## Abstract

Rational numbers, such as fractions, decimals, and percentages, are a persistent challenge in the mathematics curriculum. An underappreciated source of rational number difficulties are whole number properties that apply to some, but not all, rational numbers. I contend that mastery of rational numbers involves refining and expanding whole number representations. Behavioral evidence for the role inhibitory control and magnitude-based processing of rational numbers supports this hypothesis, although more attention is needed to task and stimuli selection, especially among fractions. In the brain, there is scant evidence on the role of inhibitory control in rational number processing, but surprisingly good correspondence, in the parietal lobe, between the handful of neuroimaging studies of rational numbers and the accumulated whole number literature. Decimals and discrete nonsymbolic representations are fruitful domains for probing the neural basis role of whole number interference in rational number processing.

Original language | English (US) |
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Title of host publication | Heterogeneous Contributions to Numerical Cognition |

Subtitle of host publication | Learning and Education in Mathematical Cognition |

Publisher | Elsevier |

Pages | 143-180 |

Number of pages | 38 |

ISBN (Electronic) | 9780128174142 |

DOIs | |

State | Published - Jan 1 2021 |

## All Science Journal Classification (ASJC) codes

- Medicine(all)
- Neuroscience(all)

## Keywords

- Decimals
- Executive functions
- Fractions
- Inhibitory control
- Neural distance effects
- Neuroimaging
- Nonsymbolic
- Rational numbers
- Symbolic