Drawing on a computer algorithm to advance future teachers’ knowledge of real numbers: A case study of task design

Abstract

In our investigation of university students’ knowledge about real numbers in relation to computer algebra systems (CAS) and how it could be developed in view of their future activity as teachers, we used a computer algorithm as a case to explore the relationship between CAS and the knowledge of real numbers as decimal representations. Our work was carried out in the context of a course for university students who aim to become mathematics teachers in high schools. The main data consists of students’ written responses to an assignment of the course and interviews to clarify students’ perspectives in relation to the responses. The analysis of students’ work is based on the anthropological theory of the didactic (ATD). Our results indicate that simple CAS-routines have a potential to help university students (future teachers) to apply their university knowledge on certain problems related to the decimal representation of real number which are typically encountered but not well explained in high school.