Resource: GeoGebra

http://www.geogebra.org/

AT A GLANCE

GeoGebra is a web-based tool that enables students not only to draw shapes, functions, and 3D objects, but provides students with the ability to move and manipulate what they have created, thus promoting inquiry. It can and should be used in a mathematics classroom from as early as the later primary years up to grade 12. Specifically, it is a great tool for students to explore geometric shapes and manipulate them without needing strong fine-motor skills or visualization abilities. In higher grade levels, GeoGebra makes plotting data and viewing graphs very efficient and effective. It is a great way to visualize concepts and see how certain parameters affect an output.

TPACK Analysis:

The Technology:

GeoGebra is a very powerful tool for visualizing mathematical concepts, patterns, and connections. It allows a user to do an incredible amount of things such as: geometric drawings, 3D shapes, moving graphics, calculate equations, graph and plot data, expand/rotate models and several other features. It takes a significant amount of time to become familiar with the possibilities of this program. On a tablet, it can be difficult to highlight exact points on the graphs or shapes. Some of the features are rather time consuming and tedious which can be frustrating for the user. The website offers a free download and a free web-browser version that students can access easily. There are also hundreds of already-prepared interactive worksheets and drawings that can be used by the teacher and students.

With this tool, students need access to a computer/tablet and the web (unless its downloaded). As an educator, this is something to consider. Will everyone have a working device and how difficult will it be to help 30 students try to navigate through an assignment in GeoGebra? If there are only a few things you want students to see done in GeoGebra, consider demonstrating them on a projector because GeoGebra can take time to become familiar with (depending on the grade level). If you plan to use GeoGebra for several units, it may be worth implementing it for inquiries in all of these units (functions, graphing, geometry, calculus, etc.). When students need to draw out shapes, graphs, data tables, or do repetitive calculations, GeoGebra is a great tool to speed up the process and offer students an alternative to drawing or writing by hand to perhaps allow them to complete their work in a neat and efficient manner.

The Content:

The possibilities with in GeoGebra cover a large portion of the content being taught in the BC secondary Mathematics curriculum and its features can also be used in other courses such as physics, chemistry, and biology. It offers several avenues for extensions and more extensive mathematical inquiries.

Below is a link to a YouTube tutorial using GeoGebra. Teachers may create several of these videos for their students to use this tool outside of the classroom, perhaps even in a flipped classroom setup.

Link (Links to an external site.)

The Pedagogy:

Current research in the field of Math Education is indicating that visual representations and dynamic manipulations of mathematical concepts enable many students to gain a deeper level of understanding of the concept more quickly. The work of Nathalie Sinclair focuses on Dynamic Geometry Environments like GeoGebra and her results indicate that students at young age can make break-through connections when geometric shapes go from static sketches to dynamics objects. While not all students are visual learners, the evidence appears to support the fact that when students can actually witness changes and manipulations in real time, they can more fully grasp and internalize these concepts.

A consideration with GeoGebra is whether or not students can stay focused on the task at hand or whether they will begin to play around with the many features of GeoGebra. It may be worth having a “fun day” as an intro where students can explore GeoGebra as they please with teacher guidance to get their curiosity satisfied. Having a specific seating arrangement may be helpful in managing the class and having weaker students sit near other students who may be able to offer help as needed.

When using GeoGebra, it is important to gauge the specific abilities and limitations of each class before engaging in a class wide inquiry using GeoGebra. Using the program on a projector is a great way for students to get the benefits of the tool without having to manage the entire class and keep them on track. After showing students how to use the tool in class, GeoGebra can be a great avenue to allow students to explore things further on their own time outside of class. This tool has endless opportunities for students to explore and make connections and new discoveries.

Heads-Up:

Luckily GeoGebra is free and does NOT require a login. It can be used directly in the Web-browser or downloaded onto any PC or tablet. It is NOT yet available on cell phones. One Heads-Up that I will highlight is that students can share/publish the work done in GeoGebra. So make sure that students are staying on task and keeping their work appropriate.