Percival G. Matthews, Ph.D. - US grants

DESCRIPTION (provided by applicant): Mathematical competence is an important determinant of life chances. Recent research suggests that understanding fractions particularly understanding their relative sizes is critical for the development of mathematical competence. Unfortunately, children and adults often encounter considerable difficulties understanding fractions. To explain these widespread difficulties, many researchers have argued for an innate constraints account of fraction cognition. On this account, fractions are difficult to understand because they lack an intuitive basis, whereas whole number understanding can be grounded in our perceptual abilities to process numerosities (i.e., collections of countable objects). Thus, innate constraint theorists argue that fraction learning is challenging because it does not benefit from existing cognitive abilities similar to those that facilitate whole number learning and that fractions must instead be learned through adapting whole number understanding. In short, they argue that fractions are somehow less natural than whole numbers. The proposed research will investigate a competing hypothesis, the cognitive primitives' account, which integrates previously unrelated findings from neuroscience, developmental psychology and education. This hypothesis contends that cognitive systems tuned to the processing of non-symbolic fractions (such as the relative lengths of two lines or the relative areas of two figures) are present before children begin formal instruction. The existence of these primitive non-symbolic fraction processing abilities suggests that they might serve as a foundation for understanding the magnitudes of symbolic fractions. On this view, children may be equipped with cognitive mechanisms that support fraction concepts prior to formal education in the same way that the ability to process numerosities equips them to learn about whole numbers. If substantiated, this hypothesis can inform interventions designed to improve fraction learning and may contribute to the detection and treatment of math learning difficulties. To test the predictions of the cognitive primitives account, the project will use behavioral tasks to investigate children's (6-year-olds an 10- to 11-year-olds) abilities to perceive the magnitudes of non-symbolic fractions. It will also aim to develop a training program that pairs non-symbolic fractions with symbolic fractions to teach children about the magnitudes of symbolic fractions. These findings will have important implications for our understanding of number processing and for designing interventions that are optimal for promoting fraction learning. If perceptual sensitivity to non-symbolic fractions can provide a foundation for the acquisition of symbolic fraction knowledge, then instruction should attempt to exploit these primitive abilities. If deficits in these non-symbolic abilities contribut to math learning difficulties, then screening should include measures of non-symbolic abilities and interventions should be designed to strengthen these abilities.

Project Summary Mathematical competence is an important determinant of life chances in modern society, and knowledge of fractions is a foundational skill for establishing mathematical competence. Despite the importance of fraction knowledge, children and adults often encounter considerable difficulties understanding fractions. To explain these widespread difficulties, many researchers have argued for an innate constraints account. They propose that fractions are difficult because they do not correspond to any preexisting categories in our brain, unlike whole numbers, which correspond to sets of countable things. Thus, they argue fraction concepts are challenging because they do not benefit from existing cognitive abilities and instead must be learned through adapting children's whole number understanding. The study team proposes a competing hypothesis, the cognitive primitives account, which integrates previously unrelated findings from neuroscience, developmental psychology and education. We argue that a primitive ability that we dub the ratio processing system (RPS) is tuned to the processing of non-symbolic fractions?such as the relative length of two lines or the relative area of two figures?and is present even before formal instruction. On this view, children are equipped with cognitive mechanisms that support fraction concepts in the same way that the ability to process countable sets equips them to learn about whole numbers. To test the predictions of these competing hypotheses, this project will follow two cohorts of children (2nd graders until 5th grade and 5th graders until 8th grade) using behavioral and brain imaging methods to (a) trace the development of non-symbolic fraction processing abilities, (b) determine how symbolic fraction knowledge builds on these abilities and (c) investigate whether individual differences in the RPS predict later math achievement. To test whether the acuity or recruitment of these non-symbolic architectures plays a role in fraction difficulties as well as general math learning difficulties, the study team will compare the behavioral performance and neural activity on a battery of cognitive tasks. This research has important implications for our understanding of number processing and for designing educational practices that are optimal for fraction learning. Improving fractions understanding would help children to clear a critical hurdle in the acquisition of higher-order mathematical competencies that impact educational, employment, and even health outcomes. If cognitive primitives for non-symbolic fractions can provide a foundation for the acquisition of symbolic fraction ability, then instruction should attempt to recruit these primitives. If deficits in these primitives contribute to math learning difficulties, then screening should include measures of non-symbolic abilities and interventions should be designed to address these abilities.