Session One:
Geometric Thinking
Facilitators: Ryota Matsuura, Dicky Ng (Boston University)

The goal of this institute is to provide teachers with a better feel for the subject of geometry. Teachers will have the opportunity to explore problems by making, testing, and proving conjectures using different tools including the Geometer's Sketchpad. Teachers will walk away from this institute not only with the mathematical insight, but also an appreciation for the art of discovery which they can bring back to their classrooms. Problems are designed to be accessible to teachers at any level and yet challenging to experienced teachers.

Some very deep mathematical results can be investigated and confirmed with simple arithmetic. In this institute, we will investigate several different contexts applicable to school mathematics. Some of the topics we'll investigate are patterns in Pascal's Triangle (like, is the sum of the entries in a row ALWAYS a power of 2?), Pythagorean triples (integer valued sides of right triangles), divisibility rules (like, why does the sum of the digits of an integer tell you whether it's divisible by 9?), and cryptography (the science of encoding and decoding secret messages).

Algebra is more than a high school course. It's more than just a series of disconnected topics. Algebraic habits of mind are pervasive throughout the K-12 curriculum. We will trace the development of some major algebraic concepts from early elementary school though high school and beyond. We are looking forward to discussions that include perspectives from teachers of all levels. The course will take a hands-on, problem-solving approach.

For more information and registration, contact Karina Dymina at karina@focusonmath.org.