The association between symbolic and nonsymbolic numerical magnitude processing and mental versus algorithmic subtraction in adults

• Do mental and algorithmic computation differentially rely on number sense?
• Association with number sense is not different for both computation methods.
• Elementary arithmetic fact knowledge entirely mediated these associations.

There are two well-known computation methods for solving multi-digit subtraction items, namely mental and algorithmic computation. It has been contended that mental and algorithmic computation differentially rely on numerical magnitude processing, an assumption that has already been examined in children, but not yet in adults. Therefore, in this study, we examined how numerical magnitude processing was associated with mental and algorithmic computation, and whether this association with numerical magnitude processing was different for mental versus algorithmic computation. We also investigated whether the association between numerical magnitude processing and mental and algorithmic computation differed for measures of symbolic versus nonsymbolic numerical magnitude processing. Results showed that symbolic, and not nonsymbolic, numerical magnitude processing was associated with mental computation, but not with algorithmic computation. Additional analyses showed, however, that the size of this association with symbolic numerical magnitude processing was not significantly different for mental and algorithmic computation. We also tried to further clarify the association between numerical magnitude processing and complex calculation by also including relevant arithmetical subskills, i.e. arithmetic facts, needed for complex calculation that are also known to be dependent on numerical magnitude processing. Results showed that the associations between symbolic numerical magnitude processing and mental and algorithmic computation were fully explained by individual differences in elementary arithmetic fact knowledge.