Like other enthusiasts of mathematics, I’m captivated by the way that mathematical ideas can explain things in the physical world around me, and by the way that I can carry out mathematical thought experiments in my mind and then apply the results to control my external physical environment.
In the Dynamic Number project, one of our goals has been to create activities in which students actually experience mathematical objects by creating them, manipulating them, and investigating them. (George Lakoff and Rafael Núñez describe, in Where Mathematics Comes From, how students' abstract mathematical concepts are grounded in … Continue Reading ››
As an 18-year veteran teacher in Philadelphia public schools, my initial reaction when I first saw Sketchpad was “This would have completely changed the way I taught geometry.” I phrase it differently today: “This would have completely changed the way students experience mathematics.” a perspective that differs in two important details. First, I now understand that the … Continue Reading ››
As a fourth-grader in 1977, I had a love-hate relationship with my Addison-Wesley textbook. Its contents overflowed with arithmetic problems, but every so often an entertaining brainteaser appeared to break the monotony of drill practice. These puzzles were clearly marked: Each appeared in a box set aside from the main text and featured a bespectacled … Continue Reading ››
Ms. Walter, my junior high math teacher, sure knew how to get my attention on the first day of class. She told us we would be studying all about sex. Well no, let me restate: She said we'd learn about sets, but my seventh-grade ears heard otherwise. It didn't take long for my confusion to … Continue Reading ››
It’s time for the NCTM Annual Meeting! For the past two and a half years, my colleague Scott Steketee and I have been collaborating with elementary teachers in New York and Philadelphia as they field test curriculum materials for the Dynamic Number project. We’ll be showcasing our work at three sessions during the upcoming … Continue Reading ››
Functions are hard for students. Students seem to master various families of functions – linear, polynomial, exponential, trigonometric, and so forth. They can graph them, evaluate them, transform them, and answer a variety of questions about them. But ask even our better students a question that’s out of the ordinary and we’re likely to be taken … Continue Reading ››
What’s the narrative? That question, so fundamental to any novel, may not sound as relevant when applied to mathematics. Take, for example, the topic of factors: 1, 2, 4, and 8 are factors of eight; 3, 5, and 7 are not. Where is the inherent drama in these relationships? In most elementary mathematics curricula, there … Continue Reading ››