Let GeoGebra Transform Your Mathematics 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?As mathematics educators, we regularly meet people socially who, upon discovering our vocation, volunteer to us, unasked, their experience of mathematics lessons at school. The general consensus is that 70+ percent of people struggled - or struggle with our loved subject.
Many strategies are available that help students better understand mathematical principles. The challenge is that most of these strategies demand significant pedagogical change, especially for teachers currently using a traditional Procedures-first approach. The plug-in-a-data-projector-and-show-the-file method
As has been explained here and in the introduction to this article, utilising 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 from the teacher.
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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 concerns 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) a GeoGebra file in action at the top of this article. The original GeoGebra file, created by John Dillon (a past 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) a GeoGebra file in action at the top of this article. The original GeoGebra file, created by John Dillon (a past 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-utilised. The primary reason, I suspect, is due to the 'You don't know what you don't know' factor. 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 - to name a few.
One issue for teachers is that GeoGebra, although easy to use once you know how is not particularly user-friendly to learn alone. And this is despite the mountain of available free resources. As a result, many teachers use ONLY pre-made files and miss out on the power of being about to unleash their creativity through GeoGebra to produce conceptually-based files specifically to suit their students, their teaching style and their creativity.
One issue for teachers is that GeoGebra, although easy to use once you know how is not particularly user-friendly to learn alone. And this is despite the mountain of available free resources. As a result, many teachers use ONLY pre-made files and miss out on the power of being about to unleash their creativity through GeoGebra to produce conceptually-based files specifically to suit their students, their teaching style and their 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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