The Math Education Blog
Last week was the fourth session of my spring Advanced Secondary Math Methods class at the University of Pennsylvania. Each year I assign a semester project in which groups of three students use lesson-study techniques—on a small scale—to create, test, refine, teach, evaluate, and document specific shared instructional products, composed of a (possibly multi-day) lesson...
Today I leave for my first proper vacation in a year and a half. Last time I took such a vacation, Key sold its high school textbooks to Kendall Hunt and transformed from a publishing company to a educational technology company. This time I just hope to survive the end of the world. 🙂 Before...
Tomoko Fuse is a Japanese origami artist whose designs are highly geometric. A Google search for her origami models reveals a plethora of boxes and intricate three-dimensional structures, many of which are folded from multiple sheets of paper and then assembled together. As an avid origami folder, I’ve always admired Fuse’s work. But nothing prepared...
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. But it turns out that my separation...
I had the immense good fortune this year to attend ICME, the International Congress on Mathematical Education. The Congress is held every year divisible by 4, and this iteration (the twelfth) was held in Seoul, Korea. It is quite something to be at a meeting of nearly 4000 mathematics educators from 84 different countries, and...
In a recent blog post, Karen Greenhaus describes how it’s possible to construct familiar corporate logos using Sketchpad. You might start with a rhombus, for example, and then reflect it twice to obtain the Mitsubishi logo. Karen’s post got me thinking about other creative uses of transformations with Sketchpad. In particular, Sketchpad 5 allows you to...
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...
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...
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...
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...