Stephen ARNOLD
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Live Mathematics and STEM on the Web

Best Integrated Geometry, Algebra and Graphing and STEM (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 teaching and learning tools for mathematics and STEM. Feel free to use them and share them with your students.

  
     
  
     

GXWeb

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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...

  
  

GeoGebra

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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.

  

  

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

  

  
  

TI CC2650 SensorTag Monitor and GeoGebra

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If you would like to use GeoGebra as a tool for STEM, then what about pairing it with the amazing data collection available using the TI CC2650 SensorTag?

The TI SensorTag is a small, inexpensive device which packs a powerful punch - it is a BlueTooth Low Energy (BLE) tool with sensors for temperature, humidity, barometric pressure, accelerometer, magnetometer, gyroscope and more. Used with iPad or Chrome browser on Mac, Android or ChromeBook, students can easily collect, view and analyse a wealth of real world data for mathematics and science, from the middle years through to seniors. From building their own weather station, to exploring the mathematics and physiology of exercise and dance the opportunities for rich mathematical exploration are truly exciting. All in a tiny device that fits in your hand and costs around $AUD40!

We can now use GeoGebra to enable data collection and exploration with the SensorTag within the Chrome browser on Mac, Android and ChromeBooks!

  

  
  
  

TI LaunchPad Terminal and GeoGebra

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Another great STEM application can grow from students learning to code for MicroController Unit (MCU) boards, like the TI LaunchPad series or Arduino boards.

TI LaunchPads are microcontroller development kits from Texas Instruments. They come in a variety of flavors to address various project needs. All LaunchPad kits include everything needed to begin developing applications in minutes, priced from $USD9.99 to $USD19.99. That's right - Blink LEDs and spin motors, all for less than $USD20. These units can be the basis for everything from simple coding to connecting a variety of sensors and other peripherals. They are easily programmed via USB from Mac or PC, and can be linked to BLE (Bluetooth Low Energy) modules, and even wifi to send and receive data both locally and remotely.

We can now use Web Bluetooth to enable free and effective communication with these programmed boards, using the Chrome browser on Mac, Android and ChromeBooks! Coupled with the versatile mathematical capabilities and programmability of GeoGebra, students can control these boards remotely, using them to collect and analyse data, even to control BLE robots! Step-by-step tutorials lead from beginner to robotics developer!

  
  

TI LaunchPad and GeoGebra Piano Keyboard

You might also like to try a combination of Web Bluetooth, GeoGebra and music using Michael Morris-Pearce's excellent web piano keyboard! Explore the mathematics and STEM basis for music with this free online tool!

These LaunchPad BLE documents should work well using the Google Chrome browser on a recent Mac (mid-2012+), Android device or ChromeBook. They will work on iPad with the WebBLE app, but this is an experimental build and may not always work seamlessly. For example, I find that I need to CONNECT, then DISCONNECT, and then CONNECT again to establish a reliable connection using WebBLE. However, after this, it generally works well.

I got mine running on my Mac without too much trouble: you do need to go in and switch on Chrome’s experimental flag to support web Bluetooth but this was pretty straightforward.

You can enable it turning on the enable-experimental-web-platform-features flag: In the Chrome browser, type in the web address chrome://flags/. This action results in a list of experimental browser features available to you. You want the Web Bluetooth one.

If you have any questions or would like to share your experience with this utility, please drop me an email!

  
  

Desmos

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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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...And some other JavaScript/HTML5 mathematics goodies..

  


  

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