THE MAGIC NUMBER FOUR AND TEMPORO-PARIETAL DAMAGE: NEUROLOGICAL IMPAIRMENTS IN COUNTING TARGETS AMONGST DISTRACTORS

Individuation of object parts in aging

Research on enumeration with isolated objects has indicated that young and older adults can report up to three elements with similar efficiency (subitizing effect). Recent studies on subitizing in young adults have shown that individuation occurs over parts of an object as efficiently as over physically disconnected objects, suggesting that spatial separation is a sufficient requirement for efficient individuation. Do young and older adults share this sufficient requirement? In two experiments, we tested for the presence of subitizing in an enumeration task with a varying number of distinct objects and object parts. In Experiment 1, results indicated the presence of a bilinear function (with an inflection point between 3 and 4 elements, a proxy for subitizing) in the response speed of young and older adults, and in both stimulus conditions. In addition, the enumeration slope in older participants was steeper for object parts than for objects in the subitizing range, possibly due to perceptual degradation (e.g., in contour detection). The pattern found generalizes to other stimuli (Experiment 2), thus highlighting the robustness of the present findings. Overall, the results indicate that while some perceptual factors (such as contour detection or curvature polarity) may hamper subitizing speed of older individuals relative to young adults, the subitizing span remains at approximately three to four elements for multiple objects and object parts in both young and older adults. Thus, individuation of multiple objects and object parts is a mechanism relatively resistant to aging.

Effects of Age on Searching for and Enumerating Targets that Cannot be Detected Efficiently

We investigated the effects of old age on search, subitizing, and counting of difficult-to-find targets. In Experiment 1, young and older adults enumerated targets (Os) with and without distractors (Qs). Without distractors, the usual subitization-counting function occurred in both groups, with the same subitization span of 3.3 items. Subitization disappeared with distractors; older adults were slowed more overall by their presence but enumeration rates were not slowed by ageing either with or without distractors. In contrast, search rates for a single target (O among Qs) were twice as slow for older as for young adults. Experiment 2 tested and ruled out one account of age-equivalent serial enumeration based on the need to subvocalize numbers as items are enumerated. Alternative explanations based on the specific task differences between detecting and enumerating stimuli are discussed.

Compensating arithmetic ability with derived fact strategies in Broca's aphasia: a case report

We investigated derived fact strategy use in RR, an aphasic patient with severely impaired working memory (no phonological loop), and 16 neurologically healthy matched controls. Participants were tested on derived fact strategy use in multi-digit addition, subtraction, multiplication, and division. RR's accuracy only differed from controls in multiplication. He was as quick as controls in addition and subtraction when able to use the strategies, though significantly slower in addition, division, and multiplication without strategies. Our findings suggest the phonological loop is non-essential for multi-digit arithmetic, and derived fact strategies can help speed up arithmetic in individuals with impaired working memory.

Impact of high mathematics education on the number sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.

The Neuroanatomy of Visual Enumeration: Differentiating Necessary Neural Correlates for Subitizing versus Counting in a Neuropsychological Voxel-based Morphometry Study

This study is the first to assess lesion–symptom relations for subitizing and counting impairments in a large sample of neuropsychological patients (41 patients) using an observer-independent voxel-based approach. We tested for differential effects of enumerating small versus large numbers of items while controlling for hemianopia and visual attention deficits. Overall impairments in the enumeration of any numbers (small or large) were associated with an extended network, including bilateral occipital and fronto-parietal regions. Within this network, severe impairments in accuracy when enumerating small sets of items (in the subitizing range) were associated with damage to the left posterior occipital cortex, bilateral lateral occipital and right superior frontal cortices. Lesions to the right calcarine extending to the precuneus led to patients serially counting even small numbers of items (indicated by a steep response slope), again demonstrating an impaired subitizing ability. In contrast, impairments in counting large numerosities were associated with damage to the left intraparietal sulcus. The data support the argument for some distinctive processes and neural areas necessary to support subitization and counting with subitizing relying on processes of posterior occipital cortex and with counting associated with processing in the parietal cortex.

Bilateral field advantage in visual enumeration

A number of recent studies have demonstrated superior visual processing when the information is distributed across the left and right visual fields than if the information is presented in a single hemifield (the bilateral field advantage). This effect is thought to reflect independent attentional resources in the two hemifields and the capacity of the neural responses to the left and right hemifields to process visual information in parallel. Here, we examined whether a bilateral field advantage can also be observed in a high-level visual task that requires the information from both hemifields to be combined. To this end, we used a visual enumeration task—a task that requires the assimilation of separate visual items into a single quantity—where the to-be-enumerated items were either presented in one hemifield or distributed between the two visual fields. We found that enumerating large number (>4 items), but not small number (<4 items), exhibited the bilateral field advantage: enumeration was more accurate when the visual items were split between the left and right hemifields than when they were all presented within the same hemifield. Control experiments further showed that this effect could not be attributed to a horizontal alignment advantage of the items in the visual field, or to a retinal stimulation difference between the unilateral and bilateral displays. These results suggest that a bilateral field advantage can arise when the visual task involves inter-hemispheric integration. This is in line with previous research and theory indicating that, when the visual task is attentionally demanding, parallel processing by the neural responses to the left and right hemifields can expand the capacity of visual information processing.

Neuropsychological evidence for a dissociation in counting and subitizing

There is a long and ongoing debate about whether subitizing and counting are separable processes. In the present paper we report a single case, MH, who presents with a dissociation in subitizing and counting. MH was spared in his ability to enumerate small numbers accurately along with a marked inability to count larger numbers. We show that non-visual counting was intact and visual counting improved when a motor record of counting could be maintained. Moreover, when larger numbers of items were spatially grouped into 2 subitizable units, performance dramatically improved. However, color grouping did not aid MH's performance, despite his being sensitive to color segmentation. In addition, MH made more re-visits of inspected locations than controls, and he was less aware of a re-visitation being made. The data cannot be explained in terms of general working memory problems (verbal working memory was relatively spared), or general number comprehension problems (e.g., simple sums and counting of auditory items was intact); but they can parsimoniously be accounted for in terms of impaired visuo-spatial memory. The findings support the argument that at least some processes are specific to counting and are not required for subitization - in particular spatial coding and memory for previously inspected locations.

Enumeration in Alzheimer's disease and other late life psychiatric syndromes

Previous studies suggest that visual enumeration is spared in normal aging but impaired in abnormal aging (late stage Alzheimer's disease, AD), raising the task's potential as a marker of dementia. Experiment 1 compared speeded enumeration of 1-9 random dots in early stage AD, vascular dementia (VAD), depression, and age-matched controls. Previous deficits were replicated but they were not specific to AD, with the rate of counting larger numerosities similarly slowed relative to controls by both AD and VAD. Determination of subitizing span was complicated by the surprisingly slower enumeration of one than of two items, especially in AD patients. Experiment 2 showed that AD patients' relative difficulty with one item persisted with further practice and extended to the enumeration of targets among distractors. However, it was abolished when pattern recognition was possible (enumerating dots on a die). Although an enumeration test is unlikely to help differentiate early AD from other common dementias, the unexpected pattern of patients' performance challenges current models of enumeration and requires further investigation.

Effects of color heterogeneity on subitization

Small numbers of items can be enumerated rapidly and accurately via a process termed subitizing. In two experiments, we examined the effect of target color heterogeneity on subitizing efficiency. In contrast to the findings of Puts and de Weert (1997), we found that observers were no less efficient at subitizing displays containing red and green items than they were at subitizing displays of a single color. We propose that these findings are consistent with subitization operating on items represented within a location master map that codes where objects are but not what they are. The data are discussed in relation to recent findings concerning the detection of single-feature targets and the functional architecture of early visual processing.

Counting in everyday life: discrimination and enumeration

Enumerating the number of items in a set accurately and quickly is a basic mathematical skill. This ability is especially crucial in the more real-life situations, where relevant items have to be discriminated from irrelevant distracters. Although much work has been done on the brain mechanisms and neural correlates of the enumeration and/or discrimination process, no agreement has been reached yet. We used event-related potentials (ERPs) to show the time course of brain activity elicited by a task that involved both enumeration and discrimination at the same time. We found that even though the two processes run to some extent in parallel, discrimination seems to take place mainly in an earlier time window (from 100 ms after the stimulus onset) than enumeration (beyond 200 ms after the stimulus onset). Moreover, electrophysiological evidence based on the N2 and P3 components make it reasonable to argue for the existence of a dichotomy between subitizing (for sets of less than four items) and counting (for sets of four and more items). Source estimation suggests that subitizing and counting, though being distinct brain processes, do recruit similar brain areas.

Effects of Alzheimer's disease on visual enumeration

Speeded enumeration of visual objects typically produces fast and accurate performance for up to 3 to 4 items (subitization) but slower and less accurate performance thereafter (counting). We investigated enumeration ability in patients with Alzheimer's disease (AD) and in age-matched controls. AD patients were slower overall than controls. The subitizing span was significantly reduced in AD patients compared with controls (2.3 vs 3.5 items) and counting rate was significantly slower (451 vs 349 ms/item). Error rates were similar in the two groups except at numerosity 3, when AD patients made errors but controls did not (consistent with their subitizing spans). Within the AD patient group, several aspects of performance correlated significantly with Mini-Mental State Examination scores. Together, the results provide a striking contrast with studies showing preservation of enumeration ability in normal aging.

The Efficiency of Feature-Based Subitization and Counting

The enumeration of small numbers of objects (approximately 4) proceeds rapidly, accurately, and with little effort via a process termed subitization. Four experiments examined whether it was possible to subitize the number of features rather than objects present in a display. Overall, the findings showed that when features are presented randomly and are uncorrelated with object numerosity, efficient enumeration is not possible. This suggests that the visual system does not have parallel access to multiple feature maps and that subitization processes operate exclusively on representations coding the locations of objects. The data are discussed with respect to theories of visual enumeration and search.

Aging and enumeration: A selective deficit for the subitization of targets among distractors

The term subitization has been used to refer to the fast and accurate enumeration of up to about 4 items. Beyond 4 items, enumeration becomes more serial and less accurate, with each additional item adding to the total enumeration time. The effects of aging on visual enumeration of targets (Os) were assessed with and without the presence of distractors (Xs). Young participants (n = 30; 18-27 years) showed the usual subitization-counting enumeration function, both with and without the presence of distractors. In contrast, for older participants (n = 35; 65-79 years), evidence for subitization was found only when distractors were absent. This occurred even though they could detect an individual target among distractors in parallel across the field. The results are discussed in relation to recent theories of visual selection and enumeration.

Working memory in spelling: Evidence from backward typing

Theories of spelling (Margolin, 1984; Nolan & Caramazza, 1983) propose a working memory system for storing order and identity information of letters during the spelling process. Capacity limitations related to the use of such a graphemic buffer were explored. Participants had to type words backwards. Longer pauses between key presses were assumed to signal points at which graphemic buffer contents were refreshed. Five- and six-letter words were divided by a major pause into chunks of two and three letters, partly coinciding with syllables. Articulatory suppression had no effect on performance. Increasing the length of the stimuli to seven to eight letters resulted in major pauses occurring at syllable boundaries, and performance becoming vulnerable to articulatory suppression but not foot tapping. Forward typing resulted in a similar pause pattern. The results suggest that chunks of approximately three letters can be handled at any one time. For short words the task seems to rely on non-phonological modes of coding, whereas longer words appear to require the use of a phonological code, possibly for keeping track of progress through the word.