This “ICME-13 Topical Survey” aims to give a view of some of the main evolutions of the research in the field of learning and teaching Calculus, with a particular focus on established research topics associated to limit, derivative and integral. These evolutions are approached with regard to the main trends in the field of mathematics education such as cognitive development or task design.

The research in the field of Calculus education covers almost all of the general issues investigated in the area of mathematics education. The most important trend is related to Calculus design, which puts forward several considerations to build and to implement alternatives by taking into account the results of existing research in the whole field.

Specifically, this overview of research includes a description of the main theoretical frameworks used in the field of Calculus education; descriptions of punctual evolutions approached through the main trends in the field, with a particular attention to the concepts of limits, derivatives, and integrals; a description of the state of Calculus instruction from both the European and American perspectives; a brief summary of the research progress and some new issues initiated by this progress.

As a complement to the main text, an extended bibliography with some of the most important references about this topic is included.