Understanding of limits and differentiation as threshold concepts in a first-year mathematics course

Threshold concepts remain relatively unexplored in mathematics, despite suggestions that the troublesome nature of such concepts pose a critical barrier to student understanding of mathematics. Many studies have identified student difficulties with limits, and their findings point to a strong likelihood that limits do indeed constitute a threshold concept in mathematics. This paper describes the initial results in a study that sought to investigate students’ understanding of limits and differentiation from the prospective of Threshold Concepts. While the findings to date do not provide conclusive evidence for limits as a threshold concept, they do reinforce the troublesome nature of the limit concept, and suggest some important implications for the teaching of limits consistent with previous studies.