Project co-director Professor Richard Noss of the London Knowledge Lab, Institute of Education, University of London explains. "Great minds from Zeno to Galileo have found the concept of infinity difficult to understand," he says. "Infinity is such an abstract concept that children are assumed to be incapable of understanding it. Our hypothesis was that by using alternative representational infrastructures we could make such ideas easier to understand. And the curious child can learn some deep, interesting and different mathematics without first having mastered algebra and more advanced mathematics."
The WebLabs team constructed a system to allow the virtual representation of abstract ideas using a Web-based interface. They took an established, cartoon-type programming language, ToonTalk, which borrows heavily from the video games arena and presents a virtual world and animated characters with which to interact.
The WebLabs team tuned a number of aspects of the language to suit project needs more closely. They also developed over 50 tools, all written in ToonTalk, that allow students to test their theories without having to write complex programming.
An example of the ToonTalk enhancements they added was a way of displaying repeating decimals such as 1/3. The team needed to find a notation for the repeating portion of the number, and a way of avoiding truncation of the decimal expansion portion. "We invented the idea of shrinking digits," says Noss. "Digits are displayed in gradually decreasing size until they reach the size of a pixel. In this way, the idea that an infinite number of digits follow the decimal point is conveyed visually."
The team also found a way to move data generated within ToonTalk into standard external tools, such as Excel, for further analysis or graphing. With a few mouse clicks the student can record the data to the Windows clipboard in a format that can be directly pasted into Excel.
To facilitate online cooperation between different groups of students, the team designed a Web-based collaboration system called WebReports, which allows students to share working models of their ideas. WebReports can include formatted text, comments and multi-media objects, and most importantly – ToonTalk models.
These ToonTalk models are embedded in the reports as images which link to the actual code object. When a ToonTalk model is clicked, it automatically opens in a student's own ToonTalk environment – which can be another classroom in another country. The student can manipulate the model, modify it and respond with comments that may include his/her own model. Project co-director Professor Celia Hoyles, also of the London Knowledge Lab, suggests: "This last point is crucial – rather than simply commenting on another's ideas, the student can rebuild the other student's attempts to model a given task or object."
WebLabs has brought to the fore the crucial importance of good design in tools and activities when examining how teachers and students can benefit from ICTs. "With these sorts of innovative projects the ideas continue to grow as technology changes. You just have to ensure you have the researchers and teachers who will 'spread the core message," says Hoyles.
Contact:
Richard Noss
The Institute of Education
United Kingdom
Tel: +44-207-7632150
Email: r.noss@ioe.ac.uk
http://www.weblabs.eu.com