Math Development

Children with higher mathematics scores at 7 years of age tend to command a higher salary as adults and experience better psychological and health outcomes. Despite the importance of mathematical skills, there are gaps in (a) our knowledge regarding the early predictors of later mathematical success, and (b) how to help pre-schoolers build solid foundations for mathematics learning. These issues will be examined in three interconnected projects. Using behavioural and neuroimaging techniques, in Project 1, we will examine the neuroanatomical correlates of numeracy development from 4.5 to 6.5 years of age with a view towards identifying markers that will predict mathematics learning difficulties. Such markers will also be used to understand differences in rates of growth in numeracy skill and in responses to intervention. A domain-general cognitive capability that has consistently predicted mathematical achievement is our ability to process and remember information simultaneously: working memory. Studies have shown that even amongst pre-schoolers, working memory and mathematical achievement exhibit variation across socio-economic strata. However, the processes that underlie these relations are unclear. In Project 2, we examine candidate processes related to parenting quality and examine how variation across socio-economic strata influences growth in working memory and numeracy. Using a cross-sequential longitudinal design, we will supplement efforts from an on-going study. Capitalising on findings from the other two projects, in Project 3, we will design a computerised working memory and numeracy intervention protocol for pre-schoolers. Using a randomised controlled design with an immediate and delayed evaluation, we will collect both behavioural and neuroimaging data; first to evaluate the efficacy of the intervention, but also to identify the characteristics of children who exhibit different patterns of response to intervention.

The purpose of this study is to investigate kindergarteners' understanding of whole number and fraction magnitude. In particular, the study focusses on the interplay of symbolic and non-symbolic magnitude processing skills and the acquisition, development, and interrelation of whole number and fraction magnitude. Whilst the past 10-15 years have witnessed the emergence of a highly influential line of research on number magnitude, it is still unknown how symbolic and non-symbolic magnitude processing skills jointly develop (and interact) over the preschool years does acuity in non-symbolic processing boost symbolic processing, or vice versa? It is also unknown how such skills affect the acquisition of fraction knowledge. This is relevant, given that understanding fraction magnitude requires a refinement of the concept of whole number, and children's difficulties with fractions persist into adulthood. Such understanding of fractions is thought to start in the form of non-symbolic fraction understanding early in development, presents persistent difficulties for children and is critical for subsequent math learning (CCSSI, 2010; NCTM, 2000). Longitudinal measures of whole number magnitude processing skills (symbolic and non-symbolic) and fraction magnitude (symbolic and non-symbolic) will afford opportunities to chart how those skills jointly develop, i.e., whether those relations become stronger or weaker over time and affect children's math achievement. A cross-lagged panel design and mediation models will be used to that end. Findings from the current research proposal may provide insights into the appropriateness of early stimulation of fraction magnitude understanding in kindergarteners. Whilst the new MOE kindergarten curriculum (NEL framework) equips teachers with a variety of activities to support the understanding of whole number magnitude (matching, comparing, ordering, and representing numbers in a variety of ways), it lacks activities that stimulate children's understanding of other types of numbers. Critically, one of the most persistent problems for children with mathematical difficulties is solving problems involving fractions (NCTM, 2000).

Unlike learning words for objects, learning the meaning of number words such as one, two and three takes years to master. Although children produce number words early and can typically count from one to ten by the age of 2 to 3, numerous studies have shown that the mastery of number words can take, on average, 2 to 3 years (see Sarnecka, 2015, for reviews). Studies have robustly shown that children learn the first few number words one at a time, and after learning the meaning of three or four, children are said to have acquired counting and the meaning of the rest of the number words. This is a significant step in children's number development, because recent studies have shown that the earlier children acquire counting, the better they are at understanding Arabic numerals, which are foundational in mathematics (Geary, 2018). Nevertheless, little is known about what predicts children's learning of the first few number words, and how we may facilitate their learning. This is important, because the earlier children learn the first few number words, the sooner they will be at acquiring the meaning of counting. In addition, it remains unknown how learning more than one language affects number word learning. A growing number of children are now raised in a bilingual language environment. However, thus far, only two studies have examined bilingual children's number development, and they have found conflicting findings with respect to whether number knowledge transfers between languages (Sarnecka, Negen, & Goldman, 2017; Wagner, Kimura, Cheung, & Barner, 2015). Given the significance of learning number word meanings in the development of later mathematics, and the fact that bilingual number development remains largely unexplored, the proposed project examines when and how 2- to 5-year-old bilingual children learn number words in four studies. The goal of the proposed project is twofold: (1) to document the developmental trajectory of number word learning in a bilingual population - Singapore, and (2) to investigate external factors (e.g., language input of teachers and parents, visual comparisons) and internal factors (e.g., children's engagement level) that may facilitate children's learning of number word meanings. We also aim to address the role of language dominance in bilingual number development. Overall, the four proposed studies will provide insights into number development in bilingual children in Singapore. Our findings on whether input and child-related factors predict the acquisition of number word meanings will also have implications for monolingual children's number development.

In our previous work, we designed and evaluated a computer-based training programme based on the Running Span and Keep Track paradigms. Conducted with children from the Learning Support Programme for Mathematics (LSM), we found training resulted in improvements at immediate post-test, which was sustained and significant six months post-training. Nonetheless, intervention did not result in better mathematics performance relative to control. In the proposed study, we will be working with our MoE colleagues to refine the training further. Several major changes will be made to the protocol. First, duration of intervention will be reduced to 10 - 15 minutes per session to allow training to be used during class time by teachers. With the significantly reduced training time per session, the length of the overall training will be lengthened . Training effects will be evaluated by comparison between performances on working memory and mathematics tasks prior to training, 6, 12, and 18 months into training. Second, a numeric training protocol will be used for children whose difficulties are related primarily to basic numeracy. Third, we will test a protocol in which working memory based training is combined with basic numeracy training. The multiple data points will afford opportunities to chart the development of fundamental math skills in this group of children, which have been shown to be at risk of long term delays.