Beyond Span: How Working Memory Precision Reshapes Pathways to Mathematics Through Its Interplay With Quantity Processing

Background: Research on working memory (WM) in mathematics skills has focusedextensively on span-based capacity, overlooking representational fidelity, WM precision, which is crucial during precise numerical development. Inconsistent findings exist regarding the interplay between domain-general WM and number sense on mathematics skills. Aims: Based on the Pathways to Mathematics model, we tested three hypotheses: (1) direct effects of WM span and precision on mathematics skills; (2) moderation effect of number sense in the association between WM span or precision and mathematics skills; (3) indirect effects of WM span and precision on mathematics through number sense.Sample: Participants were 285 Chinese third graders. Method: Measurements included WM span, WM precision, number sense, math factsfluency, word problems tasks. Results: After controlling for nonverbal intelligence and receptive vocabulary, structural equation modelling results indicated that WM span directly predicted math facts fluency and word problem solving, while WM precision indirectly influenced word problem solving via number line estimation. Moreover, WM precision moderated the effect of non-symbolic comparison on math facts fluency, with a positive effect observed only in children with high WM precision. Conclusion: These findings extended the Pathways to Mathematics model by incorporating WM precision as a core cognitive mechanism and demonstrating integration between distinct pathways (WM and quantity processing) on mathematic skills, suggesting that educators should move beyond WM capacity and consider the quality of students' mental representations when identifying math difficulties. Teaching strategies that focus on improving precise visual and numerical representations during math instruction may better support children struggling with mathematics.