From developmental theory to effective training: long-term and transfer effects of promoting the quantity-to-number word linkage in first-graders at risk for mathematical difficulties

The model of quantity-to-number word linkage (QNL model) identifies relevant milestones in the process of early numerical acquisition and describes a developmental sequence that can guide the fostering of foundational mathematical abilities in at-risk children. While there is substantial evidence for the predictive value of the quantity-number competencies (QNC) described by the model, evidence supporting the preventive potential of interventions targeting these QNC is so far largely restricted to short-term effects. Findings regarding their long-term preventive impact, especially in terms of transfer to mathematical school achievement, are still limited. This quasi-experimental study aimed to address this gap by evaluating the long-term transfer effects of an intervention program that is strictly derived from the QNL model of mathematical development [QNL training; in German "Mengen, zählen, Zahlen" (MZZ)].

We assessed the quantity-number competencies of 575 first-graders and identified 119 of them as being at risk for mathematical learning difficulties, who were then assigned to three experimental conditions. Sixty one children received 12 sessions of the QNL training, while 30 underwent training in inductive reasoning. Another 28 children served as a control group, receiving no specific intervention.

Multi-level analyses confirmed both significant short-and long-term effects in the specifically trained quantity-number competencies as well as transfer effects on subsequent mathematical school achievement. In accordance with previous findings, transfer effects of the QNL training on mathematical school achievement were not yet evident immediately after the intervention but turned out to be significant after a delay of 6 months and remained stable even 15 months after training. Effect sizes ranged from d = 0.32 to d = 1.12. These findings both underscore the preventive potential of interventions that are strictly driven by developmental theory and, conversely, support the theoretical assumptions of the QNL model.