# Camilla Gilmore's research while affiliated with Loughborough University and other places

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## Publications (95)

Young children frequently make a peculiar counting mistake. When asked to count units that are sets of multiple items, such as the number of families at a party, they often count discrete items (i.e., individual people) rather than the number of sets (i.e., families). One explanation concerns children’s incomplete understanding of what constitutes...

Individuals solve arithmetic problems in different ways and the strategies they choose are indicators of advanced competencies such as adaptivity and flexibility, and predict mathematical achievement. Understanding the factors that encourage or hinder the selection of different strategies is therefore important for helping individuals to succeed in...

Existing studies have shown mixed evidence for the role of the home numeracy environment (HNE) in supporting children’s early numeracy skills. To address some of the limitations of the existing literature, the present study used a multi-method approach to assess the parent-led HNE. Parents of children aged 3–5 years completed a questionnaire to ass...

Young children frequently make a peculiar counting mistake. When asked to count abstract units, such as the number of families at a party, they often count discrete items (i.e. individual people) rather than the number of abstract units (i.e. families). A proposed explanation concerns children’s incomplete understanding of what constitutes a unit,...

Most longitudinal evidence explores the average level of development, suggesting that the relationships between a limited number of variables applies to all learners in the same way. This is the first longitudinal study that investigates multiple component numeric skills within a preschool population using a person-centered approach (i.e., a latent...

Children born very preterm (VP; <32 weeks’ gestation) have poorer mathematics achievement than term-born peers. This study aimed to determine whether VP children’s mathematics difficulties persist from primary to secondary school and to explore the nature of mathematics difficulties in adolescence. For this study, 127 VP and 95 term-born adolescent...

This article synthesizes findings from an international virtual conference, funded by the United States National Science Foundation, focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children’s outcomes, the purpose of the conference was to discuss actiona...

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. Howe...

Individuals use diverse strategies to solve mathematical problems, which can reflect their knowledge of arithmetic principles and predict mathematical expertise. For example, ‘6 + 38 − 35’ can be solved via ‘38 − 35 = 3’ and then ‘3 + 6 = 9’, which is a shortcut-strategy derived from the associativity principle. The shortcut may be critical for und...

Objective:
To assess whether adolescents born very preterm (VP; <32 weeks' gestation) have an excess of mathematics anxiety compared with their classmates born at term.
Methods:
This cohort study included 127 adolescents born VP (51% male, mean age 13.9 years, SD 0.7) and 95 term-born classmates (56% male, mean age 13.7 years, SD 0.7) who comple...

Many mathematics problems can be solved in different ways or by using different strategies. Good knowledge of arithmetic principles is important for identifying and using strategies that are more sophisticated. For example, the problem "6 + 38 - 35" can be solved through a shortcut strategy where the subtraction "38 - 35 = 3" is performed before th...

An ongoing debate concerns whether novel mathematical concepts are better learned using contextualised or decontextualised representations. A barrier to resolving this debate, and therefore to progress in the discipline, has been the paucity of validated methods of measuring students’ understanding of mathematical concepts. We developed an innovati...

Previous research has demonstrated that working memory performance is linked to mathematics achievement. Most previous studies have involved children and arithmetic rather than more advanced forms of mathematics. This study compared the performance of groups of adult mathematics and humanities students. Experiment 1 employed verbal and visuo-spatia...

An impediment to conducting high‐quality quantitative research studies in education is the paucity of valid measures of learning gains. Studies often seek to investigate students’ deep, conceptual understanding yet many measures assess only surface, procedural understanding. One reason is that the development of validated measures of conceptual und...

Objectives:
Children born preterm are at higher risk for special educational needs and poor academic attainment compared with term-born peers, yet education professionals receive limited training and have poor knowledge of preterm birth. We have developed an interactive e-learning resource and evaluated its efficacy in improving teachers' knowledg...

Conceptual knowledge of key principles underlying arithmetic is an important precursor to understanding algebra and later success in mathematics. One such principle is associativity, which allows individuals to solve problems in different ways by decomposing and recombining sub-expressions (e.g. ‘a + b − c’ = ‘b − c + a’). More than any other princ...

Parents are frequently advised to use number books to help their children learn the meaning of number words and symbols. How should these resources be designed to best support learning? Previous research has shown that number books typically include multiple concrete representations of number. However, a large body of mathematics education research...

Correlations between conceptual understanding, mathematics achievement and all quantitative and domain-general skills.
(PDF)

A large body of research has identified cognitive skills associated with overall mathematics achievement, focusing primarily on identifying associates of procedural skills. Conceptual understanding, however, has received less attention, despite its importance for the development of mathematics proficiency. Consequently, we know little about the qua...

Hierarchical linear regression predicting WIAT Numerical Operations (Model 3a) and Mathematical Reasoning (Model 3b) subtests by quantitative and domain-general skills.
(PDF)

Recent studies have highlighted the influence of visual cues such as dot size and cumulative surface area on the measurement of the approximate number system (ANS). Previous studies assessing ANS acuity in ageing have all applied stimuli generated by the Panamath protocol, which does not control nor measure the influence of convex hull. Crucially,...

Nonsymbolic comparison tasks are widely used to measure children’s and adults’ approximate number system (ANS) acuity. Recent evidence has demonstrated that task performance can be influenced by changes to the visual characteristics of the stimuli, leading some researchers to suggest it is unlikely that an ANS exists that can extract number informa...

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 mathem...

Large individual differences in children’s mathematics achievement are observed from the start of schooling. Previous research has identified three cognitive skills that are independent predictors of mathematics achievement: procedural skill, conceptual understanding and working memory. However, most studies have only tested independent effects of...

List of addition problems for all conditions.
(PDF)

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies emp...

Leibovich et al. argue persuasively that researchers should not assume that approximate number system (ANS) tasks harness an innate sense of number. However, some studies have reported a causal link between ANS tasks and mathematics performance, implicating the ANS in the development of numerical skills. Here we report a p -curve analysis, which in...

Achievement in mathematics is predicted by an individual's domain-specific factual knowledge, procedural skill and conceptual understanding as well as domain-general executive function skills. In this study we investigated the extent to which executive function skills contribute to these three components of mathematical knowledge, whether this medi...

Background:
Children born extremely preterm are at high risk for intellectual disability, learning disabilities, executive dysfunction and special educational needs, but little is understood about the comorbidity of intellectual and learning disabilities in this population.
Aims:
This study explored comorbidity in intellectual disability (ID) an...

The dot comparison task, in which participants select the more numerous of two dot arrays, has become the predominant method of assessing Approximate Number System (ANS) acuity. Creation of the dot arrays requires the manipulation of visual characteristics, such as dot size and convex hull. For the task to provide a valid measure of ANS acuity, par...

The importance of improving students’ understanding of core concepts in mathematics is well established. However, assessing the impact of different teaching interventions designed to improve students’ conceptual understanding requires the validation of adequate measures. Here we propose a novel method of measuring conceptual understanding based on...

Performance on number line tasks, typically used as a measure of numerical representations, are reliably related to children's mathematical achievement. However, recent debate has questioned what precisely performance on the number line estimation task measures. Specifically, there has been a suggestion that this task may measure not only numerical...

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 wh...

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 relati...

The most common method of indexing Approximate Number System (ANS) acuity is to use a nonsymbolic dot comparison task. Currently there is no standard protocol for creating the dot array stimuli and it is unclear whether tasks that control for different visual cues, such as cumulative surface area and convex hull size, measure the same cognitive con...

Each year, 15 million babies worldwide are born preterm. Preterm birth is associated with adverse neurodevelopmental outcomes across the life span. Recent registry-based studies suggest that preterm birth is associated with decreased wealth in adulthood, but the mediating mechanisms are unknown. This study investigated whether the relationship betw...

Symbolic (i.e., with Arabic numerals) approximate arithmetic with large numerosities is an important predictor of mathematics. It was previously evidenced to onset before formal schooling at the kindergarten age (Gilmore et al., 2007) and was assumed to map onto pre-existing nonsymbolic (i.e., abstract magnitudes) representations. With a longitudin...

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...

To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities.
The Bavarian Longitudinal Study (B...

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Mathematical Thinking and Learning on 7/05/2015, available online: http://www.tandfonline.com/10.1080/10986065.2015.1016810.

Recent reports suggest that delayed school entry (DSE) may be beneficial for children with developmental delays. However, studies of the effects of DSE are inconclusive. This study investigated the effects of DSE versus age-appropriate school entry (ASE) on children's academic achievement and attention in middle childhood.
In total, 999 children (4...

AimThe knowledge and information needs of education professionals were assessed to determine how prepared they feel to support the growing number of preterm children entering schools today.Method
In a national survey, 585 teachers and 212 educational psychologists completed the Preterm Birth-Knowledge Scale (PB-KS) to assess knowledge of outcomes f...

Research has established that executive functions, the skills required to monitor and control thought and action, are related to achievement in mathematics. Until recently research has focused on working memory, but studies are beginning to show that inhibition skills—the ability to suppress distracting information and unwanted responses—are also i...

Dot comparison tasks are commonly used to index an individual’s Approximate Number System (ANS) acuity, but the cognitive processes involved in completing these tasks are poorly understood. Here, we investigated how factors including numerosity ratio, set size and visual cues influence task performance. Forty-four children aged 7–9 years completed...

Background
Children born very preterm (<32 weeks) are at high risk for mathematics learning difficulties that are out of proportion to other academic and cognitive deficits. However, the aetiology of mathematics difficulties in very preterm children is unknown. We sought to identify the nature and origins of preterm children's mathematics difficult...

Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an o...

The successful learning and performance of mathematics relies on a range of individual, social and educational factors. Recent research suggests that executive function skills, which include monitoring and manipulating information in mind (working memory), suppressing distracting information and unwanted responses (inhibition) and flexible thinking...

Background Children born preterm are at high risk for adverse cognitive and behavioural outcomes. Teachers are increasingly responsible for identifying problems and providing long-term support, yet no studies have assessed how prepared they feel to meet the needs of these children.
Methods A 33-item scale to assess knowledge of the outcomes and edu...

Objective Children born very preterm (VP; <32 weeks) are at risk for attention deficit/hyperactivity disorders (ADHD). ADHD in VP children have a different clinical presentation to ADHD in the general population, and therefore VP children with difficulties may not come to the teacher's attention in school. We have assessed ADHD symptoms to determin...

Previous research has demonstrated that working memory plays an important role in arithmetic. Different arithmetical strategies rely on working memory to different extents-for example, verbal working memory has been found to be more important for procedural strategies, such as counting and decomposition, than for retrieval strategies. Surprisingly,...

Nonsymbolic comparison tasks are commonly used to index the acuity of an individual's Approximate Number System (ANS), a cognitive mechanism believed to be involved in the development of number skills. Here we asked whether the time that an individual spends observing numerical stimuli influences the precision of the resultant ANS representations....

Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS) which allows individuals to represent and manipulate non-verbal numeric...

Children born very preterm have poorer attainment in all school subjects, and a markedly greater reliance on special educational support than their term-born peers. In particular, difficulties with mathematics are especially common and account for the vast majority of learning difficulties in this population. In this paper, we review research relat...

A cumulative body of research has shown that children typically shift from an operational to a relational conception of the equals sign as they move through schooling. Jones (2008) argued that a truly relational conception of the equals sign comprises a substitutive component and a sameness component. Here we present two studies that build on this...

Background:
Extremely preterm (EP, <26 wk gestation) children have been observed to have poor academic achievement in comparison to their term-born peers, especially in mathematics. This study investigated potential underlying causes of this difficulty.
Methods:
A total of 219 EP participants were compared with 153 term-born control children at...

A sophisticated and flexible understanding of the equals sign (=) is important for arithmetic competence and for learning further mathematics, particularly algebra. Research has identified two common conceptions held by children: the equals sign as an operator and the equals sign as signaling the same value on both sides of the equation. We argue h...

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 spec...

Geometrical concepts are critical to a host of human cognitive achievements, from maps to measurement to mathematics, and both the development of these concepts, and their variation by gender, have long been studied. Most studies of geometrical reasoning, however, present children with materials containing both geometric and non-geometric informati...

Recent theories in numerical cognition propose the existence of an approximate number system (ANS) that supports the representation and processing of quantity information without symbols. It has been claimed that this system is present in infants, children, and adults, that it supports learning of symbolic mathematics, and that correctly harnessing...

At the British Society for Research into Learning Mathematics day conference held at the London Institute of Education in March 2011 we presented evidence for the existence of a substitutive conception of the equals sign. During the session, Jeremy Hodgen (Figure 1) questioned the use of active and passive items in the instrument, suggesting our re...

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical ma...

Children take years to learn symbolic arithmetic. Nevertheless, non-human animals, human adults with no formal education, and human infants represent approximate number in arrays of objects and sequences of events, and they use these capacities to perform approximate addition and subtraction. Do children harness these abilities when they begin to l...

When children learn to count and acquire a symbolic system for representing numbers, they map these symbols onto a preexisting system involving approximate nonsymbolic representations of quantity. Little is known about this mapping process, how it develops, and its role in the performance of formal mathematics. Using a novel task to assess children...

Some theories from cognitive psychology and mathematics education suggest that children's understanding of mathematical concepts develops together with their knowledge of mathematical procedures. However, previous research into children's understanding of the inverse relationship between addition and subtraction suggests that there are individual d...

Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the inver...

In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12+9-9 yields 12. Her...

Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations, and their performance suffers if this nonsymbolic system is impaired. Nonsymbolic nu...

Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between t...

The development of conceptual understanding in arithmetic is a gradual process and children may make use of a concept in some situations before others. Previous research has demonstrated that when children are given arithmetic problems with an inverse relationship they can infer that the initial and final quantities are the same (e.g. 15+8–8=□). Ho...