Past Teacher Courses

Given 6 points, can you connect each pair with a red or blue string, yet form no “monochromatic” triangles (whose vertices are from those points)? For what acute angle x does 8 sinx cosx cos2x cos4x = 1? A (right circular) cylindrical hole is drilled directly through the center of a sphere; if the height of the cylinder is 6”, what is the volume of sphere remaining?

Gil Kessler will conduct a 3-session course for high school and middle school math teachers interested in adding to their collection of ideas, problems, and puzzles for themselves and their students. The material can be used to enrich lessons and homeworks, as well as challenge math team members. The presentation will be at a level accessible to all, with content ranging from easy to impossible (just kidding!), but always enjoyable.

This course is independent of any previous enrichment courses, all are welcome.

Join us at Bard this summer for a week-long residential program focused on the investigation of inequalities and optimization. Enjoy an environment of creative and insightful mathematical problem solving for middle school and high school math teachers who wish to deepen their mathematical understanding. No prior experience with inequalities required, just an interest in doing mathematics in a community of teachers. Workshops and activities led by NYMC instructors and Bard math professors.

Math & Dinner sessions are gatherings for teachers, to discuss some mathematics, work on some problems, and have dinner together. This pair of sessions is free, but please register using the link above, so that we know how many people to expect.

Gauss said "Mathematics is the queen of the sciences and number theory is the queen of mathematics." To take it further, quadratic forms would be the queen's crown, with quadratic reciprocity the crown jewel. A major area of research for many mathematicians, notable contributors included Fermat, Euler, Legendre, and Gauss. Gauss referred to quadratic reciprocity as the "golden theorem".

This two-session mini-course will take you on an introductory incursion into this classical area of the theory of numbers. The goal is to motivate from an historical perspective the theory of binary quadratic forms as developed by Fermat, Euler, Legendre, and Gauss. We will present the highlights of the more elementary portions of the theory, including quadratic reciprocity, in order to whet the appetites of those who wish to pursue more deeply this still lively area of mathematics.

When can 4 different Fibonacci numbers be the sides of a quadrilateral? What are the two smallest integer-sided triangles that agree in 5 parts (sides, angles), yet are not congruent? Ever prove things using “Mass Points”?

Gil Kessler will conduct a 6-session course for high school and middle school math teachers interested in adding to their collection of ideas, problems, and puzzles for themselves and their students. The material can be used to enrich lessons and homeworks, as well as challenge math team members. The presentation will be at a level accessible to all, with content ranging from easy to impossible (just kidding!), but always enjoyable.

This course is intended for math teachers, whether new or experienced. Participants will be taken on a mathematical journey through topics in number theory, algebra, and geometry, exploring fundamental notions and special topics. Problem posing and problem solving are emphasized throughout. Particular attention is given to the structural underpinnings of mathematics that are relevant to sound and effective teaching.

Although mathematical content is mostly on a high school level, motivated middle school teachers are welcome to register as well.

These all-day problem workshops will feature a wealth of specially selected problems ranging from relatively simple to very challenging. Solutions, extensions and associated topics will be included. The sessions are a nice follow-up to the Math Team for Teachers mini-course offered last year, although prior attendance is not a pre-requisite.

The mathematical content of these sessions is mostly on a high school level. The registration fee covers both sessions, and lunch on both days.

This week-long residential program is focused on creative and insightful mathematical problem solving for middle school math teachers. The high level mathematics activities and classes are led by NYMC instructors and Bard math professors.

Participants will engage in a wide variety of mathematical investigation, problem solving, and classes that explore and develop a deep appreciation and understanding of the Theorem of Pythagoras and its consequences. Specific topics include geometric dissections, quadratic number system extensions, Diophantine equations, historical development, and a study of Euclid's original proof, which dates back over 2000 years.

This three session mini-course will take participants through a variety of wonderful mathematics problems. Participants will see both classic well-known problems, and little-known gems.

There will be an additional related "Math & Dinner" session on Wednesday 3/17 (see registration below). It will be open for free to all interested math teachers. This is a perfect opportunity to bring along colleagues.

Not a course! Just informal gatherings for teachers, to discuss some mathematics, work on some problems, and have dinner together. Please register using the link above, so that we know how many people to expect.

March 17, 5pm, "A Pleasing Potpourri of Paradoxes and Puzzles", by Gil Kessler. This talk will be open to both Great Problems mini-course participants and non-participants as well. Come see a selection of unusual problems, then join us for dinner at a nearby restaurant.

April 21, 5pm. "Exploration of Unique Factorization, Part I", with Ben Blum-Smith. The "Fundamental Theorem of Arithmetic" is the name for the familiar fact that every natural number factors into primes in just one way. We'll begin with some provocative problems exploring the importance of this fact, and then take a historical journey to understand why a proof of it is necessary.

April 28, 5pm. "Exploration of Unique Factorization, Part II", with Ben Blum-Smith, in Room 202. This picks up directly where the April 21 session leaves off. Participants will be led to collectively create one of the classic proofs of the Fundamental Theorem of Arithmetic. The proof will reveal some surprising connections between factorization and other aspects of arithmetic.

May 12, 5pm. "Solving the Cubic", with Japheth Wood. Although solution methods for quadratic equations had been known to the ancient Babylonians, it wasn't until the 16th century that solutions for the cubic began to surface in Renaissance Italy. Come join us to learn the fascinating history of the cubic and see for yourself how it works!

May 19, 5pm. "Exploration of Unique Factorization, Part III", with Ben Blum-Smith. We will prove the unique factorization theorem and extend its reach beyond the integers (We might even get to see why it fails in Z[√-5]). There will be a recap for participants who were not at the April 21 and 28 sessions, so everyone is welcome to attend.

We are pleased to offer a math circle session for middle school teachers at Stuyvesant HS this election day. We hope you can join us for an enjoyable day of mathematics, as always in a supportive environment. Space is limited, so please write to japheth@nymathcircle.org soon if you are interested. Your RSVP is required to attend.

Topics from first year Calculus are revisited and viewed from several perspectives.

Emphasis is placed on the underlying structural principles and pervasive unifying themes. Both classic and non-routine problems are presented together with some special theorems and non-standard proofs. In addition, we will offer tips for presentation and course design.

This course would be especially helpful to those teaching or planning to teach Calculus, and will provide insight and practical suggestions based on many years of experience teaching it.

This mini course is for teachers who intend to coach a Math Team, a Math Club, or a related extracurricular activity. It can also be taken by those who simply enjoy doing mathematics and solving math team type questions. Participants will learn how to conduct a Math Team, and will become acquainted with different types of competitions, and with many available sources and resources.

Some mathematical topics essential for Math Team will be presented, accompanied by a wealth of examples. Techniques for training students, motivational devices, and philosophy of the Math Team experience will be addressed. Appreciation of problem solving is a key component. Special emphasis is placed upon potential for student growth as a consequence of Math Team.

Not a course! Just informal gatherings for teachers, to discuss some mathematics, work on some problems, and have dinner together. Two sessions are planned:

August 6th, 5pm, Interactive Math Investigation, by Jesse Johnson and Ben Blum-Smith. Jesse and Ben recently attended the Math Circle Summer Teacher Training Institute, run by Bob and Ellen Kaplan (who visited both our teachers' and students' classes this spring) and will share their favorite topic with us. As always, the style of this evening of mathematics will be interactive, with everybody welcome to participate in deriving (from scratch) a classical result from ancient Greek mathematics.

August 13th, 5pm, Pianos and Mathematics, by Jeff Suzuki, Brooklyn College. Why does Asian music sound so distinctive, and a C-D chord sound so jarring? What are flats, sharps, and what do they have to do with irrational numbers? This talk will begin with an introduction to music theory and its mathematical challenges. Along the way, we'll learn how to tune a piano (or at least, learn why a piano is tuned the way it is) and explore some of the many connections between mathematics and music.

This course is a continuation of Math Enrichment for Teachers II started in Fall 2008. See description.

We are forming a math circle for middle school math teachers, with the aim of building a community of teachers interested in developing problem solving skills, deepening content knowledge and discussing pedagogy. The Middle School Math Teachers' Circle will meet on the second Wednesday of each month, followed, at the end of July, by a three day immersion workshop at Union College.

If you'd like to register for the summer workshop but can't attend the monthly meetings, use the registration link above, and mention this in the comment box on the form.

This course is intended for math teachers, whether new or experienced, who wish to enrich their classes. Participants will continue a mathematical journey through number theory, algebra, and geometry, exploring fundamental notions and some special topics. Both new participants and those continuing the Fall course are welcome.

The course will include several guest speakers. Problem posing and problem solving will be emphasized throughout, and opportunity will be provided to work on challenging problems during class time.