The relationship between numerical mapping abilities,maths achievement and socioeconomic 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.     

Factor analysis by generalized least squares

Aitken's generalized least squares (GLS) principle, with the inverse of the observed variance-covariance matrix as a weight matrix, is applied to estimate the factor analysis model in the exploratory (unrestricted) case. It is shown that the GLS estimates are seale free and asymptotically efficient. The estimates are computed by a rapidly converging Newton-Raphson procedure. A new technique is used to deal with Heywood cases effectively.The work on this project was done when the first author was Research Statistician at Educational Testing Service, Princeton, N. J. The second author was in part supported by a grant from the Research Committee of the University of Wisconsin Graduate School. The authors wish to thank Michael Browne for many helpful comments and Marielle van Thillo for valuable assistance in the numerical computations.     

Response latency,confidence, and ROCs in auditory signal detection

Response latencies were obtained from 10 Ss in auditory signal-detection experiments. The response latencies were inversely related to certainty that a signal was (or was not) presented. The S’s decision criterion was found to have an influence on response latency, which was consistent with the hypothesis that stimuli close to the current criterion elicit longer response latencies than stimuli more distant from the criterion. Comparisons among receiver operating characteristics derived from binary decisions, from the latencies of binary decisions, and from confidence ratings show that response latencies and binary decisions together yield more information about the stimulus than does the binary decision alone. However, the increment in information gained from the measurement of response latencies is in general (though not for every S) smaller than that gained by shifting from yes-no responses to a confidence-rating procedure.     

Search processes for detecting repeated items In a visual display

Evidence for successive serial exhaustive searches was found in a task requiring detection of repeated letters in visually presented lists of varying length. The time per comparison was 25 msec. Important differences in processing appeared between instances of adjacent repeated letters and instances of nonadjacent repeated letters.     

Extraretinal feedback and visual localization

The effect of saccades on visual localization was tested before, during, and after the eye movements. After saccades, localization errors were much less than the distance that the eyes had moved. It is argued that these results demonstrate that extraretinal feedback affects visual localization. The results also suggest that the feedback is related to acceleration rather than to position. Implications for inflow and outflow theories are discussed.     

A signal detection analysis of the effects of hearing on the visual recognition of two-digit numbers

A signal detection measure of visual recognition was used to assess the visual recognition of two-digit numbers in three different conditions: (1) voicing of the number as it was presented visually; (2) voicing of a different number than the one presented; and (3) no voicing. The three treatment means were significantly different, with matched voicing resulting in the best performance and no voicing, in the worst. There was no evidence that the treatments differentially affected response criteria.