Operational Momentum in Numerosity Production Judgments of Multi-Digit Number Problems

Abstract

The current study demonstrates a numerosity production task and investigates approximate mental calculations with two-digit numbers. Participants were required to produce random dot patterns to indicate the size of two-digit numbers and the results of addition and subtraction problems. The stimuli in the calculation task consisted of problems requiring a carry operation (e.g., 24 + 18) or no-carry problems (e.g., 24 + 53) or zero problems (e.g., 24 + 0). Our analysis revealed that the outcomes of additions were estimated to be larger than the outcomes of subtractions. Interestingly, this judgment bias was present for no-carry and zero problems but not for carry problems. Taken together, the presented data provide empirical support for the presence of an operational momentum effect (OM effect) in multi-digit number arithmetic. These findings and the dissociation of the OM effect for carry and no-carry problems are discussed in the context of recent models on multi-digit number processing.

Causal role of the posterior parietal cortex for two-digit mental subtraction and addition: A repetitive TMS study

“…We predict a bilateral contribution of the posterior parietal cortex, with some specialization. Consistently with the idea that two-digit additions determine attentional shift along the MNL compared to two-digit subtraction (Masson and Pesenti, 2014;Lindemann and Tira, 2015), we expect to find a greater rightward asymmetry for the involvement of HIPS, especially during complex additions, due to the fact that the right HIPS is involved not only in the quantity system (e.g., Feher et al, 2007;Menon et al, 2000), but also in processing the order information along the MNL (Knops and Willems, 2014). We also expect to find the involvement of VIPS, especially during complex additions, as this area underpins the use of the MNL (Salillas et al, 2009(Salillas et al, , 2012.…”

“…Thus, in our case it is possible that solving complex subtractions involved attentional shifts (to the left) to a lesser extent than addition because all the numbers involved in our two-digit problems were large. In addition, in support of the involvement of attentional shift for complex mental additions, Lindemann and Tira (2015) observed an operational momentum effect especially for two-digit addition. Furthermore, Anelli and colleagues (2014) found that rightward body motions triggered mainly addition outcomes, while the leftward ones did not trigger the subtraction outcomes.…”

“…They have also shown the so-called operational momentum effect, a bias in over-and under-estimating the results of addition and subtraction, respectively, especially for two-digit additions (Lindemann and Tira, 2015). The idea is that ancient neural circuits, such as for example, calculation (Dehaene and Cohen, 2007).…”

A role for attentional reorienting during approximate multiplication and division

“…Crucially, participants misplaced addition outcomes to the right and subtraction outcomes to the left, compared to baseline that required indicating the numbers' positions without preceding arithmetic operation. When actively producing dot patterns corresponding to the outcome of multi-digit problems, participants produced relatively larger estimates for addition problems as compared to subtraction problems with identical correct outcome (Lindemann & Tira, 2011). Together, this implies that mental arithmetic is subject to systematic biases that may have their origin in the application of spatial coordinate transformation mechanisms to numerical quantity information that can be conceived of as positions on the MNL.…”

“…However, OM has also been found in symbolic notation (Knops, Dehaene, Berteletti, & Zorzi, 2014;Knops, Viarouge, & Dehaene, 2009) which has been interpreted as evidence for a common underlying mechanism. OM has also been observed with paradigms that require translating the cognitively generated numerical estimate into a position on a labeled line (Pinhas & Fischer, 2008), or actively producing the outcome via a dot generating manual device (Lindemann & Tira, 2011). In the labeled line task, participants indicated the position of the outcome of visually presented addition and subtraction problems on a line that was labeled with zero on the left and 10 on the right.…”