The answer depends on your lecturer

ABSTRACT

This article is concerned with the approaches to the root concept that lecturers in calculus, linear algebra and complex analysis employ in their instruction. Three highly experienced university lecturers participated in the study. In the individual interviews the participants referred to roots of real numbers, roots of complex numbers, roots as real functions and roots as complex functions. However, participants’ approaches to the root concept were mathematically not equivalent and the lecturers resisted to the approaches of their peers. The choices of approach were shaped by different types of pedagogical considerations, such as the mathematical ideas that appear in the courses that lecturers teach, textbook approaches and lecturers’ interpretations of students’ further academic needs. Several cases were indicated where the participants consciously compromised mathematical rigour and limited the scope of their instruction when teaching general mathematics courses.

KEYWORDS:

• Root concept
• definitions and notations
• teacher knowledge

Acknowledgements

I wish to thank Elza, Dave and Leo for their participation in the study. I am grateful to Adrian Simpson and to anonymous reviewers for their through criticism and insightful suggestions.

Disclosure Statement

No potential conflict of interest was reported by the authors.

ORCiD

Igor' Kontorovich http://orcid.org/0000-0002-3353-5445