Exploring undergraduate engineering students’ mathematical problem-posing: the case of integral-area relationships in integral calculus

ABSTRACT Previous studies have suggested that problem-posing activities could be used to improve the teaching, learning, and assessment of mathematics. The purpose of this study is to explore undergraduate engineering students’ problem posing in relation to the integral-area relationship. The goal is to help fill a gap in tertiary level research about students’ mathematical problem posing, particularly of engineering students. The mathematical problem posing of 135 undergraduate engineering students was explored using four problem-posing tasks and semi-structured interviews. The findings indicate that many of the problems the students posed were solvable and in a pure mathematics context, while those problems students attempted to set in a real-world setting did not provide a realistic situation. In addition, students faced a number of difficulties when posing problems related to the integral-area relationship and mathematics in general, and several students had a limited understanding of the applications and uses of the integral-area relationship in the real-world. This study suggests that using problem-posing activities in teaching and assessment can help identify engineering students’ mathematical understanding and misunderstanding. Furthermore, using problem-posing tasks can help developing engineering students’ understanding of the applications of integral calculus. More broadly, the findings suggest that problem-posing tasks could be used more often, alongside problem-solving tasks, as part of the teaching and assessment of mathematics at the university level.