To possess the concept of number sense is to quickly understand, approximate, and manipulate numerical quantities (Dehaene, 1996). A number of studies have shown major evidence of the capacity of neonates and infants to discriminate and perceive object number in controlled settings (Xu and Spelke, 2000; Starkey, Spelke and Gelman, 1983; Carey, 2009). An excellent example of the innate nature of number sense is a study conducted by Antell and Keating (1983), who argue that new born infants have the ability to differentiate numerical invariability in small sets. They found that neonates with a mean age of 53 hours old already possess the ability to display a notion of number. This study, alongside many others, supports validity of the theory that humans are born with an inclined ability to distinguish number variation and also multiple studies have been conducted on providing evidence that non-human animals carry a principle of number representation (Brannon and Terrace, 1998; Hauser, MacNeilage and Ware, 1995). A valid example is the research conducted by Matsuzawa (1985) on the abilities to use numbers by a chimpanzee. The results stated that Ai, the subject in consideration, was able to pair number to the items he was presented with, showing that he has great recollection abilities. Therefore, from the positive results from these researches, it can be demonstrated that the presence of number ability in animals proves the strength of our main discussion, number sense is in fact innate. On the other hand, other studies have shown opposite evidence that stands against the proposition of number sense being an instinctive ability (Cohen and Marks, 2002; Núñez, 2011).
In this literature review, we will therefore discuss, analyse and argue that number is a quintessential abstract entity (Carey, 2009), supporting a nativism view and opposing Piaget’s theory that children do not have the ability to represent number until early school years. Based upon his findings, skill is built through logical abilities that develop later in life as they do not have an understanding of true number sense (Piaget, 1952), based upon the given examinations concerning this issue.
The studies presented in this literature utilize a habituation paradigm or a violation of it in order to analyse how infants react to what they are exposed, such as number representations. In Carey (2009), it is articulated that the subjects will look longer at a novel stimulus rather than a familiar one, because they are surprised to see something they have not familiarized with in an earlier time. A clear study using this exemplar was conducted by Xu and Spelke (2000). Babies with a mean age of 6 months and 4 days were presented with sets of six habituation displays, with 8 or 16 dots that differed in size and shape. During the experiment, each infant was exposed to both familiar numerosity and novel numerosity. The results showed that most babies looked longer at the new sets of dots (M = 6:2 s, SD 5.1) rather that the ones they had observed before (M = 4:7 s, SD 4.2). This paper also suggests that the limit of 3 is not a restriction for infants and they are able to distinguish numericities as long as the ratio is large enough.
On the basis of these results, multiple studies have recorded that babies have difficulties and are able to identify and differentiate smaller ratios but have difficulties with bigger ones. Starkey and Cooper (1980) present an experiment where babies between 4- to 7-month-olds were habituated and dishabituated to arrays with different number of dots. They focused on the ratios 2:3 and 4:6, as this has been object of multiple investigations, and the results showed that, once again, babies focused significantly on the novel and smaller number condition, leading to believe that infants do appear to be limited when they come across larger numerosity. Moreover, a two vs three dots discrimination appeared to be found positive already in neonates (Antell and Keating, 1983). Other studies also observed, using the habituation model in older babies aged between 6- to 12-month old, that they are able to discriminate between two vs three, three vs four but they are unable to differentiate a four vs five set of objects. (Starkey, Spelke, & Gelman, 1990; Strauss & Curtis, 1981), widening the scale of discrimination that babies are able to identify.
Another positive study that has been considered as a pioneering study for his new ideas is Wynn (1992). A looking-time procedure was operated in order to comprehend infants’ cognitive abilities and this process had the extent to explore the babies’ capacities to understand both simple additions and subtractions such as 1 + 1 = 2 and 2 – 1 = 1. During the experiment, babies, with mean age of 5 months 1 day, were firstly presented with a single object which then disappeared behind a dark screen, followed by the placement of a second object. The results showed that when the occlusion was removed, they looked longer when an unexpected number of objects was presented to them. Moreover, a great deal of time has also been spent conducting experiments on nonhuman animals in order to classify their numerical abilities and studies show, despite the fact they lack linguistic features, they share a knowledge in counting with humans. Nonetheless the explanation of the success of infants is still in the process of fully understanding, it is clear that they possess abilities which make them sensitive to small numerical changes and additionally, they are able to track the shift of bodies over time and space (Wynn, 1992). Hauser, MacNeilage and Ware (1995) mirrored the same methodology that has been used by Karen Wynn on infants to run an experiment with wild rhesus monkeys. The results attained showed a very similar result compared to the infants: the time spent looking the impossible condition was significantly higher (mean = 168.7 frames) than the one during the possible condition was presented to them (mean = 79.9 frames). However various subjects failed in this experiment, it is still due to validate an ability of this species to represent number and some of its arithmetical properties. Another study with the purpose of determining whether animals are capable of numerical discrimination has been conducted by Meck and Church (1983) and their experiments used a psychophysical procedure in order to analyse the timing processes of rats. The subjects were firstly trained in pressing two levers which would deliver signals that differed in duration and number of segments (left = 2-sec; right = 8-sec). Meck and Church (1983) were also tested on number discrimination as well as duration discrimination in which they tested equally perceptive of a 4:1 ratio of times and counts. This made possible the understanding that there is a mechanism inside rats that is used during both the process of counting and timing. These findings showed that animals are capable of using different modalities of operation to understand and accumulate knowledge about numbers.
With the development of theory of number being innate and being an essence that humans are born with, and although multiple studies confirm and assess this concept, a variety of researches have been conducted with the intention of discrediting this belief (Cohen and Marks,2002). They propose that infants do not possess the abilities of addition and subtraction at a young age and they only show familiar traits and preferences during investigation. They run three experiments concerning the reason why babies would look longer when presented with an unexpected and false result. The first experiment run showed results that mainly repeated the original finding from Wynn (1992a), reason why a second experiment was run in order to examine the chances of babies only showing a preference for a higher number of elements rather than a smaller one. Testing on 16 5-month-old healthy infants, they presented them with four different outcomes (0,1,2,3) and the results show a significant growth in attention as the number of items got higher. Based on these results, which match the results from pre-tests ad test trials of Wynn (1992a) once again, it is argued that the subjects in the study were not habituated thoroughly. Their inclination to look longer the more items they could see is a validation of the belief that habituation does not have a major impact on babies’ reaction times. Their third and last experiment was designed with the scope of understanding whether familiarity would appear again. It was analysed what would happen if the subjects were habituated with either 1 or 2 objects before testing. This study showed that without any form of subtraction or addition, evidence of a familiarity effect and tendency to look longer when there are more items on stage can be observed in the subjects.
This is a controversial theory that particularly attacked Wynn’s (1992a) experiments and findings that infants behold number sensitivity. Clearfield and Mix (1999) have also run a number of experiments with 6- to 8-month-old infants which conveyed that the subjects dishabituated to the object properties such as length or mass, but number change did not have an impact. Their claim was based upon the hypothesis that children might habituate to a continuous quantity rather than the number displayed in front of them. A similar result seems to appear in Feigenson, Carey and Spelke (2002). They tested whether babies were sensitive to a numerical variation or they just noticed an object-based difference in dimensions, length, surface or volume. The convergence of the results of all of their experiments came to a plausible conclusion that infants respond highly when a visible surface has doubled, yet the numerical outcome is what they were expecting.
A rather interesting approach claims that all human beings share the awareness that number map onto linear space (Dehene et al., 2008a), and that numbers are represented in the form of a mental number line (Dehane et al., 2003; Zorzi et al., 2002). Núñez (2011) argues that the mental process of number interpretation is not genetically determined, but instead, is based on cognitive mechanisms and external representations. His theory, founded on historically and archaeologically based research, looking back on the Babylonian times to remote indigenous groups, is driven by the idea that humans have cognitive mechanisms that have evolved in time and as such, do not characterize all humans in the history of mankind and all cultures. Therefore, the consolidations of certain devices able to discriminate numerosity for example, and its utilization are not able to explain about the nature of mental number line but more likely to support the idealization that number line and mental representations are acquired during cultural and educational development. Nonetheless, the arguments made against number sense not being an innate human feature, it is still visible that humans are born with a capacity to distinguish and visualise number changes when exposed to it and from a young age, even though with some limits as shown from studies (Xu and Spelke, 2000; Starkley, Spelke and Gelman, 1990).
Despite some mixed results discussed in this literature review, the research presented suggests that the concept of number is indeed innate and, is within neonates from birth based on a great deal of evidence. Despite the fact their understanding might be limited in their first few years of life, they are still capable of encoding a small number of arrays presented to them (Xu and Spelke, 2000; Starkley, Spelke and Gelman, 1990; Carey, 2009). To support the currently analysed thesis, the experiments conducted on non-human animals such as chimpanzee, rats and monkeys, are essentials for the comprehension and studying of the properties of number. The results also support the theory that number is an evolutionary system in which number itself is encoded by magnitude representations, and this is proved by the fact that the subjects track number and no other property of the arrays they are displayed with (Dehaene, 1996).