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

Abstract

Abstract‘Groupitizing’ refers to the observation that visually grouped arrays can be accurately enumerated much faster than can unstructured arrays. Previous research suggests that visual grouping allows participants to draw on arithmetic abilities and possibly use mental calculations to enumerate grouped arrays quickly and accurately. Here, we address how subitizing might be involved in finding the operands for mental calculations in grouped dot arrays. We investigated whether participants can use multiple subitizing processes to enumerate both the number of dots and the number of groups in a grouped array. We found that these multiple subitizing processes can take place within 150 ms and that dots and groups seem to be subitized in parallel and with equal priority. Implications for research on mechanisms of groupitizing are discussed.

Unimpaired groupitizing in children and adolescents with dyscalculia

“…Some note of cautions should be made at this point. Despite similar groupitizing advantages has been found for both approximate estimation 17 – 20 , 25 and exact serial counting tasks 14 , 16 , they can still rely on different mechanisms. It is therefore important to underline that, as we only measured groupitizing with an approximate estimation task, our results cannot be directly generalised to counting tasks.…”

“…There is evidence suggesting that groupitizing leverages on subitizing. For example, both groupitizing and subitizing require attentional resources 16 and a recent study has shown that it is possible to groupitize small groups of items, suggesting a link between the two phenomena 25 . Interestingly, subitizing has recently been shown to be unrelated to mathematical abilities of typically developing children 26 and not impaired in a sample of individuals with dyscalculia 27 .…”

Groupitizing reflects conceptual developments in math cognition and inequities in math achievement from childhood through adolescence

“…In the years since McCandliss' study of groupitizing in children, extensive research in adults have uncovered two key processes involved in groupiziting -the first linked to access to cardinal values of subsets, and the second linked to more conceptual mathematical processes involved in combining cardinal values of subsets into exact cardinal values of entire sets. In particular, recent studies showed that groupitizing involves subitizing processes at an early stage (Anobile et al, 2020;Maldonado Moscoso et al, 2020;Wege et al, 2021). Note that, fascinatingly, groupitizing does not limit to visual scenes but can be found in auditory sequences too, through subitizations of grouped auditory targets (Anobile et al, 2021).…”

“…To manipulate how subgroups are combined, we asked how groupitizing is impacted when grouped arrays of the same value were formed by 2 versus 3 subgroups. Subitizing processes have been shown to occur in parallel across twoand even three-group displays (Wege et al, 2021), which opens up the possibility of direct access to the cardinality of an entire set, with similar latencies for two and three subgroup sets. However, recent findings suggest that groupitizing demonstrates several remarkable parallel e↵ects that also impact symbolic arithmetic (Ciccione & Dehaene, 2020) including a large e↵ect caused by the number of operands (e.g., two versus three operand addition).…”

Small number enumeration processes of deaf or hard-of-hearing students: A study using eye tracking and artificial intelligence

“…The enumeration of sets in subsets (groups) is called groupitizing (Starkey and McCandliss, 2014 ) or “conceptual subitizing” (Clements, 1999 ) since conceptual processes of the part-whole relationship are involved. Groupitizing allows sets of items to be perceived quasi-simultaneously, that is, by subitizing subsets (Anobile et al, 2020 ; Wege et al, 2022 ). Furthermore, enumeration of small sets can involve the recall of familiar patterns, such as dice patterns.…”