Mathematics is a wonderful game. It's one that can stretch students' minds and expose them to the beauty and unexpected delights that lie behind every good problem. I've always gravitated to colleagues who share my love of math's playful, game-like side, so I quickly made friends with Toni Cameron when we met at P.S. 503 in … Continue Reading ››

In how many different ways can you build a rhombus that stays a rhombus when its vertices are dragged? This assignment, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties of the quadrilateral. While the rhombus task works … Continue Reading ››

When students find the nth roots of a complex number, they use de Moivre's Theorem and a fair bit of calculation and trigonometry. In this blog post, I'm going to approach the topic from a more visual perspective and make use of the following geometric way to think about complex number multiplication: To multiply two complex … Continue Reading ››

On the NCTM discussion site myNCTM, there's currently an extended discussion about "Division and multiplication of fractions." As the discussion has continued, I've grown concerned with what I see as a fundamental problem with the way we often introduce multiplication as repeated addition: "Multiplying 4 by 5 means we're combining five groups of four items. … Continue Reading ››

A recent post on the my NCTM discussion group asked about tools to help students visualize and understand addition and subtraction of integers. I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … Continue Reading ››