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

(B) Exemplar websites
A number of comprehensive online courses on statistics have been developed; similar sites on pure mathematics are beginning to appear.

2.9 ExploreMath
ExploreMath provides an online interactive mathematics course catering for students at high school, post 16 and first year college. It uses the Macromedia Shockwave plug-in to "bridge the digital divide between free course pages and the web's finest mathematical multimedia." In doing so, it does meet all four of our criteria for a good educational website. Figure 16 shows a typical display. The quadratic curve y=ax²+bx+c can be manipulated by dragging the boxes along the green lines. Further information about vertex and intercept can be displayed if required and the graph scaling can be altered to suit. Finally, buttons are provided to facilitate copying the entire display or just the graph to the clipboard, and coordinate data can be captured from the graph and pasted into other documents - see Table 1 which as been pasted into this document directly from the website.


Figure 16: ExploreMath

Table 1 x y-5.0000 -2.5000-4.0000 -3.6000-3.0000 -4.1000-2.0000 -4.0000-1.0000 -3.30000.0000 -2.00001.0000 -0.10002.0000 2.40003.0000 5.50004.0000 9.20005.0000 13.5000
ExploreMath can also be used by a teacher or tutor to create courseware. To do this the user must first join the site by creating a free account and then follow a sequence of set-up pages to create or customise their course. The finished product will provide instructions for the student on what work is expected of them, recommended links and deadlines. To work on this course, students must carry out the following steps:
1. Go to the ExploreMath site
2. Click on "find course pages"
3. Enter the user name - in this case enter MathsNet - and click on "search"
4. Click on "MathsNet online courses"
5. Start the course

2.10 Math online
Math Online describes itself as "a gallery of interactive learning material for school and distance learning". The gallery includes coordinate geometry, vectors, trigonometry, functions and calculus, most of which use Java applets to create interactivity. The site also has an interactive test section consisting of multiple choice tests and other types such as "drag and drop". Figure 17 shows a typical interactive display. This one shows a function together with its first and second derivatives. When the sliders are operated, the graphs transform accordingly.


Figure 17: Math online

The buttons at the top give access to background information and suggested exercises. The site has a download facility whereby you can download Math online in its entirety to your hard disk to run off line.

2.11 Online geometry
The Geometry Centre , from the University of Minnesota, is now closed but its website remains! AngliaCampus includes modules on transformation geometry (reflections, rotations, enlargements and translations) based on the Cinderella software. At the ScienceU Geometry Center you are encouraged to browse through an exhibit, or jump right in and start experimenting with shapes, patterns and symmetry.

2.12 General sites
The Math Forum describes itself as "An Online Math Education Community Center" and has as its goal to build an online community of teachers, students, researchers, parents, educators, and citizens at all levels who have an interest in math and math education. It contains a variety of resources across the curriculum and age range. Cut-The-Knot also offers a miscellany of materials ranging across the mathematics curriculum.

2.13 CAST
CAST is an entire Statistics online course that uses Java applets to illustrate key concepts. Figure 18 shows least squares regression, wherein the points can be moved and the errors (shown as squares) and regression line are then recalculated.


Figure 18: CAST

2.14 Other online statistics courses
Inferential statistics is essentially a full length statistics text book. The Rice Virtual lab in Statistics or RVLS , is also an extensive online statistics course. It includes an online statistics book with links to other statistics resources on the web; simulations/demonstrations using Java applets that demonstrate various statistical concepts; case studies of examples of real data with analyses and interpretation; analysis lab containing some basic statistical analysis tools.