NEWTON: An interactive environment for exploring mathematics

In recent years there has been much interest in incorporating computers into the teaching of college-level mathematics classes. In particular, there has been great interest in the use of computer algebra systems in introductory calculus. While educators believe that computer algebra systems have great potential in the calculus sequence, the limitations of such software have often made them difficult to use in the classroom. This thesis discusses the design, implementation, and evolution of a computational environment for use in teaching introductory mathematics. This system, called N scEWTON, runs on Macintosh computers and consists of a user-friendly interface to the symbolic mathematics package Maple, supplemented by an extensive library of Maple code. As an interface specifically designed for educational purposes, the driving motivation behind its development was to allow students access to the full power of a computer algebra system, without mastering the idiosyncrasies of the system and struggling to enter information. To accomplish this, we have provided the student with an easy to use interface which adds features specific to its intended educational use. A prototype system entered classroom use in 1991. While well received, the system was limited in functionality and proved to be difficult to maintain. The system has been completely redesigned, reimplemented, and extended for use in linear algebra, numerical analysis, and differential equations courses. The current N scEWTON interface is based on the concept of an interactive book, and the user can freely mix text, formulas and graphics in collapsible sections on worksheets. Multiple windows allow users and work with several formulas at once. A syntax-directed editor is provided which allows easy two-dimensional input and editing of mathematical formulas. Formulas are easily constructed and modified, appearing as they do in textbooks. Users do not interact with Maple directly and need know nothing of Maple\u27s syntax and command structure. Mathematical operations are selected from menus, and plots and animations are generated from dialog boxes. Other unique aspects of the system include dialogs for techniques of integration and differentiation and the automatic documentation of solutions