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GeoGebra: An Interactive Dynamic Mathematics Tool

Page history last edited by Geoff Roulet 10 years, 6 months ago


GeoGebra History and Community


  • Initially developed by Markus Hohenwarter, Johannes Kepler University, Linz, Austria
  • Today supported by a large international team


  • Open-source software - free to download
  • Written in Java - Runs on multiple platforms: Windows and Apple
  • New version being written in HTML5 - Will run as a web application on tablets




GeoGebra: Interactive, Linked and Dynamic Representations


  • GeoGebra provides algebra, graphing, geometry, spreadsheet, and statistics tools
  • Representations or models generated with these tools are dynamically linked - Making a change in one representation is reflected in changes in the others.
  • In the example below for the topic of parabolas and quadratic equations the shape and location of the curve (parabola) can be changed by dragging the Focus and/or Directrix (drag point D). As the parabola changes the corresponding function for the curve, the Conic BallPath in the Algebra window, is updated. At the same time, the coordinates of the ball on the curve change and are recorded in the Spreadsheet.
  • Clicking on the image below will bring up a new tab holding this image as an active GeoGebra applet.
  • Drag the Focus and Directrix to construct a parabola that passes through the five red points.
  • You can always return to the original starting point by clicking on the reset icon  in the upper right corner of the Graphics window.




This example is from an article that appeared in the June 2013 issue of the Ontario Mathematics Gazette. The full article is available by clicking the following link.


Roulet, G., & Lazarus, J. (2013). Linking representations using GeoGebra. Ontario Mathematics Gazette, 51(4), 28-33.



Examples of GeoGebra Constructions for the Ontario Curriculum


  • It is quite easy for you and your students to begin work with GeoGebra as application of most of the core tools is relatively straight forward.
  • A good way to begin is by following a set of well described steps for a particular construction.
  • We suggest you take this approach by selecting and completing one or more of the three investigations given in the PDF documents linked below. The order of the investigations parallels the complexity of the required GeoGebra constructions.  


  Investigation 1: Circumcircle of a Triangle   Investigation 2: Derivative and Tangent of a Function   Investigation 3: Transformations of Exponential Functions  



GeoGebra Quick Tips



Views and Perspectives

    • Three main views: graphics view (2), algebra view, and spreadsheet view. CAS view also available.
    • All objects dynamically linked across views.
    • Perspectives: shortcut to most-used view setups (right-hand arrow). 

Move Tool and Toolbar

    • Move tool: Used to select and drag objects in graphics view. Use the move tool at any time by clicking Esc.
    • Toolbar: Divided into toolboxes, each containing one or more tools. Open a toolbox by clicking the arrow in the bottom right.


Zoom and Shift Key

    • Scroll up or down to zoom in or out.
    • Hold Shift and click and drag to move graphics view. Hold Shift and click and drag on an axis to rescale, the x:y ratio will the displayed for you. 

Renaming and Object Properties

    • Highlight an object and begin typing to rename 
    • Highlight an object and either right-click or type Ctrl+E to open the Object Properties window, where colour, style, label, and much more can be edited. 


    • Open Edit Graphics View to Clipboard to copy a picture of graphics view, click and drag using the move tool to first select a specific area of graphics view to copy. 
    • Open File Export to save as a webpage, picture, or animated GIF. 

Input Bar

    • Used to create and redefine mathematical objects such as points, functions, etc. 
    • Any tool can also be used through an input bar command.




Sharing GeoGebra Learning Objects


GeoGebra is written in Java and future versions will use HTML5. This means that GeoGebra integrates well with the web. The File > Export tools of GeoGebra allow you to capture the code and embed it in a webpage. Using a webpage editor you can add instructions and questions for students. Your page with active GeoGebra applet may then be shared with your students by uploading it to a course website. The basketball activity above is an example of an Exported applet. Clicking on the link below will take you to a more complete dynamic worksheet holding a related video and student instructions.


Score a Basket


Detailed instructions and an instructional video providing the steps for the Export process can be found by going to the Exporting a Dynamic Worksheet page in this wiki.


If you have a course website the platform that supports the site; an LMS such as D2L, Moodle, or Blackboard or a wiki service such as PBworks or Wikispaces, may permit the GeoGebra code to be embedded directly into your course pages. The File > Export tools of GeoGebra support the copying of code for embedding in other web applications.


For detailed instructions and an instructional video showing how to copy GeoGebra code and embed this in a PBworks wiki page go to the embed a GeoGebra applet page. For parallel instruction for embedding in a Wikispaces page go to Embed a GeoGebra applet in a wiki page. If your LMS administrator has set the required permissions similar steps will work in these environments.



GeoGebraTube: A Growing Source of GeoGebra Learning Objects


Educators across the globe are using GeoGebra to generate learning objects and sharing these via the GeoGebraTube website. There you will find thousands of GeoGebra applets that can be used to support students' developing understanding in not only mathematics. Along with the applet, contributors also post instructions and related student worksheets. To help with searching, contributors also attach tags to their work indicating the related topic(s) and type of resource.


Many of the GeoGebraTube materials can be used in the Ontario mathematics curriculum. The link below will take you to a Google Doc created by Meghan Donnelly in which you will find links to selected GeoGebraTube materials and a listing of Ontario mathematics curriculum related to these.

Introduction to GeoGebraTube


This Google Doc is an open document and you are encouraged to add additional links to GeoGebraTube materials and the Ontario curriculum.


Note: GeoGebraTube materials are contributed in many different languages. If a search in English materials does not give you what you are looking for try other languages. Since the structure of GeoGebra menus is fixed you should still be able to use the applet and in many cases it is not difficult to translate the instructions and student worksheet.


GeoGebraTube materials can be downloaded to run on your and your students' computers or they may be embedded in pages on your course website. When you do use a GeoGebraTube item please credit the source and author.


You are encouraged to contribute any GeoGebra learning objects you create. To do this follow the File > Export > Dynamic Worksheet as Webpage (html) … steps described above and then select . The GeoGebraTube site will then guide you through the steps for submitting your resource.



Curve Matching: Samples of Student Work


In this activity students in a Grade 11 Functions, University course (MCR3U) used sliders and regression analysis to construct algebraic functions with curves that fit pictures embedded in the GeoGebra graphics window. Using the File > Export > Dynamic Worksheet as Webpage (html) steps outlined above, students can display their work via the web as has been done for the samples linked below. Clicking on each image below will bring up a new tab holding the active GeoGebra applet created by the student.







Student Collaboration


Student sharing of GeoGebra work can be expanded to include online collaborative explorations and problem solving. In this process students embed their GeoGebra work and explanations in wiki pages. Collaborating students can pick up their teammates' applets continue working with them and then re-post their additional contributions to the exploration. Students' providing of explanations can be further enhanced by using a screen recording and sharing tool such as Jing.


A journal article by Jill Lazarus and Geoff Roulet describing such a collaboration process in a Grade 10, Academic Principles of Mathematics course (MPM2D) appeared in the June 2013 issue of the Ontario Mathematics Gazette. This article can be accessed by clicking on the link below.


Lazarus, J., & Roulet, G. (2013). Communication in a blended math-talk community: Extending the boundaries of classroom collaboration. Ontario Mathematics Gazette, 51(4), 34-40.


An online demonstration of collaboration using a wiki, GeoGebra, and Jing, along with the technical details can be found at the Collabmath wiki.


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