Numerical predictors of arithmetic success in grades 1–6

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1–6. In grades 1–2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing.     

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.

     

The role of numerosity in processing nonsymbolic proportions

The difficulty in processing fractions seems to be related to the interference between the whole-number value of the numerator and the denominator and the real value of the fraction. Here we assess whether the reported problems with symbolic fractions extend to the nonsymbolic domain, by presenting fractions as arrays of black and white dots representing the two operands. Participants were asked to compare a target array with a reference array in two separate tasks using the same stimuli: a numerosity task comparing just the number of white dots in the two arrays; and a proportion task comparing the proportion of black and white dots. The proportion task yielded lower accuracy and slower response, confirming that even with nonsymbolic stimuli accessing proportional information is relatively difficult. However, using a congruity manipulation in which the greater numerosity of white dots could co-occur with a lower proportion of them, and vice versa, it was found that both task-irrelevant dimensions would interfere with the task-relevant dimension suggesting that both numerosity and proportion information was automatically accessed. The results indicate that the magnitude of fractions can be automatically and holistically processed in the nonsymbolic domain.     

Number gestures predict learning of number words

When asked to explain their solutions to a problem, children often gesture and, at times, these gestures convey information that is different from the information conveyed in speech. Children who produce these gesture‐speech “mismatches” on a particular task have been found to profit from instruction on that task. We have recently found that some children produce gesture‐speech mismatches when identifying numbers at the cusp of their knowledge, for example, a child incorrectly labels a set of two objects with the word “three” and simultaneously holds up two fingers. These mismatches differ from previously studied mismatches (where the information conveyed in gesture has the potential to be integrated with the information conveyed in speech) in that the gestured response contradicts the spoken response. Here, we ask whether these contradictory number mismatches predict which learners will profit from number‐word instruction. We used the Give‐a‐Number task to measure number knowledge in 47 children (M_age = 4.1 years, SD = 0.58), and used the What's on this Card task to assess whether children produced gesture‐speech mismatches above their knower level. Children who were early in their number learning trajectories (“one‐knowers” and “two‐knowers”) were then randomly assigned, within knower level, to one of two training conditions: a Counting condition in which children practiced counting objects; or an Enriched Number Talk condition containing counting, labeling set sizes, spatial alignment of neighboring sets, and comparison of these sets. Controlling for counting ability, we found that children were more likely to learn the meaning of new number words in the Enriched Number Talk condition than in the Counting condition, but only if they had produced gesture‐speech mismatches at pretest. The findings suggest that numerical gesture‐speech mismatches are a reliable signal that a child is ready to profit from rich number instruction and provide evidence, for the first time, that cardinal number gestures have a role to play in number‐learning.     

A translational application of music for preschool cognitive development: RCT evidence for improved executive function,self-regulation,and school readiness

The benefits of active music participation and training for cognitive development have been evidenced in multiple studies, with this link leveraged in music therapy approaches with clinical populations. Although music, rhythm, and movement activities are widely integrated into children's play and early education, few studies have systematically translated music therapy-based approaches to a nonclinical population to support early cognitive development. This study reports the follow-up effects of the Rhythm and Movement for Self Regulation (RAMSR) program delivered by generalist preschool teachers in low socioeconomic communities. This randomized control trial (RCT) involved 213 children across eight preschools in disadvantaged communities in Queensland, Australia. The intervention group received 16–20 sessions of RAMSR over 8 weeks, while the control group undertook usual preschool programs. Primary outcome measures included executive function (child assessment of shifting, working memory, and inhibition) and self-regulation (teacher report), with secondary outcomes of school readiness and visual-motor integration. Data were collected pre- and post-intervention, and again 6 months later once children had transitioned into school. Results demonstrated significant intervention effects across the three time points for school readiness (p = 0.038, η_p² = 0.09), self-regulation (p < 0.001, η_p² = 0.08), and inhibition (p = 0.002 η_p² = 0.23). Additionally, the feasibility of building capacity in teachers without any music background to successfully deliver the program was evidenced. These findings are important given that children from low socioeconomic backgrounds are more likely to need support for cognitive development yet have inequitable access to quality music and movement programs.

Research Highlights

• Initial effects of self-regulation from a rhythm and movement program were sustained following transition into school for children from disadvantaged backgrounds.
• Delayed effects of inhibition and school readiness from a rhythm and movement program appeared 6 months post-intervention as children entered school.
• Generalist teachers can successfully implement a rhythm and movement program, which boosts critical developmental cognitive skills.

     

Natural reference: A phylo‐ and ontogenetic perspective on the comprehension of iconic gestures and vocalizations

The recognition of iconic correspondence between signal and referent has been argued to bootstrap the acquisition and emergence of language. Here, we study the ontogeny, and to some extent the phylogeny, of the ability to spontaneously relate iconic signals, gestures, and/or vocalizations, to previous experience. Children at 18, 24, and 36 months of age (N = 216) and great apes (N = 13) interacted with two apparatuses, each comprising a distinct action and sound. Subsequently, an experimenter mimicked either the action, the sound, or both in combination to refer to one of the apparatuses. Experiments 1 and 2 found no spontaneous comprehension in great apes and in 18‐month‐old children. At 24 months of age, children were successful with a composite vocalization‐gesture signal but not with either vocalization or gesture alone. At 36 months, children succeeded both with a composite vocalization‐gesture signal and with gesture alone, but not with vocalization alone. In general, gestures were understood better compared to vocalizations. Experiment 4 showed that gestures were understood irrespective of how children learned about the corresponding action (through observation or self‐experience). This pattern of results demonstrates that iconic signals can be a powerful way to establish reference in the absence of language, but they are not trivial for children to comprehend and not all iconic signals are created equal.     

Numerical and nonnumerical estimation in children with and without mathematical learning disabilities

There are currently multiple explanations for mathematical learning disabilities (MLD). The present study focused on those assuming that MLD are due to a basic numerical deficit affecting the ability to represent and to manipulate number magnitude ( Butterworth, 1999 , 2005 ; A. J. Wilson & Dehaene, 2007 ) and/or to access that number magnitude representation from numerical symbols ( Rousselle & No?l, 2007 ). The present study provides an original contribution to this issue by testing MLD children (carefully selected on the basis of preserved abilities in other domains) on numerical estimation tasks with contrasting symbolic (Arabic numerals) and nonsymbolic (collection of dots) numbers used as input or output. MLD children performed consistently less accurately than control children on all the estimation tasks. However, MLD children were even weaker when the task involved the mapping between symbolic and nonsymbolic numbers than when the task required a mapping between two nonsymbolic numerical formats. Moreover, in the estimation of nonsymbolic numerosities, MLD children relied more than control children on perceptual cues such as the cumulative area of the dots. Finally, the task requiring a mapping from a nonsymbolic format to a symbolic format was the best predictor of MLD. In order to explain these present results, as well as those reported in the literature, we propose that the impoverished number magnitude representation of MLD children may arise from an initial mapping deficit between number symbols and that magnitude representation.     

Learning strategy differentially impacts memory connections in children and adults

Even once children can accurately remember their experiences, they nevertheless struggle to use those memories in flexible new ways—as in when drawing inferences. However, it remains an open question as to whether the developmental differences observed during both memory formation and inference itself represent a fundamental limitation on children's learning mechanisms, or rather their deployment of suboptimal strategy. Here, 7–9-year-old children (N = 154) and young adults (N = 130) first formed strong memories for initial (AB) associations and then engaged in one of three learning strategies as they viewed overlapping (BC) pairs. We found that being told to integrate—combine ABC during learning—both significantly improved children's ability to explicitly relate the indirectly associated A and C items during inference and protected the underlying pair memories from forgetting. However, this finding contrasted with implicit evidence for memory-to-memory connections: Adults and children both formed A-C links prior to any knowledge of an inference test—yet for children, such links were most apparent when they were told to simply encode BC, not integrate. Moreover, the accessibility of such implicit links differed between children and adults, with adults using them to make explicit inferences but children only doing so for well-established direct AB pairs. These results suggest that while a lack of integration strategy may explain a large share of the developmental differences in explicit inference, children and adults nevertheless differ in both the circumstances under which they connect interrelated memories and their ability to later leverage those links to inform flexible behaviours.

Research Highlights

• Children and adults view AB and BC pairs related through a shared item, B. This provides an opportunity for learners to connect A–C in memory.
• Being encouraged to integrate ABC during learning boosted performance on an explicit test of A–C connections (children and adults) and protected from forgetting (children).
• Children and adults differed in when implicit A–C connections were formed—occurring primarily when told to separately encode BC (children) versus integrate (adults), respectively.
• Adults used implicit A–C connections to facilitate explicit judgments, while children did not. Our results suggest developmental differences in the learning conditions promoting memory-to-memory connections.

     

Triangulating causality between childhood obesity and neurobehavior: Behavioral genetic and longitudinal evidence

Childhood obesity is a serious health concern that is not yet fully understood. Previous research has linked obesity with neurobehavioral factors such as behavior, cognition, and brain morphology. The causal directions of these relationships remain mostly untested. We filled this gap by using the Adolescent Brain Cognitive Development study cohort comprising 11,875 children aged 9–10. First, correlations between the age- and sex-specific 95th BMI percentile (%BMIp95) and neurobehavioral measures were cross-sectionally analyzed. Effects were then aggregated by neurobehavioral domain for causal analyses. Behavioral genetic Direction of Causation modeling was used to test the direction of each relationship. Findings were validated by longitudinal cross-lagged panel modeling. %BMIp95 correlated with impulsivity, motivation, psychopathology, eating behavior, and cognitive tests (executive functioning, language, memory, perception, working memory). Greater %BMIp95 was also associated with reduced cortical thickness in frontal and temporal brain areas but with increased thickness in parietal and occipital areas. Similar although weaker patterns emerged for cortical surface area and volume. Behavioral genetic modeling suggested causal effects of %BMIp95 on eating behavior (β = 0.26), cognition (β = 0.05), cortical thickness (β = 0.15), and cortical surface area (β = 0.07). Personality/psychopathology (β = 0.09) and eating behavior (β = 0.16) appeared to influence %BMIp95. Longitudinal evidence broadly supported these findings. Results regarding cortical volume were inconsistent. Results supported causal effects of obesity on brain functioning and morphology. The present study highlights the importance of physical health for brain development and may inform interventions aimed at preventing or reducing pediatric obesity.

Research Highlights

• A continuous measure related to obesity, %BMIp95, has correlations with various measures of brain functioning and structure
• Behavioral genetic and longitudinal modeling suggest causal links from personality, psychopathology, and eating behavior to %BMIp95
• Results also indicate directional links from %BMIp95 to eating behavior, cognition, cortical thickness, and cortical surface area
• Obesity may play a role for healthy brain development during childhood

     

Arithmetic knowledge from the spontaneous attention to relations

Children's knowledge of arithmetic principles is a key aspect of early mathematics knowledge. Knowledge of arithmetic principles predicts how children approach solving arithmetic problems and the likelihood of their success. Prior work has begun to address how children might learn arithmetic principles in a classroom setting. Understanding of arithmetic principles involves understanding how numbers in arithmetic equations relate to another. For example, the Relation to Operands (RO) principle is that for subtracting natural numbers (A ? B = C), the difference (C) must be smaller than the minuend (A). In the current study we evaluate if individual differences in arithmetic principle knowledge (APK) can be predicted by the learners' spontaneous attention to relations (SAR) and if feedback can increase their attention to relations. Results suggest that participants’ Spontaneous Attention to Number (SAN) does not predict their knowledge of the RO principle for symbolic arithmetic. Feedback regarding the attention to relations did not show a significant effect on SAR or participants’ APK. We also did not find significant relations between reports of parent talk and the home environment with individual differences in SAN. The amount of parent's talk about relations was not significantly associated with learner's SAR and APK. We conclude that children's SAR with non‐symbolic number does not generalize to attention to relations with symbolic arithmetic.     

Co‐thought gestures in children's mental problem solving: Prevalence and effects on subsequent performance

Co‐thought gestures are understudied as compared to co‐speech gestures yet, may provide insight into cognitive functions of gestures that are independent of speech processes. A recent study with adults showed that co‐thought gesticulation occurred spontaneously during mental preparation of problem solving. Moreover, co‐thought gesturing (either spontaneous or instructed) during mental preparation was effective for subsequent solving of the Tower of Hanoi under conditions of high cognitive load (i.e., when visual working memory capacity was limited and when the task was more difficult). In this preregistered study ( https://osf.io/dreks/ ), we investigated whether co‐thought gestures would also spontaneously occur and would aid problem‐solving processes in children (N = 74; 8–12 years old) under high load conditions. Although children also spontaneously used co‐thought gestures during mental problem solving, this did not aid their subsequent performance when physically solving the problem. If these null results are on track, co‐thought gesture effects may be different in adults and children.     

Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non‐symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta‐analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two‐level random‐effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non‐symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non‐symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school‐aged children and for adults.     

Early gesture selectively predicts later language learning

The gestures children produce predict the early stages of spoken language development. Here we ask whether gesture is a global predictor of language learning, or whether particular gestures predict particular language outcomes. We observed 52 children interacting with their caregivers at home, and found that gesture use at 18 months selectively predicted lexical versus syntactic skills at 42 months, even with early child speech controlled. Specifically, number of different meanings conveyed in gesture at 18 months predicted vocabulary at 42 months, but number of gesture+speech combinations did not. In contrast, number of gesture+speech combinations, particularly those conveying sentence‐like ideas, produced at 18 months predicted sentence complexity at 42 months, but meanings conveyed in gesture did not. We can thus predict particular milestones in vocabulary and sentence complexity at age by watching how children move their hands two years earlier.     

“I'm an ogre so I'm very hungry!” “I'm assistant ogre”: The Social Function of Sibling Imitation in Early Childhood

Siblings' imitative behaviors were investigated in 39 middle‐class dyads during six 90‐min home sessions at both Time 1 (M age: older sibling = 4.4 years; younger sibling = 2.4 years) and Time 2 (2 years later). Although younger siblings imitated most often at T1 and T2, older siblings' imitation increased proportionally over time in comparison to younger siblings. Findings highlight the affiliative nature of imitation that occurred during reciprocal play interactions, via positive responses, and the content of the imitation. Finally, age was controlled by comparing first‐born siblings aged 4 at T1 to second‐born siblings aged 4 at T2. Findings demonstrated that sibling imitation had distinct characteristics despite the age match and partner effects. Sibling imitation is a dynamic, interactive social behavior and may be a powerful source of learning for young children.

Highlights

• The role of sibling imitation in ongoing play in early childhood is highlighted.
• Sibling imitation is a dynamic and affiliative behavior that promotes interaction during play.
• Naturalistic observations of sibling imitation document that it is a powerful source of learning for young children.

     

The approximate number system is not predictive for symbolic number processing in kindergarteners

The relation between the approximate number system (ANS) and symbolic number processing skills remains unclear. Some theories assume that children acquire the numerical meaning of symbols by mapping them onto the preexisting ANS. Others suggest that in addition to the ANS, children also develop a separate, exact representational system for symbolic number processing. In the current study, we contribute to this debate by investigating whether the nonsymbolic number processing of kindergarteners is predictive for symbolic number processing. Results revealed no association between the accuracy of the kindergarteners on a nonsymbolic number comparison task and their performance on the symbolic comparison task six months later, suggesting that there are two distinct representational systems for the ANS and numerical symbols.     

Cognitive process-based subtypes of developmental coordination disorder (DCD)

The purpose of the study was to identify the cognitive subtypes demonstrated by children with developmental coordination disorder (DCD) using the Planning-Attention-Simultaneous-Successive Processing (PASS) theory and the Cognitive Assessment System (D-N CAS). Participants were 108 children aged 5- and 6-years old, 54 with DCD and 54 without DCD, all attending typical kindergartens. They were examined on 31 cognitive-motor variables. Hierarchical-agglomerative and iterative partitioning cluster analyses including 9 motor and 7 cognitive variables revealed the following six subtypes:

• oC1 = children at risk (having considerable difficulty with jumping and minor difficulty with manual dexterity and simultaneous coding);
• oC2 = children on the mean (all cognitive-motor scores close to the mean);
• oC3 = free from cognitive-motor problems (all scores above average);
• oC4 = manual dexterity, planning and simultaneous coding difficulties;
• oC5 = manual dexterity, dynamic balance, and planning difficulties;
• oC6 = generalized cognitive-motor dysfunction (all scores considerably below average).

It is well known that DCD is a heterogeneous condition. However, whenever cognitive processes were lower than average, cognitive-motor relationship was evident in subgroups C1, C4, C5 and C6. Early identification of task-specific cognitive-motor difficulties may be essential for early educational intervention practices in order to anticipate and improve learning, academic and performing difficulties.     

Approximate number sense,symbolic number processing,or number–space mappings: What underlies mathematics achievement?

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children’s performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well children compared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.     

The interrelationships of mathematical precursors in kindergarten

This study evaluated the interrelations among cognitive precursors across quantitative, linguistic, and spatial attention domains that have been implicated for math achievement in young children. The dimensionality of the quantity precursors was evaluated in 286 kindergarteners via latent variable techniques, and the contribution of precursors from each domain was established for small sums addition. Results showed a five-factor structure for the quantity precursors, with the major distinction being between nonsymbolic and symbolic tasks. The overall model demonstrated good fit and strong predictive power (R² = 55%) for addition number combinations. Linguistic and spatial attention domains showed indirect relationships with outcomes, with their effects mediated by symbolic quantity measures. These results have implications for the measurement of mathematical precursors and yield promise for predicting future math performance.     

Food for thought: a study of food consumption in postmodern US culture

• The objective of this research is to examine the symbolic meanings of contemporary food consumption and provide an in‐depth understanding of related practices. Specifically, we view food as a prominent cultural category representative of postmodernism and approach our study using a postmodern perspective. The paper provides an insight into how US consumers relate to food and highlights the symbolic dimension of food in a culture that is often depicted as highly individualistic. Offering a theoretical framework rooted in an ethnographic account of food consumption we uncover its postmodern complexities that take into account social, cultural, and contextual dimensions. Food is discussed in the context of relationships, desire, and a globalized commodity.

Copyright © 2007 John Wiley & Sons, Ltd.     

Working memory and number line representations in single-digit addition: Approximate versus exact,nonsymbolic versus symbolic

How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills.