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.     

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.     

Differential specialization of the cerebral hemispheres for the perception of sameness and difference

The Johns Hopkins University, Baltimore, Maryland 21218 Pairs of letters were presented 4 deg left or right of fixation, and Ss were asked to indicate as quickly as possible whether the letters in a pair were the same or different. Reaction times for “different” responses were faster when stimuli were in the left visual field than in the right, but reaction times for “same” responses were faster when stimuli were in the right visual field than in the left. These results may indicate that the right hemisphere is better specialized for difference detection, while the left hemisphere is better specialized for sameness detection.     

Concurrent variation of response bias and sensitivity in an operant-psychophysical test

The yes-no signal detection procedure was applied to a single-response operant paradigm in which rats discriminated between a standard auditory intensity and attenuated comparison values. The payoff matrix was symmetrical (with reinforcing brain stimulation for correct detections and brief time-out for errors), but signal probability and intensity differences were varied to generate a family of isobias and isosensitivity functions. The d’ parameter remained fairly constant across a wide range of bias levels. Isobias functions deviated from a strict matching strategy as discrimination difficulty increased, although an orderly relation was maintained between signal probability value and the degree and direction of response bias.