Mini-Courses

to known values and discuss how to resolve any minor discrepancies. This course is primarily for Earth science, physics, or mathematics teachers.

Paul McDowell studied mathematics and astrophysics at the University of Toronto and then worked in business systems. He progressed from programmer to V.P. and Chief Information Officer. As Managing Director of a major international consulting firm, Paul led global transformations. Most recently, Paul was at the world’s largest hedge fund, building new people/work systems. Paul’s career and passions are about understanding the Universe, simplifying the complex, and unleashing human capability. Paul graduated from Ryerson University with studies in Computing Systems. His hobbies include mathematics, model trains, running, and film-making.

Lawrence Whitfield taught high school mathematics in Zambia, Africa, for six years and then became a software developer. While progressing from software developer to project management to senior management, he enjoyed mathematics as a hobby throughout. Ever intrigued by Earth-Sun geometry, Lawrence challenged his astrophysicist friend to quantify these movements via mathematical equations. This was a successful process with the side benefit of mastering Geogebra. Lawrence developed several renditions of the Earth-Sun movement available on his YouTube channel. Lawrence contributed to SoME and SoME2 via 3Blue1Brown. Lawrence has an Honours B.Sc. in Mathematics and Computer Science.

Elissa Levy is an MƒA Early Career Teacher and science teacher at Hunter College High School in Manhattan.

Tilings, Tessellations, and Origami Facilitators: MƒA Master Teachers Grace Chang and

Kevin Peters

THURSDAYS, APR 27, MAY 11, MAY 25 MƒA  MATHEMATICS

Have you ever tried to design a tessellation or tiling?

In this course, we will create tessellations by twisting paper to form different shapes and then repeating them in various arrangements to create intricate patterns. In the first session, we will fold a square twist on a square grid and use it to create an iso-area tessellation. In the second session, we will fold a triangle twist on an isometric grid and then tessellate the paper with triangles. And in our final session, we will fold a hexagon twist and experiment with different possibilities for tessellating paper using an isometric grid. Throughout, we will discuss some of the mathematical properties of paper folding and how to apply these properties and constraints to exploring and making our own tilings and designs. Previous experience folding paper is helpful but not required.

Grace Chang is an MƒA Master Teacher and mathematics teacher at Neighborhood School in Manhattan.

Kevin Peters is an MƒA Master Teacher and mathematics teacher at 47 The American Sign Language and English Secondary School in Manhattan.

True Origins of the Pythagorean Theorem Facilitator: Christina Eubanks-Turner, Ph.D.

TUESDAYS, APR 4, APR 18, APR 25 ONLINE  MATHEMATICS

Traditional ways of organizing content in the history of mathematics hold a Eurocentric bias common in producing, disseminating, and evaluating scientific knowledge (Powell & Frankenstein, 1997). Much of the focus in a traditional history of mathematics course focuses on Greek beginnings in introducing “rigorous” mathematics through proof. This prevailing Eurocentric, male-centered view of mathematics obscures history and denies the communities and cultures that played significant roles in the development of mathematical knowledge (Joseph, 1987). In this course, we will look beyond these Eurocentric views as we explore the origins and uses of the Pythagorean Theorem and present evidence demonstrating knowledge of the Theorem that preceded Pythagoras. We will also examine other wellknown mathematical theorems and ideas attributed to Europeans, which Non-European mathematicians actually discovered.

Dr. Christina Eubanks-Turner is a Professor of Mathematics and Graduate Director of the M.A. in Teaching Mathematics program at Loyola Marymount University. Her primary research areas include mathematics, mathematics education, and broadening participation in mathematics. She has extensive experience working with pre-service and in-service teachers from small and large urban districts across the US. She teaches mathematics content courses for K-12 preservice teachers. She has taught various graduate-level mathematics courses for in-service middle and secondary teachers. She has led several teacher professional development workshops in collaboration with education faculty and school district leaders. Her mathematics education research focuses on best practices for supporting the development of mathematical knowledge for teaching.

Unlocking Intermediate Number Theory: Beyond Common Divisors and Multiples

Facilitator: MƒA Master Teacher Scott Matthews

THURSDAYS, MAY 4, MAY 11, MAY 25

MƒA 

Mathematics

The locker problem is a well-known, high school-level, elementary number theory problem involving divisors of numbers. One by one, students numbered 1 to 1000 walk by a row of lockers numbered 1 to 1000, all of which are initially closed. The first student opens every locker. The second student closes every second locker. The third student changes every third locker; if it’s closed, they open it; if it’s open, they close it. That same pattern continues for all 1000 students. Which lockers are left open after all 1000 students have walked the row of lockers? In this course, we will work collaboratively to solve problems related to numbertheoretic functions, including the divisor function, the sum of divisors function, and Euler’s totient function. Then we will find solutions to Diophantine equations, if they exist, with the help of the Euclidean algorithm. Lastly, we will use modular arithmetic to develop Fermat’s Little Theorem, Wilson’s Theorem, and Euler’s Theorem. This course is open to all teachers, as we’ll cover the basics of number theory. If you are interested in more deeply exploring number theory, join us!

Scott Matthews is an MƒA Master Teacher and mathematics teacher at Brooklyn Technical High School in Brooklyn.