent, inquisitive, and persistent, then we need to provide them with the means to acquire these skills. An inquiry-based learning (IBL) approach to teaching mathematics puts these issues front and center and places an explicit focus on students producing, rather than consuming, mathematics. In this talk, we will address the following questions: What is IBL? Why use IBL? What are some of the challenges of IBL? I will also relay my personal experience and discuss how I came to IBL. Time permitting, we will also discuss some examples of what an IBL classroom might look like in practice.

This talk was given as the opening address at the Spring 2016 Joint ArizMATYC and MAA–Southwest Section Conference on Friday, April 8, 2016 at Coconino Community College in Flagstaff, AZ.

Transcript

1. transitioning students from consumers to producers Joint MAA-Southwestern ArizMATYC Conference 2016 Dana C. Ernst Northern Arizona University April 8, 2016
2. setting the stage
3. directions Directions ∙ Get in groups of size 3–4. ∙ Group members should introduce themselves. ∙ For each of the questions that follow, I will ask you to: 1. Think about a possible answer on your own. 2. Discuss your answers with the rest of your group. 3. Share a summary of each group’s discussion. 2
4. question one What are the goals of a university education? What are the goals of a university education? What are the goals of a university education? 3
5. question two What do you reasonably expect your students to remember from your courses in 20 years? What do you reasonably expect your students to remember from your courses in 20 years? What do you reasonably expect your students to remember from your courses in 20 years? 4
6. question three What is the value of making mistakes in the learning process? What is the value of making mistakes in the learning process? What is the value of making mistakes in the learning process? 5
7. productive failure #pf “Any creative endeavor is built on the ash heap of failure.” — Michael Starbird “Any creative endeavor is built on the ash heap of failure.” — Michael Starbird “Any creative endeavor is built on the ash heap of failure.” — Michael Starbird 6
8. 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 & 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. Lofty Goals ∙ Transition students from consumers to producers! ∙ I want to provide the opportunity for a transformative experience. ∙ I want to change my students’ lives! 7
9. what is ibl?
10. what is 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 & typically involves student presentations. ∙ Example: Moore Method, after R.L. Moore. 9
11. what is ibl? ∙ Students should as much as possible be responsible for: 1. 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. 10
12. what is ibl? 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? 11
13. my version of ibl ∙ 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. 12
14. my version of ibl ∙ 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. 13
15. my version of ibl 14
16. my version of ibl 15
17. my version of ibl 16
18. my version of ibl 17
19. my version of ibl 18
20. my version of ibl 19
21. 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? 20
22. let’s back up…
23. how did i get here? ∙ When I was a child, I hated mathematics. I NEVER would have predicted that I would be where I am today. ∙ I was slowly won over by Bob Sachs at George Mason University. ∙ MS in mathematics at NAU. ∙ Taught for 2 years at Front Range Community College in Longmont/Boulder, CO. ∙ PhD in mathematics from University of Colorado Boulder. ∙ My current mathematical research involves Coxeter groups and their associated algebras, as well as combinatorial game theory. ∙ Taught for 4 years at Plymouth State University in NH. ∙ Returned to NAU in 2012. 22
24. how did i get here? ∙ When I started teaching, I mimicked experiences I had as a student. I lectured. ∙ Number of IBL classes as student: 0 ∙ By most metrics, I was a successful teacher (e.g., high evaluations, several awards). Why change? “Things my students claim that I taught them masterfully, they don’t know.” — Dylan Retsek “Things my students claim that I taught them masterfully, they don’t know.” — Dylan Retsek ∙ First exposed to IBL/Moore Method during a Project NExT workshop run by Carol Schumacher (Kenyon College). ∙ Taught 1st full-blown IBL class in Fall 2009. ∙ Currently Special Projects Coordinator for AIBL & mentor for new IBL practitioners. “Things my students claim that I taught them masterfully, they don’t know.” — Dylan Retsek 23
25. oh, by the way…
26. oh, by the way… 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. ∙ Roughly 900 U.S. citizens earned a PhD in math in 2014. (Up 24% since 2008!) Conclusion? Education is a self-populating institution! You are peculiar! You are peculiar! You are peculiar! 25
27. why ibl?
28. why ibl? “Much more important than specific mathematical results are the habits of mind used by the people who create those results. Although it is necessary to infuse courses and curricula with modern content, what is even more important is to give students the tools they will need in order to use, understand, and even make mathematics that does not yet exist.” “Much more important than specific mathematical results are the habits of mind used by the people who create those results. Although it is necessary to infuse courses and curricula with modern content, what is even more important is to give students the tools they will need in order to use, understand, and even make mathematics that does not yet exist.” Cuoco, Goldenberg, & Mark in Habit of Mind: An Organizing Principle for Mathematics Curriculum. “Much more important than specific mathematical results are the habits of mind used by the people who create those results. Although it is necessary to infuse courses and curricula with modern content, what is even more important is to give students the tools they will need in order to use, understand, and even make mathematics that does not yet exist.” 27
29. why ibl? 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 & Selden 1995/1999/2003, Dreyfus 2001, Sowder & Harel 2003, Weber 2001/2003, Weber & Alcock 2004, Tall 1994 28
30. 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. The Twin Pillars 1. Deep engagement in rich mathematics, 2. Opportunities to collaborate. 29
31. why ibl? The Colorado Study by Sandra Laursen et al. IBL Interviews SALG Pre/Post Tests Transcripts Gender Observations Non-IBL 30
32. 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.” 31
33. why ibl? Freeman et al. 2014 “The studies analyzed here document that active learning leads to increases in examination performance that would raise average grades by a half a letter, and that failure rates under traditional lecturing increase by 55% over the rates observed under active learning.” “The results raise questions about the continued use of traditional lecturing as a control in research studies, and support active learning as the preferred, empirically validated teaching practice in regular classrooms.” 32
34. personal reflections
35. 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! 34
36. 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. 35
37. personal reflections ∙ 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 36
38. closing
39. ibl resources ∙ Academy of IBL (inquirybasedlearning.org) ∙ IBL mentoring ∙ Mini-grants ∙ IBL Workshops (iblworkshop.org) The Academy of Inquiry-Based Learning was recently awarded a $2.5 million grant from the NSF to run workshops through 2020 ∙ Discovering the Art of Mathematics (artofmathematics.org) ∙ Journal of Inquiry-Based Learning in Mathematics (jiblm.org) 38