Grouping Mechanisms in Numerosity Perception

Abstract

Enumeration of a dot array is faster and easier if the items form recognizable subgroups. This phenomenon, which has been termed “groupitizing,” appears in children after one year of formal education and correlates with arithmetic abilities. We formulated and tested the hypothesis that groupitizing reflects an ability to sidestep counting by using arithmetic shortcuts, for instance, using the grouping structure to add or multiply rather than just count. Three groups of students with different levels of familiarity with mathematics were asked to name the numerosity of sets of 1–15 dots in various arrangements, for instance, 9 represented as a single group of 9 items, three distinct groups of 2, 3, and 4 items (affording addition 2+3+4), or three identical groups of 3 items (affording multiplication 3×3). Grouping systematically improved enumeration performance, regardless of whether the items were grouped spatially or by color alone, but only when an array was divided into subgroups with the same number of items. Response times and error patterns supported the hypothesis of a multiplication process. Our results demonstrate that even a simple enumeration task involves mental arithmetic.

Finding the subitizing in groupitizing: Evidence for parallel subitizing of dots and groups in grouped arrays

“…Starkey and McCandliss (2014) found that groupitizing was positively associated with children's arithmetic abilities, an association also shown in adults (Anobile et al, 2020;Ciccione & Dehane, 2020;. Proposed mechanisms for the association between groupitizing and arithmetic abilities include the extension of the subitizing range through arithmetic abilities , the use of fast repeated addition (Wender & Rothkegel, 2000), conceptual knowledge about the composition of large numbers from small numbers (Starkey & McCandliss, 2014, Clements & Sarama, 2009, Wästerlid, 2020 and the use of mental multiplication (Ciccione & Dehaene, 2020). All of these proposed mechanisms concern how numerical information is used to quickly enumerate the total number of items in the array.…”

“…Our findings suggest the likely reason is that this particular way of visual grouping supports parallel subitizing of dots and groups, which in turn provides operands for mental calculations. The groupitizing effect can also be found if arrays are grouped by temporal proximity or separated colors , Ciccione & Dehaene, 2020, but seems to be heavily impaired when items are grouped by shape or color, but interspersed (Liu, Zheng, Huang & Cicchini, 2020).…”

“…A central idea in many groupitizing studies is that grouped arrays can be enumerated faster than unstructured arrays, because visually grouping of dots into smaller sets allows participants to use mental calculation, such as adding up of the numbers of dots in each group PARALLEL SUBITIZING IN GROUPED ARRAYS 4 (Anobile et al, 2020, Wender & Rothkegel, 2000 or multiplying the number of dots per group by the number of groups (Ciccione & Dehaene, 2020). Finding the operands for such mental calculations is a matter of enumerating small sets fast and accurately.…”

“…Our study suggests that the parallel subitizing of dots and groups in grouped arrays may provide the enumeration processes that is necessary for groupitizing via mental multiplication. Ciccione and Dehaene (2020) proposed that visually grouping dots into identical groups allowed participants to use the number of groups and dots per group as operands in the retrieval of multiplication facts (such as 4 × 3 = 12). Multiplication facts are highly trained and can be retrieved from memory very fast and accurately (Campbell & Graham, 1985).…”

“…Multiplication facts are highly trained and can be retrieved from memory very fast and accurately (Campbell & Graham, 1985). Grouped arrays with identical groups can be 'groupitized' within 1000-1500ms (Ciccione & Dehaene, 2020), but the retrieval of multiplication facts alone takes roughly 1000ms (Verguts & Fias, 2005). Groupitizing via mental multiplication therefore requires a particular way of extracting numerical information from grouped arrays: it requires an enumeration process that very fast and accurately (i) enumerates the number of dots per group and (ii) enumerates the number of groups in a grouped array.…”