
In recent years, our computerbased ability to connect and manipulate representations of knowledge in mathematics have become ever more powerful and flexible. The reification of mathematical knowledge in computerbased learning environments, and accompanying enrichment of mathematical experience due to progress in interface design and knowledge representation (ie internal structures), widen and deepen access to experiential learning. Some of these environments even involve tools or models that adapt to the learner or guide their learning. Such developments raise questions regarding the use of these tools in the classroom: How can teachers and others assess and make sense of what students learn? How can they manage computerintensive classroom situations? How is mathematical knowledge transformed when instantiated in such computational environments (the computational transposition of mathematics)? How can teachers bridge between low technology and high technology approaches to teaching and learning? Dealing with such questions is essential to the productive use of technology by teachers and designers of instruction.We would like the Topic Group to examine these questions from the research point of view as well as from practice. Since the design and implementation of computerbased interactive learning environments results from the collaboration of at least two communities, computerscientists and mathematics educators, TG 19 will address each of them regarding the difficulties and success in the past and the problems to be investigated by research and development in the future?
Among the possible key issues to addressed we identify:
 Microworlds and the new realism of mathematics
 Managing didactical interaction
 Person/machine interaction and acquisition of a mathematical language
 Distance learning, collaborative learning and distributed or virtual classrooms
 Problems, limits, and potentials of the teacher/machine partnership
 Understanding learners' understanding and the issue of learner modeling
 Computational transposition of mathematics and related epistemological issues
 the contribution and limits of AI
 the contribution and limits of the WWW as a CBILE
The issue of the evolution of the curriculum due to technology may be mainly addressed within WG15.
For further information contact either of the three organisers :
 Nicolas.Balacheff@imag.fr
 JKAPUT@umassd.edu
 recio@matsun1.unican.es
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