Longitudinal associations between parental mathematics anxiety and attitudes and young children's mathematics attainment.

The associations between parental mathematics anxiety and attitudes and children's mathematics attainment in early primary school were explored. Initially, parents of preschool children (Mage = 3;11 [years;months]) completed a questionnaire indexing parental mathematics anxiety and attitudes and the frequency of preschool home number experiences. The children completed mathematics assessments in their first year (n = 231, Mage = 5;2) and second year (n = 119, Mage = 6;3) of schooling and a mathematics anxiety questionnaire in their third year of schooling (n = 119, Mage = 6;7). A questionnaire indexing the frequency of primary school home number experiences was completed by 119 of the parents in their children's second year of schooling (Mage = 6;0). All indices of parental mathematics anxiety and attitudes predicted children's mathematics attainment in their first school year. These associations were independent of parental mathematics attainment and were not mediated by the frequency of preschool home number experiences. Furthermore, the positive association between preschool home number experiences and children's mathematics attainment was not weaker in the context of high parental mathematics anxiety or negative parental mathematics attitudes. One index of parental mathematics attitudes predicted children's mathematics attainment in their second school year, but this association was not significant when prior attainment was controlled. There was a stronger association between maternal mathematics anxiety and girls' attainment versus boys' attainment. Parental mathematics anxiety did not predict children's mathematics anxiety. The findings suggest that children whose parents have high mathematics anxiety or negative mathematics attitudes are more likely to have lower mathematics attainment in their first year of school. However, the mechanism underpinning this association is not yet established.

Response-irrelevant number, duration, and extent information triggers the SQARC effect: Evidence from an implicit paradigm.

Spatial-Numerical Association of Response Codes (SNARC) and Spatial-Quantity Association of Response Codes (SQARC) effects are evident when people produce faster left-sided responses to smaller numbers, sizes, and durations and faster right-sided responses to larger numbers, sizes, and durations. SQARC effects have typically been demonstrated in paradigms where the explicit processing of quantity information is required for successful task completion. The current study tested whether the implicit presentation of task-irrelevant magnitude information could trigger a SQARC effect as has been demonstrated previously when task-irrelevant information triggers a SNARC effect. In Experiment 1, participants (n = 20) made orientation judgements for triangles varying in numerosity and physical extent. In Experiment 2, participants (n = 20) made orientation judgements for triangles varying in numerosity and for a triangle preceded by a delay of varying duration. SNARC effects were observed for the numerosity conditions of Experiments 1 and 2 replicating Mitchell et al. SQARC effects were also demonstrated for physical extent and for duration. These findings demonstrate that SQARC effects can be implicitly triggered by the presentation of the task-irrelevant magnitude.

The differential recruitment of short-term memory and executive functions during time, number, and length perception: An individual differences approach.

Developmental, behavioural, and neurological similarities in the processing of different magnitudes (time, number, space) support the existence of a common magnitude processing system (e.g., a theory of magnitude, ATOM). It is, however, unclear whether the recruitment of wider cognitive resources (short-term memory, STM; and executive function) during magnitude processing is similar across magnitude domains or is domain specific. The current study used an individual differences approach to examine the relationship between STM, executive function, and magnitude processing. In two experiments, participants completed number, length, and duration bisection tasks to assess magnitude processing and tasks that have been shown to assess STM span and executive component processes. The results suggest that the recruitment of STM and executive resources differed for the different magnitude domains. Duration perception was associated with access, inhibition, and STM span. Length processing was associated with updating, and number processing was associated with access to semantic memory. For duration and length, greater difficulty in the magnitude judgement task resulted in more relationships to STM and executive function. It is suggested that duration perception may be more demanding of STM and executive resources because it is represented sequentially, unlike length and number which can be represented nonsequentially.

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study.

The extent to which phonological, visual-spatial short-term memory (STM), and nonsymbolic quantitative skills support the development of counting and calculation skills was examined in this 14-month longitudinal study of 125 children. Initial assessments were made when the children were 4 years 8 months old. Phonological awareness, visual-spatial STM, and nonsymbolic approximate discrimination predicted growth in early calculation skills.These results suggest that both the approximate number system and domain-general phonological and visual-spatial skills support early calculation. In contrast, only performance on a small nonsymbolic quantity discrimination task (where the presented quantities were always within the subitizing range) predicted growth in cardinal counting skills. These results suggest that the development of counting and the development of calculation are supported by different cognitive abilities.

The impact of the development of verbal recoding on children's early writing skills.

BACKGROUND: The spontaneous recoding of visual stimuli into a phonological code to aid short-term retention has been associated with progress in learning to read (Palmer, 2000b). AIM: This study examined whether there was a comparable association with the development of writing skills. SAMPLE: One hundred eight children (64 males) in the second year of the UK educational system (mean age 5:8 years, SD = 4 months) were recruited to the study. METHODS: The children participated in tasks to assess their general cognitive abilities, reading skills, and their predominant short-term memory (STM) strategy for retaining visually presented stimuli. On the basis of their memory profile, children were classified as either engaging in verbal recoding of the stimuli (N = 31) or not (N = 77). Writing performance was indexed as alphabet transcription, spelling, and early text production skills. RESULTS: Children classified as verbal recoders demonstrated better spelling performance and produced more individual letters, words, and T-units in their texts than did children who persisted with a visual memory strategy. In contrast, the alphabet transcription abilities of the groups did not differ. Hierarchical regression analyses revealed that variance in text production skills was associated with STM capacity and that moreover, significant independent variance in the number of words and T-units in the children's texts was predicted by individual differences in verbal recoding abilities. CONCLUSION: The results suggest that the development of verbal recoding skills in STM may play a role in children's early progress in writing, particularly their text generation skills.

Different components of working memory have different relationships with different mathematical skills.

A comprehensive working memory battery and tests of mathematical skills were administered to 90 children-41 in Year 1 (5-6 years of age) and 49 in Year 3 (7-8 years of age). Working memory could explain statistically significant variance in number writing, magnitude judgment, and single-digit arithmetic, but the different components of working memory had different relationships with the different skills. Visual-spatial sketchpad (VSSP) functioning predicted unique variance in magnitude judgments and number writing. Central executive functioning explained unique variance in the addition accuracy of Year 1 children. The unique variance explained in Year 3 multiplication explained by phonological loop functioning just missed conventional levels of significance (p=.06). The results are consistent with the VSSP having a role in the development of number writing and magnitude judgments but a lesser role in early arithmetic.

Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia.

We review significant empirical studies of the arithmetic abilities of children with dyslexia. These studies suggest that the academic impairments of children with dyslexia are not limited to reading and spelling, but also include aspects of mathematics. A consistent finding across a number of studies is that children with dyslexia have difficulty recalling number facts. The results of the reviewed studies are analysed, both in terms of the weak phonological representations hypothesis, and the triple-code theory of mathematical cognition. It is suggested that the phonological processing deficits of individuals with dyslexia impair aspects of mathematics that rely on the manipulation of verbal codes (e.g. counting speed, number fact recall), whilst other aspects of mathematics that are less reliant on verbal codes (e.g. estimation, subitising) are unimpaired. Suggestions for testing this hypothesis are put forward.

The mental and written arithmetic abilities of adults with dyslexia.

The abilities of 19 adult students with dyslexia and 19 students without dyslexia to recall number facts were compared. Despite being matched for estimated IQ, the dyslexic students were less accurate than the non-dyslexic students when answering subtraction and multiplication questions. When the dyslexic students answered addition and subtraction questions correctly they did so more slowly than the non-dyslexic students. It was concluded that dyslexic adults have greater difficulty recalling number facts than non-dyslexic adults. No statistically significant correlations were found between the dyslexic students' performance on the tests of number fact recall and their performance on tests of auditory-verbal and visual-spatial memory.