Arithmetic Training Does Not Improve Approximate Number System Acuity

Abstract

The approximate number system (ANS) is thought to support non-symbolic representations of numerical magnitudes in humans. Recently much debate has focused on the causal direction for an observed relation between ANS acuity and arithmetic fluency. Here we investigate if arithmetic training can improve ANS acuity. We show with an experimental training study consisting of six 45-min training sessions that although feedback during arithmetic training improves arithmetic performance substantially, it does not influence ANS acuity. Hence, we find no support for a causal link where symbolic arithmetic training influences ANS acuity. Further, although short-term number memory is likely involved in arithmetic tasks we did not find that short-term memory capacity for numbers, measured by a digit-span test, was effected by arithmetic training. This suggests that the improvement in arithmetic fluency may have occurred independent of short-term memory efficiency, but rather due to long-term memory processes and/or mental calculation strategy development. The theoretical implications of these findings are discussed.

More Space, Better Mathematics: Is Space a Powerful Tool or a Cornerstone for Understanding Arithmetic?

“…However, no such cross-over effect was observed in another large-scale study with children randomly assigned to different groups including training on exact numerosities (Obersteiner, Reiss, & Ufer, 2013). Another recent study corroborated this negative result that extensive arithmetic training and substantial improvements in arithmetic performance were not reflected in matching ANS acuity changes (Lindskog, Winman, & Poom, 2016). A possible indication of these inconsistent results would be to focus on the processes involved in mathematical operations and not only on the assumed numerical representation.…”

Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

“…Nuances in the casual nature of this relation are also important to note. For instance, while training nonsymbolic number appears to improve math performance, training math skills does not lead to enhanced numerical acuity (Lindskog, Winman, & Poom, 2016), and adults' math abilities appear to improve only when the nonsymbolic number training involves manipulating approximate quantities, rather than just comparing them (Park & Brannon, 2014). Importantly, this relation would still be likely if a domain-specific module, such as the ANS, were responsible for numerical processing.…”

Neurodevelopmental differences in task-evoked number network connectivity: Comparing symbolic and nonsymbolic number discrimination in children and adults

“…This pattern of results indicates that children may require the mapping of both symbolic and nonsymbolic numerical referents to an amodal and abstract magnitude representation, while developmental maturation could serve two main effects: a decoupling of the functional circuitry supporting symbolic (memory-based) and nonsymbolic (visuospatial) number processing; and the establishment of integrated circuits for retrieval, working memory, and visuospatial processes for format-independent number processing ( Kaufmann et al, 2011 ). Moreover, these results could be of explanatory value for reported absences of transfer effects between symbolic arithmetic ability and ANS acuity in adults ( Lindskog et al, 2016 ), implying that symbolic and nonsymbolic numerical cognition may become decoupled over developmental time. While the current results describe connectivity patterns between theoretically motivated regions and provide hypotheses for their cognitive-behavioral implications, future research should attempt to broaden the scope of developmental connectivity differences in number processing.…”