The aim of the present paper is to show that, contrary to the main current approach to numerical cognition, the link between space and numbers cannot be reduced to the concept of a mental number line (MLN). A distinction between low-level numerical skills, that involve MLN processing, and higher level arithmetical skills, which are related to algorithmic processing, is needed in order to understand the different contribution given by visuo-spatial skills. I suggest that cognitive skills related to symbolic manipulation should be analyzed on their own in order to better understand the importance of spatial representation for arithmetical processing and, to this purpose, I propose a model of algorithmic skills that could be useful to study some typical features of symbolic manipulation, such as the influence of spatial schemes and the role for external resources in working memory offloading.