Funded Grants

Theoretical and Pedagogical Implications of the Nonsymbolic Ratio Processing System

Symbolic numbers emerged late enough on the human evolutionary time scale that they clearly could not have influenced the evolution of our species. Still, humans are remarkably efficient at processing numbers. Indeed, we are so familiar with numbers that we exhibit numerical Stroop effects: when asked to determine which of two digits is physically larger, educated adults are slower and less accurate when the physically smaller digit has the larger numerical value. This means humans are so competent with numbers that we automatically process their magnitudes (or sizes), even when they are irrelevant to the task at hand. How is it that the human brain can support such fluid processing of numerical symbols when it clearly did not evolve to do so? What basic capacities existed that have been recycled to form a basis for supporting number concepts? My research seeks to uncover answers to these questions, particularly as they apply to fractions and other numbers that cannot be reached by counting.

One frequently proffered answer regarding the origins of our number sense points to some basic perceptual abilities that allow humans and other species to rapidly estimate the sizes of sets of discrete objects. One such ability, subitizing, allows us to rapidly and exactly enumerate small sets of objects. Another, the approximate number system (or ANS), allows us to rapidly determine the approximate sizes of much larger sets (e.g., an array of sixty dots). Several researchers have argued that the acquisition of numerical concepts rests upon these evolutionarily inherited enumeration abilities that serve as “neurocognitive startup tools” for number concepts. These theorists privilege whole numbers, concluding that other classes of numbers, such as fractions and irrational numbers, exceed the innate constraints of these core abilities. Thus, the countable numbers have been dubbed the “natural” numbers, and others are deemed the products of human artifice, as exemplified by the mathematician Kronecker’s famous proclamation that, “God made the integers; all the rest is the work of man” (Bell, 1986, p. 477).

My work investigates an alternative to these innate constraints accounts of the human number sense. Specifically, I and others have begun to detail the human ability to perceptually access the magnitudes of nonsymbolic ratio magnitudes (i.e., ratios composed of pairs of nonsymbolic stimuli, such as two line segments with lengths in a 2:3 ratio). This work stands to contribute to basic science and to applied education research in multiple ways. First, it extends accounts of the primitive human number sense to include relationally defined magnitudes, like fractions. Second, it seeks to situate theories of numerical processing into theories regarding human perception of size more generally, be it the number of dots in an array, the area of a circle, or the loudness of a sound. Finally, it offers new hypotheses on how educators might rely on this basic perceptual ability to improve instruction about important concepts like fractions.