2.3 Spreadsheets
Spreadsheets are mentioned explicitly in the new UK National Curriculum for Mathematics (within "Number and Algebra"). In many schools with networked computers, this is will probably imply use of Microsoft Excel. Though there is no doubting the power of Excel to perform varied mathematical tasks and to enable data to be analysed efficiently, the program remains a technology barrier in schools. Even at the BETT exhibition in London this year (a showcase for state of the art use of ICT in Education), the presenters on the Microsoft stand were taking their audience slowly step by step through each detail in the precise process of setting up a file. You cannot simply hand a student over to a spreadsheet and tell them to get on with it. The Internet should be offering a way forward, but so far there is little sign of an educational site providing an online spreadsheet. This may be due to the fact that spreadsheets are the most applicable of all mathematics software to the "real" world and therefore have great financial worth. Spreadsheets are too valuable to give away. One partial exception to this is Formula One.

2.3.1 Formula One
Formula One is a Java program, produced by TideStone Technologies , primarily for the American business market. As with dynamic geometry and algebra, the educator/programmer can create a spreadsheet embedded in a web page with interactivity limited to whatever they require. Formula One is expensive and not as yet clearly projected towards education. See Figure 9 (also on the web ) for an example.

Multiplication

2.4 VRML
VRML, or virtual reality markup language, is the means by which 3 dimensional images can be displayed and manipulated with a browser. Usually this manipulation will include the ability to zoom in and out, to move the object from side to side and to rotate the object. All movements will occur on screen in a believably 3 dimensional way. There are many "flavours" of VRML programming available currently on the Internet, most of which require a plug-in to be downloaded by the user and installed on their computer. One version, shown in Figure 10, that does not require a plugin, is called JGV . Another version, from Internet Explorer is shown in Figure 11. The creation of a typical VRML file is not for the faint-hearted programmer, but the results often provide a stunningly intuitive method of appreciating the nature of solid geometric objects. In this respect VRML fits perfectly into this paper's view on ideal web pages. Far more elaborate polyhedra are catalogued at the Virtual Polyhedra website.

2.5 Logo
Microworlds, from LCSI is a interactive software package based on the concept of logo turtle graphics, but providing, with the aid of a browser plugin, interactive projects embedded in web pages. See Figure 12 (also on the Web ) for an example where the user can drag and drop the tangram pieces onto the silhouetted shape, display the solution and access more problems. For further development the school can buy the software and create their own interactive pages.

2.6 Applets
The above sections summarise good practice in specific areas of mathematics, produced by business enterprises working in education. Scattered around the World Wide Web are many isolated examples of excellent interactive mathematics. Most will use Java programming to create material embedded in webpages. (In fact almost all of the above uses Java too.) It is this scattered nature of the web that makes some excellent material practically impossible to use, since both at school and at home, the user needs a coherent interface; they need to find their resources gathered together within an organised whole. Often these applets are there as demonstrations of the medium or of an amateur enthusiast's skills rather than part of coherent curriculum content. The fluid nature of the Internet means that, whilst the quality may be outstanding, the material may well vanish from the Internet when interests or financial commitments change. To solve this problem, it may require commercial enterprises to invest money in collecting together such scattered resources. Here are a few selected highlights. If any are not found at the address given, then the above point is proven! The Manipula site contains some excellent Java applets. Figure 13 shows an example of a construction which enablers the use to dissect a quadrilateral into two parts of equal area. Figure 14, from Math Cove , shows a typical simple applet illustrating aspects of transformations and angles that are immediately appealing.

Other examples that show the variety available on the Web from using Java are: Buffon's needle , Central limit Theorem , Cubic polynomials , Integration and Vectors.

2.7 Flash & Shockwave
Flash technology, developed by Macromedia , particularly in version 4, (and Shockwave from Macromedia too) allows the educator/programmer to produce interactive mathematical activities that are quick to load and understood by both Netscape and Internet Explorer - and even Dreamcast and Playstation 2 games consoles too! This is a cutting-edge technology, heavily promoted in the e-commerce world. Developments in education should be expected soon. Figure 15 shows a basic Flash file. Clicking on the buttons will cause the elephant to undergo the requested transformation. Another early example illustrates tangrams . A primary school, Ambleside , in the UK has also developed material on numeracy using Flash.