Matthias Kawski Legacy R.L.Moore Denver, June 2014
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IBL Experiments in the Math Circle at ASU Tempe
Matthias KawskiSchool of Mathematical & Statistical Sciences
Arizona State UniversitySupported in part thru the National Science Foundation via grants through the NAMC
Matthias Kawski Legacy R.L.Moore Denver, June 2014
Outline
• Brief personal introduction • Math Circles
• history and heritage: Bulgaria, Russia• national umbrella: NAMC http://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
Matthias Kawski Legacy R.L.Moore Denver, June 2014
• 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
Personal background
Matthias Kawski Legacy R.L.Moore Denver, June 2014
• “intellectual need” (Guershon Harel)• “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(adv calc stud’s: invent “compactness” natural definition!)
• mathematics is a social enterprise: practice teamwork!• trying “modified Moore” in topology, complex, algebra
Teaching/learning: subscribe to
Matthias Kawski Legacy R.L.Moore Denver, June 2014
Math Circles• 100 years plus in Bulgaria• Russia, Kolmogorov school• after-school tradition: ballet, swim, piano, soccer
what 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”
Matthias Kawski Legacy R.L.Moore Denver, June 2014
National Association of MCs• community• workshops
& conferencestraining, network
• clearinghouse (problems, lesson plans)
• $$$ support
Matthias Kawski Legacy R.L.Moore Denver, June 2014
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)
Matthias Kawski Legacy R.L.Moore Denver, June 2014
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 research
not competition-style questions with q.e.d. “DONE”
Matthias Kawski Legacy R.L.Moore Denver, June 2014
• 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
Faculty and student roles: IBL ?
Matthias Kawski Legacy R.L.Moore Denver, June 2014
• 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
Some criteria for topic selection
Matthias Kawski Legacy R.L.Moore Denver, June 2014
MC @ ASU Tempe: Spring 2014
Matthias Kawski Legacy R.L.Moore Denver, June 2014
MC @ ASU Tempe: Spring 2012
Matthias Kawski Legacy R.L.Moore Denver, June 2014
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 !
Matthias Kawski Legacy R.L.Moore Denver, June 201418
Double bubble conjecture ….
Carol Edwards with multi-bubbles
Matthias Kawski Legacy R.L.Moore Denver, June 2014
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
Matthias Kawski Legacy R.L.Moore Denver, June 2014
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
Matthias Kawski Legacy R.L.Moore Denver, June 2014
Stable matching theory
• again a nicemotivator, asextra icing on the cake
Matthias Kawski Legacy R.L.Moore Denver, June 2014
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
Matthias Kawski Legacy R.L.Moore Denver, June 2014
Parting comments• faculty use MathCircle as a teaching laboratory
experimenting 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 directions
make it difficult to write a script (no worksheets)• often only a-posterior recollections what we did,
reflections on what worked well (dissemination).