The Impact of Technology in Topics Foundational to Calculus at the Secondary Level

Antonio R. Quesada
Department of Theoretical & Applied Mathematics
The University of Akron
Akron, Ohio 44325-4002, USA

Abstract. The integration of technology into the teaching & learning of mathematics impacts every aspect of instruction, from course content to teaching methods and assessment. As a result, some of the assumptions made about mathematics curricula, in a time prior to the integration of technology in the classroom, are no longer valid. Currently, the ability to bridge cumbersome calculations via technology, allows students at various levels of secondary school, to meaningfully explore concepts and problems previously proposed to more advanced mathematics students, and to extend the breadth and depth treatment of these concepts. Thus, topics such as optimization, matrix applications, linear and non-linear regression, recursion etc. are now accessible to secondary students at different levels prior to calculus. In this presentation we will show examples that illustrate how the numerical and graphical capabilities of hand-held graphing technology, as well as dynamic geometry software, can be used to introduce key concepts foundational to Calculus at the secondary level. Moreover, we will see that it is possible to introduce some of these concepts using different representations, in a way that is similar to how they were developed and are better understood, namely, using approximations.