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.     

The missing-fundamental illusion at isoluminance.

The missing-fundamental illusion describes how a square wave with its fundamental Fourier component removed appears as a square wave. This illusion is normally explained with reference to the bandpass nature of the luminance-contrast-sensitivity function, together with a 'default-to-square-wave' rule. Since the chromatic-contrast-sensitivity function is low-pass, we should not expect a missing-fundamental illusion at isoluminance. Using a simultaneous-detection-and-identification paradigm to eliminate contrast as a cue to discrimination, we nevertheless found that chromatic missing fundamentals and square waves could not be separately identified at detection threshold: just under twice the contrast required to detect the stimuli was needed to identify them. To test whether this was due to insufficiently narrow chromatic-channel bandwidths, we measured detection and identification thresholds for chromatic F and 3F sine-wave gratings. In this case identification was possible almost at detection threshold, suggesting that channel bandwidth limitations were not the critical factor. It is suggested that the weak missing-fundamental illusion observed at isoluminance probably reflects the operation of mechanisms similar to those that are responsible for the chromatic Craik-Cornsweet illusion.