By Ann Dowker

ISBN-10: 0203324897

ISBN-13: 9780203324899

ISBN-10: 1841692352

ISBN-13: 9781841692357

Criteria in numeracy are a relentless trouble to academic policy-makers. although, why are variations in arithmetical functionality so marked? In person alterations in mathematics, Ann Dowker seeks to supply a greater realizing of why those modifications in skill exist, encouraging a extra knowledgeable method of tackling numeracy problems. This booklet stories present learn via the writer and through others just about arithmetical skill and provides powerful proof to aid a componential view of mathematics. Focusing totally on young ones, yet together with dialogue of arithmetical cognition in fit adults and neuropsychological sufferers, all the important parts of arithmetic is lined. inside of this quantity, findings from developmental, academic, cognitive and neuropsychological stories are built-in in a distinct method. This publication covers matters similar to: Counting and the significance of person variations. mathematics proof, methods and varied types of reminiscence. explanations of, and interventions with, mathematical problems. the results of tradition, language and event. the tutorial implications of those findings are mentioned intimately, revealing unique insights that would be of serious curiosity to these learning or gaining knowledge of within the parts of schooling, neuroscience and developmental and cognitive psychology.

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There have been a few attempts to classify the mental processes involved in learning and doing arithmetic. The classifications differ in detail and in the number of processes that they involve, but they concur that arithmetic cannot be treated as a single system or process. Ginsburg (1972, p. 10) proposed at least four ‘relatively autonomous cognitive systems’: a system for calculation procedures, a system for estimation, a system of formal knowledge (involving explicit knowledge of arithmetical facts and concepts such as place value) and a system of informal knowledge (involving arithmetical concepts such as ‘more’ and ‘less’, which are acquired by all children without a need for formal teaching).

Indeed, some attempts to model human mathematical cognition through artificial intelligence programs have emphasized flexibility and inventiveness in strategy use rather than honing in on one optimal strategy. Defays’ (1995) ‘Numbo’ program is a notable example. Do numerically gifted people make mistakes in arithmetic? Professional academic mathematicians are one group who have been selected and selfselected for talent in at least some aspects of mathematics, although not necessarily arithmetic.

When they get bitty. ’ (Claire, aged 28) Fractions and decimals pose difficulty for many children and adolescents (Hart, 1981) and are often confusing even to adults who have received extended education in mathematics. As indicated earlier, Hitch (1978) found that industrial apprentices had a lot of difficulty with mathematics. Moreover, unlike most other arithmetical tasks, fraction and decimal arithmetic, and conceptual tasks involving ‘ratio, proportion and percentage’ showed only a weak correlation with grades obtained on the CSE mathematics examination (an examination given at that time to British school leavers of average or somewhat above average ability).

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Individual Differences in Arithmetical Abilities: Implications for Psychology, Neuroscience and Education by Ann Dowker

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