GeoGebra is a learning tool for mathematics that is used all over the world. It’s a free geometry, algebra and calculus application, created for teachers and students from primary school to university level.
Elisabeth Engum jumped for joy when she learned that GeoGebra applets could be embedded into learning platforms. She even made a video showing us how to incorporate them into itslearning (see below).
Elisabeth, now Global Head of Pedagogy at itslearning in Norway, was a math and geoscience teacher for eight years. She reports, “GeoGebra allows teachers to create challenging and fun tasks for students. The great thing about it is that it allows students to play around with formulas and functions within its applets.” (Applets are small software applications.) For example, in the GeoGebra applet below, you can estimate whether or not the boy will make a basket. Just change the values of the different parameters by dragging the dots on the lines and you can determine the future trajectory of the basketball.
Try it yourself! Slide the dots (a, t and h) along the lines in the interactive GeoGebra applet below:
Try to position the red line below so that it follows the curve of the basketball in flight. Will the ball go through the hoop or not?
GeoGebra applets are great for demonstrating the practical application of mathematical formulas. Elisabeth explains, “If you want to learn how to use GeoGebra, there are a lot of excellent websites that will teach you. I’ve made my own tutorial describing how to embed GeoGebra applets into learning platforms so that teachers can create different activities for their students.”
In the video below, Elisabeth shows you how to make a GeoGebra applet exploring the quadratic function (ax2 + bx + c). She then explains how to embed applets into itslearning assignments, notes, etc. so that students can experiment with them within the platform. “You can include an applet in itslearning surveys, for example. Ask your students to explore the applet by dragging the gliders. Have them explain in their own words what effect changing each of the values has on the quadratic function.”
GeoGebraTube is the official repository website of GeoGebra products. It contains over 60,000 materials including interactive presentations, games and lessons made with GeoGebra. Applets can be uploaded to GeoGebraTube and exported as files, suitable for use in itslearning. You can also search GeoGebraTube for other teachers’ materials and embed them into itslearning. This is especially useful for secondary school and upper secondary school teachers.
GeoGebra certification courses
GeoGebra, itslearning and Kikora (a digital math teaching tool) are collaborating to train and certify math teachers in the use of GeoGebra. Their course includes Kikora instructional videos and GeoGebra assignments, all integrated into itslearning. No software installations, user names or passwords are necessary, so it’s easy to get started. Teachers can see their own progress during self-instruction. Official “GeoGebra User” certification is awarded to qualified teachers. More and more teachers are acquiring the skills to make their own quality teaching materials!
GeoGebra software is free and can be downloaded from GeoGebra.org. It can be used to make conjectures and to learn how to prove geometric theorems. Constructions can be made with points, vectors, segments, lines, etc. and can be changed dynamically afterwards. Elements can be entered and modified directly onscreen, and projects can be exported in several formats. GeoGebra has expanded its offerings to include iPad, Android and Windows Store app versions.