Enumeration: Shape information and expertise Roy Allen * , Peter McGeorge The School of Psychology, College of Life Sciences and Medicine, University of Aberdeen, William Guild Building, Kings College, Aberdeen AB24 2UB, Scotland, United Kingdom article info Article history: Received 13 December 2005 Received in revised form 28 March 2008 Accepted 5 April 2008 Available online 20 May 2008 PsycINFO classification: 2323 2346 Keywords: Attention Enumeration Subitizing Expertise Perceptual grouping Multiple object tracking abstract This study examined the interaction between grouping information and expertise in a simple enumera- tion task. In two experiments, participants made rapid judgements about the number of items present in a visual display. Within each display, items were grouped into a canonical representation (e.g., triangle, square, and pentagon) or were arranged linearly. In both experiments, grouping information facilitated enumeration performance, replicating previous findings in the literature. In Experiment 2, the facilitative effect of grouping information was found to be greater for Air Traffic Controllers (ATCs) than for matched novices, though they were no better than novices on linear arrays. This may be because linear, like canon- ical arrays, hold unique numerosity information, but only when they contain the minimum number of points necessary to define a line (i.e., 2). So ATCs’ performance on linear arrays containing more than two items does not benefit from a facilitative effect of grouping information. That their experience of being ATCs, in terms of years served, was shown to account for the expertise effect suggests that such visuospatial expertise is acquired through frequent exposure to spatial arrays. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction When asked to make a rapid decision about how many items are presented in a visual display, people typically show a distinc- tive pattern of response times and accuracy (e.g., Trick & Pylyshyn, 1993, 1994). For displays containing small numbers of items (up to 3 or 4), accuracy tends to be close to ceiling and response times are fast and relatively constant. For displays containing greater num- bers of items, accuracy generally decreases and response times in- crease as a function of each additional item in the display. Kaufman, Lord, Reese, and Volkmann (1949) coined the term subi- tizing to describe the rapid and accurate enumeration of small numbers of items and to distinguish it from the processes of count- ing or estimating involved in quantifying larger (>4) numbers of items. Mandler and Shebo (1982) proposed that subitizing was the re- sult of geometric cues in the arrangement of items in the display leading to fast pattern recognition and access to associated infor- mation on numerosity (i.e., a triangular pattern is associated with the number three; a square with the number four, etc.). They pre- sented participants with displays in which items were arranged either in a familiar pattern, such as is seen on the face of a die, or randomly. Participants demonstrated a pattern recognition advantage in that they responded faster and more accurately to the familiar patterns than to random arrangements. Similar re- sponses were reported by Wender and Rothkegel (2000) who, in addition, demonstrated that when presented with more complex displays, participants would, where possible, partition these into small canonical patterns prior to enumeration. In fact, that enu- meration is easier when the elements group in a manner conducive to form recognition has been extensively explored (see, for exam- ple, van Oeffelen & Vos, 1982; Vos, van Oeffelen, Tibosch, & Allik, 1988). The fact that subitizing appears restricted to displays containing up to about four items has been attributed to the difficulties that arise when generating canonical patterns for displays of greater numbers of items. As the number of items within a display in- creases, the number of possible configurations into which they can be arranged becomes too large to facilitate the development of simple representative patterns. For example, Logan and Zbrodoff (2003) demonstrated that perceived similarity between different configurations of the same number of elements decreased as the number of elements in the displays increased. Similarity between displays containing three items was very high but then fell dramat- ically as the number of elements per display increased beyond this point. Difficulties in generating a canonical pattern notwithstanding, there is evidence suggesting that the pattern recognition advan- tage can be extended, albeit to a small extent, by practice. For example, Mandler and Shebo (1982) demonstrated that, with around 50 trials using fixed patterns, response times to displays 0001-6918/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.actpsy.2008.04.003 * Corresponding author. Tel.: +44 (0)1224 272665; fax: +44 (0)1224 273426. E-mail address: roy.allen@abdn.ac.uk (R. Allen). Acta Psychologica 129 (2008) 26–31 Contents lists available at ScienceDirect Acta Psychologica journal homepage: www.elsevier.com/locate/actpsy