Abstract
Two experiments examined whether the processing of the magnitude of fractions is global or componential. Previously, some authors concluded that adults process the numerators and denominators of fractions separately and do not access the global magnitude of fractions. Conversely, others reported evidence suggesting that the global magnitude of fractions is accessed. We hypothesized that in a fraction matching task, participants automatically extract the magnitude of the components but that the activation of the global magnitude of the whole fraction is only optional or strategic. Participants carried out same/different judgment tasks. Two different tasks were used: a physical matching task and a numerical matching task. Pairs of fractions were presented either simultaneously or sequentially. Results showed that participants only accessed the representation of the global magnitude of fractions in the numerical matching task. The mode of stimulus presentation did not affect the processing of fractions. The present study allows a deeper understanding of the conditions in which the magnitude of fractions is mentally represented by using matching tasks and two different modes of presentation.
Highlights
Current evidence about how fractions are represented in the human brain is controversial
We aimed to determine whether fraction magnitude processing was componential or () relied on the global fraction magnitude in a new experimental setting
Numerical distance effects observed in matching tasks are thought to be directly related to the mental representations of numbers (Van Opstal and Verguts, 2011) and are more appropriate than comparison tasks to assess the processing of numbers
Summary
Current evidence about how fractions are represented in the human brain is controversial. Numerical abilities are currently thought to rely on an innate biological system representing approximate magnitude (Dehaene, 1997). Gallistel et al (2005) extended this view by suggesting that the magnitude coding system has properties co-extensive with mathematical real numbers and allows the approximate representation of ratios, a claim supported by evidence from preverbal children (McCrink and Wynn, 2007) as well as primates (Vallentin and Nieder, 2008). Fractions constitute a major stumbling block in maths education (Mack, 1993), and this difficulty suggests that the link between fraction symbols and their magnitude (i.e., their rational value) is not acquired . A question has recently been raised whether adults process fractions by accessing their global magnitude or only the value of their component numerals
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