After a four-year hiatus, I’m teaching Geometry once again. I have always loved this course, because it’s such a unique branch of high-school mathematics. It doesn’t deal much with arithmetic, variables, and functions; rather, it requires students to employ logic and clear thinking to prove theorems. There’s even room for some “elegance”!
We are currently learning the basic building blocks of Euclidean geometry: points, lines, and planes, and the postulates concerning them. In previous years, I have incorporated Geometer’s Sketchpad into my teaching, but this year I’m switching to GeoGebra. I love Sketchpad, and I’m very comfortable working with it (take a tour of my YouTube videos featuring it), but I can’t justify asking my students to pay a hefty license fee to use it, when GeoGebra is open source. GeoGebra also has a built-in CAS, and its developers provide major updates regularly. Throw in all the lessons and files available on GeoGebraTube, and it’s very hard to resist making the switch.
After making sure all of my Geometry students had the latest version of GeoGebra installed, we worked through the basic features of it. Within a few minutes they were creating some impressive artwork with it. Today, I issued the first of what I plan to be a regular series of GeoGebra challenges: create a rectangle (not a square) that remains a rectangle regardless of how they drag corners and sides. It’s harder than it sounds, and it requires them to think about what makes a rectangle a rectangle.