How I Use It
I have used GeoGebra to teach and expand upon the concept of fractal mathematics for a wide range of students by using it in an
online course format. The ability of GeoGebra to both demonstrate a concept and also to allow students to create fractal patterns of their own was very useful for bringing this concept to life for the students. It was also flexible enough that I could use it for a wide range of student ages and abilities; the younger students could simply move the slider and see the patterns change and older students could follow directions to make their own patterns and explore them more in-depth.
By allowing students the ability to create the fractals (Cantor Set, Koch Snowflake and Sierpinski Triangle) in a step by step way it allowed them to see the self-repeating patterns in action and to discover how fractals are built in a very hands on way. It also allowed them to 'play around' and have fun with different patterns to see if they could make their own fractal patterns in new and unique ways. The students really liked being able to see each step and to alter the different dimensions of the image to more clearly see how the patterns repeat. It was also useful for younger students who could simply move the slider and see how the image changed; without having to know the exact equations used.
It was a great visual tool that allowed the students to explore a concept not commonly taught in school in a fun, and highly visual, way.
I really like GeoGebra for a number of reasons. First and foremost is that it allows students to really see, and manipulate, equations, numbers and formulas in a way that highlights what they really mean and what they are trying to tell us. It also speeds up some of the time consuming processes associated with drawing graphs and images by hand, which can quickly become frustrating for students. Instead it allows them to quickly create and manipulate images on their computer or device.
Secondly, GeoGebra has a number of pre-made worksheets available on their website that allows students to explore concepts without having to set up the images and formulas themselves. This can be highly useful for teachers that have a large amount of information to get through with their students but often not a lot of time. However, the worksheets available on the GeoGebra website do range in quality and usability and require careful selection by the teacher before providing them to students.
Finally, GeoGebra itself (the company) is incredibly supportive of those who wish to use their platform. They provide the software for free and there are a lot of apps and extensions constantly being created that improve the reach of the program (including a new AR app that is fantastic).
However, I do have two main issues with the program. First, there can be a steep learning curve depending on what you want to do and, while the online resources do help with this, the teacher does need to be quite knowledgable with the program before providing it to their students in order to really get the full effect. If not, the students can quickly become frustrated and the 'picky' aspects of the program can undermine its overall purpose. Secondly, I did find that once a concept was covered the students quickly became bored with the tool. For the pre-made resources this often included moving the slider once or twice and then losing interest. For the step by step instructions once the image was created the students were ready to move on to other topics or resources.
Overall, I really like using GeoGebra. It showcases math in a new and interactive way and really brings math to life, especially Geometry. It's a great tool for bringing equations to life across multiple math areas and I highly recommend it for students and teachers alike!