Evidence for distinct magnitude systems for symbolic and non-symbolic number

Abstract

Cognitive models of magnitude representation are mostly based on the results of studies that use a magnitude comparison task. These studies show similar distance or ratio effects in symbolic (Arabic numerals) and non-symbolic (dot arrays) variants of the comparison task, suggesting a common abstract magnitude representation system for processing both symbolic and non-symbolic numerosities. Recently, however, it has been questioned whether the comparison task really indexes a magnitude representation. Alternatively, it has been hypothesized that there might be different representations of magnitude: an exact representation for symbolic magnitudes and an approximate representation for non-symbolic numerosities. To address the question whether distinct magnitude systems exist, we used an audio-visual matching paradigm in two experiments to explore the relationship between symbolic and non-symbolic magnitude processing. In Experiment 1, participants had to match visually and auditory presented numerical stimuli in different formats (digits, number words, dot arrays, tone sequences). In Experiment 2, they were instructed only to match the stimuli after processing the magnitude first. The data of our experiments show different results for non-symbolic and symbolic number and are difficult to reconcile with the existence of one abstract magnitude representation. Rather, they suggest the existence of two different systems for processing magnitude, i.e., an exact symbolic system next to an approximate non-symbolic system.

Improving Preschoolers’ Arithmetic through Number Magnitude Training: The Impact of Non-Symbolic and Symbolic Training

“…Thus, taken altogether, our results are in line with the dual-representation view, according to which symbolic and non-symbolic processing rely on two distinct number magnitude representations; symbolic numbers activating an exact number representation and non-symbolic numerosities the ANS [22]. Indeed, the unique representation view anticipated a similar increase of performance in symbolic and non-symbolic magnitude processing after both symbolic and non-symbolic conditions, which is not what we observed.…”

“…According to this view, both symbolic and non-symbolic magnitude comparisons show ratio effects [11, 17, 18] and similar brain areas would be activated for both types of stimuli ([19–21], see [2, 17] for a review). These studies suggest that symbolic and non-symbolic magnitude processing activate one approximate magnitude representation system, the ANS [22]. Finally, the unique-representation view postulates that the ANS underlies math learning [13, 23] as ANS acuity has been shown to correlate with individual differences in mathematics competences [15, 24] and to be lower in people presenting specific math learning disability or dyscalculia [25–27].…”

“…In addition, recent brain imaging studies using more precise techniques failed to find overlapping representations between dots and digits [35]. According to this view, dot sets activate an analogue and approximate representation such as the ANS [22]. However, recent studies question the extent to which this representation would really code for number magnitude [36].…”

The Stability of Individual Differences in Basic Mathematics‐Related Skills in Young Children at the Start of Formal Education

“…Although it appears that numerical ordering skills become particularly important from around the age of 6 or 7 (Attout & Majerus, ; Lyons, Price, Vaessen, Blomert, & Ansari, ; Sasanguie & Vos, ), there is also now emerging evidence in support of a role of nonnumerical ordering in mathematical development in the case of younger children (Attout, Noël, & Majerus, ; Morsanyi, van Bers, O'Connor, & McCormack, ; O'Connor, Morsanyi, & McCormack, ). Nonnumerical order processing measures can be broadly divided into two categories: those involving the retrieval of a familiar sequence from long‐term memory, such as the order of familiar daily events, familiar everyday sequences, the months of the year, or letters (Morsanyi, O'Mahony, & McCormack, ; O'Connor et al, ; Sasanguie, De Smedt, & Reynvoet, ; Vos, Sasanguie, Gevers, & Reynvoet, ), and those involving the retrieval of a novel, arbitrary sequence from short‐term memory (order working memory [WM] task; Attout & Majerus, , ; Attout et al, ). O'Connor et al () found that both numerical and nonnumerical ordering measures were related to early mathematical achievement in 4–5‐year‐old children.…”

Disentangling the Mechanisms of Symbolic Number Processing in Adults’ Mathematics and Arithmetic Achievement

“…The task is based on Sasanguie and Reynvoet (; see also Sasanguie, De Smedt, et al. ). Participants heard a number word (range: 1–9) and simultaneously a dot array was visually presented on a computer screen.…”