Core Knowledge Theory

Introduction

The core knowledge theory addresses the old age question regarding the capacities available from the time one is born, and those that are acquired later through experience. The key focus of this approach is whether the unique human capacities manifest from the onset of early development and whether the existing differences in abilities between human and other species arise later during development (Spelke, 2017; Strickland et al. 2017). There are three shared characteristics in the core knowledge domains that are crucial for understanding human cognitive development and could be explored further with psychology dissertation help. The first core knowledge is task specific, implying that all systems functions with the end goal of solving limited sets of problems. For instance, the number system has capabilities of discriminating quantities on the basis of their ratio, even though it is worth noting that this is different from counting ability. This essay critically discusses the domain of number, drawing from different empirical studies.

Natural number system

The natural number system supportive of counting is a relatively complex construction requiring integration from the object and number systems and also induction on how numbers relate with their referents (Dehaene et al. 2006). The other characteristic is that the different domains of core knowledge are encapsulated in such a way that each single system operated with a fair degree of independence from the other cognitive systems. The advantage of this is that core abilities are universal and are acquired rather effortlessly even with the least experience. On the downside, a limitation of encapsulation is that these abilities are neither flexible nor precise (Vallortigara, 2012).

Owing to the fact that core representations of number are ever present during the course of development, Dobbs (2005), argues that they should not be dependent on formal mathematics education. That gives rise to the question of how the core system of number is associated with the number systems that are learned in school. The modern study of numerical development in children was launched by Gelman and Meck (1983), who carried out major studies that formed the foundation of counting among children. Gelman established that, when presented with a collection of objects, infants were able to count them in a systematic and flexible manner. The children also complied when they were instructed to start counting from different objects; this shows that they are cognizant of the fact that it was possible to count the same items in varying orders. However, the children repudiate counts that go against the unalterable order of the words in their count list and those that either skip or reject words or objects. Nativist theories provide sound explanations for the existing universality of natural number system across different cultures. Additionally, they explain why children are observed to gain access to the number system way before they begin their formal education.

Nativist theory

Most of the research by nativist theorists involves an easy approach: the Give-N task (Le Corre and Carey, 2007). This involves first asking children to count a collection of objects, which is accompanied by recording the used words. They are then shown a stack of objects and required to present their specific quantity, using the number words they previously obtained while counting. The majority of the involved children in these studies are observed to produce one fish whenever required of them from when they are just two years, even though they take more time to learn what two means and be able to produce two fish when demanded. Once they have successfully produced the two, they spend more time before they are able to produce three, and so on. Therefore, it is evident that children are engaged in counting and recital of number words, way before developing a full understanding of counting as an enumeration procedure and that number words indicate cardinal values that are precise.

Human cognition

The responses of infants to surprising events are recognized as relatively critical in the characterisation of early thought. Among the main ways through which core knowledge affects learning is by the reduction of the learning space that confronts observers (Strickland et al. 2017). With the presence of multiple numbers of objects, object parts, features and relations that could be learned about, violations of expectations could be focused on the cognitive resources of a learner on the aspects of the world regarding which they possessed the wrong prior model – and therefore on which they made wrong predictions.

Experiments involving children have established that from as early as when infants are just six months old, they are capable of detecting 1:2 ratio changes in large numbers, for example, 4 and 8, 8 and 16, 16 and 32, but cannot detect a 2:3 ratio (Brannon and Van de Walle, 2001; Kolkman et al. 2013, Siegler and Lortis-Forgues, 2014; Siegler and Braithwaite, 2017). By the time these infants reach 9 months, they are able to detect 2:3 ratio changes and their detection precision increases to a 7:8 ratio in adults. It is possible to use these numerical discriminations for purposes of predicting performance across different stimuli and this includes actions, tones, and objects. From these examples, there is evidence of the abilities to abstract numerical information across different perceptual inputs and the ratio-based signature in all of them is the same. Just like with the knowledge on objects, it is apparent that the developmental change in magnitude is one of elaboration and refinement. Evidence drawn from infants and other different species points to these representational skills having ontogenetic and phylogenetic continuity.

The structuring of the core number system revolves around tenets that oppose both agent and object systems, showing its characteristic signature limits. There are three contending classes of principles that have so far been suggested for purposes of characterising this system (Dehaene & Changeux, 1993; Meck & Church, 1983; Church & Broadbent, 1990). It is worth noting that each proposal explains the main characteristics of numerical representations, and therefore, there are continuous debates of their relative merits. There exists general agreement on three main attributes of the representations of core numbers. The first is that number representations are not precise, and their lack of precision grows linearly and is accompanied by increments in the cardinal value. Based on various presuppositions, Henik et al. (2012), report that from the scalar variability, a ratio limit to the discriminality of sets with cardinal values that are different is produced. The other property is that number representations are abstract and are applicable to varied beings encountered through various sensory modes, and these include an array of sound sequences, objects, and perceived and produced action sequences. The third property is that it is possible to compare and subsequently combine number representations through addition and subtraction operations.

These types of number representations have been observed in human infants, children, adults, and also in adult non-human primates (Siegler and Braithwaite, 2017). Infants have been observed to discern between large numbers of actions, objects and sounds, during the control of continuous quantities, and a ratio limit is additionally observed from their discrimination. Additionally, infants have the capabilities of adding and subtracting large numbers and objects (Batchelor, 2014). Adult humans and monkeys are seen to segregate between large numbers of sounds and have a ratio limit. The numerical representation precision ratio improves with development, from 2.0 in six-months old infants to 1.15-1.3 in human adults, even though this is dependent on the task.

All humans, from professional mathematicians, to new-born infants, spontaneously describe the cardinal values of sets of sequences and objects with precision that is ratio-limited. Multiple experiments have been carried out involving new-borns and all these point to this ability. Izard et al. (2009) familiarised infants drawn from a maternity hospital with syllable sequences. Changes were noted in the particular syllables from one sequence to the other, and the same was also observed for the duration of syllable sequence, even though the number of syllables remained constant. Alternating visual rays appeared as the infants listened to the different sequences with either 4 or 12 objects of variable, even though sizes and shapes are comparable. Infants were observed to spend more time looking at the object array with a number correspondence to the sound sequences. As a result of the differences in auditory and visual arrays in terms of format and modality, and because they could not be matched based on continuous, intensive and extensive quantities like sequence duration, contour length, and item size, these looking patterns proved infants were able to detect the existing numerical correspondence in the arrays, therefore, numerically distinguishing 4 and 12. Additional experiments point to new-born infants having the capabilities to distinguish between 6 and 18, even though they could not differentiate between 4 and 8. The abilities to discriminate between two numbers begin from the first days after birth and in the earlier days, this is dependent on the ratio of the numbers.

Another study by Oakes et al. (2013) reports that infants illustrate the visual forms sequences and arrays as ensembles that have approximate numerical magnitudes. A size limit is evident in the abilities to process individual objects, with most adults being incapable of holding more than four objects in their minds at once, whereas infants can respond to number in larger arrays. Therefore, infants often fail in the representation of numerical sizes of small object sets. For instance, new-born infants are incapable of matching the sequences of 2 sounds to arrays of 2 as compared to 6 objects, when tests are carried out under the same conditions. When both adults and children are presented with sets that are small, they all tend to focus on individual objects, subsequently suppressing representations of the numerical magnitude of the set. However, it is worth noting that adults and infants, in equal measure have the capabilities of focusing on small sets` numerical values, in the event presentation conditions make tracking individual objects difficult. As such, the numerical representations of new-born infants are not dependent on, and may even refuse to allow selective attention to the individual members of the sets to which they are applicable. The majority of the studies carried out on sensitivity to number have involved older adults, who go about detecting number in displays that are relatively diverse, and these include action sequences, arrays of 3D objects, and clouds of dots (Sarnecka, 2016).

Conclusion

Just like with the knowledge humans possess on objects, they also possess knowledge about numbers. Humans are able to tell of the existing difference between 8 and 16 dots without even having to count. They can make this judgement quickly and in an accurate way. There are multiple other species that are good in making these types of judgements and they include nonhuman primates, pigeons and rats. For instance, monkeys possess the abilities of representing and comparing approximate numerosities. This ability to discriminate as per this paper, appears to be based on analogue magnitudes. That is, the discriminability of two values is determined by the proportion and not the absolute difference between them (Sarnecka, 2016). For instance, adults are more capable of discriminating 100 dots from 200 dots (1:2 ratio) in comparison to 200 to 300 dots (a 2:3) ratio, although the difference between the two comparisons is just 100 dots. There exists developmental challenges in this abilities precision. Infants also find it easy to discriminate 1:2 ratios.

In summary, Infants pay more attention and therefore, look longer at numerically changing displays as compared to numerically constant displays. They are also able to distinguish increments from decreases in number. Additionally, infants are able to successively do additions and subtractions of arrays presented to them, facilitating a rough estimation of their sums and differences. Even as new-borns, infants are able to match arrays whose numbers increase to objects whose lengths increase. Infants are also observed to be conscious of the commensurate sizes of objects and subjects that contain large sets of objects with either two or more colours. They could utilise these proportions in estimating the probability that random sampling will be done on individual objects of each colour.

References

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