Challenging issues in the teaching and learning of Calculus and Analysis

The importance of Analysis and the nuances involved in its teaching and learning continue to be a fruitful topic of interest for the mathematics education community at the university level. This chapter shows the variety and depth of research conducted recently, as reflected in the INDRUM meetings in 2016 and 2018. Transition from secondary school to university is a crucial issue in mathematics education, and within this the teaching and learning of Calculus and introductory Analysis is one of the most investigated topics. It might seem that once students overcome this initial transition, that they would have less difficulties when studying other courses related to Analysis. This seems not to be the case. Participants at the INDRUM conferences have considered further transition points: for example, when students are introduced to new kinds of functions such as multivariable functions; when they are introduced to Analysis on the real line; and when they study Topology or Complex Analysis. All of these transitions have their own characteristics and we explore them in this chapter.