Individual differences in numerical abilities in preschoolers

This study investigated individual differences in different aspects of early number concepts in preschoolers. Eighty 4-year-olds from Oxford nursery classes took part. They were tested on accuracy of counting sets of objects; the cardinal word principle; the order irrelevance principle; and predicting the results of repeated addition and subtraction by 1 from a set of objects. There were marked individual differences for most tasks. Most children were reasonably proficient at counting and 70% understood the cardinal word principle. Based on the results of a repeated addition and subtraction by 1 task, the children were divided into three approximately equal groups: those who were already able to use an internalized counting sequence for the simplest forms of addition and subtraction; those who relied on a repeated 'counting-all' procedure for such tasks; and those who were as yet unable to cope with such tasks. In each group, significant relationships between some, but not all, of the numerical tasks were found. However, for almost any two tasks, it was possible to find individuals who could carry out either one of the tasks but not the other. Thus, even before formal instruction, arithmetical cognition is not unitary but is made up of many components.     

Use of derived fact strategies by children with mathematical difficulties

339 children aged 6 and 7 at Oxford primary schools took part in a study of arithmetic. 204 of the children had been selected by their teachers as having mathematical difficulties and the other 135 children were unselected. They were assigned to an Addition Performance Level on the basis of a calculation pretest, and then given Dowker's (1998) test of derived fact strategies in addition, involving strategies based on the Identity, Commutativity, Addend + 1, Addend − 1, and addition/subtraction Inverse principles. The exact arithmetic problems given varied according to the child's previously assessed calculation level and were selected to be just a little too difficult for the child to solve unaided. The technique was used of giving children the answer to a problem and then asking them to solve another problem that could be solved quickly by using this answer, together with the principle under consideration. The children were also given the WISC Arithmetic subtest and the British Abilities Scales Basic Number Skills Subtest. Performance on the standardized arithmetic tests was independently affected by both Addition Performance Level and group membership (unselected children versus those with mathematical difficulties). Derived fact strategy use was affected by Addition Performance Level, but there was no independent effect of group membership.     

Abstraction and perceptual individuation in primed word identification are modulated by distortion and repetition: A dissociation

One experiment investigated the effects of distortion and multiple prime repetition (super-repetition) on repetition priming using divided-visual-field word identification at test and mixed-case words (e.g., goAT). The experiment measured form-specificity (the effect of matching lettercase at study and test) for two non-conceptual study tasks. For an ideal typeface, super-repetition increased form-independent priming leaving form-specificity constant. The opposite pattern was found for a distorted typeface; super-repetition increased form-specificity, leaving form-independent priming constant. These priming effects did not depend on the study task or test hemifield for either typeface. An additional finding was that only the ideal typeface showed the usual advantage of right hemifield presentation. These results demonstrate that super-repetition produced abstraction for the ideal typeface and perceptual individuation for the distorted typeface; abstraction and perceptual individuation dissociated. We suggest that there is a fundamental duality between perceptual individuation and abstraction consistent with Tulving's (1984 Tulving, E. 1984. Precis of elements of episodic memory. The Behavioral and Brain Sciences, 7: 223–268. [Crossref], [Web of Science ®] , [Google Scholar]) distinction between episodic and semantic memory. This could reflect a duality of system or process.     

The role of cues to differential absolute size in children's transitive inferences

To investigate the role that "nonlogical" cues might play in transitive inference, 6- and 7-year-olds were given a three-term transitive task in which perceptual cues to differential absolute size were either present or absent. Relationships between the taught premises and the relational information that was physically present were manipulated using four basic conditions: "congruent," "inverse," "pretended," or "persuaded." Both age groups showed identical overall premise memory, but the younger group tended to reason more on the basis of the perceptual information rather than on the successfully encoded premise information. Contrasts between the various conditions showed that categorical effects can be circumvented in three-term problems with appropriate controls, that there may be qualitative as well as quantitative differences in transitive inference with age, and that transitive inference is not based solely on memory. The findings also indicate that, although 7-year-olds are competent in "logic-based" transitive inference, they experience great difficulty on tasks involving pretend information.     

Abstraction and perceptual individuation in primed word identification are modulated by distortion and repetition: a dissociation

One experiment investigated the effects of distortion and multiple prime repetition (super-repetition) on repetition priming using divided-visual-field word identification at test and mixed-case words (e.g., goAT). The experiment measured form-specificity (the effect of matching lettercase at study and test) for two non-conceptual study tasks. For an ideal typeface, super-repetition increased form-independent priming leaving form-specificity constant. The opposite pattern was found for a distorted typeface; super-repetition increased form-specificity, leaving form-independent priming constant. These priming effects did not depend on the study task or test hemifield for either typeface. An additional finding was that only the ideal typeface showed the usual advantage of right hemifield presentation. These results demonstrate that super-repetition produced abstraction for the ideal typeface and perceptual individuation for the distorted typeface; abstraction and perceptual individuation dissociated. We suggest that there is a fundamental duality between perceptual individuation and abstraction consistent with Tulving's (1984) distinction between episodic and semantic memory. This could reflect a duality of system or process.