VIA APL (A PROGRAMMING LANGUAGE)
Howard A. Peelle · 2016
Mathematics is a language for formal communication among scientists and engi neers and can be taught effectively via a formal language. A Programming Language (abbreviated APL) is a relatively new multipurpose programming language now available on both minicomputers and large time-sharing systems, with major appli cations in business, scientific research, and education. Originally conceived as a notation for describing algorithms (Iverson 1962), APL is a particularly appropriate language for teaching mathematics. APL provides the user with many symbols for forming concise and unambiguous mathematical expressions. Its syntax is simple, uniform, and easily learned by students. The design of APL affords even greater rewards because of its consistency, generality, and elegance?qualities that have been admired by mathematicians and teachers of mathematics alike. APL is further attractive as an interactive language implemented on computers because it provides an active learning environment?one in which the student may engage directly in problem solving and, in a sense, do mathematics. APL gives power to the educational process by relegating computational tedium to the machine?leaving the student free to study important concepts and leaving the teacher free to provide guidance and motivation. This is the unique contribution of the computer: not just to transmit knowledge (as in conventional computer-assisted instruction), but to allow the student to experience mathematics directly and to be creative in studying it. Because its roots are in mathematics, APL gives quick and natural access to many areas of mathematics. We will illustrate the use of APL for teaching mathematics with selected examples from the areas of logic, set theory, algebra, number theory, and calculus. But first, we will give a brief introduction to APL and a brief descrip tion of the glass box approach.