1 / 25

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

viveka
Download Presentation

IBL Experiments in the Math Circle at ASU Tempe

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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).

More Related