Spatial tests involving the comparison of diagrams of interlaced ropes or knots at varying orientations were given to (n=21) subjects, mostly English college undergraduates, to determine an ordering in terms of complexity of tasks involving the mental manipulation of the knots. Certain knot shapes were processed faster than others and greater…

Analysis of (n=92) university students' construction of visual representations (Venn diagrams) of eight set expressions found competent and error-prone students constructed and used procedures to complete set translation tasks, and two-thirds of observed errors arose from consistent implementation of ill-formed procedures. (Author/MKR)

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore…