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Welcome to my blog! My name is Evanthia Basias, and I have been teaching secondary school mathematics at Hunter College High School, grades 7 through 12 in Manhattan, NY since 1979. I am amazed with technology’s influence on mathematics education since I began teaching and how it can be used to help visualize and explore mathematics.
Even though I have presented workshops on how to use the TI graphing calculator to enhance calculus instruction, I feel technology is advancing too quickly and more online calculators and graphing software is now available and somewhat easier to use in the classroom. I enjoy learning and challenging myself with new technology . For this reason, I attended the 2016 Anja S. Greer Conference on Mathematics and Technology from June 25 to July 1st for secondary mathematics teachers at Exeters Academy. The primary emphasis of the conference is mathematics focusing on the impact and applications of technology in the classroom and the role of technology in mathematics and science curricula. I participated in two classes on how to use GeoGebra, which is a free, easy software to illustrate and enhance algebra, precalculus, trigonometry and calculus instruction. I learned some key features of GeoGebra while creating class exercises, labs and demonstrations, illustrations and nice diagrams for handouts or tests, and finding, modifying, collecting applets for the library. I was excited to learn about 3-D features of the program which are not available in Desmos and in graphing calculators. By the end, I developed and I hope to continue to discover alternate and powerful ways to make it easier for students to visualize math.
My goal in this blog is to bring some of these ideas back to you. This blog is not only limited to GeoGebra. Any other technology is welcome(Desmos, TI-Graphing Calculators, Geometer Sketchpad, e.t.c.), used effectively in mathematics instruction and I am looking forward to sharing ideas with all of you.
Marc Renault, supported by Shippensburg University made a complete library of applets for Calculus I that are suitable for in-class demonstrations and/or student exploration. He created these applets using GeoGebra software for creating dynamic visualizations of mathematical ideas.
My favorite applet I have used successfully in the classroom was the chain rule applet. It is a dynamic way to demonstrate the chain rule using an x-wheel, a u-wheel, and a y-wheel. You can change the speed of the x-wheel, and you can connect the wheels with belts and change their radii. This model is a great exploration of the chain rule and enhances an intuitive understanding of where the formula comes from. The best part is crossing the belts in the applet!
The Intuitive Notion of the Chain Rule
Marc Renault has a library of calculus applets created with Geogebra on his website:
GeoGebra Calculus Applets
Other Calculus Applets
This applet demonstrates the epsilon-delta definition of the limit. (In particular, we are exploring whether lim f(x)=L as x approaches c)
Epsilon Delta Definition of the Limit
GeoGebra is a user friendly website to use. This is what the page looks like when it opens.
GeoGebra was created by a student to earn his PhD. The agreement made with the professor was to make all GeoGebra creations available to the public for easy access. The first button allows to research GeoGebra programs according to topic. The second button allows to start the program, and the third button gives an option to download GeoGebra onto a desktop, notebook or mobile device.
For the Anja Greer conference I have attended, we were asked to download GeoGebra onto our computers beforehand. The online version of GeoGebra is not the same as the downloaded version. I found participants preferred to work with the online version of GeoGebra. The two programs are alike but do not work exactly the same for everything.
We also created an account with GeoGebra so that we can save materials we found on the site. It was very easy to search for materials on line. Click the “materials” button, and then the search key (magnifying glass). Type in any topic in the search bar, and all of the GeoGebra programs created for that topic will appear. As in any search, it is important to check out the programs of interest.
The moderators of the GeoGebra courses mentioned that the best way to learn how to create GeoGebra programs was to find the ones we like, and discover how the program was created by looking at the commands used.
We used these two guides to get started with GeoGebra: