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Size Matters in Numerical Cognition

Final Report Summary - SMINC (Size Matters in Numerical Cognition)

In recent years, research in numerical cognition has expanded, and we have witnessed a flourishing field produce major advances toward unraveling the building
blocks of numerical cognition and its development. Research in the area of numerical cognition has led to a widely accepted view of the existence of innate, domain-specific, core numerical knowledge based on the ability to perceive and manipulate discrete quantities (e.g. enumeration of dots). This core knowledge involves the intraparietal sulcus (IPS) in the brain and it is thought that a deficiency in this core knowledge might be the basis for arithmetic disability. However, advances in research suggested that this wide agreement needs to be examined carefully. In particular, arrays of items always carry non-countable continuous properties (e.g. area, density, how much liquid is in a glass) and as a result, there is a high correlation between numerosity and these continuous properties (the more numerous array of dots is also denser than the less numerous array). It is not simple to disentangle numerosity and non-countable dimensions and hence, when an infant shows that he or she prefers one array of items, it is not clear if the preference is related to numerosity or to another property (e.g. density). In addition, size seems to be an essential property of objects in the world around us: elephants are big, and mice are small. Moreover, size seems to have an intimate relationship to numbers and numerosity. If we are asked to decide which of two digits is larger, an irrelevant difference in the physical size of the digits affects such a decision. It takes longer to decide that 8 is larger than 3 if the 8 is also physically smaller than the 3, than if it is larger than the 3. These and other results led us to study the involvement of non-countable continuous properties, such as size and density, in numerical cognition and its development. We found that various continuous properties do affect judgments of numerosity even when they are completely irrelevant to the task at hand. For example, when participants are asked to judge which of two arrays has more dots, density and similar irrelevant properties modulate numerosity judgements. This occurs not only when the arrays contain large numbers of dots but also when they contain only small numbers of dots (four dots or less). Similarly, irrelevant physical sizes of objects (their size on the computer screen) modulate judgments regarding their conceptual size. Moreover, it seems that there are specialized areas of the brain involved in size perception. Our current theoretical suggestion is that the sense for numbers is not innate but rather develops with experience. Instead, there seems to be a magnitude sense that appears very early in development. The core capacities of this magnitude sense are the ability to perceive and evaluate sizes and amounts. This magnitude sense probably facilitates the development of an exact numerical system.