students to remember from your courses in 20 years? What do you reasonably expect to your students to remember from your courses in 20 years? What do you reasonably expect to your students to remember from your courses in 20 years? 3
freshmen in US. • 1.8 million bachelors degrees annually. • Less than 1% of BA/BS are in math. • Roughly 900 US citizens earn a PhD in math each year. Conclusion? We are peculiar! We are peculiar! We are peculiar! 4
only takes a few minutes to do all math problems • Only geniuses can understand math • Math is about memorization • If I go slow, then I’m dumb • If I get stuck, then I’m dumb • Faster is smarter • The teacher is the authority • Math is not a creative subject • It’s about answer getting 5
list of pairs of words, but do not write anything down. bread/b tter ocean/breeze leaf/tree music/l rics sweet/sour sh e/sock phone/bo k movie/actress chi s/salsa gasoline/engine high school/college pen il/paper river/b at turkey/stufﬁng fruit/vegetable be r/wine computer/chip television/rad o l nch/dinner chair/couch 6
pairs of words, write down as many pairs as you can. You do not need to remember where any missing letters were nor which column/what order a pair was in. • Looking at the table on the next slide count how many pairs are in column A versus column B. 7
sweet/sour sh e/sock movie/actress phone/bo k gasoline/engine chi s/salsa high school/college pen il/paper turkey/stufﬁng river/b at fruit/vegetable be r/wine computer/chip television/rad o chair/couch l nch/dinner Table 1: Word list from The Talent Code. 8
studies show that on average people remember 3 times as many pairs in column B, the one with missing letters. Maybe a room full of mathematicians will have wildly different results, but … You are peculiar! You are peculiar! The claim is that a microsecond of struggle (cognitive demand) makes all the difference. What does this have to do with teaching? You are peculiar! 9
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. 2. If we really want students to be independent, inquisitive, & persistent, then we need to provide them with the means to acquire & practice these skills. Lofty Goals 1. Transition students from consumers to producers! 2. Provide opportunity for a transformative experience. 11
Student engagement in meaningful mathematics, 2. Student collaboration for sense-making, 3. Instructor inquiry into student thinking, 4. Equitable instructional practice to include all in rigorous mathematical learning and mathematical identity-building. 12
possible be responsible for: 1. Guiding the acquisition of knowledge, 2. Validating the ideas presented (instructor not sole authority). Common Vehicles to IBL 1. Student presentations. 2. Small group work. This is not an “either-or” choice. Most IBL instructors implement some combination. 13
make design decisions about: 1. The tasks students will engage in. 2. How students will engage with those tasks, with each other, and with you. • Your decisions will be inﬂuenced by many obstacles & opportunities: • Class size? • Signiﬁcant content pressure? • Conﬁguration of room? • Who are your students? • Your implementation may vary from course to course. 18
IBL was implemented, student out- comes 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 elim- inates a sizable gender gap that disfavors women students in lecture-based courses.” “Despite variation in how IBL was implemented, student out- comes 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 elim- inates a sizable gender gap that disfavors women students in lecture-based courses.” “Despite variation in how IBL was implemented, student out- comes 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 elim- inates a sizable gender gap that disfavors women students in lecture-based courses.” 20
about the continued use of tradi- tional lecturing as a control in research studies, and support active learning as the preferred, empirically validated teach- ing practice in regular classrooms.” “The results raise questions about the continued use of tradi- tional lecturing as a control in research studies, and support active learning as the preferred, empirically validated teach- ing practice in regular classrooms.” “The results raise questions about the continued use of tradi- tional lecturing as a control in research studies, and support active learning as the preferred, empirically validated teach- ing practice in regular classrooms.” 21
on institutions of higher education, mathemat- ics departments and the mathematics faculty, public policy- makers, and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms.” “…we call on institutions of higher education, mathemat- ics departments and the mathematics faculty, public policy- makers, and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms.” “…we call on institutions of higher education, mathemat- ics departments and the mathematics faculty, public policy- makers, and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms.” 22
must gather the courage to advocate beyond our own classroom for student-centered instructional strategies that promote equitable access to mathematics for all students. We stand at a crossroads, and we must choose the path of trans- formation in order to fulﬁll our professional responsibility to our students.” “We must gather the courage to advocate beyond our own classroom for student-centered instructional strategies that promote equitable access to mathematics for all students. We stand at a crossroads, and we must choose the path of trans- formation in order to fulﬁll our professional responsibility to our students.” “We must gather the courage to advocate beyond our own classroom for student-centered instructional strategies that promote equitable access to mathematics for all students. We stand at a crossroads, and we must choose the path of trans- formation in order to fulﬁll our professional responsibility to our students.” 23
for digesting most new material out of class by working on a sequence of problems. • 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 • Nearly all class time devoted to students presenting proposed solutions/proofs. 25
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. 26
of issues that bubble to the surface that we blissfully ignore when lecturing. Feature not a bug! • When we have access to student thinking we can build on and extend their understanding. • Student 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.” “You will become clever through your mistakes.” — German proverb 34
what the students can expect from you, is vital. • Having a Student Buy-In Plan is key. • 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 everyone with immediate feedback about how things are going. 35
environment where risk taking is encouraged and productive failure is valued? • What constraints do you have on physical space? • How much scaffolding will you provide on problems? • Will you utilize group work? How will you choose groups? How large will the groups be? • Will you utilize student presentations? How will you choose presenters? How will you assess presenters? • Are students expected to generate proofs of theorems? Will proofs be assessed on exams? • What’s your plan for obtaining student buy-in? 36
IBL is doable. • IBL is fun. • IBL isn’t all or nothing. You can make incremental changes. • IBL assumes a growth mindset. • IBL fosters a growth mindset. • IBL can be transformative. “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 37
Summer IBL Workshops Registration is now open! Registration is now open! • June 18–21, 2019: University of St. Thomas, St. Paul, Minnesota, cohosted with MAA NCS • June 25–28, 2019: Portland Paramount, Portland, Oregon • July 9–12, 2019: Staybridge Suites, Los Angeles, California • Mentoring via AIBL • Journal of Inquiry-Based Learning in Mathematics (JIBLM) • IBL SIGMAA • Mathematics Learning by Inquiry • MAA Instructional Practices Guide Registration is now open! 40