Non-symbolic magnitudes are represented spatially: Evidence from a non-symbolic SNARC task.

A core proposition in numerical cognition is numbers are represented spatially. Evidence for this proposition comes from the "spatial numerical association of response codes" effect (SNARC) in which faster responses are made by the left/right hand judging whether one of a pair of Arabic digits is smaller/larger than the other. Less is known if a similar SNARC effect exists for non-symbolic magnitudes; and research that has been conducted used stimuli which could be translated into symbolic terms. To overcome this limitation, we employed a referent-to-target judgment paradigm in which a referent dot array (n = 30 dots) was follow by a second array of dots (e.g., n = 45 or 15 dots)-participants judged if the second array contained fewer or more dots than the referent array. Dot arrays with fewer dots were judged more quickly with the left hand compared to the right hand (i.e., a SNARC effect). Not all participants demonstrated a SNARC effect, however. Neither visuospatial working memory nor math ability was associated with the presence/absence of a non-symbolic SNARC effect. Implications of the non-symbolic SNARC effect for accounts of numerical cognition are discussed.

Stability and change in markers of core numerical competencies.

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental signatures, is unknown. To investigate these issues, the DE and NC RT signatures of 159 children were assessed 7 times over 6 years. Cluster analyses identified within-task and across-age subgroups. DE signatures comprised 4 parameters: (a) the RT slope within the subitizing range, (b) the RT slope for the counting range, (c) the subitizing range (indicated by the point of slope discontinuity), and (d) the overall average DE RT response. NC RT signatures comprised 2 parameters (NC intercept and slope) derived from RTs comparing numbers 1 to 9. Analyses yielded 3 distinct DE and NC profiles at each age. Within-age subgroup profiles reflected differences in 3 of the 4 DE parameters and only 1 NC parameter. Systematic changes in parameters were observed across ages for both tasks, and both tasks broadly identified the same subgroups. Sixty-nine percent of children were assigned to the same subgroup across age, even though parameters themselves changed across age. Subgroups did not differ in processing speed or nonverbal reasoning, suggesting that DE and NC do not tap general cognitive abilities but reflect individual differences specific to the domain of numbers. Indeed, both DE and NC subgroup membership at 6 years predicted computation ability at 6 years, 9.5 years, and 10 years.

Five- to 7-year-olds' finger gnosia and calculation abilities.

The research examined the relationship between 65 5- to 7-year-olds' finger gnosia, visuo-spatial working memory, and finger-use in solving single-digit addition problems. Their non-verbal IQ and basic reaction time were also assessed. Previous research has found significant changes in children's representational abilities between 5 and 7 years. One aim of the research was to determine whether changes in finger representational abilities (finger gnosia) occur across these ages and whether they are associated with finger-use in computation. A second aim was to determine whether visuo-spatial working memory is associated with finger gnosia and computation abilities. We used latent class profile analysis to identify patterns of similarities and differences in finger gnosia and computation/finger-use abilities. The analysis yielded four finger gnosia subgroups that differed in finger representation ability. It also yielded four finger/computation subgroups that differed in the relationship between finger-use and computation success. Analysis revealed associations between computation finger-use/success subgroups, finger gnosia subgroups, and visuo-spatial working memory. A multinomial logistic regression analysis showed that finger gnosia subgroup membership and visuo-spatial working memory uniquely contribute to a model predicting finger-use in computation group membership. The results show that finger gnosia abilities change in the early school years, and that these changes are associated with the ability to use fingers to aid computation.