matthias kawski legacy r.l.moore denver, june 2014 ibl experiments in the math circle at asu tempe...
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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
Math Circles across the country
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
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: very diverse
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 2014
Sorting networks: great motivation
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
Warm-up session: Hall’s theorem
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
Julia RobinsonMath Festivalat ASU Tempe
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).