Programmed control systems are ubiquitous in the present-day world. In current educational practice, however, these systems are hardly being addressed, and little is known about children's spontaneous understandings about such systems. Therefore, we explored pupils' understandings prior to instruction in three concrete settings: a car park, an…

Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…