A pedagogical example of second-order arithmetic sequences applied to the construction of computer passwords by upper elementary grade students

Abstract

The purpose of this paper is (1) to present how general education elementary school age students constructed computer passwords using digital root sums and second-order arithmetic sequences, (2) argue that computer password construction can be used as an engaging introduction to generate interest in elementary school students to study mathematics related to computer science, and (3) share additional mathematical ideas accessible to elementary school students that can be used to create computer passwords. This paper serves to fill a current gap in the literature regarding the integration of mathematical content accessible to upper elementary school students and aspects of computer science in general, and computer password construction in particular. In addition, the protocols presented here can serve as a hook to generate further interest in mathematics and computer science. Students learned to create a random-looking computer password by using biometric measurements of their shoe size, height, and age in months and to create a second-order arithmetic sequence, then converted the resulting numbers into characters that become their computer passwords. This password protocol can be used to introduce students to good computer password habits that can serve a foundation for a life-long awareness of data security. A refinement of the password protocol is also presented.