More gist, better math: Fuzzy-trace theory-based investigation of the relationship between long-term memory and mathematical skills

Despite extensive research on the cognitive basis for mathematical activity, the associations between long-term memory and math skills remain relatively understudied. In our fuzzy-trace theory-driven study, we addressed this issue by investigating the relationships between long-term memory for numbers and prominent math skills, namely approximate number processing, arithmetic fluency, and math reasoning, along with math self-concept. Individuals who performed better in the numerical memory task demonstrated better math reasoning, a higher math self-concept, and were more arithmetically fluent. We did not find an association between memory and approximate number processing. Crucially, our memory task, based on the conjoint recognition model, allowed us to go beyond merely measuring overall performance and, as a result, to test fine-grained memory processes related to two memory traces: verbatim (remembering exact numbers) and gist (remembering a general intuition about a number's magnitude). While both gist and verbatim processes correlated with math reasoning, the associations involving gist-based processes were more prominent, which is consistent with one of the main assumptions of fuzzy-trace theory. This pattern was further supported by the results of the cluster-based analysis. On the other hand, even though math self-concept was positively associated with overall numerical memory performance, it correlated significantly only with verbatim-based process. Overall, our study shows the nuanced role of long-term memory processes in mathematical skills and demonstrates the power of fuzzy-trace theory and multinomial processing tree modeling in the fine-grained investigation of mathematical cognition.