ibl experiments in the math circle at asu tempe

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


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

http://www.mathcircles.org/




http://math.la.asu.edu/~mathcircle

http://math.la.asu.edu/~mathcircle


• 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


• “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

http://www.discovery.utexas.edu/rlm/






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”


Math Circles across the country


National Association of MCs• community• workshops

& conferencestraining, network

• clearinghouse (problems, lesson plans)

• $$$ support


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)


Math Circle: very diverse


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”

http://math.la.asu.edu/~mathcircle/


• 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 ?


• 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


MC @ ASU Tempe: Spring 2014

https://math.la.asu.edu/~mathcircle/events.php#calendar


MC @ ASU Tempe: Spring 2012

https://math.la.asu.edu/~mathcircle/events.php#calendar


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 !


Sorting networks: great motivation


Double bubble conjecture ….

Carol Edwards with multi-bubbles


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


Warm-up session: Hall’s theorem


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


Stable matching theory

• again a nicemotivator, asextra icing on the cake


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


Julia RobinsonMath Festivalat ASU Tempe


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).

ibl experiments in the math circle at asu tempe

Documents

moore denver

tomatthias kawski legacy

namc matthias kawski

road matthias kawski

r university

discrete math

math club

modified moore