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Tag: geogebra

Geogebra simulations in math

I love using Geogebra! Take a look at the diagram below (use the slider to change the value of n) and then think about how difficult this one simple interactive diagram would be to recreate without the technology.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

For more Geogebra resources, either check out the official Geogebra website (http://www.geogebra.org/) or the awesome resources shared below to get a feel for what you can do with Geogebra.

http://www.ualberta.ca/~urban/Projects/Math/Tech%20in%20Math.htm by @stefras

http://mrhonner.com/2011/06/19/pendulum-animation/ by @MrHonner

http://www.geogebra.org/en/upload/index.php?&direction=0&order=&directory=english/Daniel_A_Kaufmann by @dak721

 

Don’t have Geogebra? Try it out here

I’ve embedded a web version of Geogebra (a free, cross-platform, geometry and algebra tool) below. It will take a little bit to load, and will only work in a web browser, but it is an easy way to test out Geogebra without installing it.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Geogebra Open Presentation writing

Google Docs has a really cool feature I’d like to try out.  The idea is that I have a presentation on Geogebra that I would like to host.  There was a lot of interest before, and unfortunately I had to cancel, but I’d like to try again.  I’m not a Geogebra expert however, just an enthusiastic intermediate level user.  I’d like to create a presentation for beginners to use, but don’t want to miss anything important.

That’s where you come in, if you are interested.  The idea is, I’ve created a presentation, which you can access at:

http://docs.google.com/Presentation?id=dhkzc87c_7g8r8cz83

You can contact me through an online form at https://davidwees.com/contact and ask for permission to edit the presentation, and I’ll send you an invitation.  You’ll have to start by creating an account at http://docs.google.com, but that’s pretty easy to do.  Once you have the invitation, you can edit/add to/delete from the presentation.  I’ve started with a basic structure, but there’s obviously lots of room for improvement.

Here is what we have so far:

Online Geogebra training

Hi folks,

I’m planning on doing an online training session, we’ll see if I get anyone to sign up!  The first 20 people to post a comment here will be registered in this free training session in Geogebra.  This limit of 20 people is only because http://dimdim.com restricts the free online sessions to 20 people.  I’m not, by any means, an expert in the program, but I am happy to share what I have learned in 2 years of using the program.

  1. Post a comment to this post indicating what time works best for you.  You need to fill in your email field, which is hidden from everyone except me, the owner of this blog.  I’ll use your email address to send you the Dimdim meeting invitation, so it is important that you include it.
  2. Go to http://dimdim.com and sign up for an account.  You will of course need to use the same email address as step 1.  You should try it out first to check to make sure there are no problems ahead of time.  I’ll of course be testing this myself.   Update: We  might use Mikogo instead, it seems easier to use.
  3. Oh and I suppose I should mention that you really want Geogebra installed.  You can get it from http://geogebra.org and happily, it is free.
  4. I’ll also be putting up some resources on the blog, linked to this post, once I get a chance to organize them.  You should make sure to come back here and download those resources.

Of course this training session is dependent on my internet connection remaining up.  I guess if there are problems, we can always reschedule.  

 

Update:

Hello all,

A little over three years ago I decided I wanted to experiment with online learning, and I decided I would start this experiment with a training session for Geogebra, which is still software I love to use in my teaching. A week after I made announcements everywhere about the training session, my Dad died, and I never ran the session. Three years later, I’m still receiving registration requests for the program so I know there is still interest. At one point, all of you registered for this training opportunity.

I’m still personally interested in what this would look like from my perspective, but I already know of a terrific resource for learning Geogebra for beginners so I see little point in duplicating effort. Linda ran an excellent (and free) course last year, and I recommend using it as a resource for getting started with Geogebra. You can access it here: http://moodlemeets.learnnowbc.ca/course/view.php?id=3

It’s free, but you have to create a login at http://learnnowbc.ca in order to access the course. The course is archived, but there are lots of discussions archived in the forums, and you may find many of your questions answered there.

If you are still stuck, you can take a further plunge and if you have not already done so, sign up for Twitter and then search for #mathchat in the search box on Twitter. Many of the mathematics educators that post with the #mathchat hashtag use Geogebra regularly and may be able to answer your questions. Hopefully you’ve also already found http://geogebratube.com/ which already contains 10,000 Geogebra resources that are free to use and modify as you see fit.

Thank you,

David Wees

 

How can Geogebra be used to help students understand and visualize mathematics problems?

In your inquiry e-folio, reflect upon knowledge representation and information visualization based on your post above and the discussion it generated with your peers. Ensure that you refer to the software you chose to explore.

In my ETEC 533 class, we are in the middle of a really cool unit, and our task of this unit was to share a digital learning tool or resource with everyone else in the class.  I chose to share an open source geometry program I have used a lot, Geogebra.  Unfortunately my post has yet to generate any discussion, possibly because of the large number of other geometry packages available, and the therefore limited interest in this particular one.

This handy geometry package is free, cross platform, and very easy to use. It allows for the creation of geometric objects, which have various properties (including position, color, size, etc…) and which can be either a dependent or an independent object.  Independent objects can have associated dependent objects, and when you modify the independent object, the dependent geometric object is modified as well.

For example, suppose we created two points in the plane as independent objects, and then created an associated line through the two points as a dependent object.  When we move the position of either of the two points the line will change to match this movement.  This allows students to end up with a deeper understanding of the relationship between geometric objects.

This program is very flexible, and can be used to show simple geometric relationships (like for instance the geometric fact that the sum of the interior angles of a triangle is 180 degrees) to very complex geometric properties (the limit of the sum of rectangles which approximate the area underneath a curve is equal to the exact area under the curve).  Geogebra is then therefore useful in a wide variety of different contexts and branches of mathematics.

When students are using dynamic geometry software, such as Geogebra, they invariably end up with a deeper understanding of the material (Pütz 2001).  This is probably because they are given a strong visual representation of the object, that comes associated with a more tactile impression that comes with using the mouse to move and adjust the object.  Obviously there is a "wow" factor involved in the use of any new program, where the students are engaged with an activity simply because it is new, but it has been my experience that the use of these geometry packages ends up leading to a long lasting understanding of geometry.

Another advantage of Geogebra is that it allows the user to export the current file into a web ready format (a java applet) which can then be uploaded to a web server.  This provides the ability for students and teachers to discuss and analyze each other’s work, and allows for the creation of a social discussion about the work. 

Geogebra also allows a "construction protocol navigation bar" to be added to the file, which means that users can step the geometric construction process, one piece at a time.  This is a tremendous advantage of Geogebra as it allows a user observing someone else’s work to have some insight into the process they went through to create it. 

Geogebra allows students to actively and through the sharing of the work online, socially construct an understanding of geometry.  This program allows for simple visualizations of possibly complex geometric concepts, and helps enhance a student’s understanding of those concepts.

References

Pütz, C. (2001). Teaching Descriptive Geometry: Principles and Effective Methods Demonstrated by the Example of Monge Projection, XV Conference on Graphics, Sao Paulo Brazil, November 5-9, 2001.

Hannafin, Robert D. & Scott, Barry N. (2001). Teaching and Learning with Dynamic Geometry Programs in Student-Centered Learning Environments. Computers in the Schools, 17 (1), 121-141. Retrieved March 18, 2009, from http://www.informaworld.com/10.1300/J025v17n01_10

Ways to use Geogebra in a mathematics classroom

There are a lot of good open source programs out there, but not many of them have direct application to a mathematics classroom the way Geogebra does.  Geogebra is a software package for creating and manipulating geometric objects.  It also allows for graphing of funcitons and manipulating the functions in all sorts of interesting ways.  It runs on the Java framework, which means if you have Java installed on your computer, you can run Geogebra, which makes it any Java enabled operating system.  This means the very same program will run on Windows, Mac, Linux or Solaris, although the installer is different for each operating system.

If you are planning on using the program with your students, it is nice to know that they can install the program for free, and that it is very likely to work on their computer.  The only caveat is that you need to make sure the students have the right version of Java installed if they have any problems as this can sometimes be an issue.

Geogebra has all of the standard Geometry software functions.  You can add lines, circles, ellipses and all other sorts of geometric functions to the document.  You can also make one object a dependent of another object which means that changes in the original object propagate to its dependent objects.  So in other words, if a you draw a line segment which depends on the location of point A and point B, changing either point A or point B modifies the line segment.

There are 2 cool things I like about Geogebra.  The first is that you can export your working file as a dynamic worksheet on a web page, which means you can easily make what you are working on web ready.  The second feature which I use all of the time is the ability to export my current file as a picture in PNG (and a few others) format.  This allows me to use Geogebra to create graphs for inclusion in my online posts, something my students and I use Geogebra for all the time.

Geogebra also has an input textfield, which means that every command you can use the interface to enter, you can also type in.  Some commands are done much more easily through the input textfield, things like entering y = x^2 + 3x which uses the nature notation to graph a function.  Entering Function[x^2, 0, 2] graphs the function over the domain from 0 to 2 for x.  Very handy.

Using Geogebra with your classroom is an affordable way to bring high quality geometry software to your classroom at an extremely affordable price (its free!!).  I’ve only scratched the surface of what Geogebra is capable of doing, I suggest you try it out yourself.  Maybe when I have time I’ll create some tutorials on using it.