Common magnitude representation of fractions and decimals is task dependent

Abstract

Although several studies have compared the representation of fractions and decimals, no study has investigated whether fractions and decimals, as two types of rational numbers, share a common representation of magnitude. The current study aimed to answer the question of whether fractions and decimals share a common representation of magnitude and whether the answer is influenced by task paradigms. We included two different number pairs, which were presented sequentially: fraction-decimal mixed pairs and decimal-fraction mixed pairs in all four experiments. Results showed that when the mixed pairs were very close numerically with the distance 0.1 or 0.3, there was a significant distance effect in the comparison task but not in the matching task. However, when the mixed pairs were further apart numerically with the distance 0.3 or 1.3, the distance effect appeared in the matching task regardless of the specific stimuli. We conclude that magnitudes of fractions and decimals can be represented in a common manner, but how they are represented is dependent on the given task. Fractions and decimals could be translated into a common representation of magnitude in the numerical comparison task. In the numerical matching task, fractions and decimals also shared a common representation. However, both of them were represented coarsely, leading to a weak distance effect. Specifically, fractions and decimals produced a significant distance effect only when the numerical distance was larger.

The role of attentional networks in the access to the numerical magnitude of fractions in adults / El rol de las redes atencionales en el acceso a la magnitud numérica de fracciones en adultos

“…This numerical distance effect would be an index of access to a representation of the magnitude of numbers along a mental number line (Dehaene, 1997). A distance effect has also been reported in the case of the fractions (Zhang, Fang, Gabriel, & Szűcs, 2016).…”

“…Este efecto de distancia entre números sería indicativo del acceso a una representación de la magnitud de los números en una línea numérica mental (Dehaene, 1997). En el caso de las fracciones también se ha reportado un efecto de distancia (Zhang, Fang, Gabriel, & Szűcs, 2016).…”

“…Este efecto de distancia entre números sería indicativo del acceso a una representación de la magnitud de los números en una línea numérica mental (Dehaene, 1997). En el caso de las fracciones también se ha reportado un efecto de distancia (Zhang, Fang, Gabriel, & Szűcs, 2016). Hasta ahora los esfuerzos se han concentrado en entender el modo en que el conocimiento matemáticoasociado a números naturales obstaculiza (y en otros casos facilita) las operaciones con fracciones.…”

Children’s reasoning about decimals and its relation to fraction learning and mathematics achievement.

“…Because students in Class 1 were highly accurate, they could be accessing an internal representation of magnitude. However, students in Class 2 and 3 did not appear to reason about decimal magnitudes holistically (Zhang, Fang, Gabriel, & Szűcs, 2016); rather, given their performance described above, they applied (or misapplied) rules regarding whole number and place value. When different rules conflicted with one another (e.g., .06 vs. .4–place value helps performance but whole number bias hurts performance), students with a partial (Class 2) or poor (Class 3) understanding performed at chance, suggesting they simultaneously possessed different strategies that competed with one another for application.…”

“…Because students in Class 1 were highly accurate, they could be accessing an internal representation of magnitude. However, students in Class 2 and 3 did not appear to reason about decimal magnitudes holistically (Zhang, Fang, Gabriel, & Szu ˝cs, 2016); Note. SEM ϭ structural equation model.…”