Ask a random sample of 50 people between the ages of 10 and 30 how well they understood mathematics at school and I think you’ll agree that mathematics education has some improving to do in the ‘imparting mathematical understanding to students’ department. Many tangible strategies are available which help students to better understand mathematical principles. The downside is that these strategies demand significant pedagogical change on behalf of the teacher, especially for teachers using a “traditional procedures” based approach.

GeoGebraGif_UnitCircleTrig 670x345

The original GeoGebra file used for the dynamic image above was created by John Dillon, NSW, course participant, September 2009.

However, utilizing GeoGebra using the plug-in-a-data-projector-and-show-the-file method, is a powerful addition to the mathematics classroom, increasing engagement and deepening understanding in students. The huge upside is that using GeoGebra in this way requires no change in approach by teachers. All that is required is for the teacher to connect a data projector and demonstrate some files! And for the record, connecting a data projector to a computer does not constitute pedagogical change!

Below are three ways in which GeoGebra can be utilized in the mathematics classroom:

  • Project and demonstrate pre-made GeoGebra files.
  • Create partly constructed files designed for investigation of mathematical ideas and have students complete and explore the files.
  • Have students create and explore files of their own as part of an investigation task.

This article is concerned with the easiest of the three methods, namely plug-in-a-data-projector-and-show-the-file. For those interested in running student-led GeoGebra investigations, I recommend the article Five tips for designing student-lead GeoGebra investigations.

Consider the dynamic image (gif) at the top of this article, a repeating video of a GeoGebra file in action. The file, created by John Dillon, an August 2009 course participant, is a brilliant illustration of the principles behind the unit circle and trigonometric graphs. Given we are talking about simply projecting the file as a 2-minute addition to whatever instruction the teacher normally offers, can there be any argument against utilizing such a file for this unit?

Below is another GeoGebra file, designed by course participant, Frederic Jaccard, for younger students. It’s a lovely way to see the relative dimensions of various figures change while keeping the area constant.

The original GeoGebra file used for the dynamic image above was created by Frederic Jaccard, Xavier College, NSW, December 2014 course participant.

For more examples of dynamic GeoGebra files in action check out the articles linked below. The files strengthen the argument that all math teachers with access to a projectable computer should be utilizing GeoGebra (or similar). Yet I’m convinced there are a great many who, at the time of writing, are not. I invite anyone to show that the number of mathematics teachers who are regular users of GeoGebra (or similar) is greater than 50% worldwide.

My assumptions about math teachers who are not utilizing GeoGebra (or similar) fall under one or more of the following categories:

  1. They do not yet know about GeoGebra (or similar software).
  2. They hold misconceptions about GeoGebra (or similar), and as a result, have decided that GeoGebra is not for them (i.e they assume GeoGebra is a tool only to be used for complicated, high-end mathematics, and/or that it is too difficult to use).
  3. They are aware of GeoGebra (or similar) and have tried to learn how to use it but were not very successful.
  4. They do not have access to a computer and a data projector.

Overcoming assumption 4 may prove difficult in some situations. It would help if schools realized that 90% of the advantages of an interactive whiteboard lie with the data projector and that therefore it would be better to have a data projector in every classroom rather than an IWB in a quarter of the classrooms! However, assumption 4 would account only for a small percentage of the non-GeoGebra-using math teachers. It is mostly a lack of awareness which prevents GeoGebra from being utilized by ‘all and sundry’, i.e. assumptions 1, 2 and 3. This article is an attempt to raise awareness.

I encourage you to take a quick look at another excellent demonstration of a file designed to foster conceptual understanding. It’s theSurfboard file, created by December 2013 participant Anne Wolkowitsch. You will find it half way down this article along with a suggested approach for demonstrating it. I highly recommend you take a look because the file and suggested approach offer an excellent example of a conceptual approach in action.

Would you like GeoGebra to transform your math teaching? (There’s a course for that!)

If you are interested in becoming proficient with GeoGebra then  this course is for you. Note also that the course is set up so that multiple teachers from the one department can participate as a team.

Here’s what one teacher had to say after completing the course:

“This course has taught me so much. I have been inspired to include the use of
GeoGebra in my lessons so my students’ learning will be engaging, interactive,
collaborative and investigative.”

—Dianne Ley, Gilroy College, 18.2.15

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