Numerical relational and counting skills both develop nonlinearly between mid-Kindergarten year 1 and the end of Grade 1, with NRS decelerating and CS accelerating¶

Claim · All claims
Evidence · 1 study (2 entries) · associational r2 · q3
Currency · newest study 2026 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? In the population sample, NRS and CS both developed nonlinearly, with NRS decelerating and CS accelerating towards the end of Grade 1 without reaching ceiling. → Verkerk 2026 q3 i? Adding a quadratic term substantially improved model fit for both NRS and CS relative to linear-only growth models. → Verkerk 2026 (2)

Evidence¶

Verkerk 2026¶

Verkerk, J. C., van de Rijt, B., & van Viersen, S. (2026). Development of numerical relational and counting skills as components of early numeracy. Learning and Instruction. https://doi.org/10.1016/j.learninstruc.2025.102313

q3 · i? · associational · r2

Latent growth curve models on six time points of the Dutch population sample (N = 1252) using ENT-3 regression factor scores showed that "numerical relational and counting skills both developed nonlinearly", with NRS decelerating and CS accelerating towards the end of Grade 1.

"In the population sample, numerical relational and counting skills both developed nonlinearly, with numerical relational skills decelerating and counting skills accelerating towards the end of Grade 1 without reaching ceiling."

Verkerk 2026 (2)¶

Verkerk, J. C., van de Rijt, B., & van Viersen, S. (2026). Development of numerical relational and counting skills as components of early numeracy. Learning and Instruction. https://doi.org/10.1016/j.learninstruc.2025.102313

q3 · i? · associational · r2

Univariate LGCM comparison in the population sample: the quadratic model fit substantially better than the linear baseline, with Δχ2 (4) = 44.08 for NRS and Δχ2 (4) = 55.03 for CS, both p < .001, supported by lower AIC and BIC values.

"the addition of a quadratic effect of time resulted in a substantial improvement in model fit for both NRS (Δχ2 (4) = 44.08, p < .001) and CS (Δχ2 (4) = 55.03, p < .001)"

Discussion¶

Learner Variables¶

• Number Sense — predictor: learners who differ on it differ in outcomes

Related Claims¶

• At-risk learners show lower initial levels and delayed growth in early numeracy components, especially counting skills, relative to typically developing peers — related
• Initial levels and growth in numerical relational skills contribute to counting skill development, suggesting NRS may precede CS — related
• Correlations between NRS and CS decrease slightly over time, being stronger in kindergarten than in Grade 1 — related
• Children with higher initial levels in NRS or CS show slower subsequent linear growth in the same component — related
• The interdependence between numerical relational and counting skills is weaker in at-risk learners — related
• Early numeracy shows a two-factor structure (NRS and CS) on the Dutch ENT-3, with the two-factor model outperforming a one-factor model at several time points — related