Trial-level analysis replicates discrete-trials effects: fluency decreases with problem size, is faster for addition than subtraction, and increases across grade¶

Claim · All claims
Evidence · 1 study (2 entries) · associational r3 · q3
Currency · newest study 2025 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? In linear-mixed effects models, RPM decreased by an average of 2.03 problems per minute per one-unit increase in problem size and was faster for addition than subtraction, with older students more fluent than younger students. → Ethan Roy 2025

Evidence¶

Ethan Roy 2025¶

Ethan Roy, Mathieu Guillaume, Amandine Van Rinsveld, Project iLead Consortium & Bruce D. McCandliss. (2025). Tablet-based arithmetic fluency assessment reveals developments in math cognition and math achievement from childhood to adolescence. npj Science of Learning. https://doi.org/10.1038/s41539-025-00314-5

q3 · i? · associational · r3

Linear-mixed effects model of RPM with random intercepts per participant, fixed effects of problem size, operation, and grade. The article reports "an average decrease in RPM of 2.03 problems per minute with a one-unit increase in problem size" (partial R2 = 0.020), and grade and operation main effects, all FDR-corrected; partial R2 from regression is not treated as an effect size.

"Students tended to speed up when solving smaller problems, with an average decrease in RPM of 2.03 problems per minute with a one-unit increase in problem size (R2partial = 0.020, t(10,780) =−16.47,padj <0.001"

Ethan Roy 2025 (2)¶

Ethan Roy, Mathieu Guillaume, Amandine Van Rinsveld, Project iLead Consortium & Bruce D. McCandliss. (2025). Tablet-based arithmetic fluency assessment reveals developments in math cognition and math achievement from childhood to adolescence. npj Science of Learning. https://doi.org/10.1038/s41539-025-00314-5

q3 · i? · associational · r3

Same mixed-effects model examining operation effects on RPM. The article reports addition was answered at a "slightly, yet significantly, faster rate compared to subtraction problems" (partial R2 = 0.003), noting operation is confounded with problem size because subtraction problems generally have smaller solutions; no standardized effect size is printed.

"This model also revealed that, on average,students correctly answered addition problems at a slightly, yet significantly, faster rate compared to subtraction problems (R2partial = 0.003, t(10,800) =−6.62,padj < 0.001, Fig.2a)"

Discussion¶

Related Claims¶

• Students across all grades answer exceptional problems (ties, successor, identity) faster than common problems — related
• The problem-size effect on fluency is slightly steeper for subtraction than addition problems — related
• Children shift from counting to memory-based retrieval strategies in single-digit addition over a 1.2-year interval in middle childhood — related
• Older participants learn faster across all territories while younger participants learn better in the environment where a hidden agent generates positive outcomes — related