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IBL Experiments in the Math Circle at ASU Tempe

IBL Experiments in the Math Circle at ASU Tempe. Matthias Kawski School of Mathematical & Statistical Sciences Arizona State University. Supported in part thru the National Science Foundation via grants through the NAMC. Outline. Brief personal introduction Math Circles

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IBL Experiments in the Math Circle at ASU Tempe

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  1. IBL Experiments in the Math Circle at ASU Tempe Matthias Kawski School of Mathematical & Statistical Sciences Arizona State University Supported in part thru the National Science Foundation via grants through the NAMC

  2. Outline • Brief personal introduction • Math Circles • history and heritage: Bulgaria, Russia • national umbrella: NAMChttp://www.mathcircles.org/ • Math Circle at ASU Tempe http://math.la.asu.edu/~mathcircle • local demographics and our choices, our objectives • sample sessions& topics • Parting thoughts

  3. Personal background • Differential geometric control theory (1986) • 26 years at ASU, over 30 different courses taught • calculus reform, CAS and dynamic visualization • integrated curricula in engineering (1992-2002)just-in-time, problem solving, inquiry, mini-lecture • travel worldwide as much to teaching/learning workshops & conferences as for control theory

  4. Teaching/learning: subscribe to • “intellectual need” (GuershonHarel) • “never prove a theorem that the students did not ask you to prove.” (Jerry Uhl) [mine demand proof of Stokes ! ] • MAT 300: “Chapter Zero” (Carol Schumacher) • 9thAnnual Legacy of R. L. Moore Conference (2006): “And where do the definitions and theorems come from?” • but: experiment, observe, conjecture, make definitions are integral to math that all students must experience(advcalc stud’s: invent “compactness” natural definition!) • mathematics is a social enterprise: practice teamwork! • trying “modified Moore” in topology, complex, algebra

  5. Math Circles • 100 years plus in Bulgaria • Russia, Kolmogorov school • after-school tradition: ballet, swim, piano, soccerwhat about “math club” ? • math for fun - not for grades, no credit, no prizes • in US, first on coasts, since late 80s, immigrants • recently: NMAC, MSRI, NSF, “circle on the road”

  6. Math Circles across the country

  7. National Association of MCs • community • workshops & conferencestraining, network • clearinghouse (problems, lesson plans) • $$$ support

  8. Math Circle at ASU Tempe • ASU: only R university in 4M+ population metro area(expect about 50 future math PhDs now in PHX HSs ) • need: many MathCircles w/diverse themes, ages, goals • ours to make best use of unique resource: ASU R-fac (stud’s who cannot be served by others in community) • here: advanced topics for highly motivated students(e.g. NavajoCircles different level, same engagement)

  9. Math Circle: very diverse

  10. Math Circle at ASU Tempehttp://math.la.asu.edu/~mathcircle/ • learn to think and solve problems like pros • highly motivated high-school age students • 8 to 11 weekly meetings/semester • connect w/ diverse group of research mathematicians • “orthogonal” to school curricula (cf. Courant/Robbins) • focus on problem solving: discrete math, algebra, elementary number theory, geometry, topology • open-ended problems, towards researchnot competition-style questions with q.e.d. “DONE”

  11. Faculty and student roles: IBL ? • committed to bringing in diverse session leaders diverse math, sometimes outside “speakers”, but • but generally students do most of the work, and often suggest new direction of inquiry.asking new question is as valued as answering! • still themes/topics are initiated by faculty, who provide guidance which questions are likely worth pursuing, which are dead-ends

  12. Some criteria for topic selection • genuine math, engaging, accessible • open-ended, students ask new questions • preferably: opening to long lines of inquiry,ideally connected to current / recent active R • “orthogonal” to school curricula • a little “recreational math” or “historical math” • frequently: adapt NAMC resources to IBL format

  13. MC @ ASU Tempe: Spring 2014

  14. MC @ ASU Tempe: Spring 2012

  15. Sorting networks • Very accessible (some use blue masking tape on floor to sort students …). Relevance to microchips helps. Problem solving: find more efficient (optimal networks) -- nicely open-ended, still active research. News of Abel price exciting !

  16. Sorting networks: great motivation

  17. Double bubble conjecture …. Carol Edwards with multi-bubbles

  18. Tiling: parity, coloring, induction • not only young kids immediately start to work, and discover “impasses” which necessitate math • classic example for induction, necessary (not sufficient) conditions, coloring. very open ended

  19. Warm-up session: Hall’s theorem

  20. Hall's marriage theorem • start w/ hands-on exploration, and try to come up with (greedy) algorithm • following week work on a general abstract proof

  21. Stable matching theory • again a nicemotivator, asextra icing on the cake

  22. Billiards inside polygons (rectangles) Another safe start – w/ connections to closed geodesics on R-manifolds unexpected where this will lead, primality, absorbing sets for dynamical systems

  23. Julia RobinsonMath Festivalat ASU Tempe

  24. Parting comments • faculty use MathCircle as a teaching laboratoryexperimenting with different ways to deliver, intention: take experience back to classrooms • students changed, adopted style of the pros:reflective, deliberate, open-ended R, new Qs • research/inquiry not bound by tight lesson plans • open ended questions, and new directionsmake it difficult to write a script (no worksheets) • often only a-posterior recollections what we did, reflections on what worked well(dissemination).

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