Mathematical difficulties as decoupling of expectation and developmental trajectories

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science

From Empire to Globalization: The New Zealand Experience

Globalization, Courts, and Judicial Power Symposiu

Risk and the Rule of law

In this article the author argues for the importance of law even in the face of a global pandemic, suggests some ways that law helps to reveal and articulate the moral issues at stake, and sketches the legal controversies surrounding the Covid-19 lockdown

Government to State: Globalization, Regulation, and Governments as Legal Persons

Globalization and Governance: The Prospects for Democracy, Symposiu

Government to State: Globalization, Regulation, and Governments as Legal Persons

Globalization and Governance: The Prospects for Democracy, Symposiu

Nature/nurture and the origin of individual differences in mathematics:evidence from infant and behavioural genetics studies

In this chapter, we discuss empirical evidence addressing the nature-nurture debate from two different perspectives: infant studies and behavioural genetics. Current evidence suggests that there are two cognitive systems for encoding numerical information, and perhaps core systems for geometry. However, questions remain about whether these systems are both present at birth and hence the degree of determinism and the mechanisms by which they connect to later mathematics are still far from established. Behavioural genetics studies offer a valuable way to assess the origin of individual differences in mathematical cognition and to discriminate between genetic and environmental contributions. We thus review relevant evidence on core quantitative knowledge, mathematical abilities and cross-domain relations from twin studies. We conclude by suggesting that while there is convincing evidence of nature’s general and specific role in mathematics, it is clear that environment plays a fundamental role too. The real question for the future is not whether mathematics has a natural core but how to optimise the interaction between nature and nurture so that differential domain-specific and domain-general predispositions can meet an ideal environment to blossom into competent mathematics

What children learn from adults’ utterances:an ephemeral lexical boost and persistent syntactic priming in adult–child dialogue

We show that children’s syntactic production is immediately affected by individual experiences of structures and verb–structure pairings within a dialogue, but that these effects have different timecourses. In a picture-matching game, three- to four-year-olds were more likely to describe a transitive action using a passive immediately after hearing the experimenter produce a passive than an active (abstract priming), and this tendency was stronger when the verb was repeated (lexical boost). The lexical boost disappeared after two intervening utterances, but the abstract priming effect persisted. This pattern did not differ significantly from control adults. Children also showed a cumulative priming effect. Our results suggest that whereas the same mechanism may underlie children’s immediate syntactic priming and long-term syntactic learning, different mechanisms underlie the lexical boost versus long-term learning of verb–structure links. They also suggest broad continuity of syntactic processing in production between this age group and adults

The relationship between numerical mapping abilities, maths achievement, and socio-economic status in 4- and 5-year-old children

Background: Early numeracy skills are associated with academic and life-long outcomes. Children from low-income backgrounds typically have poorer maths outcomes, and their learning can already be disadvantaged before they begin formal schooling. Understanding the relationship between the skills that support the acquisition of early maths skills could scaffold maths learning and improve life chances. Aims: The present study aimed to examine how the ability of children from different SES backgrounds to map between symbolic (Arabic numerals) and non-symbolic (dot arrays) at two difficulty ratios related to their math performance. Sample: Participants were 398 children in their first year of formal schooling (Mean age = 60 months), and 75% were from low SES backgrounds. Method: The children completed symbolic to non-symbolic and non-symbolic to symbolic mapping tasks at two difficulty ratios (1:2; 2:3) plus standardized maths tasks. Results: The results showed that all the children performed better for symbolic to non-symbolic mapping and when the ratio was 1:2. Mapping task performance was significantly related to maths task achievement, but low-SES children showed significantly lower performance on all tasks. Conclusion: The results suggest that mapping tasks could be a useful way to identify children at risk of low maths attainment.</p