1 / 81

MAA Intermountain Section Meeting March 24, 2007

Organizing a High School Math Circle. MAA Intermountain Section Meeting March 24, 2007. PETER E. TRAPA Department of Mathematics University of Utah. What is a Math Circle?. Provisional definition:. What is a Math Circle?. Provisional definition:

denton
Download Presentation

MAA Intermountain Section Meeting March 24, 2007

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. Organizing a High School Math Circle MAA Intermountain Section MeetingMarch 24, 2007 PETER E. TRAPA Department of MathematicsUniversity of Utah

  2. What is a Math Circle? • Provisional definition:

  3. What is a Math Circle? • Provisional definition: • a program for K-12 students devoted to mathematical training and exploration. Particular emphasis is placed on direct interaction with mathematicians.

  4. What is a Math Circle? • Provisional definition: • a program for K-12 students devoted to mathematical training and exploration. Particular emphasis is placed on direct interaction with mathematicians. • Typically the methods and materials used are non-standard, at least compared with usual K-12 curriculae.

  5. Examples • Three that I’ll discuss today: • The Boston Math Circle • The Berkeley Math Circle • The Utah Math Circle

  6. Examples • But many others exist, including: • Davis (UC Davis) • New York (Lehman College, CUNY) • Miami (Florida International U) • Mobile (U of Southern Alabama) • Palo Alto (Castilleja School) • San Diego (UCSD, Art of Problem Solving) • San Franscisco (USF) • San Jose (collaboration with AIM) • St. Louis (Washington U)

  7. Toward a National Network? • MSRI is interested in building and • maintaining a national-level “Math Circle • Infrastructure”.

  8. Toward a National Network? • MSRI is interested in buliding and • maintaing a national-level “Math Circle • Infrastructure”. • Small “seed grants” from MSRI are now • available for starting new Math Circles.

  9. Why all the interest in Math Circles?

  10. Why all the interest in Math Circles? • Typical high school math curriculae are • almost exclusively template based.

  11. Why all the interest in Math Circles? • Typical high school math curriculae are • almost exclusively template based. • This is extremely effective for some • purposes.

  12. Why all the interest in Math Circles? • Typical high school math curriculae are • almost exclusively template based. • This is extremely effective for some • purposes. • But it’s terrible for others.

  13. Downsides of template-based learning

  14. Downsides of template-based learning • Encourages very short attention spans.

  15. Downsides of template-based learning • Encourages very short attention spans. • Implemented algorithms take • precedence over their conceptual • formulation.

  16. Downsides of template-based learning • Encourages very short attention spans. • Implemented algorithms take precedence over their conceptual formulation. • Creativity is often limited to the confines of the template.

  17. But this is not what mathematicians do!

  18. But this is not what mathematicians do! • Instead we are trained to think deeply • about simple things.

  19. But this is not what mathematicians do! • Instead we are trained to think deeply • about simple things. • This idea is completely absent in • template-based learning.

  20. A Different Model: The Russian Experience In Russia, a highly evolved and extremely efficient mathematical training infrastructure exists.

  21. A Different Model: The Russian Experience In Russia, a highly evolved and extremely efficient mathematical training infrastructure exists. • Early Identification • Special Schools • Math Circles

  22. A Different Model: The Russian Experience In Russia, a highly evolved and extremely efficient mathematical training infrastructure exists. • Early Identification • Special Schools • Math Circles • The objective is not limited to producing only research mathematicians.

  23. Example (courtesy of Josh Zucker)

  24. Example (courtesy of Josh Zucker) • St. Petersburg’s School 239: • 2500 sixth-graders take the district Olympiad. • 25 or so are tracked into their own math course • and math circle.

  25. Example: 8th grade algebra class

  26. Example Problems If it is true that (a2 - 1) x ≥ 3a - 1 for all x, what value(s) of a are possible. What is an inequality whose solution set will be (-infinity, -2) union [3, infinity).  Solve |2x - 1| > 3x. 

  27. Example of Math Circle Problems • Vlad draws diagonals of unit squares in an 8x8 grid of squares.  Nikita sees to it that they have no common points (including ends).  What is the maximum number of diagonals that Vlad can draw?

  28. Example of Math Circle Problems • Asterisks are arranged in some squares of an n by n grid.  In each vertical, horizontal, and diagonal (even diagonals of only one square count), the number of asterisks in it is known.  For which n is it possible to determine where the asterisks are?

  29. Can any of this be emulated here? • .

  30. The Boston Math Circle

  31. The Boston Math Circle • Started in 1994 by math educators Bob • and Ellen Kaplan.

  32. The Boston Math Circle • Started in 1994 by math educators Bob • and Ellen Kaplan.

  33. The Boston Math Circle • Started in 1994 by math educators Bob and • Ellen Kaplan. • No official university affiliation • (although resources are provided by • Harvard, MIT, Northeastern, Tufts,….)

  34. The Boston Math Circle • Started in 1994 by math educators Bob and • Ellen Kaplan. • No official university affiliation (although • resources are provided by Harvard, MIT, • Northeastern, Tufts,….) • Grown into a rather large enterprise

  35. Typical Spring Schedule • Four pre-algebra courses • Divided, roughly, into grades 3-4, 5-6 • 10 sessions, one hour each

  36. Typical Spring Schedule • Four pre-algebra courses • Divided, roughly, into grades 3-4, 5-6 • 10 sessions, one hour each • One advanced course • for high school students • 10 sessions, three hours each

  37. Approach for younger students • A “seed” topic is a springboard for • open-ended explorations.

  38. Approach for younger students • A “seed” topic is a springboard for • open-ended explorations. • Sample topics for kids aged 5-10: • Are there numbers between numbers? • Primes • Infinity

  39. Approach for younger students • A “seed” topic is a springboard for • open-ended explorations. • Sample topics for kids between 5 and 10: • Are there numbers between numbers? • Primes • Infinity • Ages 12-14 (some algebra): • complex numbers • Fibonacci sequence • continued fractions

  40. Approach for High School Students • Almost exclusively devoted to a single • topic.

  41. Approach for High School Students • Almost exclusively devoted to a single • topic. • Sample courses: • Algebraic Geometry • Complex Analysis • Knot Theory • Hyperbolic Geometry • Group Theory • Quantum Mechanics

  42. The Boston Math Circle charges tuition • Each pre-algebra courses • $225 tuition • Each advanced course • $450 tuition • About $20/hour per student

  43. To start your own Math Circle… • From the Boston Math Circle webpage: • “Want to start your own Math Circle? • Founders Robert and Ellen Kaplan can be • hired as consultants to help get you going. • Feel free to contact Bob and Ellen Kaplan • directly to learn more about what they can do • for you. They are willing to travel to your • locale to help out. Their per-diem fee is • $1000 plus expenses.”

  44. The Berkeley Math Circle

  45. The Berkeley Math Circle • Founded in 1998 with the support of MSRI (Hugo Rossi, Zvezda Stankova, and others).

  46. The Berkeley Math Circle • Founded in 1998 with the support of MSRI (Hugo Rossi, Zvezda Stankova, and others). • Closely followed the Russian-type model.

  47. The Berkeley Math Circle • Founded in 1998 with the support of MSRI (Hugo Rossi, Zvezda Stankova, and others). • Closely followed the Russian-type model. • In particular contests were absolutely central.

  48. The Berkeley Math Circle • Founded in 1998 with the support of MSRI (Hugo Rossi, Zvezda Stankova, and others). • Closely followed the Russian-type model. • In particular contests were absolutely central. • This led to the creation of the Bay Area Math Olympiad (BAMO).

  49. The Berkeley Math Circle • Founded in 1998 with the support of MSRI (Hugo Rossi, Zvezda Stankova, and others). • Closely followed the Russian-type model. • In particular contests were absolutely central. • This led to the creation of the Bay Area Math Olympiad (BAMO). • Draw heavily on faculty from Berkeley, Stanford, UCSF, etc.

  50. The Berkeley Math Circle • Founded in 1998 with the support of MSRI (Hugo Rossi, Zvezda Stankova, and others). • Closely followed the Russian-type model. • In particular contests were absolutely central. • This led to the creation of the Bay Area Math Olympiad (BAMO). • Draw heavily on faculty from Berkeley, Stanford, UCSF, etc. • Free.

More Related