"CAS, Educational Microworlds, and the Internet"

Nurit Zehavi 
Weizmann Institute of Science, Israel 
Email: ntzehavi@weizmann.weizmann.ac.il


Constructing learning environments that incorporate CAS, elements of 
educational microworlds, and the Internet can boost the implementation 
and utilization of these technologies in mathematics education. The  
desire to provide educational materials over the Internet has led us 
to consider integrating our experience in developing open tutoring 
systems and in creating non-routine problems to be solved using a CAS. 
An open tutoring system should enable students to find solutions in  
their own ways, and an on-line guidance, in the form of hints, should 
provide support. Investigating non-routine questions using CAS 
encourages diverse mathematical thinking and independent work. With  
this in mind we have analyzed the types of mathematical knowledge that 
were applied in solving specific problems and identified the 
relationships and the 'Webs of meanings' involved in the solution 
processes. We utilized computer software tools commonly used in the  
Internet, such as html, CGI, Java Script, and e-mail to design an 
interactive guidance system in the format of Web pages. The pilot 
studies in this new development dealt with Magic circles obtained by 
composing linear functions, and with a specific sequence of Extrema  
problems. The progress so far indicates that the work to be done is  
indeed a triple challenge.