Psychological studies have been carried out to assess the ability of an individual to percept numerical values. Evidence shows that some numbers can only be available for adult perception however there are certain numerical concepts which could be observed by infants, adults and animal species. The article “Core systems of number” by L. Feigenson et al. (2004) reviews certain neuropsychological and behavioral findings that these perception abilities are based on two core systems of number representation which we will discuss further in detail.
As was put by Roger Bacon (c. 1219–1294) “The knowledge of mathematical things is almost innate in us”, showing that, in fact, people were interested in numbers’ perception from ancient times. Attempts are still made to understand the simultaneous difficulty and easiness in understanding of mathematical rules. In the reviewed article we will tackle the two core systems which will bring us nearer to the understanding of numerical phenomena L. Feigenson et al. (2004). As was shown in habituation paradigm tests (Appendix 1) in the core system 1 in infants, even 6 –months old children seem to have inborn perception in numbers, however, they responded only to testing of numerical values ignoring non-numerical dimensions. Being tested with alternating arrays, infants showed successful response to numbers. Further tests resulted in the findings of explicit response to continuous variables discriminating numerosities of four and higher suggesting that this number perception in infants strongly depends on abstract representation of quantities. Recognizing consistent patterns between sets of numbers infants’ perception yields an expected outcome of simple mathematical issues calculating the numbers (Appendix1, Figure 1b). However, there is still a room for further research concerning infants’ ability to distinguish numerosities. Despite the calculated ratio-dependent performance in infants (Appendix 2) no plain evidence is provided explaining when an infant counts discrete and/or continuous properties of a number array.
Core system 1 in adults and older children outlined that adults/older children (about 5 year of age) are more apt to distinguish set of Arabic figures pointing out bigger or smaller numbers and are able to compare symbolic numerosities mapping their symbolic meaning to their numerical magnitude. As was discussed Core system 1 in infants, older children and adults shows explicit ability of the testees to compute and enumerate certain sets of symbolic, linear and logarithmic numerosities and establish inter-relations between them.
Tests of Core system 2 in infants carried out with 10 and 12 months old infants showed that making them to choose between two amounts of objects (Appendix 1, Figure 1c) yield the following results: habituation task was successful when infants had to discriminate 2 vs 3 objects but not 4 vs 6 despite of the identical ratio differentiation. Infants of the above mentioned age were proved to have a 3 item limitation ability when were asked to search for hidden objects because they look for exact number of hidden items which should be 3 or less in either location not basing this search on continuous variables. While infants’ perception of numerosities is narrowed to 3 items for adults in Core system 2 this ability is broadened to 1-4, afterwards the rate of erroneous response rise sharply. As was shown by L. Feigenson et al. (2004) subitizing ability in adults is supposed to be responsible for accurate calculation and allows differentiating small vs larger numbers; however, there are several approaches to the ability of accurate measurement of 1-4 numerosities by adults. Alternative approach suggests that number variability of numerosities 1-4 is quite small therefore little room for errors is left. Core systems 1 and 2 have also certain dissociations concerning processing of small and lager numbers while large number is varying depending on ratio of numerosities and small number relates to absolute quantity limiting this quantity to 3. Another important aspect of studies concerns core system’s shared heritage showing that this phenomenon is common across species pointing out phylogenetic history of numbers’ perception not only in human beings but also for animals. Core system 1 in non human animals presented evidence that for animals (like rats) numerical magnitude representations are abstract like for human beings. Primates (rhesus monkeys) demonstrated ability to count elements in ascending numerical order with great accuracy which was close to the results obtained from adults (Appendix 3). Accordingly for Core system 2 primates showed 4- item limitation when tried to find objects hidden in different locations. Like for human beings monkeys preferred to choose a larger quantity of objects proving those two distinct systems for number representation is common across human and non human species. These findings are extremely important for understanding of brain activity and neuronal network functioning because it could help children and adults having acalculia, dyscalculia and Turner’s syndrome problems to overcome these difficulties in the future by improving current neuroimaging methods and systems.
The researched article has touched extremely important issues of numerical magnitudes, however, current studies are not sufficient to answer all the questions, they offer only suggestions. First of all numbers are elements of the cores system representation which becomes active in infancy. Further, numbers could be hard to master when they go beyond the systems’ borders and demand verbal counting and symbolic perception. Despite the progress in mathematical concept a lot of issues still escape our understanding.
Works Cited
Feigenson, Lisa., Dehaene, Stanislas and Spelke, Elizabeth. Language and Conceptual Development series: Core systems of number. TRENDS in Cognitive Sciences 8.7 (2004): 307-314. Print
Appendix 1
Appendix 2
Appendix 3
