Interactive mathematics online for school and home

A paper by Bryan Dye. This has been submitted to the International Conference ICME-9 in Tokyo on July 31st to August 6th 2000. The section on dynamic geometry forms 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, B Websites
3. Issues affecting the success of Online education
4. Conclusion

1. A vision for future online materials
Less than 15 years ago, using a computer in school meant tackling a whole range of technological issues: faulty machinery, excess cabling, missing disks, software of variable quality and suitability. And consequently, computer use in schools was left to the obsessive, optimistic, patient, "techie" member of staff to persevere with. A lot has changed since then.

My vision for fifteen years on would be one seamless Online medium for doing mathematics interactively. This medium would involve at its centre some future development or evolution of the browser, whereby many and varied types of mathematical activity, ranging from geometric and graphical to algebraic and statistical, are all handled by the same interface. No longer will the student have to learn first how to operate the technical aspects of many different pieces of software; instead they will be able to choose their own route through a mathematical environment, capable at any stage of doing mathematics immediately. This is not a revolution about technology at all but about accessibility of content. This environment will be a changing and developing medium produced globally by teams of educators and programmers to fit to agreed rules or principals of operation. The "Windows" operating system and the World Wide Web are two current examples.

1.1 School and/or home service
TV advertising campaigns in the UK are raising expectations. Major UK investment in Online education is coming from commercial publishers and from other conventional online media (BBC, ITV and Channel 4). More than merely a replacement for a conventional school textbook scheme, Online will encompass it and open up limitless potential for varied and differentiated tasks with a high degree of feedback.
What Online offers that the conventional classroom cannot is depth, interactivity and individual customizability - "MY learning". How this customizability is handled must depend on whether the student is accessing it from school, as a member of a class, or from home as an individual. This is a crucial difference based on the simple premise that at school the teacher is in charge whereas at home the student is.

1.1.1 A school service
Customizability at school must be at the control of the teacher. The teacher may be giving individual students tasks to complete or may be using a network of computers in much the same way as in the past. The cost of access to the Internet is only a minor issue now as schools are able to buy as a package full 24 hour a day access from ISPs and soon will be no issue at all. With current developments in computer network technology, decisions on which means of Online access to use should be based simply on educational need.
This paper assumes that the teacher will plan use of Online materials in exactly the same way as any other part of their teaching. There is no suggestion here that the teacher should hand over responsibility to some other person or organisation or computer; this paper is not about "integrated learning systems". The teacher should expect to have access to levels of customization beyond the students' control. They should be able to determine what materials are accessible, how progress is recorded and be able to read detailed logs of each individual student's achievements. In addition, the content provider will be giving them regular feedback and advice on what is available and how it could be used. The teacher should expect the student to have the means (through email or equivalent) to make requests of the teacher and inform the teacher of progress.

1.1.2 A home service
From home, the student logs on to their educational site and is presented with their own customized homepage. It is here that "MY learning" can become fully effective. They become engaged in an environment of their own choosing, on tasks tailored to their needs, which "remember" them from session to session. By means of a personal profile, students state their preferences for topic areas at the outset, and then are informed on their learning homepage when such materials are available. Considering the technology available now on the web, it should be relatively easy to maintain a comprehensive database. As an example, the websites Atomz and Freefind maintain databases of the entire contents of other websites, which can be used to create a full search engine for those other sites. The databases up updated automatically as frequently as once a week. Latest additions are catalogued separately. These services are provided free. See MathsNet's homepage for examples of such use.
Tasks could change monthly to encourage a feeling of dynamism - September could be "Algebra Online Month". A yearlong course could be timetabled from month to month, or be available at any time to run for the following year. The development of time sequencing of this kind could help students with short attention. A particular area of study could be available only for an hour and a particular time of day.

1.2 Is the Internet just another electronic medium?
The Internet, or what ever it evolves into, is potentially the overarching online medium, in that it can, and should, include all others. Skeptics in education may ask why we need the Internet when we already have CD-ROMs full of software designed specifically for education. This paper sees Online as a smooth and simple interface between users and resources. Online can bring all those software packages to the attention of potential users, through user-friendly interactive pages. Those who wish to investigate further, to develop detailed expertise, either in themselves or their students, can either subscribe to a dedicated website, AngliaCampus for example, or purchase and download the software and go from there. Traditionally, software has been promoted the reverse way: buy this amazing package and then struggle to find a use for it. The Internet is all about accessibility. Users expect to find stuff they can use and for free. This should remain a basic notion.
Since the ideals described in this paper insist that all interactivity be contained in one interface, that interface should include as much explanatory text as needed. The supplier of the educational content may not be the same person who created the interactivity. Editorial control at the top level should enhance the usability of each item. For example, in Figure 2 below, the right hand side of the screen contains programmed interactivity - points that can be dragged. A programmer or, better, a teacher with some programming skills will have produced this part. Once completed it may well become a "blackbox" to all other users, i.e., beyond editing. However, the left-hand side of Figure 2 contains text only and is simply part of the web page. This means it is available for editing by anyone. It can be updated at any time or customised for different users. If the profile entered by the individual student as part of their "MY learning" process contains some indicator of ability or age, then the text accompanying each interactive activity can be automatically adjusted to fit.

1.3 Four criteria
A good educational website will be the product of a coordinated team working to a common goal. The team will include teachers, advisers, editors, designers, programmers and users. Four basic criteria are suggested to decide if an educational website is making good use of new interactive technology:
1.3.1 Technology.
The user requires minimal technical knowledge. The focus should be the curriculum content. This is an issue for the programmers involved in educational websites.
1.3.2 Design
The design should be transparent. Access to the curriculum content should not be limited by the language (both in terms of linguistics and reading age) used or the design. This is an issue for the designers and editors involved in educational websites.
1.3.3 Content
The amount of curriculum content should be considerable. There should be both width and depth. In the midst of the sprawling and ever expanding Internet, there must be enough content on an educational website to make it worth accessing. Teachers and advisors should determine the content.
1.3.4 Development
The website itself should be constantly developing and the user also can, if desired, develop the content further on their own websites or intranets. This may require downloading a dedicated software package or customizing existing material to create their own Online material.

It would appear likely that the technology, design and development criteria are, at least in the first instance, within the control of the publishing body, but the content criterion can be tackled by a wider team, teachers in the main. Technology and design considerations will be centred on the choice of "viewer", currently the web browser. Content and development will be sensitive to the shifting demands of exam syllabi and government curriculum requirements.