Number sense at 12 months predicts 4-year-olds’ maths skills

Preverbal infants spontaneously represent the number of objects in collections. Is this ‘sense of number’ (also referred to as Approximate Number System, ANS) part of the cognitive foundations of mathematical skills? Multiple studies reported a correlation between the ANS and mathematical achievement in children. However, some have suggested that such correlation might be mediated by general-purpose inhibitory skills. We addressed the question using a longitudinal approach: we tested the ANS of 60 12 months old infants and, when they were 4 years old (final N = 40), their symbolic math achievement as well as general intelligence and inhibitory skills. Results showed that the ANS at 12 months is a specific predictor of later maths skills independent from general intelligence or inhibitory skills. The correlation between ANS and maths persists when both abilities are measured at four years. These results confirm that the ANS has an early, specific and longstanding relation with mathematical abilities in childhood.

Research Highlights

• In the literature there is a lively debate about the correlation between the ANS and maths skills.
• We longitudinally tested a sample of 60 preverbal infants at 12 months and rested them at 4 years (final sample of 40 infants).
• The ANS tested at 12 months predicted later symbolic mathematical skills at 4 years, even when controlling for inhibition, general intelligence and perceptual skills.
• The ANS tested at 4 years remained linked with symbolic maths skills, confirming this early and longstanding relation in childhood.

     

No intrinsic number bias: Evaluating the role of perceptual discriminability in magnitude categorization

Accumulating evidence suggests that there is a spontaneous preference for numerical, compared to non-numerical (e.g., cumulative surface area), information. However, given a paucity of research on the perception of non-numerical magnitudes, it is unclear whether this preference reflects a specific bias towards number, or a general bias towards the more perceptually discriminable dimension (i.e., number). Here, we found that when the number and area of visual dot displays were matched in mathematical ratio, number was more perceptually discriminable than area in both adults and children. Moreover, both adults and children preferentially categorized these ratio-matched stimuli based on number, consistent with previous work. However, when number and area were matched in perceptual discriminability, a different pattern of results emerged. In particular, children preferentially categorized stimuli based on area, suggesting that children's previously observed number bias may be due to a mismatch in the perceptual discriminability of number and area, not an intrinsic salience of number. Interestingly, adults continued to categorize the displays on the basis of number. Altogether, these findings suggest a dominant role for area during childhood, refuting the claim that number is inherently and uniquely salient. Yet they also reveal an increased salience of number that emerges over development. Potential explanations for this developmental shift are discussed.

Research Highlights

• Previous work found that children and adults spontaneously categorized dot array stimuli by number, over other magnitudes (e.g., area), suggesting number is uniquely salient.
• However, here we found that when number and area were matched by ratio, as in prior work, number was significantly more perceptually discriminable than area.
• When number and area were made equally discriminable (‘perceptually-matched’), children, contra adults, spontaneously categorized stimuli by area over number (and other non-numerical magnitudes).
• These findings suggest that area may be uniquely salient early in childhood, with the previously-observed number bias not emerging until later in development.

     

Memories of the dictatorship in Spain. An analysis of the narratives from three generations / Memorias de la dictadura en España. Un análisis de las narrativas de tres generaciones

Abstract

This study will investigate the narratives related by the members of three different generations within two different families on their memories of the Franco dictatorship. The first generation lived through Francoism, the second the democratic transition, and the third were born in a democratic country. Based on a social and discursive conception of memory and identity, this study is carried out using semi-structured interviews as a data collection tool, which we then thematically analyse, together with aspects of the participants’ positions and voices. The interviews are connected according to the factors of generation and family, and we analyse the similarities and differences. This is how the influence of both is seen in each individual’s memories and identities, in addition to how their political ideology is configured.     

关于古代术数中内算与外算易位问题的探讨

在古代,传统术数(也称数术)中的内算与外算是一个整体。在两千多年的历史时期中,从教育史、从业者的身份认同与知识结构,以及史籍对二者的记载和二者在数术整体功能中的权重等方面来看,"外算"是以"内算"的婢女身份出现的。从《四库全书》起,这一观念发生改变,而在阮元等人所编《畴人传》中,内算与外算之关系发生了易位。通过对晚明前清中西术数、中西文化会通的考察而发现,这一易位有其必然性。但是从人类文化的未来发展来看,二者关系及各自前景值得深入思考。     

The relationships between quantity‐number competencies,working memory,and phonological awareness in 5‐ and 6‐year‐olds

In this study, the interdependencies among phonological awareness, verbal working memory components, and early numerical skills in children 1 year before school entry are addressed. Early numerical skills were conceptualized as quantity‐number competencies (QNC) at both basic (QNC Level 1) and advanced (QNC Level 2) levels. In a sample of 1,343 children aged 5 and 6, structural equation modelling provided support for the isolated number words hypothesis (Krajewski & Schneider, 2009, J. Exp. Child Psychol., 103, 516–531). This hypothesis claims that phonological awareness contributes to the acquisition of QNC Level 1, such as learning the number word sequence, but not of QNC Level 2, which requires the linkage of number words to quantities. In addition, phonological awareness relied on verbal working memory, especially with regard to the phonological loop, central executive, and episodic buffer. The results were congruent with the idea that phonological awareness mediates the impact of verbal working memory on QNCs. The relationships between verbal working memory, phonological awareness, and QNCs were comparable in monolingual and bilingual children.