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.

Public Health Relevance

Knowledge of fractions provides an important foundation for developing mathematical competence, yet many children and adults struggle to understand fractions. This study will investigate how children's perceptual abilities can support learning about fractions. The results will 1) provide new insights into the nature of children's number sense, 2) help develop more effective methods for teaching fraction concepts, and 3) help deepen our understanding of math learning difficulties (including math disabilities) and methods for treating them.

National Institute of Health (NIH)
Small Research Grants (R03)
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Cognition and Perception Study Section (CP)
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Mann Koepke, Kathy M
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University of Wisconsin Madison
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United States
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