icme9

Interactive mathematics online for school and home

An updated online version of the original paper submitted to the International Conference ICME-9 in Tokyo on July 31st to August 6th 2000. The section on dynamic geometry originally formed the basis of a presentation at the conference "Good Practice in the Use of ICT in Schools" at the RSA, London on March 6th 2000.

Abstract
1. A vision for future online materials
2. Current examplars:
A Techologies: Dynamic Geometry, Dynamic Algebra, Spreadsheets, VRML, Logo, others;
B Websites
3. Issues affecting the success of Online education
4. Conclusion



2.2 Dynamic algebra
Dynamic algebra software has been available for many years. Mathematica from Wolfram Research has recently announced a Java package to extend its capabilities and thus make it more Web-friendly. Mathcad and Derive are other examples. Such software can perform many algebraic tasks, such as simplifying, factorising, solving, differentiating, integrating and graphing. As with dynamic geometry, its use in schools - in the UK at least - has been limited, partly due to technological barriers and partly because in many ways this software "does" mathematics for you and leaves the student as a passive observer. However, new possibilities are developing with software such as LiveMath (previously known as MathView) and the associated plug-in for Netscape and Internet Explorer. Besides providing the user with the means to investigate algebra and graphing interactively, LiveMath also allows the educator/programmer to control exactly the degree of interactivity that the user is permitted. LiveMath is a standalone program - see Figure 6 - wherein various components (the 36 in this simple example) can be altered and lines following will change dynamically.





Figure 6

Figure 6: LiveMath
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LiveMath can also be embedded in a web page with the same interactivity.






Figure 7: LiveMath embedded in a browser.
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Graphs can be investigated in the same way (Figure 8). In this figure the quadratic equation, x²+5x+6=0, can be edited and the graph view itself can be changed by zooming in or out or moving the axes. As occurred earlier with dynamic geometry, the display in Figure 8 is split in two halves. The right-hand side contains the programmed mathematics, but the left contains text available to anyone to edit to suit the expected audience. Further examples of dynamic algebra using LiveMath can be found at MathsNet's algebra site and at Angliacampus. As with dynamic geometry, the student or teacher who wishes to develop this area of mathematics further can purchase and download the software and create their own dynamic geometry.




Instructions
Find the two solutions to this equation by using the graph. Look for where the graph crosses the x-axis.
Then change the equation and solve it again.
Can you find an equation that cannot be solved?
Can you find an equation which has only one solution?

Figure 8 Graphing with LiveMath
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