Overview
Curator: Darrell Glover
Description of Resource: (from website) “GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package.” The GeoGebra website also has a large “Materials” section that has user created lessons and activities for others to utilize.
Technical & Cost considerations: GeoGebra is a free resource available for download over the internet. While the site has various activities that will work on any device with an internet connection, the GeoGebra program itself can be run offline. In addition to personal computer downloads, there are GeoGebra apps available for Apple and Android devices.
Evaluation
1. Learning Activity Types
- LA-Practice – there are resources on the GeoGebra site that utilize the tool for procedural practice
- LA-Present – GeoGebra’s easy graphing and tool interfaces, in addition to its clear presentation, make it ideal for introducing new concepts in a variety of mathematical strands
- LA-Present-Demo – teachers can easily demonstrate many new mathematical ideas with the various tools available
- LA-Present-Explain – the program does not explicitly explain what each of the various tools does but it does provide a small illustration next to each selection to help the user identify the tool’s purpose
- LA-Explore – the easy interface allows users to explore the abilities of the program and to explore ideas from different strands of mathematics
- LA-Apply – many of the activities in the “Materials” section on the GeoGebra site are given as word problems where the user can concoct a mathematical solution and use the program to solve it
2. What mathematics is being learned?
Standards
There are a wide variety of concepts that GeoGebra is able to illustrate, therefore, there is no reason to take up multiple pages listing each individual standard that it can satisfy. However, it is safe to say that an overwhelming number of NCTM and/or Common Core State Standards are addressed in different ways depending on how the program is used. These standards have stressed the need to better link algebra and geometry and by giving both representations, the program’s name is well earned for improving this.
Proficiency Strands
- conceptual understanding – various representations of data make it easier for the user to make conceptual connections among different mathematical ideas and the program’s ease of use makes it easier to concentrate on the concepts v. the need to spend time drawing graphs
- procedural fluency – there are GeoGebra materials available on their website whose purpose is simple procedural practice
- strategic competence – the simple user interface allows for easy exploration of different approaches to solving problems
- adaptive reasoning – the various tools and clear graphics on GeoGebra make it easier to identify and reflect on possible explanations while the connected algebraic representation allows for users to justify their conclusions
- productive disposition – when combined with materials on the GeoGebra site, the tool can provide many opportunities to tie mathematical concepts into the real world; for example, I did an exercise with GeoGebra in one class where I tried to figure out the equation of the parabola the Gateway Arch in St. Louis represents by fitting a curve to its picture
3. How is the mathematics represented?
GeoGebra uses multiple representations throughout its program. The main interface consists of a graphical representation with an algebraic function in the text box to the left. Spreadsheets of values are also available for use. Once drawn, many of the graphics are able to be manipulated with the functions dynamically updating as it happens and users can also utilize slider bars and other manipulative items to make connections and provide instant feedback.
4. What role does technology play?
The greatest advantage that technology gives to GeoGebra is the automation of many drawing and solving tasks. For example, the process of transcribing a circle around a triangle in GeoGebra is as easy as clicking on the three vertexes of the triangle. Likewise, as soon as that’s done, the algebraic function of the circle is immediately given. These two processes, by hand, would take vastly more time than the 15 seconds it does in the program. This example also illustrates how well the program does at representing knowledge. The ability to manipulate a figure and see the corresponding changes immediately can allow for much more exploration of different geometric concepts and exploration of many more examples in the same amount of time.
One potential disadvantage is that it can be argued that GeoGebra does too much for the user. For example, the user would never need the ability to algebraically solve for the roots of a polynomial as there is a button specifically for that purpose (among numerous others).
Affordances of Technology for Supporting Learning
- Computing & Automating – graphing is extremely simple and can be done in multiple ways (point and click or input equations, for example); many other concepts can be computed faster such as intercepts and roots
- Representing Ideas & Thinking – users can easily represent ideas, from a word problem for example, by graphing various shapes or using the programs many other applications
- Accessing Information – the GeoGebra site has much information on applications for the program, as well as numerous submitted activities that take advantage of it
- Communicating & Collaborating – users can share ideas for problems, applications, and activities on the GeoGebra site for others to utilize
- Capturing & Creating – users can create their own GeoGebra applications, problems, and projects
5. How does the technology fit or interact with the social context of learning?
While the program can only be manipulated by one user at a time, the many uses of GeoGebra lend itself to small group, collaborative discussions. The ability to easily draw and manipulate the various graphs should allow much more time for exploration and explanation and can make it a useful tool for a teacher to utilize during whole class discussions as well.
6. Additional Comments
GeoGebra has the potential to be a game changer when it comes to intertwining the strands of algebra and geometry. As opposed to the endless number of time-consuming, hand-written drawings, GeoGebra should allow users to focus much more on making connections on the conceptual side of the subject.