Publications List (March 1999)

What is Organic Mathematics?

Mathematics is more important now than it has ever been. More mathematics is done both inside and outside of universities. Admittedly not all of it is called mathematics--among other things, it might be called robotics, or financial analysis, or operations control, or engineering, --but when we look closely there is no doubt that we are living in the truest Golden Age for mathematics to date. There are indications that this Golden Age is giving way to yet another due to the influence of technology. Mathematics has fundamentally affected technology, most notably computers. It is now clear that the converse will also be true. Technology, usefully falling into five major categories, has already changed mathematics dramatically, and the pace of change is accelerating.

Internet, Executable Content, and the Future of Mathematical Science Communication

Internet technology has already produced large changes in the way that we do mathematical science: Collaborative projects are now coordinated via electronic mail, and in most sciences, initial publication is via online preprint archives. The present technology for true one-to-one collaboration, however, is expensive and difficult to manage, thus limiting its utility. The internet is about to enter a period of great change as new programming technology becomes available. This technology, called executable content, allows internet distribution of advanced communication applications.

Middle School Students Using Tomorrow's Technology

Intending to create a constructionist environment for interactive learning, we are developing a JavaBeans-based tool building kit. It supports teachers' and students' use of Lego-like components to construct purposeful tools for teaching and learning mathematics. Due to the nature of the technology, it requires the user adopt an object-oriented, event-driven framework - a reasonable requirement for C++ and Java programmers but not typical for most middle school students.

Despite apparent technological handicaps and obstacles to learning, we were surprised at how readily the students assimilated the concepts and applied them creatively. This far and away exceeded our expectations and pointed at the tremendous potential borne by such constructionist technologies.

Premature Adoption of a Constructive Educational Technology: A Case Study

Is it feasible for middle school students to use component-oriented software tools to construct their own mathematical explorations and experiments? In order to explore the potential of a new constructive educational technology for mathematics, a program of guided collaboration between middle school students on Bowen Island near Vancouver Canada and researchers at Simon Fraser University was established. Novel and recently developed bridging methodologies were introduced to overcome the lack of maturity in the software. The goal was to predict its feasibility as an in-class resource for learning mathematics and to engage the students in the software design process.

Guided Collaboration: A Case Study

Prime motivations of previous studies are to design new software environments. Our prime motivation was different; we used guided collaboration as a means of evaluating, developing AND learning. While the assessment of the technology's potential was at the heart of the project, many notable observations and conclusions were made in the process. These led to a collections of recommendations, originally intended to improve our future field trials.