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 in multiplication and division, but not in addition, subtraction, or 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. This pattern was further supported by 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. We discuss our results in relation to the findings of previous fuzzy-trace theory-driven studies on mathematical cognition, highlighting discrepancies between them and their possible origins. Overall, our study shows the nuanced role of long-term memory in mathematical skills and demonstrates the power of fuzzy-trace theory in the fine-grained investigation of mathematical cognition.