Subitizing as pattern recognition: evidence for automaticity when non-symbolic number stimuli are canonically arranged

Subitizing allows detecting the quantity of a small set of elements (up to four) with the accuracy of counting and the velocity of estimation. Recent studies have supported a theory which considers subitizing as a visual mechanism of pattern recognition, sensitive to spatial disposition of elements. These studies have found an increase in response rate and accuracy in the assessment of quantity when elements to be enumerated are arranged in an orderly fashion. Whether the numerosity of orderly arranged elements is accessed automatically, without the requirement of attentional resources, is a relevant issue not yet empirically investigated. The current study investigated the relation between subitizing and automaticity in a target detection task where distractors were non-symbolic number stimuli (dot patterns), with two different arrangements, random or canonical (like dice faces), having the same or different numerosity in the number target. We found that with canonical patterns, in the subitizing range, response times were faster in compatible trials, and slower in incompatible trials, compared to random patterns which did not influence response times in any condition. This result revealed that when elements in a visual display form easily recognizable patterns, their numerosity is accessed automatically

The effect of feature saliency on haptic subitizing

‘Subitizing’ refers to fast and error-free numerosity judgment for small (<4) sets of items. For larger sets, the slower process of ‘counting’ is used. Counting has a serial character, whereas subitizing is believed to have a parallel character. While subitizing was initially found in vision, it has been shown to exist in touch as well. In vision, it has been demonstrated that adding distractor items to a set of target items influences numerosity judgment of the target items. Subitizing was in this case only possible if the distractor item is highly salient among the targets. In the present study, we investigated the effect of adding a distractor item on haptic judgement of a set of target items. To this end, we asked subjects to judge the number of spheres grasped in their hand. Either a cube or an ellipsoid could be added to the set. A cube among spheres has been shown to be highly salient, while an ellipsoid among spheres is not. Our results show that adding a distractor item led to an increase in the response time slopes regardless of the distractor shape. Subitizing was, however, only possible in the case of a salient distractor. This is in agreement with results from vision

The cultural challenge in mathematical cognition

In their recent paper on “Challenges in mathematical cognition”, Alcock and colleagues (Alcock et al. [2016]. Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41) defined a research agenda through 26 specific research questions. An important dimension of mathematical cognition almost completely absent from their discussion is the cultural constitution of mathematical cognition. Spanning work from a broad range of disciplines – including anthropology, archaeology, cognitive science, history of science, linguistics, philosophy, and psychology – we argue that for any research agenda on mathematical cognition the cultural dimension is indispensable, and we propose a set of exemplary research questions related to it

Object individuation by iconic content: How is numerosity represented in iconic representation?

Abstract: Fodor argues that perceptual representations are a subset of iconic representations, which are distinguished from symbolic/discursive representations. Iconic representations are nonconceptual (NCC) and they do not support the abilities afforded by concepts. Iconic representations, for example, cannot support object individuation. If someone thinks that perception or some of its parts has imagistic NCC, they face the following dilemma. Either they will have to accept that this NCC does not allow for object individuation, but it represents instead conglomerations of properties and at some stage of visual processing it must interface with cognition and its conceptual capacities for the visual objects to be individuated. Or, they will have to hold that the imagistic, NCC of (or, a stage of) perception, allows for object individuation. I opt for the second thesis because I think there is strong empirical evidence that objects are individuated during early vision. I also think that early vision individuates objects by means of, what I had previously called nonconceptual perceptual demonstrative reference. I argue, first, why Fodor’s view that iconic NCC does not enable object individuation is false. I also argue, contra Fodor, that early vision allows the perception of the cardinality of sets of objects.Keywords: Early Vision; Analog Representations; Object Individuation; Arithmetic Cognition; Cardinality of Sets L'individuazione di oggetti mediante il contenuto iconico: come è rappresentata la numerosità nella rappresentazione iconica? Riassunto: Per Fodor le rappresentazioni percettive sono un sottoinsieme delle rappresentazioni iconiche, distinte dalle rappresentazioni simbolico/discorsive. Le rappresentazioni iconiche sono nonconcettuali e non supportano le abilità richieste dai concetti. Le rappresentazioni iconiche, per esempio, non supportano l'individuazione di oggetti. Se si pensa che la percezione o qualche sua parte abbia un contenuto nonconcettuale (NCC) come immagine, si ci si imbatte nel seguente dilemma. O si accetta che il NCC non permetta di individuare oggetti, ma che rappresenti conglomerati di proprietà e che (durante il processamento visivo) si interfacci con la cognizione e le sue capacità concettuali, per individuare gli oggetti visivi. O si dice che l'immagine, il NCC (o una su stadio), della percezione consenta di individuare oggetti. Propendo per la seconda tesi, poiché penso che ci sia solida evidenza empirica per cui gli oggetti vengono individuati durante le prime fasi della visione, in cui l’individuazione avviene mediante quanto definito come riferimento dimostrativo del contenuto nonconcettuale percettivo. Chiarirò le ragioni per cui la concezione di Fodor, per cui il contenuto nonconcettuale iconico non supporta l’individuazione di oggetti, è falsa. Inoltre, contra Fodor, sosterrò che le prime fasi della visione permettono la percezione della cardinalità di insiemi di oggetti.Parole chiave: Prime fasi della visione; Rappresentazioni analogiche; Individuazione di oggetti; Cognizione aritmetica; Cardinalità degli insiem

Rational analysis of the adaptive and predictive nature of memory

In his target article, Klein (2013) makes the important point that many approaches to studying memory neglect the function of memory, in particular its capacity to help predict the future. Here, we complement Klein’s argument in two ways. First, we point to an existing and well-developed research program that formalizes a functional approach to memory, exploring its adaptive nature. Second, we illustrate how this approach can be applied to analyze regularities in social interactions, which memory might exploit to predict future interactions. John R. Anderson and colleagues (Anderson and Milson, 1989, Anderson and Schooler, 1991, Anderson and Schooler, 2000 and Schooler and Anderson, 1997) developed the rational analysis of memory, in which they argued that much of memory performance, including forgetting, might be understood in terms of adaptation to the structure of the environment. The first key assumption of the rational analysis is that environmental stimuli make informational demands on the cognitive system that are met by retrieving memory traces associated with those stimuli. The second assumption is that the memory system acts on the expectation that environmental stimuli tend to reoccur in predictable ways; the pattern of past encounters can, thus, predict the future need of information. The third assumption is that the memory system makes most accessible those traces that it predicts will be most useful in the future. Consequently, memory performance should reflect the patterns with which environmental stimuli occur and reoccur in the environment. For instance, more recently encountered stimuli will likely be encountered again. An adaptive memory system should make information about those stimuli more accessible because it is more likely to be needed. Conversely, the longer time interval since the last encounter, the less likely the information will be needed in the future, and so it can and should be forgotten

Relationship between visual perceptual skill and mathematic ability

Poor mathematics performance in South African schools is of national concern. An attempt to gain insight into the problem prompted a study into the possibility of a relationship between visual perceptual skill and mathematic ability. A theoretical review revealed that inherent limitations of traditional psychological theories hinder an adequate explanation for the possible existence of such a relationship. The theory of situated cognition seems to be better suited as an explanatory model, and simultaneously clarifies the nature of both visual perception and mathematics. A small exploratory study, with a sample of 70 Grade 6 learners, provided empirical evidence towards the plausibility of the relationship. Specifically, it proved the hypothesis that visual perceptual skill positively correlates with scholastic mathematics achievement. The results of the study, interpreted within the situated cognitive framework, suggest that a conceptual emphasis in mathematics education – as opposed to a factual emphasis – might improve mathematic ability, which may credibly reflect in scholastic performance.PsychologyM. Sc. (Psychology