Disentangling the Mechanisms of Symbolic Number Processing in Adults' Mathematics and Arithmetic Achievement.

A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial-accessing underlying magnitude representation of symbols (i.e., symbol-magnitude associations), processing relative order of symbols (i.e., symbol-symbol associations), or processing of symbols per se. To address this question, in this study adult participants performed a dots-number word matching task-thought to be a measure of symbol-magnitude associations (numerical magnitude processing)-a numeral-ordering task that focuses on symbol-symbol associations (numerical order processing), and a digit-number word matching task targeting symbolic processing per se. Results showed that both numerical magnitude and order processing were uniquely related to arithmetic achievement, beyond the effects of domain-general factors (intellectual ability, working memory, inhibitory control, and non-numerical ordering). Importantly, results were different when a general measure of mathematics achievement was considered. Those mechanisms of symbolic number processing did not contribute to math achievement. Furthermore, a path analysis revealed that numerical magnitude and order processing might draw on a common mechanism. Each process explained a portion of the relation of the other with arithmetic (but not with a general measure of math achievement). These findings are consistent with the notion that adults' arithmetic skills build upon symbol-magnitude associations, and they highlight the effects that different math measures have in the study of numerical cognition.

Effects of numerical surface form in arithmetic word problems / Efectos del formato numérico en problemas aritméticos

Adults’ simple arithmetic performance is more efficient when operands are presented in Arabic digit (3 + 5) than in number word (three + five) formats. An explanation provided is that visual familiarity with digits is higher respect to number words. However, most studies have been limited to single-digit addition and multiplication problems. In this article, we examine to what extent format effects can be found in the context of arithmetic wordproblems, in which visual familiarity is reduced (Manuel had 3 marbles, and then Pedro gave to him 5). Participants with high and low arithmetic fluency solved addition and subtraction word problems in which operands were presented in both formats. The overall results showed an advantage for digits operands relative to words operands. In addition, the format effects were more evident for subtraction and low-skilled participants. These results were interpreted in terms of more rapid access of digits to numerical magnitude (AU)

Los adultos calculan más eficazmente cuando los operandos se presentan en formato arábigo (3 + 5) que cuando se presentan en formato palabras numéricas (tres + cinco). Una explicación ofrecida es la mayor familiaridad visualde los dígitos relativo a las palabras numéricas. Sin embargo, la mayoría de los estudios se han limitado a operaciones simples de cálculo con sumas y multiplicaciones. En el presente trabajo analizamos hasta qué punto se produce el efecto del formato en el contexto de un problema aritmético, en el que la familiaridad visual se elimina (Manuel tenía 3 canicas y le dieron 5). Participantes con diferente nivel de competencia en fluidez aritmética resolvieron problemas de suma y resta con los operandos en ambos formatos. Los resultados mostraron un efecto del formato, con mayor rapidez en formato dígitos que en palabras numéricas. Además los efectos fueron más evidentes en la operación de resta y en los participantes menos competentes en fluidez aritmética. Es tos resultados fueron interpretados en función de una mayor eficacia del formato dígitos para acceder a la semántica del número (AU)