A couple of days ago I got an email from my long-time friend Geri, who was spending some quality Sketchpad time with her 12-year-old grandson Niels. Geri emailed me for advice because Neils was having some trouble figuring out how to construct a pentaflake. Neither Geri nor Niels had any idea that I'd never even … Continue Reading ››
For a while now, I’ve been intrigued by the ways in which the study of geometric transformations can provide students with a very effective introduction to function concepts. Daniel and I have written a couple of articles about this topic, and we created a number of activities to take advantage of what can arguably be … Continue Reading ››
With the World Cup in our hemisphere, and the US squad having started out with a win over Ghana, my thoughts turned to the mathematics of soccer. My friend Henri Picciotto has a nice page about the shooting angle, the angle within which a shot is on goal, so I thought of … Continue Reading ››
In this guest post, Nate Burchell describes a sketch he uses with his students to explore parametric functions. In this process students work entirely in a graphical world, manipulating graphs directly rather than by way of equations. (Nate teaches in Seoul, Korea, where I enjoyed his family's hospitality when I attended ICME in … Continue Reading ››
In Where Mathematics Comes From, cognitive scientists George Lakoff and Rafael Nuñez assert that our understanding of abstract mathematical concepts relies upon our sensory-motor experiences:
“For the most part, human beings conceptualize abstract concepts in concrete terms, using ideas and modes of reasoning grounded in the sensory-motor system. The mechanism by which the … Continue Reading ››
π Day has always been a special day for me, from my earliest days. In fact, I've never figured out whether I was so eager to celebrate my first π Day that I jumped the gun and sent my mom into labor early, or whether I just wanted be sure to experience all 24 hours … Continue Reading ››
In my Advanced Methods class at Penn’s Graduate School of Education, my students are working in groups to create shared lesson plans using an inquiry approach. For a number of reasons it can be challenging for these pre-service teachers to identify appropriate topics for student inquiry, but sometimes the brainstorming they do turns into something … Continue Reading ››
I recently got a question from a question from a user about how to line up text objects. The question was both about lining up objects on a page, and about lining them up from one page to the next, so that when you switch pages things are in the same place on every page.
As … Continue Reading ››