The role of mental representations of order in mathematical cognition: a developmental approach
Many authors have focused on the importance of magnitude inthe development of mathematical abilities. However, given that ordinality isalso an important aspect of number, there are now several studies which haveshown that numerical ordering abilities are also important to mathematicaldevelopment, although relatively few developmental studies have considered thecontribution of non-numerical ordering skills, and most have not considered theimportance of ordering skills involving ordinal sequences that are familiar toeven very young children, such as the order of familiar everyday tasks andfamiliar daily events. The current thesis attempted to address the question ofwhether order-processing skills were predictive of maths achievement during thefoundation years (between the ages of 4-6) and during Key Stage 2 (between theages of 8-11). Since the school starting age of children in Northern Ireland isthe youngest in Europe, the current thesis provides an insight into skills thatare important for maths learning amongst very young children at the beginningof primary school, as well as amongst children who are preparing to leaveprimary school. The findings of the empirical chapters in this thesis support theimportance of numerical and non-numerical ordering skills across childhood. Thenovel finding was that non-numerical ordering skills, involving the ordering offamiliar content, were shown to be important to early maths learning.Furthermore, order-processing skills were also shown to be involved in thedevelopment of mathematical and reading skills IV amongst older children,showing that order- processing skills may also be involved in other academicsubjects. The findings of the current thesis suggest that order-processingskills are important to mathematical development across childhood. Orderingskills, involving the ordering of familiar content, may be a suitable candidatefor the creation of diagnostic tools to identify children with mathematical difficultiesat an early stage, as well as providing the basis for a mathematicalintervention. Further research into order-processing skills may involveassessing exactly how these skills they are related to reading development,investigating whether ordering skills are linked to other cognitive disorders(such as Gerstmann’s syndrome), as well as assessing whether order-processingskills are also linked to maths achievement in children educated vianon-mainstream educational pedagogies, such as the Steiner-Waldorf andMontessori pedagogies.
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