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This manuscript presents a study in which the new version of the computer-based training programme, The Number Race (NR), was used as an intervention for mathematically low-performing children in grade one (Mage = 86.46, SD = 3.89). In addition to ordinary teacher instruction in mathematics, the intervention group (n = 29) received NR training for 15 minute sessions, 3-4 days per week, during a four-week period.One comparison group comprising mathematically low-performing children (n = 27) and another comprising average-performing children (n = 278) received only ordinary teacher instruction in mathematics during this period. The children's mathematical skills (e.g. counting and basic arithmetic skills) were measured three times during grade one, using three parallel tests. The grouping was based on the first assessment, using the lowest 20th percentile as the cut-off point in the test. The NR intervention took place between the second and third assessments. There was no statistically significant NR intervention effect found in this study.

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Mathematical learning disabilities (MLD) are typically defined as difficulties in basic numerical skills. It has been suggested that number processing skills (i.e., enumeration and symbolic number comparison) would differentiate low achievement from more severe difficulties in mathematics. This study investigated the accuracy of number processing skills in identifying students with MLD based on arithmetic fluency and whether the classification ability of number processing skills varied as a function of grade level. Participants were 18,405 students (girls = 9,080) from third to ninth grade (9–15 years of age). Students’ basic numerical skills were assessed with an online dyscalculia screener aimed at identifying students with MLD. Confirmatory factor analyses supported a two-factor structure of the screener, with number processing skills and arithmetic fluency as the two factors. The two-factor structure was invariant across language groups, gender, and grade levels. Receiver operating characteristics curve analyses indicated that number processing skills are a fair classifier of MLD status across grade levels three to nine. The classification accuracy of number processing skills was better when predicting MLD (cut-off < 5%) compared to low achievement (cut-off < 25%) status. Results highlight the need to measure both number processing and arithmetic fluency when identifying students with MLD.

The aim of this study was to investigate individual differences in mathematical problem-solving among 3- to 5-year-old children (N = 328; n3-year-olds = 115, n4-year-olds = 167, n5-year-olds = 46). First, we examined the extent to which children in this age group were able to solve open and closed non-routine mathematical problems representing a variety of mathematical domains. Second, we investigated the extent to which underlying academic and cognitive skills (i.e., expressive and receptive language, visuospatial, and early numeracy skills) were associated with individual differences in mathematical problem-solving concurrently and longitudinally (i.e., one year later). The results showed that 4- to 5-year-olds were able to solve a variety of non-routine mathematical problems. However, though 3-year-olds were also able to solve a variety of problems, the mathematical problem-solving measure did not meet the reliability criteria, resulting in excluding 3-year-olds from further analyses. Expressive and receptive language, visuospatial, and early numeracy skills were associated with mathematical problem-solving concurrently among 4-year-olds. Among 5-year-olds, only visuospatial and early numeracy skills were associated with mathematical problem-solving. Furthermore, only prior mathematical problem-solving skills and early numeracy skills predicted mathematical problem-solving skills longitudinally. These findings indicate that preschoolers are able to solve open and closed non-routine mathematical problems representing a variety of mathematical domains. Additionally, individual differences may stem not only from differences in mathematical problem-solving skills but also from early numeracy.