Category: Poster

32 - Graphing Challenge: A Novel Twist on a Standard Idea from Algebra

Saturday, Nov 11
12:00 PM – 1:00 PM

We "know" that y=x will be the graph of a line. But what if the "notches" on our axes are non-standard? Do we still get a line if we erase the numbers on the y-axis and replace them with the numbers 1, 10, 100, ... ? This simple question begs a million more. This presentation describes a multi-week, inquiry-based unit on graphing in which students are invited to re-engage with ideas they thought they knew inside and out. Students are free to invent alternate axes and choose their own equations, putting them squarely in the driver's seat.

Paul Gafni

Mathematics Instructor
Robinson Center for Young Scholars, University of Washington
Seattle, Washington

Paul Gafni's primary professional aim is to share his passion for mathematics with K-12 students. Paul excelled in his undergraduate math program, receiving departmental recognition for Outstanding Achievement in Mathematics both as a sophomore and as a senior. After graduating magna cum laude with a B.A. in Mathematics in 2011, Paul has (so far) opted out of pursuing further academic degrees in favor of a career teaching mathematics to highly capable youth.

Paul teaches the Transition School's mathematics class at the University of Washington's Robinson Center. Transition School serves highly capable students who aim to enter university early; Paul's students generally become full time university students at age 15, if they are successful at Transition School. Aside from his work at Transition School, Paul has been working with Math for Love since 2012, running a handful of Math Circles around the greater Seattle area. He also teaches online classes with Art of Problem Solving, and works privately with a handful of students. He has been teaching since 2008, and his primary mathematical interests are Combinatorial Game Theory, Abstract Algebra, Number Theory, Graph Theory, and Combinatorics.

When he's not teaching or learning math, you might find Paul out of the country or working on art in a variety of forms. Since 2011, his travels have included Thailand, Malaysia, Laos, Cambodia, Vietnam, South Africa, Mozambique, Zimbabwe, Colombia, and Guatemala. His art focus lately has been on designing and fabricating fractal jewelry, using laser cut acrylic and birch. Past art projects include a motorized couch and a 6 foot flower wooden with 3+4+...+10=52 pentagonal petals.