Analyzing student understanding of cryptography using the SOLO taxonomy

Abstract

Although cryptography is monumentally important in keeping our information safe and secure, this interdisciplinary field of study can also be used as a powerful teaching tool by putting mathematics in a dramatic and realistic setting. Cryptography also allows for a natural way to introduce topics such as modular arithmetic, matrix operations, and elementary group theory. This paper reports the results of a preliminary qualitative study of students’ thinking and understanding of cryptography using both the SOLO taxonomy and open coding as they participated in task-based interviews. Students interviewed were assessed on how they made connections to various areas of mathematics through solving cryptography problems. Analyzing these interviews showed that students have a strong foundation in number-theoretic concepts such as divisibility and modular arithmetic. Also, students were able to use probability intuitively to make sense of and solve problems. Finally, participants’ SOLO levels ranged from uni-structural to extended abstract, with the multi-structural level being the most common (three participants). This gives evidence to suggest that students should be given the opportunity to make mathematical connections early and often in their academic careers. Results indicate that although cryptography need not be a required course for mathematics majors, concepts from this field could be introduced in courses such as linear algebra, abstract algebra, number theory, and discrete mathematics.