Not long ago, I conducted a Saturday morning PD session for some Texas teachers participating in an NSF research project. (The research is a controlled study of the relationship between students’ use of Sketchpad and their conjecturing and proving behavior. I hope we’ll have a blog post about this study itself before too long.) Because of the … Continue Reading ››

As a student, I didn’t place conic sections on my list of favorite high school topics. The standard textbook treatment of the ellipse, parabola, and hyperbola seemed uninspired. There were messy algebraic equations with multiple square roots. There was lots of terminology. Drawing a conic meant plotting several points on graph paper and connecting them with … Continue Reading ››

At around Pi-hour on Friday afternoon we successfully launched our new website. The night before (the night of the big storm for Bay Area folks), Andres and I were out with a dear former colleague and I mentioned I was going to blog about our new branding, new website, and new name. She said, “You … 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 ››

In a recent blog post, Karen Coe referred to Conrad Wolfram’s opinion that programming is to mathematics what composition is to English. I’ve taught programming and written a lot of Sketchpad code, and I appreciate Wolfram’s analogy. In English class, students read books, poems, short stories, essays, and articles—but to gain a deep appreciation for … Continue Reading ››

As an author of Sketchpad activities, I like to think that I can pose good problems for students to solve. But as I visit elementary classrooms and watch students use Sketchpad, I realize that a large part of the enjoyment they derive from using our software comes from creating their own problems and sharing them … Continue Reading ››

A quick quiz: How many fractions are there? This may sound like an absurd question, but in the context of elementary mathematics curricula, it makes a lot of sense. Think about it: Children encounter fractions like 1/2, 3/4, and 2/6 all the time, but do they ever see 1/100, 31/90, or 499/500? Unlikely. No brave soul … Continue Reading ››