Mathematics’ war - real or imaginary?

[EN] This paper investigates different methods to solve a mathematics task attempted by students enrolled for a first-year mathematics module in South Africa (n = 182). The paper examines an expected calculus solution approach and examples of interesting alternative student solutions. Task solutions were analysed according to the number of conceptual and procedural steps used to solve the task. Each step in the task solutions is described by a problem-solving category, based on the knowledge approaches used to solve the task. The results confirm that solution methods are not unique. Task solutions require both procedural and conceptual steps, and problem-solving steps are sometimes iterative. The analyses demonstrate that mathematical questions cannot be uniquely described as mainly conceptual or procedural. The analyses suggest that lecturers could consider explanation and comparison of multiple solution strategies as a way to enhance mathematical proficiency.