Operational momentum during ordering operations for size and number in 4-month-old infants

Abstract

An Operational Momentum (OM) effect is shown by 9-month-old infants during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Recent evidence has shown that this effect extends to ordering operations for size-based sequences in 12-month-olds. Here we provide evidence that OM occurs for ordering operations involving numerical sequences containing multiple quantity cues, but not size-based sequences, already at 4 months of age. Infants were tested in an ordinal task in which they detected and represented increasing or decreasing variations in physical and/or numerical size, and then responded to ordinal sequences that exhibited greater or lesser sizes/numerosities, thus following or violating the OM generated during habituation. Results showed that OM was absent during size ordering (Experiment 1), but was present when infants ordered arrays of discrete elements varying on numerical and non-numerical dimensions, if both number and continuous magnitudes were available cues to discriminate between with-OM and against-OM sequences during test trials (Experiments 2 vs. 3). The presence of momentum for ordering number only when provided with multiple cues of magnitude changes suggests that OM is a complex phenomenon that blends multiple representations of magnitude early in infancy.

Operational momentum for magnitude ordering in preschool children and adults

“…Given the constraints of such a young population (with children as young as 37 months of age), the adoption of a between-subjects design would have proved necessary to include a descending operation, as they lose interest in the task rather quickly. However, the infants tested in Macchi Cassia et al (2017) showed an underestimation tendency after habituation to descending numerical sequences which was not dissimilar from the overestimation tendency they showed after habituation to ascending sequences. Therefore, testing for the generalizability of the obtained findings to descending ordering operations in young children would be worth further investigation.…”

“…It is possible that there were indeed miscalculations arising from spatial shifts in the preschoolers, similar to the infants, but the study's design dampened them for the preschoolers. For instance, in the infant study (Macchi Cassia et al, 2017), an infant-controlled habituation procedure was employed, which gave each single participant ample time to encode and form a robust representation of the ordering operation. Moreover, during habituation infants were given multiple examples of the same ordering rule.…”

“…How, then, do we reconcile this account -a protracted interface of spatial attention and the mental number line, with spatial shifts emerging before estimation biases -with the findings on OM in infancy? For both ordering OM and addition/subtraction OM, there is evidence that infants are miscalculating outcomes in accord with the "direction" of the arithmetic operation (Macchi Cassia et al, 2017;McCrink & Wynn, 2009). Yet, this bias isn't apparent in childhood (Knops et al, 2013;Pinheiro-Chagas et al 2018; current study).…”

“…In particular, when it comes to ordering operations over magnitude, infants show evidence of operational momentum. Macchi Cassia, McCrink, de Hevia, Gariboldi, and Bulf (2016) and Macchi Cassia, Bulf, McCrink, and de Hevia (2017) have shown that, when 4-and 12month-old infants are habituated to a set of objects that progressively increases or decreases in number (Macchi Cassia et al, 2017) or physical size (Macchi Cassia et al, 2016), and are subsequently presented with ordinal sequences whose magnitude is larger or smaller compared to the initial sequence, they look longer at sequences in which the direction violates the operational momentum experienced during habituation (the smaller sequence after viewing ascension, and the larger sequence after viewing descension).…”

Moving attention along the mental number line in preschool age: Study of the operational momentum in 3‐ to 5‐year‐old children's non‐symbolic arithmetic

“…Only few studies have tested OM in children, For instance, Macchi Cassia, McCrink, de Hevia, Gariboldi, and Bulf (2016), Macchi Cassia, Bulf, McCrink, and de Hevia (2017) found that just 4-monthold infants expected larger numerosities at a given position in the sequence when previously habituated to increasing numerical sequences but expected smaller numerosities when habituated to decreasing sequences. Knops, Zitzmann, and McCrink (2013) and…”