  Vector fields are a highly abstract physical concept that is often taught
using visualizations. Although vector representations are particularly suitable
for visualizing quantitative data, they are often confusing, especially when
describing real fields such as magnetic and electric fields, as the vector
arrows can overlap. The present study examines vector understanding at the end
of secondary education. In particular, the extent to which the geometry of the
field can be derived from conventional unit vector representations and
representations with centered unit vectors is examined. To support this
understanding, two exercises were compared. The unirepresentational exercise
argued within the conventional unit vector representation, while the
multirepresentational exercise attempted to support the link between centered
and conventional unit vectors. The results show that almost all test subjects
solved the items for generating vector representations correctly, but
significant difficulties were encountered in interpreting vector
representations. Drawing and interpreting vector representations therefore
appear to be different skills that should be practiced intensively and in an
integrated way. Furthermore, the learners recognized the field's geometry much
more readily from centered unit vectors than from conventional unit vectors.
Errors occur especially when interpreting the geometry of conventional unit
vector representations of rotational fields and fields containing both sources
and sinks, while the geometries of fields containing only sinks were
interpreted quite well. The comparison between the two exercises showed that a
promising approach to deepen students' understanding would be to use an
exercise that contrasts the two representations and explains how to translate
from one representation to the other, rather than describing the main elements
of only a single representation.
