Stephen ARNOLD
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Live Mathematics on the Web

Best Integrated Geometry, Algebra and Graphing (free and online)

  
  

Over twenty years ago, I served as Project Officer for a national teacher professional development project for the Australian Association of Mathematics Teachers, working with representatives of each of the state and territory Mathematics Teacher Associations to explore and develop resources for the new phenomenon of the World Wide Web. Of the outcomes of the AAMT EdNA DAME project (Yes, Will Moroney, I am looking at you for that name!) [Education Network Australia Delivery Alternatives for Mathematics Education], two in particular retain a special fondness for me.

  • The AAMT Discussion List for Mathematics Teachers (discuss@aamt.edu.au) which, all these years later, remains a vibrant and important forum for teachers from across the country and beyond to share and learn, and

  • A project of my own, called Live Mathematics on the Web, in which I sought out and explored the possibilities for interactive browser-based mathematics learning opportunities which were beginning to appear, especially in the areas of algebra and graphing, but also for geometry and number. At the time, these tended to be based on browser plug-ins and Java applications, and a smattering of JavaScript. Only the last survives as viable in today's web experience, along with HTML5, which brings amazing opportunities for free, dynamic learning experiences for students on any platform, computer, phone or tablet.

Here I present some of the best free browser-based classroom-ready mathematics teaching and learning tools. Feel free to use them and share them with your students.

      
         
      
         

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  • GXWeb is a free browser-based symbolic geometry tool that combines constraint-based dynamic geometry with computer algebra. From Saltire Software who offer the amazing Geometry Expressions and Mathematical Illustrations, this surprisingly powerful tool for classroom learning offers students a pathway to learning and understanding algebra through visual and dynamic geometric representations.

    Imagine dynamic geometry built on a foundation of computer algebra. So side lengths, angles, etc can be defined algebraically as well as numerically, and results can be derived in general form.

    Then add constraint-based construction to make it even easier to use. Do you want a right-angled triangle? No problem - just define a general three sided figure and add the right angle later.

    Derive Pythagoras' Theorem? Easy!

    Have students explore algebraic relationships through convincing visual means using geometric constructions.

    Try GXWeb out right here by tapping on the button or the figure above - don't forget to explore the help options to get started!

    Check out my YouTube collection of great GXWeb examples!

      
      

    Did you know?

    The algebraic objects that you create in GXWeb can be copied as text or code by tapping on them, and this can then be pasted into GeoGebra (using the Input bar) or, if you are using the Desktop version, into Desmos, TI-Nspire, Mathematica...

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  • GeoGebra is an exciting blend of Algebra and Geometry using an integrated graphing and geometry environment. It is freely available for all platforms and has a wealth of supporting sites. Explore the sample files below.

      
      

    Did you know?

    The GeoGebra documents that you create can be embedded in a web page.

    AND your students can interact with those applets from the web page, allowing you to create dynamic worksheets, which might be used for feedback or assessment!

      
      

    The first few sample activities which follow demonstrate this interesting feature that supports interaction between JavaScript on the web page with GeoGebra web apps, potentially serving as a powerful tool for online assessment.

      
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    For some more detailed ideas about how to use such wonderful tools, please feel free to read:

      
      
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    Desmos: Graph functions, plot data, evaluate equations, explore transformations, and much more – for free!

     

    While Desmos does not offer the integrated algebra and geometry of GXWeb or GeoGebra, it does offer a functional geometry app.

     
        
      

    Did you know?

    Of perhaps more interest is the option for students to collaborate, viewing and sharing each others' screens while working on Desmos.

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  • Or other JavaScript/HTML5 mathematics goodies..

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