The Math Education Blog
Four years ago, my colleague Scott Steketee and I began brainstorming new Sketchpad activities for a National Science Foundation grant called Dynamic Number. Our goal was to use Sketchpad to make ideas from number, operation, early algebra, and algebra come alive through interactive models that emphasized conceptual understanding. Scott and I had lots of help....
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...
Using Sketchpad, it is very easy to start from scratch and create a polar graph. Here are the steps to create the graph shown on the right below. Choose Graph | Plot New Function. Use the Equation menu to choose r = f(θ). Type “c” (for “cos”), “2”, and “th” (for “theta”). Click OK. If your angle...
The Web Sketchpad model below (and here) shows the function f(θ) = 1 – cos 2θ in both Cartesian and polar form. For each graph, the independent variable appears as a red bar that corresponds to a particular value of x (for Cartesian) or θ (for polar). The red bar has tick marks that show...
I had the privilege this year of participating in the CADRE Fellows Program of NSF’s Community for Advancing Discovery Research in Education, and met a number of colleagues in the program whose projects, like our Data Games project, are exploring the classroom benefits of computer-game- or simulation-based-learning. (In this post, I’ll refer to technology-oriented games and simulations simply...
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...
According to a recent Wall Street Journal article, “Big Data’s Problem: Little Talent,” the technology industry faces a major dearth of employees with strong data analysis skills. The article quotes a 2011 study by McKinsey: A significant constraint on realizing value from Big Data will be a shortage of talent, particularly of people with deep...
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...