Abstract:

The traditional textbooks in mathematics, at the undergraduate level and especially the College entry level, have been the subject of justifiably serious criticism. Their use by students is typically limited to the exercise pages where assignments are referenced. Their cost, given their limited use, is forbidding for large numbers of students.

This has generated significant efforts on the part of educators to design the kind of curriculum that is accessible financially, and intellectually. Those efforts, that spanned a few decades, were funded by the National Science Foundation primarily, but other corporations have also contributed significantly. In the author's opinion, we have not reached the goal that we set forth albeit significant progress has been achieved.

It is our responsibility as educators to demonstrate confidence in the students' ability to learn mathematics and to give them the tools to be successful in their learning experiences. It is indeed our responsibility to encourage and nurture them in a subject that, for many, seem forbidding and remote, if not impossible, and has traditionally been viewed as the proper domain of only the few.

To the end of living up to these responsibilities, we must continue to be willing to take a serious look at the effectiveness of our habitual approach to teaching/learning, and to modify it in light of new opportunities, new needs, and new technologies. Any genuine teaching/learning environment must integrate three basic principles: participation, visualization, and integration.

Participation refers to the active involvement of students in the construction of their own knowledge. This process recapitulates the development of certain scientific ideas by formulating key problems in ordinary language, and encouraging students, through class discussion and computer exploration, to discover what is needed to refine that language and thereby to reconstruct the appropriate formalisms. Participation, in this sense, puts students more in control of the pace and, to some extent, the direction of their learning.

Visualization refers to the formation of stable and coherent mental pictures of abstract constructions and processes in mathematics and science. The ability to visualize constructions and processes requires practice and experience. The best students enter their courses with refined and exercised habits of visualization, and these students usually progress smoothly and quickly. But many students are forced to spend much of their time "discovering" the right pictures.

Integration is the process by which students build bridges connecting principal ideas of different disciplines, and place them into a unified conceptual context. So it has to do with synthesis and organization.

The author will present several modules to illustrate the ideas above. A web site, that will host those modules, is being updated and will be made available to all the participants.

Keywords:

Open Text, Interactive Text, Participation, Visualization.