Numerical magnitude processing impairments in genetic syndromes: a cross‐syndrome comparison of Turner and 22q11.2 deletion syndromes

Cross‐syndrome comparisons offer an important window onto understanding heterogeneity in mathematical learning disabilities or dyscalculia. The present study therefore investigated symbolic numerical magnitude processing in two genetic syndromes that are both characterized by mathematical learning disabilities: Turner syndrome and 22q11.2 deletion syndrome (22q11DS). We further verified whether the phenotypic outcomes of these syndromes emerged from the same or different cognitive processes and therefore examined whether numerical impairments were related to working memory deficits, often observed in these syndromes. Participants were 24 girls with Turner syndrome, 25 children with 22q11DS and 48 well‐matched typically developing control children. All children completed a symbolic numerical magnitude comparison task and four additional working memory tasks. Both groups of children with genetic syndromes showed similar impairments in symbolic numerical magnitude processing compared to typically developing controls. Importantly, in Turner syndrome, group differences in symbolic numerical magnitude processing disappeared when their difficulties in visual‐spatial working memory were taken into account. In contrast, the difficulties in 22q11DS were not explained by poor visual‐spatial working memory. These data suggest that different factors underlie the symbolic numerical magnitude processing impairments in both patient groups with mathematical learning disabilities and highlight the value of cross‐syndrome comparisons for understanding different pathways to mathematical learning disabilities or dyscalculia.     

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test)

The ability to compare symbolic numerical magnitudes correlates with children’s concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one- and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1–6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single- as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterion-related validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia.     

A validation of eye movements as a measure of elementary school children's developing number sense

The number line estimation task captures central aspects of children's developing number sense, that is, their intuitions for numbers and their interrelations. Previous research used children's answer patterns and verbal reports as evidence of how they solve this task. In the present study we investigated to what extent eye movements recorded during task solution reflect children's use of the number line. By means of a cross-sectional design with 66 children from Grades 1, 2, and 3, we show that eye-tracking data (a) reflect grade-related increase in estimation competence, (b) are correlated with the accuracy of manual answers, (c) relate, in Grade 2, to children's addition competence, (d) are systematically distributed over the number line, and (e) replicate previous findings concerning children's use of counting strategies and orientation-point strategies. These findings demonstrate the validity and utility of eye-tracking data for investigating children's developing number sense and estimation competence.     

Debating ethical expertise

This paper explores the relevance of the debate about ethical expertise for the practice of clinical ethics. We present definitions, explain three theories of ethical expertise, and identify arguments that have been brought up to either support the concept of ethical expertise or call it into question. Finally, we discuss four theses: the debate is relevant for the practice of clinical ethics in that it (1) improves and specifies clinical ethicists' perception of their expertise; (2) contributes to improving the perception of moral competence of non-ethicists; (3) gives insight into complementary styles of argumentation of ethicists and non-ethicists; and (4) contributes to the awareness of the problem of profession-building of (clinical) ethicists.     

Family demographic profiles and their relationship with the quality of executive functioning subcomponents in kindergarten

Executive functioning (EF), needed for goal‐oriented behaviour, thoughts, and emotions, is important for various life domains. This study examined the relationship between family demographics and EF subcomponents. A kindergarten sample was tested on subcomponents of working memory, inhibition, and cognitive flexibility. Parents provided information on demographic variables. For 78 children both EF and demographic data were available. First, demographic profiles were identified within the sample. Two profiles were found: A low‐risk profile of mainly two‐biological‐parent, high‐income families with a highly educated mother who did not smoke during pregnancy and a high‐risk profile of low‐income families with a young, low‐educated mother who more often smoked during pregnancy. Second, children with different demographic profiles were compared on EF subcomponents. Results indicate differential relations between family demographics and EF subcomponents: Whereas for most EF subcomponents no association with family demographics was found, high‐risk children performed better on response shifting and tended to perform worse on verbal memory than low‐risk children. Parenting stress decreased performance only for high‐risk children. Although this study found limited impact of family demographics for EF, further longitudinal research can provide nuanced insights about which factors influence specific EF subcomponents during which developmental periods and guide targeted prevention of EF difficulties.     

The relation between consciousness and attention: An empirical study using the priming paradigm

Dehaene et al., 2006, Koch and Tsuchiya, 2007 recently proposed taxonomies that distinguish between four processing states, based on bottom-up stimulus strength and top-down attentional amplification. The aim of the present study was to empirically test these processing states using the priming paradigm. Our results showed that attention (prime attended or not) and stimulus strength (prime presented subliminally or not) significantly modulated priming effects: either receiving top-down attention or possessing sufficient bottom-up strength was a prerequisite for a stimulus to elicit priming. When both top-down attention and sufficient bottom-up strength were present, the priming effect was boosted. The origins of the observed priming effects also varied between different processing states. We can conclude that our empirical study using the priming paradigm confirmed the presence of four processing states, which displayed a differential pattern of response priming effects and differential origins of the response priming effects.     

How is phonological processing related to individual differences in children’s arithmetic skills?

While there is evidence for an association between the development of reading and arithmetic, the precise locus of this relationship remains to be determined. Findings from cognitive neuroscience research that point to shared neural correlates for phonological processing and arithmetic as well as recent behavioral evidence led to the present hypothesis that there exists a highly specific association between phonological awareness and single‐digit arithmetic with relatively small problem sizes. The present study examined this association in 37 typically developing fourth and fifth grade children. Regression analyses revealed that phonological awareness was specifically and uniquely related to arithmetic problems with a small but not large problem size. Further analysis indicated that problems with a high probability of being solved by retrieval, but not those typically associated with procedural problem‐solving strategies, are correlated with phonological awareness. The specific association between phonological awareness and arithmetic problems with a small problem size and those for which a retrieval strategy is most common was maintained even after controlling for general reading ability and phonological short‐term memory. The present findings indicate that the quality of children’s long‐term phonological representations mediates individual differences in single‐digit arithmetic, suggesting that more distinct long‐term phonological representations are related to more efficient arithmetic fact retrieval.     

Using addition to solve large subtractions in the number domain up to 20

This study examined 25 university students’ use of addition to solve large single-digit subtractions by contrasting performance in the standard subtraction format (12 − 9 = .) and in the addition format (9 + . = 12). In particular, we investigated the effect of the relative size of the subtrahend on performance in both formats. We found a significant interaction between format, the magnitude of the subtrahend (S) compared to the difference (D) (S > D vs. S < D), and the numerical distance between subtrahend and difference. When the subtrahend was larger than the difference and S and D were far from each other (e.g., 12 − 9 = .), problems were solved faster in the addition than in the subtraction format; when the subtrahend was smaller than the difference and S and D were far from each other (e.g., 12 − 3 = .), problems were solved faster in the subtraction than in the addition format. However, when the subtrahend and the difference were close to each other (e.g., 13 − 7 = .), there were no significant reaction time differences between both formats. These results suggest that adults do not rely exclusively and routinely on addition to solve large single-digit subtractions, but select either addition-based or subtraction-based strategies depending on the relative size of the subtrahend.     

Know thyself: Metacognitive networks and measures of consciousness

Subjective measures of awareness rest on the assumption that conscious knowledge is knowledge that participants know they possess. Post-Decision Wagering (PDW), recently proposed as a new measure of awareness, requires participants to place a high or a low wager on their decisions. Whereas advantageous wagering indicates awareness of the knowledge on which the decisions are based, cases in which participants fail to optimize their wagers suggest performance without awareness. Here, we hypothesize that wagering and other subjective measures of awareness reflect metacognitive capacities subtended by self-developed metarepresentations that inform an agent about its own internal states. To support this idea, we present three simulations in which neural networks learn to wager on their own responses. The simulations illustrate essential properties that are required for such metarepresentations to influence PDW as a measure of awareness. Results demonstrate a good fit to human data. We discuss the implications of this modeling work for our understanding of consciousness and its measures.