Category Archives: GeoGebra
At Twitter Math Camp 2012, I gave a session about getting started with GeoGebra. Here are the resources from my session, including eight tutorials and links to pages with lots of other tutorials
TABLE OF CONTENTS
- Why Should you use GeoGebra?
- How do you use GeoGebra in your classroom?
- Why use GeoGebra instead of Geometer’s Sketchpad or another math visualization program?
- Where do I get GeoGebra?
- How can I learn how to use the program? <– TUTORIALS!
- How can I find ridiculously cool applets that are way above my skill level?
Why should you use GeoGebra?
The idea of learning a new technology and incorporating it into your teaching can sometimes very overwhelming. And you should never just use technology for technology’s sake, as some administrators seem to espouse. You have to have a real reason to use it. GeoGebra can improve math instruction in a million ways. The dynamic nature of the program gives you the ability to explain and explore concepts that simple pen and paper (or marker and whiteboard) can’t! I find myself using the program at least weekly, sometimes more.
How do you use GeoGebra in your classroom?
AS A DYNAMIC DEMONSTRATOR: To help students understand a tricky concept during direct instruction.
How can you get students to understand that the perpendicular bisectors of a triangle ALWAYS meet at one point? Construct a triangle with perpendicular bisectors in GeoGebra and move the vertices of the triangle around and let them observe that those lines always meet up at a point. (PS, sorry I didn’t upload these – this post took forever as it is and there are lots of examples of applets in the tutorials section below)
DYNAMIC WORKSHEET: To give students a chance to explore a concept at their own pace in small groups or individually.
One activity I do every year is let students “discover” derivative rules using a derivative tracer. They enter a function into a GeoGebra applet, which then traces out its derivative. With that, students try to guess what the equation of the derivative is. Once they collect a bunch of examples or correct derivative equations, they look for patterns to come up with a rule.
STUDENT EXPLORATIONS: To give students a powerful tool with which to complete their own investigations.
I have had students convert pictures to integrals, fit functions to data of really crazy things that they wanted to study, and calculate the volume of real world solids of revolution. Getting them comfortable with program with more guided activities earlier in the year gives them the skills to be able to do amazing things with it on their own later in the year.
CREATING WORKSHEETS/ASSESSMENTS: A tool for you to make your worksheets and assessments very professional looking.
You can copy and paste anything from GeoGebra into a Word Document, giving you the ability to put very good looking graphs and diagrams in your teaching materials.
Why use GeoGebra instead of Geometer’s Sketchpad or another math visualization program?
Well, first, it’s free. I mean, that should really be enough, but I’ll keep going. Because it’s free, you can install it on as many computers as you need (so students can use the program at home and at school). And you don’t actually need to install it – you can run GeoGebra right from a web browser, or host web applets that just require a student to have a browser with Java installed (i.e. 99% of people who own a computer and keep it even remotely up to date). Basically, no matter how annoying the tech department at your school is, GeoGebra is pretty easy to get going.
Additionally, because the program is free, it is developing quickly, and resources are easy to share and easy to come by. The community around GeoGebra is strong and constantly growing – check out GeoGebraTube, a ridiculously large repository of GeoGebra applets.
Where do I get GeoGebra?
Download it here. Click on “Webstart” to download the installer. You can also start a web applet here (in “Applet Start”) and download an offline installer for students without internet access.
How can I learn how to use the program?
Luckily, the program is incredibly intuitive. The best way to learn is to open up the program and experiment! But some people hate that and need a bit more of a push to get going (I had to teach my mom how to text with her new phone, so I think she is one of those people). That’s totally okay – my recommendation is to work through some tutorials that can show you how powerful you can be with the program. I wrote 8 tutorials that progress from GeoGebra basics to some cool intermediate to advanced things that will go a long way in creating your own applets.
GeoGebra Tutorials (written by me):
7. Uploading to GeoGebra Tube
(uploading your creations to the web to make sharable web applets)
(tutorial, finished product) <– With GeoGebra 4.0, this is even easier! There is a menu item in File–>Export–>Dynamic Worksheet as Webpage (.html), and then you can directly upload to GeoGebra Tube.
Other tutorials I have found:
- Math and Multimedia Tutorials – Over 50 GeoGebra Tutorials at all levels from the blog Mathematics and Multimedia.
- Lance Bledsoe’s Tutorials – A similar collection to mine above of basic tutorials to get you started with the program.
How can I find ridiculously cool applets that are way above my skill level?
If you aren’t all that interesting in making your own, you can still find tons and tons of great applets. Like this applet that helps derive the equation for the area of a circle…
Head to GeoGebra Tube, an official searchable database of GeoGebra applets for just about any topic imaginable. Feel free to be inspired by the amazing work that some people do with the program!!
Best of luck using this program to help make your math teaching more dynamic!
I wrote about this project back on Sam’s blog this summer when Sam gave me reign of his kingdom for a month or so, but I wanted to share the student work that I got this year from it, because it was much better than last year, and some of the work is actually really beautiful/cool/interesting (Math Art, MArTH anyone?).
The basic premise of the project is to RECREATE A PICTURE USING INTEGRALS by doing the following:
- Upload a picture into GeoGebra.
- Place points around all the outlines making sure to hit critical points
- Fit functions to the outlines.
- Use integrals to shade in the areas between the outlines.
I initially waffled about whether this was a worthwhile problem or just an exercise in integrals, but having taught AP Calculus this year, I realize how these problems of just finding the area of a weird shape are interesting and important for deep understanding of the connection between a Riemann sum and how the integral actually calculates area. So basically, if you think that this is a worthwhile problem…
Find the Area of R and S given that f(x) is blah blah and g(x) is blah blah blah squared.
…then this project is just a glorified, more interesting, more complex version of that problem. If you don’t think that problem is worthwhile, well, then you probably wont like this either. Regardless, it was a great thing to do to hammer in ideas about finding the area between curves, and a great learning mode while AP’s were occurring because attendance did not really matter all that much. It took most students 3 and a half 45-minute class periods (so about 2.5 hours), though I think that more efficient students not freaking out about standardized tests, and consistently present in the classroom, might be able to do it a little quicker.
SOME OF MY FAVORITES:
ALL OF THE STUDENT WORK:
(the good, the bad, the ugly!)