Mathematical skills play a vital role in achieving individual well-being and professional development, while also contributing significantly to societal advancement (OECD, 2016). Research has revealed that numeracy and math achievements emerge from configurations of both domain-specific and domain-general cognitive processes. Particularly, numerous studies have focused on the involvement of the memory system in mathematical cognition, revealing that working memory capacity (Peng et al., 2016, J. Educ. Psychol.) and the performance of arithmetic fact retrieval constitute robust predictors of math skills (Geary, 2011, Dev. Behav. Pediatr.). Notably, a reduced ability to memorize and retrieve basic arithmetic facts is among the diagnostic criteria for dyscalculia (DSM-5-TR, 2022, APA). Surprisingly, the contribution of more fine-grained long-term memory processes associated with verbatim (the exact information) and gist (the information’s meaning), as distinguished by the Fuzzy-Trace Theory (Reyna & Brainerd, 2023, Nat. Rev. Psychol.) to mathematical cognition has received little attention (Obidziński, Bażela, Hohol, 2025), even though the theory has already been applied in the context of early numeracy (Brust-Renck & Reyna, 2023, Risk Anal.). What is more, although credible, previous research on memory systems—namely, working memory and facts retrieval—and mathematical cognition has mostly stemmed from different theoretical frameworks, which has made it difficult to draw more general conclusions. Last but not least, previous research on the cognitive determinants and correlates of poor math skills has focused primarily on deficits, leaving compensatory mechanisms largely overlooked.
The project aims to fill these research gaps by applying the Fuzzy-Trace Theory and multinomial processing tree modeling as a unified approach to investigate the relationships between different dimensions of gist and verbatim memory and mathematical skills, with particular emphasis on possible, so far overlooked, fine-grained memory deficits and compensatory mechanisms in dyscalculia. The project will be divided into three phases. In the first two phases, we aim to conduct a series of behavioral experiments to investigate the relationships between different dimensions of numerical memory and mathematical skills in two groups: typically developing young adults (first phase) and young adults with developmental dyscalculia and matched controls (second phase).
Dimensions of numerical memory to be investigated will include verbatim and gist long-term memory for symbolic and non-symbolic numerical material, working memory in the context of verbatim and gist representation of numerical information, and arithmetic facts retrieval. All of them will be measured with entirely novel or substantially revised tasks grounded in the Fuzzy-Trace Theory. Math skills will include non-symbolic and symbolic numerical magnitude processing, arithmetic fluency, math reasoning, and spatial processing and will be assessed using well-recognized paradigms. In the final phase, we will address an additional research question regarding the possibility of classifying participants into those with dyscalculia and those without it through data mining, based on patterns found in the studies conducted during the second phase. Additionally, in the third phase we will prepare and publish a dataset containing all the collected data and submit an opinion paper summarizing all the project’s advances and the new research questions and avenues it inspires.
As the Fuzzy-Trace Theory, though widely applied in research on memory and reasoning (Brainerd, Bialer, Chang, 2022, JEP:LMC), has been somewhat overlooked by the majority of mathematical cognition researchers, the project aims to establish bridges between representatives of these vital research traditions. Importantly, it has the potential to shed new light on the cognitive mechanisms underlying individual differences in mathematical skills, with particular emphasis on the lower end of their continuum. Finally, the project results could serve as a foundation for future interventions aimed at helping individuals with dyscalculia.
