Improving preschoolers' number foundations

Mathematical competence is crucial for educational and financial success in modern societies. There is currently debate whether mathematical abilities later on in life depend on symbolic knowledge, such as counting abilities and digit recognition, or whether they rely upon non-symbolic knowledge, such as the ability to discriminate between large magnitudes that rely upon the approximate number sense (ANS). However, it is unclear whether symbolic abilities rely on non-symbolic ones (one-representation view) or whether symbolic and non-symbolic abilities are distinct systems (dual-representation view). Knowing what abilities predict mathematical success later on in life is important for the development of economically valid and efficient educational programmes, especially for those children who perform low on mathematical ability tasks or low achievers (LA). Our previous studies had shown that specially developed PLUS games, which target ANS abilities and require children to guess and see where is “more” or “less” very quickly, improved typically developing preschooler’s ANS abilities. However, it was unclear how the PLUS games compared to other training programmes, for example those that target symbolic knowledge, and whether the PLUS programme would benefit children who perform low on mathematical ability tasks. In this study we first examined which children performed low on mathematical ability tasks. Next, we compared the impact of two different training programmes on LA children’s ANS knowledge, their symbolic knowledge, and their mathematical abilities in general. One of the training programmes focused on nonsymbolic abilities using PLUS games, which targeted children’s ANS abilities, and the other programme included DIGIT games that targeted symbolic knowledge and focused on children’s counting abilities and digit knowledge. We included preschoolers as they would have received little formal education so far and thus have limited symbolic knowledge. In addition, we targeted those preschoolers who were performing below average on mathematical ability tasks and who had low ANS abilities. The inclusion of children who had both little symbolic and non-symbolic abilities allowed us to examine the foundations of mathematical abilities and to observe which training programme would benefit children’s general mathematical outcomes most. We predicted that if ANS abilities form the basis of mathematical abilities then children in the PLUS group would improve more than those in the DIGIT group. However, if non-symbolic and symbolic knowledge are two distinct systems then children in the DIGIT group should show improved mathematical abilities. Our results showed that, although there are a number of reasons why preschoolers perform low on mathematical ability tasks, most children identified as LA had low ANS abilities as well. This confirms results in previous studies that have found that ANS abilities are important for children’s mathematical abilities. The results from the training study showed that both training groups improved equally on a number of mathematical ability tasks that assess symbolic knowledge, including counting abilities, digit recognition, and understanding of counting as well as those that require non-symbolic knowledge, including ANS abilities. Finally, both groups showed improved general mathematical abilities and over 50% of LA children were no longer considered as low achievers on mathematical ability tasks six months later. Therefore, the current results suggest that LA preschoolers benefit from playing daily mathematical games that target both non-symbolic abilities, the PLUS games, as well as symbolic ones, the DIGIT games. In addition, there is a complex interaction between symbolic, non-symbolic abilities, and mathematical cognition in preschoolers in that children who played DIGIT games also showed improved nonsymbolic abilities. Future studies should examine longitudinal outcomes and assesses which LA children continue to show mathematical difficulties or whether the training programmes benefit LA children long term. In addition, larger controlled trials are needed to verify the current findings. Based upon the current results we would recommend that all preschool children engage in daily games that support mathematical development, including both PLUS and DIGIT games, as this will allow LA children to reach their full potential.