Magnitude representations and counting skills in preschool children

When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this mapping only occurs once children have cardinality understanding. One difficulty with the current literature is that studies have employed tasks that only indirectly assess children’s nonsymbolic-symbolic mappings. We introduce a task in which preschoolers made magnitude comparisons across representation formats (e.g., dot arrays vs. verbal number), allowing a direct assessment of mapping. We gave this task to 60 children aged 2;7 - 4;10, together with counting and Give-a-Number tasks. We found that some children could map between nonsymbolic quantities and the number words they understood the cardinal meaning of, even if they had yet to grasp the general cardinality principle of counting

Spontaneous focusing on numerosity and the arithmetic advantage

Children show individual differences in their tendency to focus on the numerical aspects of their environment. These individual differences in ‘Spontaneous Focusing on Numerosity’ (SFON) have been shown to predict both current numerical skills and later mathematics success. Here we investigated possible factors which may explain the positive relationship between SFON and symbolic number development. Children aged 4e5 years (N ¼ 130) completed a battery of tasks designed to assess SFON and a range of mathematical skills. Results showed that SFON was positively associated with children's symbolic numerical processing skills and their performance on a standardised test of arithmetic. Hierarchical regression analyses demonstrated that the relationship between SFON and symbolic mathematics achievement can be explained, in part, by individual differences in children's nonsymbolic numerical processing skills and their ability to map between nonsymbolic and symbolic representations of number

Non-verbal number acuity correlates with symbolic mathematics achievement: but only in children

The process by which adults develop competence in symbolic mathematics tasks is poorly understood. Nonhuman animals, human infants, and human adults all form nonverbal representations of the approximate numerosity of arrays of dots and are capable of using these representations to perform basic mathematical operations. Several researchers have speculated that individual differences in the acuity of such nonverbal number representations provide the basis for individual differences in symbolic mathematical competence. Specifically, prior research has found that 14-year-old children’s ability to rapidly compare the numerosities of two sets of colored dots is correlated with their mathematics achievements at ages 5–11. In the present study, we demonstrated that although when measured concurrently the same relationship holds in children, it does not hold in adults. We conclude that the association between nonverbal number acuity and mathematics achievement changes with age and that nonverbal number representations do not hold the key to explaining the wide variety of mathematical performance levels in adults

Challenges in mathematical cognition: a collaboratively-derived research agenda

This paper reports on a collaborative exercise designed to generate a coherent agenda for research on mathematical cognition. Following an established method, the exercise brought together 16 mathematical cognition researchers from across the fields of mathematics education, psychology and neuroscience. These participants engaged in a process in which they generated an initial list of research questions with the potential to significantly advance understanding of mathematical cognition, winnowed this list to a smaller set of priority questions, and refined the eventual questions to meet criteria related to clarity, specificity and practicability. The resulting list comprises 26 questions divided into six broad topic areas: elucidating the nature of mathematical thinking, mapping predictors and processes of competence development, charting developmental trajectories and their interactions, fostering conceptual understanding and procedural skill, designing effective interventions, and developing valid and reliable measures. In presenting these questions in this paper, we intend to support greater coherence in both investigation and reporting, to build a stronger base of information for consideration by policymakers, and to encourage researchers to take a consilient approach to addressing important challenges in mathematical cognition

Verbal count sequence knowledge underpins numeral order processing in children

Recent research has suggested that numeral order processing – the speed and accuracy with which individuals can determine whether a set of digits is in numerical order or not – is related to arithmetic and mathematics outcomes. It has therefore been proposed that ordinal relations are a fundamental property of symbolic numeral representations. However, order information is also inherent in the verbal count sequence, and thus verbal count sequence knowledge may instead explain the relationship between performance on numeral order tasks and arithmetic. We explored this question with 62 children aged 6- to 8-years-old. We found that performance on a verbal count sequence knowledge task explained the relationship between numeral order processing and arithmetic. Moreover many children appeared to explicitly base their judgments of numerical order on count sequence information. This suggests that insufficient attention may have been paid to verbal number knowledge in understanding the sources of information that give meaning to numbers

Supplementary information file for article: 'Verbal count sequence knowledge underpins numeral order processing in children'

Supplementary information file for article: 'Verbal count sequence knowledge underpins numeral order processing in children'. Abstract: This dataset is from a study of children's basic numerical skills. Children (aged 6 to 8 years) completed tasks to measure: (1) count sequence knowledge; (2) numeral order processing; (3) Rapid Automatized Naming; and (4) arithmetic. (Article under review.)</div

Parents’ and children’s mathematics anxiety

Mathematics anxiety refers to the syndrome of negative emotions that many individuals experience when engaging in tasks demanding numerical or mathematical skills. It has long been recognized by educators and researchers and has been shown to have a range of negative consequences, from poorer performance on mathematical tasks to avoidance of mathematical activities. Until recently, research into mathematics anxiety has focused on older children and adults. As such, little is known about the emergence of mathematics anxiety in early childhood. It is not clear how, or why, mathematics anxiety develops. One possibility is that parents play a role in shaping their children's attitudes and anxieties toward mathematics. Parents may transmit negative feelings toward the subject with comments such as “I've always been hopeless with numbers.” In this chapter we test this possibility by investigating the relationship between parents' and children's mathematics anxiety. First, we present an overview of mathematics anxiety with some brief historical perspectives. Next, we focus on the possible causes of mathematics anxiety, drawing on research from the general anxiety literature before narrowing down to look at the environmental influence of parents. Finally, we conclude with a summary of key findings in the field and emerging questions for future research

Disclosure Table for p curve analysis on whether the ANS is causally linked to mathematics performance

This is a disclosure table associated with a commentary in Behavioral and Brain Sciences

The ecological validity of picture SFON tasks

Data and materials associated with the paper "The ecological validity of picture SFON tasks".Details of each variable etc are available in the excel sheet.Abstract from paperResearch has identified that children differ in the extent to which they spontaneously focus on numerical aspects of the environment (Spontaneous Focusing on Numerosity, SFON) and that this correlates with their mathematics achievement. It is assumed that the mechanism underpinning this relationship is that children who spontaneously focus on numerical features of their environment will experience more self-initiated practice with number concepts. We explored this mechanism by investigating whether 4-to 5-year-old children’s verbal SFON scores on a picture description task related to their spontaneous focusing on number while engaged in play activities with their parent. We found that the scores derived from a picture description task were strongly correlated with the scores derived from the play sessions, rs=.638, 95% CI [.433, .781], providing evidence for this mechanism. We further investigated the role that verbal abilities may play in children’s performance on the picture description task, finding that general verbal abilities were not associated with verbal SFON scores. These results contribute to our understanding of the role played by verbal SFON tendencies in explaining differences in numerical development, and demonstrate the ecological validity of SFON picture tasks.</p

Data for Iconicity in mathematical notation

Data and experimental materials associated with the paper "Iconicity in mathematical notation"