An investigation into the approach of mathematics undergraduates to a non-routine task

ABSTRACT

Critical thinking and problem solving are widely recognised as valuable competencies in the twenty-first century, and indispensable skills in the workplace. In this context, we investigate the strategies employed by first-year university mathematics students when faced with a non-routine task, specifically the impossible triangle. The data collection process involved the administration of a questionnaire (70 questionnaire responses) and conducting interviews (six interviews). The study used the lens of framing to examine the interplay between the task cue and students' responses, and the Ref*AER framework to interpret the knowledge of the participants. A considerable number of students approached the task using an algorithmic mathematical frame. With reference to the Ref*AER framework, the participants' inadequate conceptions were a hindrance to the successful completion of the task. We believe that the implementation of tasks like the impossible triangle in the mathematics classroom can effectively foster students' noticing and uncover deficiencies in their knowledge.

KEYWORDS:

• Non-routine task
• activity-effect relationship
• framing

Acknowledgement

We want to express our gratitude to the reviewers for devoting the necessary time and effort to the manuscript. We sincerely thank you for your insightful comments and advice, which helped us to raise the quality of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The study has been performed in accordance with the principles stated in the Declaration of Helsinki. The study has been approved by the Department of Mathematics, University of Osijek.