One of the most difficult parts of high school mathematics is geometric proofs. This process involves memorization of many facts and definitions along with a type of mathematics that involves no formulas or processes to follow and few numbers. This involves a type of mathematical thinking that is difficult to master and is very different from what we have been asking students to do for the entirety of their previous experience in math. Fortunately, this is a pretty neat app that can ease this transition and develop in our students the type of thinking that we wish to foster.

Geogebra is a wonderful free application that is available for download at http://www.geogebra.org/cms/en/. This app allows both teachers and students to design and manipulate geometric diagrams and their accompanying algebraic notations. Geogebra has tools that can be used to model a situation in which a student is tying to prove a geometric concept. One of the best things about Geogebra is that is allow one to manipulate one variable in a diagram. This allows students to develop and test theories in the course of their proofs and give life to the diagrams in question.

Also, Geogebra has applications in the plane and in Algebra. Any of the diagrams made in Geogebra can be transferred to the coordinate plane, which could be used to teach students about translations, tessellations, and rotations. This is accompanied by the algebraic representations of the shapes and lengths created in this app. Point labels, angle and segment measures, and areas can be shown and manipulated in Geogebra.

An effective use of Geogebra could be to have the students in the computer lab working through a discovery lesson on what happens when two parallel lines intersect a transversal.

In short, this application can make geometry much more hands on and accessible for students.  It encourages students to think in a new way, to create and test theories, and allows you to incorporate multiple representations into a single, seamless lesson.