This paper focuses on the KOM framework for mathematical competencies and in particular its aids and tools competency and investigates its application to digitaltechnologies used for mathematical learning. Very little has been done on networking the KOM’s mathematics competencies framework to internationally established theories and theoretical constructs. Through an analysis of an authentic example involving digital technologies for teaching slope fields, we compare and combine the aids and tools competency with the approach of instrumental genesis and the notion of scheme. We claim that the networking of these theoretical perspectives facilitates our understanding of mathematical competencies in the digital age.