Approximate multiplication in young children prior to multiplication instruction

Qu, Chuyan; Szkudlarek, Emily; Brannon, Elizabeth M.

doi:10.1016/j.jecp.2021.105116

Cited by 16 publications

(23 citation statements)

References 46 publications

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“…Relatedly, and in contrast to ANS representations, representations generated by the OTS can be verbalised (when observing two dots, participants can report that there are two dots, whereas they are not able to do this reliably when the number of dots is outside the subitizing range). If it is the precision/verbalisability of a representation which determines whether or not it can be used to scale other quantities, then we would expect participants to succeed on small × small, small × large, large × small, n × small, small × n, n × large and large × n problems, but not large × large problems, which is indeed the pattern of results found in the literature and the current experiments (Barth et al, 2009;Ciccione & Dehaene, 2020;McCrink & Spelke, 2010;Qu et al, 2021).…”

Section: When Are Nonsymbolic Representations Multipliable?supporting

confidence: 79%

“…In summary, both our data and the data collected by Qu et al (2021) show that participants can successfully multiply two representations formed from nonsymbolic quantities within the subitizable range at above-chance levels, but are only at chance levels when multiplying two representations formed from non-subitizable quantities. These results are inconsistent with the hypothesis that two ANS representations can be multiplied, which would predict above-chance performance across all trials.…”

Section: Discussionsupporting

confidence: 51%

“…Given that our participants were able to reliably multiply OTS representations, this finding represents another piece of evidence that ANS and OTS representations differ in important ways (e.g., Carey, 2009;Hutchison et al, 2020;Lipton & Spelke, 2004;Revkin et al, 2008). Previous investigations into nonsymbolic approximate multiplication have often not distinguished between problems with operands within, across and outside the subitizing range (e.g., Katz & Knops, 2014;Qu et al, 2021). Our data suggest that this factor is important and that future researchers investigating this topic should carefully take it into account in their analyses.…”

Section: Are Ans Representations Numerical?mentioning

confidence: 69%

“…While we were writing this paper, Qu, Szkudlarek, and Brannon (2021) published an article reporting a study that investigated a similar question. They asked whether approximate nonsymbolic multiplication is possible in young children.…”

Section: Reanalyzing Qu Szkudlarek and Brannon (2021)mentioning

confidence: 99%

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Are approximate number system representations numerical?

2023

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Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by amalgamating perceptual features confounded with the set’s cardinality. In this paper, we approach the question of whether ANS representations are numerical by studying the properties they have, rather than how they are formed. Across two pre-registered within-subjects studies, we measured 189 participants’ ability to multiply the numbers between 2 and 8. Participants completed symbolic and nonsymbolic versions of the task. Results showed that participants succeeded at above-chance levels when multiplying nonsymbolic representations within the subitizing range (2-4) but were at chance levels when multiplying numbers within the ANS range (5-8). We conclude that, unlike Object Tracking System (OTS) representations, two ANS representations cannot be multiplied together. We suggest that investigating which numerical properties ANS representations possess may advance the debate over whether the ANS is a genuinely numerical system.

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Section: When Are Nonsymbolic Representations Multipliable?supporting

confidence: 79%

Section: Discussionsupporting

confidence: 51%

Section: Are Ans Representations Numerical?mentioning

confidence: 69%

Section: Reanalyzing Qu Szkudlarek and Brannon (2021)mentioning

confidence: 99%

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Are approximate number system representations numerical?

2023

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“…However, numbers are not only perceptual objects, but also a prime example of entities that we commonly transform internally during mental computations, generating new numbers as outcomes. Such internal number manipulation is not limited to symbols nor dependent on formal mathematical training, as attested by the ability of young children [20][21][22] , subjects from cultures with very limited numerical symbol use 23 , and to some extent even macaque monkeys 24 , to perform basic numerical operations over sets of objects. In the latter case, the results of the computations are approximate, contrasting with the precise nature of outputs that can be computed during formal arithmetic on symbols.…”

Section: Introductionmentioning

confidence: 99%

Human brain representations of internally generated outcomes of approximate calculation revealed by ultra-high-field brain imaging

Czajko,

Vignaud,

Eger

2023

Preprint

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Much of human culture’s advanced technology owes its existence to the ability to mentally manipulate quantities. Neuroscience has described the brain regions overall recruited by numerical tasks and the neuronal codes representing individual quantities during perceptual tasks. Nevertheless, it remains unknown how quantity representations are combined or transformed during mental computations and how specific quantities are coded in the brain when generated as the result of internal computations rather than evoked by a stimulus. Here, we imaged the brains of adult human subjects at 7 Tesla during an approximate calculation task designed to disentangle in- and outputs of the computation from the operation itself. While physically presented sample numerosities were distinguished in activity patterns along the dorsal visual pathway and within frontal and occipito-temporal regions, a representation of the internally generated result was most prominently detected in higher order regions such as angular gyrus and lateral prefrontal cortex. Behavioral precision in the task was related to cross-decoding performance between sample and result representations in medial IPS regions. This suggests the transformation of sample into result may be carried out within dorsal stream sensory-motor integration regions, and resulting outputs maintained for task purposes in higher-level regions in a format possibly detached from sensory-evoked inputs.

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