Precursors of mathematics learning: identification and intervention

The studies presented in this thesis contribute to the growing body of knowledge regarding the relationships between domain general precursors, domain specific precursors and mathematical learning. Given the previous inconsistent results about the link between ANS acuity and mathematical abilities (i.e. Kolkman et al., 2013) we were interested in the investigation of the relation between the ANS and early mathematics abilities in preschool years. This relationship was explored by using two different approaches: in Chapter 2 the relationship between ANS and different mathematical measures, measured concurrently, were investigated; Chapter 3 examined the possibility to improve the ANS abilities in preschool children by using intensive adaptive training over a relatively short period. Moreover, the transfer effects of the training on mathematical abilities were also examined. The second aim of this dissertation concerned the potential role played by STM and WM skills in supporting domain-specific precursors of mathematics. The few studies that considered the role of WM in simple quantity comparison abilities did not provide a strong basis for any firm conclusions on such a relationship (Mussolin, Nys, Leybaert, & Content, 2012; Soltà©sz, Sz?cs, & Sz?cs, 2010) since they didn't assess all of the WM components. Chapter 2 focuses on uncovering which specific WM component is involved in non-symbolic approximate quantity comparison processing in the preschool age. Moreover, in ordered to further explore the relationship between WM abilities and ANS, Chapter 3 investigated whether training focusing on the improvement of ANS abilities produced a far-transfer effect on WM abilities. Several studies found that WM abilities are related to overall mathematical skills (Gersten et al., 2005; Jordan et al., 2006; Passolunghi & Lanfranchi, 2012), therefore Chapter 4 investigated a possible causal relationship between domain-general working memory abilities and domain-specific numerical competence through a training study during the preschool years. The third aim of this dissertation was to explore the malleability of cognitive precursors of mathematical learning. In Chapter 3, the possibility to improve ANS abilities was investigated, whereas Chapter 4 aimed to verify and compare the effects on early numerical competence of two types of training. One type of training focused on the enhancement of domain-general precursors, working memory abilities; while the other focused on the enhancement of domain-specific precursors, early numeracy abilities. In the field of intellectual disabilities, some studies suggested that WM skills of children with neurodevelopmental disorders (like Down's syndrome) tend to be impaired and very poor compared to typically developing children of a similar mental age (Gathercole & Alloway, 2006). In Chapter 5, the efficacy of a school-based visuo-spatial WM training on STM and WM skills for two individuals with DS was examined. The main findings emerging from overall studies and limitations, future directions and implications of the research are finally discussed in Chapter 6. ?