Numbers, space, and spatial attention: Operational momentum in non-symbolic and symbolic mental arithmetic, and number-line estimation in preschool children

In the present article, we analyze preschoolers’ performance in three arithmetic tasks (symbolic and non-symbolic ±1, and non-symbolic ±5 arithmetic) and two number-to-position number-line estimation tasks (symbolic and non-symbolic, range 1–9). Both arithmetic and number-line estimation (NLE) are supposed to involve similar representations and processes (operating on spatial-numerical representations of numerical orders and magnitude scaling). We focused on the relationship between the various measures in arithmetic and NLE with emphasis on operational momentum (OM; overestimation and/or rightward bias in addition and underestimation/leftward bias in subtraction) in arithmetic, which, like log-to-linear shift in NLE may be a signature of the most basic numerical representations and processes. Some form of OM was revealed for all three arithmetic tasks, but no positive between-task correlation was found for this variable. Additionally in the symbolic task accuracy and OM indices were positively correlated. In both NLE tasks, the linear model fit better than the logarithmic one and performance was strongly correlated, but not related to arithmetic, except for the symbolic arithmetic accuracy and OM. We conclude that, in the preschool stage, symbolic numerical processes are grounded in non-symbolic ones; however, the operational momentum biases in mental arithmetic and scaling in the NLE task are not the result of inherent non-linear scaling of numerical representation (logarithmic mental number-line), but rather of task-and-context dependent ability to map the numbers onto spatial representations and the involvement of inner spatial attention to process them. Additionally, the demonstrated effects, including non-symbolic tasks, seem to depend more on the individual level of knowledge of counting principles than on general developmental factors represented by age. The results also provide partial replications of the study of Haman and Lipowska (2021).