## Let GeoGebra Transform Your Math Teaching

The Case For Becoming A Proficient, Inspired GeoGebra User!

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

## Mathematical understanding at school?

Ask a random sample of 50 people between the ages of 20 and 30 how well they understood mathematics at school and I think you’ll agree that we maths teachers are not doing as well as we could in regard to the ‘imparting of mathematical understanding to students’, but not from a lack of trying. Many tangible strategies are available which help students better understand mathematical principles. The challenge is that these strategies demand significant pedagogical change on behalf of the teacher, especially for teachers currently using a traditional procedures-based approach.

## The plug-in-a-data-projector-and-show-the-file method

As has been explained here and in the introduction to this article, 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 significant upside is that using GeoGebra in this way requires no significant change in the approach used by teachers.

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

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

- 1. Project and demonstrate pre-made GeoGebra files.
- 2. Create partly constructed files designed for investigation of mathematical ideas so that students can complete and explore the files.
- 3. 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 original GeoGebra 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 a teacher normally offers, can there be any argument against utilising such a file for a unit segment on 'trig graphs and the unit circle'?

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.

Consider the dynamic image (gif) at the top of this article, a repeating video of a GeoGebra file in action. The original GeoGebra 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 a teacher normally offers, can there be any argument against utilising such a file for a unit segment on 'trig graphs and the unit circle'?

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)

## Why the proficient use of GeoGebra is not widespread

Given the power of GeoGebra and the potential for significant improvements in student engagement and understanding, you'd think GeoGebra would be used extensively by most mathematics teachers today. However, my 'ear-to-the-ground' observations suggest that GeoGebra is grossly under-utilized, primarily, I suspect, due to the principle 'You don't know what you don't know'. Many who use GeoGebra, for example, use it only for the upper grades or only for graphing and geometry. Yet GeoGebra can be applied to numerous topics including fractions, ratio and proportion, similarity, number, trigonometry and bearings, statistics, Pythagoras’ theorem, dynamic explanation of all measurement formulas, and the derivation of pi.

One issue for teachers is that GeoGebra, although easy to use once you know how, is not easy to learn alone

despite the mountain of available free resources. This leads many teachers to use ONLY pre-made files and miss out on the power of being about to unleash their creativity and produce conceptually-based files specifically to suit their students, their teaching style and their own level of creativity.

One issue for teachers is that GeoGebra, although easy to use once you know how, is not easy to learn alone

despite the mountain of available free resources. This leads many teachers to use ONLY pre-made files and miss out on the power of being about to unleash their creativity and produce conceptually-based files specifically to suit their students, their teaching style and their own level of creativity.

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

Dianne Ley, Gilroy College, 18.2.15

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