Abstract
Within mathematics, fractions hold a special place. They present perennial difficulties to students, and yet, mastering fractions is a critical stepping stone towards algebra and higher-order mathematics. More than 20 years ago, Stanislas Dehaene suggested that fractions are difficult because they lack the intuitive perceptual foundation that permits us to readily comprehend whole numbers and instead may depend on formal and symbolic processes. Here, I will present research from my lab showing that fractions may indeed have a perceptual foundation, and that this perceptual foundation may be recycled to allow us to understand symbolic fractions. Behaviorally, we have shown that symbolic fractions do not need to be processed componentially and instead can be represented on a coherent mental number. We show that wholistic fraction comparisons (and translation to decimals) does not require time consuming computations, and that non-symbolic ratio perception in college students and American elementary school children predicts formal fractions skills. Using fMRI, we have further shown that non-symbolic ratio perception reliably recruits right parietal cortex, even before the onset of formal schooling, and these parietal systems become tuned to symbolic fractions after as little as two years of formal education. Despite this evidence that fractions do, indeed, have a perceptual foundation, they still present significant difficulties. I will close by arguing that fractions (and other domains) may be difficult not due to a lack of foundational systems, but rather, due to educational methods that fail to align with these perceptual foundations. Furthermore, I will argue that research in numerical cognition can (and should!) provide new pedagogical approaches that better align with the foundational systems we have discovered to help students better grasp higher-order mathematical concepts.
