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AbstractFinger counting is widely considered an important step in children's early mathematical development. Presumably, children's ability to move their fingers during early counting experiences to aid number representation depends in part on their early fine motor skills (FMS). Specifically, FMS should link to children's procedural counting skills through consistent repetition of finger‐counting procedures. Accordingly, we hypothesized that (a) FMS are linked to early counting skills, and (b) greater FMS relate to conceptual counting knowledge (e.g., cardinality, abstraction, order irrelevance) via procedural counting skills (i.e., one–one correspondence and correctness of verbal counting). Preschool children (N = 177) were administered measures of procedural counting skills, conceptual counting knowledge, FMS, and general cognitive skills along with parent questionnaires on home mathematics and fine motor environment. FMS correlated with procedural counting skills and conceptual counting knowledge after controlling for cognitive skills, chronological age, home mathematics and FMS environments. Moreover, the relationship between FMS and conceptual counting knowledge was mediated by procedural counting skills. Findings suggest that FMS play a role in early counting and therewith conceptual counting knowledge.

AbstractSpatial processing of numbers has emerged as one of the basic properties of humans' mathematical thinking. However, how and when number–space relations develop is a highly contested issue. One dominant view has been that a link between numbers and left/right spatial directions is constructed based on directional experience associated with reading and writing. However, some early forms of a number–space link have been observed in preschool children who cannot yet read and write. As literacy experience is evidently not necessary for number–space effects, we are searching for other potential sources of this association. Here we propose and test a hypothesis that the number–space link can be quickly constructed in preschool children's cognition on the basis of spatially oriented visuo‐motor activities. We trained 3‐ and 4‐year‐old children with a non‐numerical spatial movement task (left‐to‐right or right‐to‐left), where via touch screen children had to move a frog across a pond. After the training, children had to perform a numerosity comparison task. After left‐to‐right training, we observed a SNARC‐like effect (reactions to smaller numbers were faster on the left side, and reactions to larger numbers on the right side), and after right‐to‐left training a reverse effect. These results are the first to show a causal link between visuo‐motor activities and number–space associations in children before they learn to read and write. We argue that simple activities, such as manual games, dominant in a given society, might shape number–space associations in children in a way similar to lifelong reading training.

In today's society, mathematics is one of the most important competencies imparted in school. To improve children's mathematical skills, existing interventions and trainings in mathematical learning address different proficiency levels and age groups, take place in different settings, can focus on a single task or a set of different tasks, be applied for different durations, and address different types of numerical content. However, when such trainings are evaluated, this often happens only insufficiently. In this review, we derive and apply four evaluation criteria in a meta-analysis of mathematical intervention literature: (i) evaluation with the actual target group, (ii) evaluation in comparison to a performance-matched control group, (iii) evaluation in comparison to a comparable alternative intervention, and (iv) separate evaluation of subcomponents in the case of multi-componential approaches. Based on these criteria, we review current intervention approaches, paying particular attention to how they were evaluated. A meta-analysis on 39 effect sizes extracted from 37 studies revealed a reliable impact of three of the above-proposed evaluation criteria on the reported efficacy of an intervention. In contrast, sample and methodological characteristics like grade level of participants or training duration were not associated with effect sizes. These data indicate that the reported efficacy of an intervention in mathematical learning may depend not only on the type of intervention conducted, but also on the thoroughness of the evaluation procedure.