The aim of this study was to model the most crucial numerical factors to the development of mathematical skills among children aged five to eight years (i.e. kindergarten, preschool, first and second graders). We categorised numerical skills into four main groups based on the results of longitudinal studies. A series of analyses of test batteries designed to measure the development of mathematical skills in children yielded results in support of this construct. Based on our findings we propose a working model for teachers of core numerical skills that focuses on four major factors: (1) symbolic and non-symbolic number sense; (2) understanding mathematical relations (early mathematical-logical principles, arithmetic principles, mathematical operational symbols, place-value and base-ten system); (3) counting skills (knowledge of number-symbols, number word-sequence, enumeration with concrete objects); and (4) basic skills in arithmetic (arithmetic combinations, addition and subtraction skills with number symbols). The adoption of this working model could improve the efficacy of the assessment of numerical skills of children, but also help educators to structure their support more comprehensively.

This research investigated the similarities and differences between countries in young children’s early numeracy skills related to age, culture, and gender. The participants were five‐year‐old children from Beijing (People’s Republic of China), England, and Finland. The rationale for the cross‐cultural comparison originates from research results with older children showing that Asian children outperform children from America or Europe, and from the lack of such information concerning younger children. The results showed that in all locations older children performed better than the younger children. Cultural differences were found: young children from Beijing outperformed those from England and Finland in overall early numeracy performance, as well as in sub‐tests for understanding of quantities and relations (i.e. relational skills), and counting skills. Finnish children had better scores than English children in the whole early numeracy scale and in the relational scale. The results are discussed in relation to culture, instruction in preschools, and learning support at home, as well as the effects of language characteristics. The culture’s appreciation of and approach to mathematics learning in early childhood is a plausible explanation for the cross‐cultural differences found in this study.

This systematic review investigates the characteristics of effective mathematics interventions for students with intellectual disabilities (ID) age 5 to 12, focusing on early numeracy, arithmetic, and arithmetical problem solving skills. Twenty studies from 2008–2020 were reviewed: 17 had a single-subject design and three a group-comparison design. The studies included a total of 135 students with ID. Consistent with previous studies, the analysis showed that interventions with systematic and explicit instruction with feedback and the use of manipulatives are effective instructional approaches and strategies for students with ID. This study reveals that effective interventions are well-structured, high intensity learning sequences adapted to the students’ achievement level. The intensity of an intervention requires careful consideration of the number of intervention sessions per week and their duration. Further studies should investigate which instructional strategy is most effective for each type of skill and the optimum intensity of interventions.