Classroom Tools - Geogebra and Cabri Jr.

The Texas educational standards or Texas Essential Knowledge and Skills (TEKS) consider technology to be one of the techniques¹ for working with spatial figures and their properties, as well as, one of the underlying processes for all mathematic content areas. Therefore, TEKS for high school geometry specifies that students use technology “to solve meaningful problems by representing and transforming figures and analyzing relationships” and “in problem solving contexts.”

Acceptable forms of technology include, but are not limited to, calculators with graphing capabilities, data collection devices, and computers. Data collection devices often require that they be used in conjunction with a graphing calculator or computer, whereas, a computer or a graphing calculator can work independently of each other. However, all three can be combined and work as a single system to increase the capabilities of the devices.

There are also software packages, internet tools, and apps available to facilitate the integration of technology into the curriculum itself. In the context of geometry, these tools are referred to as dynamic geometry software (DGS) because they are able to represent figures, illustrate transformations and demonstrate how certain relationships will respond to manipulations.

With numerous factors that must be considered, the choice of which technology or DGS to use is by no means an easy decision. The very first factor that I consider is accessibility. Will all of my students have relatively easy access to a particular DGS? Furthermore, will my students have to purchase the DGS or special hardware to run the program?

My first choice will usually be a software package that is free. If a school or district has a considerable population of economically disadvantaged students, purchase packages become a matter of accessibility and, by extension, equality². What is more, some software packages that are available for free via the internet are still not accessible to all students (i.e. economically disadvantaged) because they cannot afford internet access at home. This must also be considered in the decision process. However, if a purchase package is available to students at the campus computer lab, the cost of purchase and accessibility from home becomes a non-issue in most cases.

The next factors I consider when choosing a software package are available features and ease-of-use or “user-friendliness”. What does this DGS offer that others do not? Is the extra feature absolutely necessary? How much training will my students need before they can use a particular DGS? How much training will I need before I can use a particular DGS? The quality and/or features of a particular DGS versus another DGS must be considered because it can be a matter of quality and equality of education, especially when associated with a difference in price.

The final factor that I will discuss is support. What kind of technical and/or user support will be provided with a particular DGS? What kind of training will be available for students or will they have to figure it out on their own? What kind of training will be available for me? I find few things as wasteful as money spent on technology that sits idle because teachers and/or students simply do not know how to use it.

I could see the Cabri Jr. app and Geogebra being used in my classroom. All of my students have access to TI-83+ calculators (during classroom time) which would provide them access to the free Cabri Jr. app. This would offer students the opportunity to explore transformations, constructions, and manipulations on their own. Although the graphic quality is quite low, the dynamic nature of the illustrations can do more for student understanding than a static image. Also, the simplicity of the app makes it very user-friendly which would allow students to spend more time exploring and less time trying to figure out how to make it work.

I do not have enough computers for each of my students. I do not even have enough computers to allow my students to work in small groups. Therefore, I would use the free Geogebra package as a presentation tool to illustrate dynamic, geometric relationships. Using Geogebra I would create illustrations that I could share with the entire class. The example I think of is showing the relationship between the unit circle and trigonometric functions (see Technology-Supported Mathematics Learning Environments chapter 10).

Endnotes

¹   the mathematical techniques and underlying processes include: multiple representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), technology, applications and modeling, and numerical fluency.

²  “equality” refers to quality of education. Are all students receiving an equitable education regardless of socioeconomic status?