Lisa Fast

Pathways to Mathematics: Longitudinal Predictors of Performance.

A model of the relations among cognitive precursors, early numeracy skill, and mathematical outcomes was tested for 182 children from 4.5 to 7.5 years of age. The model integrates research from neuroimaging, clinical populations, and normal development in children and adults. It includes 3 precursor pathways: quantitative, linguistic, and spatial attention. These pathways (a) contributed independently to early numeracy skills during preschool and kindergarten and (b) related differentially to performance on a variety of mathematical outcomes 2 years later. The success of the model in accounting for performance highlights the need to understand the fundamental underlying skills that contribute to diverse forms of mathematical competence.

Do home numeracy and literacy practices of Greek and Canadian parents predict the numeracy skills of kindergarten children

Children’s experiences with early numeracy and literacy activities are a likely source of individual differences in their preparation for academic learning in school. What factors predict differences in children’s experiences? We hypothesised that relations between parents’ practices and children’s numeracy skills would mediate the relations between numeracy skills and parents’ education, attitudes and expectations. Parents of Greek (N = 100) and Canadian (N = 104) five‐year‐old children completed a survey about parents’ home practices, academic expectations and attitudes; their children were tested on two numeracy measures (i.e., KeyMath‐Revised Numeration and next number generation). Greek parents reported numeracy and literacy activities less frequently than Canadian parents; however, the frequency of home numeracy activities that involved direct experiences with numbers or mathematical content (e.g., learning simple sums, mental math) was related to children’s numeracy skills in both countries. For Greek children, home literacy experiences (i.e., storybook exposure) also predicted numeracy outcomes. The mediation model was supported for Greek children, but for Canadian children, the parent factors had both direct and mediated relations with home practices.

Knowledge of counting principles: How relevant is order irrelevance?

Most children who are older than 6 years of age apply essential counting principles when they enumerate a set of objects. Essential principles include (a) one-to-one correspondence between items and count words, (b) stable order of the count words, and (c) cardinality-that the last number refers to numerosity. We found that the acquisition of a fourth principle, that the order in which items are counted is irrelevant, follows a different trajectory. The majority of 5- to 11-year-olds indicated that the order in which objects were counted was relevant, favoring a left-to-right, top-to-bottom order of counting. Only some 10- and 11-year-olds applied the principle of order irrelevance, and this knowledge was unrelated to their numeration skill. We conclude that the order irrelevance principle might not play an important role in the development of childrens conceptual knowledge of counting.

Development of Mathematical Knowledge in Young Children: Attentional Skill and the Use of Inversion.

The principle of inversion, that a + b − b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (2005). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion.