Threshold concepts and undergraduate mathematics teaching

Traditionally, many undergraduate mathematics courses have been defined in terms of mathematical content and the techniques in which students should become proficient or theorems they should be able to prove. This can result in a reliance on shallow or rote learning by students, despite the fact that the main goal of a mathematics lecturer is usually to foster mathematical understanding in their students. In contrast, it is suggested that placing an emphasis on the threshold concepts involved in a course can enable teachers and students to focus on what is fundamental to the study and mastery of their subject.