Assessing the impact of LEGO® construction training on spatial and mathematical skills.

Lego construction ability is associated with a variety of spatial skills and mathematical outcomes. However, it is unknown whether these relations are causal. We aimed to establish the causal impact of Lego construction training on: Lego construction ability; a broad range of spatial skills; and on mathematical outcomes in 7-9-year-olds. We also aimed to identify how this causal impact differs for digital versus physical Lego construction training. One-hundred and ninety-eight children took part in a six-week training programme, delivered twice weekly as a school lunch time club. They completed either physical Lego training (N = 59), digital Lego training (N = 64), or an active control condition (crafts; N = 75). All children completed baseline and follow-up measures of spatial skills (disembedding, visuo-spatial working memory, spatial scaling, mental rotation, and performance on a spatial-numerical task, the number line task), mathematical outcomes (geometry, arithmetic, and overall mathematical skills) and Lego construction ability. Exploratory analyses revealed evidence for near transfer (Lego construction ability) and some evidence for far transfer (arithmetic) of Lego training, but overall transfer was limited. Despite this, we identified key areas for further development (explicit focus on spatial strategies, training for teachers, and embedding the programme within a mathematical context). The findings of this study can be used to inform future development of Lego construction training programmes to support mathematics learning.

Mathematics Skills in Epilepsy: A Systematic Review and Meta-Analysis.

Mathematics incorporates a broad range of skills, which includes basic early numeracy skills, such as subitizing and basic counting to more advanced secondary skills including mathematics calculation and reasoning. The aim of this review was to undertake a detailed investigation of the severity and pattern of early numeracy and secondary mathematics skills in people with epilepsy. Searches were guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Twenty adult studies and 67 child studies were included in this review. Overall, meta-analyses revealed significant moderate impairments across all mathematics outcomes in both adults (g= -0.676), and children (g= -0.593) with epilepsy. Deficits were also observed for specific mathematics outcomes. For adults, impairments were found for mathematics reasoning (g= -0.736). However, two studies found that mathematics calculation was not significantly impaired, and an insufficient number of studies examined early numeracy skills in adults. In children with epilepsy, significant impairments were observed for each mathematics outcome: early numeracy (g= -0.383), calculation (g= -0.762), and reasoning (g= -0.572). The gravity of impairments also differed according to the site of seizure focus for children and adults, suggesting that mathematics outcomes were differentially vulnerable to the location of seizure focus.

Associations and indirect effects between LEGO® construction and mathematics performance.

There is a known association between LEGO® construction ability and mathematics achievement, yet the mechanisms which drive this association are largely unknown. This study investigated the spatial mechanisms underlying this association, and whether this differs for concrete versus digital construction. Between January 2020 and July 2021, children aged 7-9 years (N = 358, 189 female, ethnicity not recorded) completed spatial and mathematics tasks, and either a concrete or digital Lego construction task. Mediation analyses examining direct and indirect pathways (through spatial skills) between Lego construction ability and mathematics explained 8.4% to 26.6% of variance in mathematics scores. Exploratory moderated mediation analyses revealed that only the indirect path through mental rotation differed between Lego conditions. Findings are discussed in relation to theories of spatial-numerical associations and the potential of Lego training for mathematics improvement.

Counting many as one: Young children can understand sets as units except when counting.

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 a unit, resulting in a preference for discrete items. Here we demonstrate that children's incomplete understanding of counting also plays a role. In an experiment with 4- and 5-year-old children (N = 43), we found that even if children are able to name sets, group items into sets, and create one-to-one correspondences with sets, many children are nevertheless unable to count sets as units. We conclude that a nascent understanding of the abstraction principle of counting is also a cause of some children's counting errors.

Is the ANS linked to mathematics performance?

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 indicates that these experimental studies do not contain evidential value.

Explaining the relationship between number line estimation and mathematical achievement: The role of visuomotor integration and visuospatial skills.

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 representations but also proportional judgment skills; if this is the case, then individual differences in visuospatial skills, not just the precision of numerical representations, may explain the relationship between number line estimation and mathematical achievement. The current study investigated the relationships among visuospatial skills, visuomotor integration, number line estimation, and mathematical achievement. In total, 77 children were assessed using a number line estimation task, a standardized measure of mathematical achievement, and tests of visuospatial skills and visuomotor integration. The majority of measures were significantly correlated. In addition, the relationship between one metric from the number line estimation task (R(2)LIN) and mathematical achievement was fully explained by visuomotor integration and visuospatial skill competency. These results have important implications for understanding what the number line task measures as well as the choice of number line metric for research purposes.

Universal gestational age effects on cognitive and basic mathematic processing: 2 cohorts in 2 countries.

OBJECTIVE: 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. STUDY DESIGN: The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). RESULTS: For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: -2.99, -1.70) and 2.76 (95% CI: -3.40, -2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: -2.20, -1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. CONCLUSIONS: Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling.

Preterm Birth and Adult Wealth: Mathematics Skills Count.

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 between preterm birth and low adult wealth is mediated by poor academic abilities and educational qualifications. Participants were members of two British population-based birth cohorts born in 1958 and 1970, respectively. Results showed that preterm birth was associated with decreased wealth at 42 years of age. This association was mediated by decreased intelligence, reading, and, in particular, mathematics attainment in middle childhood, as well as decreased educational qualifications in young adulthood. Findings were similar in both cohorts, which suggests that these mechanisms may be time invariant. Special educational support in childhood may prevent preterm children from becoming less wealthy as adults.

Nature and origins of mathematics difficulties in very preterm children: a different etiology than developmental dyscalculia.

BACKGROUND: Children born very preterm (<32 wk) are at high risk for mathematics learning difficulties that are out of proportion to other academic and cognitive deficits. However, the etiology of mathematics difficulties in very preterm children is unknown. We sought to identify the nature and origins of preterm children's mathematics difficulties. METHODS: One hundred and fifteen very preterm children aged 8-10 y were assessed in school with a control group of 77 term-born classmates. Achievement in mathematics, working memory, visuospatial processing, inhibition, and processing speed were assessed using standardized tests. Numerical representations and specific mathematics skills were assessed using experimental tests. RESULTS: Very preterm children had significantly poorer mathematics achievement, working memory, and visuospatial skills than term-born controls. Although preterm children had poorer performance in specific mathematics skills, there was no evidence of imprecise numerical representations. Difficulties in mathematics were associated with deficits in visuospatial processing and working memory. CONCLUSION: Mathematics difficulties in very preterm children are associated with deficits in working memory and visuospatial processing not numerical representations. Thus, very preterm children's mathematics difficulties are different in nature from those of children with developmental dyscalculia. Interventions targeting general cognitive problems, rather than numerical representations, may improve very preterm children's mathematics achievement.

The long-term consequences of preterm birth: what do teachers know?

AIM: The 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 following preterm birth. Total scores (range 0-33) were compared between groups and the impact of demographic characteristics on knowledge was analysed. Training and information needs were also assessed. RESULTS: Teaching staff (mean 14.7, SD 5.5) had significantly lower knowledge scores than educational psychologists (mean 17.1, SD 5.0; p<0.001); both had significantly lower scores than neonatal clinicians surveyed previously (mean 26.0, SD 3.6; p<0.001). Education professionals' poorest areas of knowledge related to the most frequent adverse outcomes following preterm birth. Only 16% of teaching staff had received training about preterm birth and more than 90% requested more information. Having a special educational needs role and being employed at least 16 years were associated with higher knowledge scores. INTERPRETATION: Education professionals have poor knowledge of the needs of children born preterm and most feel ill-equipped to support them in school. As teachers have primary responsibility for providing long-term support for children born preterm, this is of significant public health and educational concern.

Delayed school entry and academic performance: a natural experiment.

AIM: 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. METHOD: In total, 999 children (492 females, 507 males; 472 born preterm) were studied as part of a prospective population-based longitudinal study in Germany. Using a natural experimental design, propensity score matching was applied to create two matched groups who differed only in terms of DSE versus ASE. Teacher ratings of achievement in mathematics, reading, writing, and attention were obtained in Year 1, and standardized tests were administered at 8 years of age. RESULTS: There was no evidence of a difference in the odds of DSE versus ASE children being rated as above average by teachers in Year 1. In contrast, the standardized mean test scores for DSE children were lower than ASE children's mean scores in all domains (mathematics: B=-0.28 [-0.51 to -0.06)], reading: B=-0.39 [-0.65 to -0.14], writing: B=-0.90 [-1.07 to -0.74], and attention: B=-0.58 [-0.79 to -0.36]). INTERPRETATION: DSE did not affect teacher-rated academic performance. However, missing 1 year of learning opportunities was associated with poorer average performance in standardized tests at 8 years of age. Future research is needed to determine the long-term effect of DSE on academic achievement.

Multiple number-naming associations: How the inversion property affects adults' two-digit number processing.

Some number-naming systems are less transparent than others. For example, in Dutch, 49 is named "negenenveertig," which translates to "nine and forty," i.e., the unit is named first, followed by the decade. This is known as the "inversion property," where the morpho-syntactic representation of the number name is incongruent with its written Arabic form. Number word inversion can hamper children's developing mathematical skills. But little is known about its effects on adults' numeracy, the underlying mechanism, and how a person's bilingual background influences its effects. In the present study, Dutch-English bilingual adults performed an audiovisual matching task, where they heard a number word and simultaneously saw two-digit Arabic symbols and had to determine whether these matched in quantity. We experimentally manipulated the morpho-syntactic structure of the number words to alter their phonological (dis)similarities and numerical congruency with the target Arabic two-digit number. Results showed that morpho-syntactic (in)congruency differentially influenced quantity match and non-match decisions. Although participants were faster when hearing traditional non-transparent Dutch number names, they made more accurate decisions when hearing artificial, but morpho-syntactically transparent number words. This pattern was partly influenced by the participants' bilingual background, i.e., their L2 proficiency in English, which involves more transparent number names. Our findings suggest that, within inversion number-naming systems, multiple associations are formed between two-digit Arabic symbols and number names, which can influence adults' numerical cognition.

Mathematics difficulties in extremely preterm children: evidence of a specific deficit in basic mathematics processing.

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 11 y of age. All children were assessed by a psychologist on a battery of standardized cognitive tests and a number estimation test assessing children's numerical representations. RESULTS: EP children underperformed in all tests in comparison with the term controls (the majority of Ps < 0.001). Different underlying relationships between performance on the number estimation test and mathematical achievement were found in EP as compared with control children. That is, even after controlling for cognitive ability, a relationship between number representations and mathematical performance persisted for EP children only (EP: r = 0.346, n = 186, P < 0.001; control: r = 0.095, n = 146, P = 0.256). CONCLUSION: Interventions for EP children may target improving children's numerical representations in order to subsequently remediate their mathematical skills.

Symbolic arithmetic knowledge without instruction.

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 number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required. Here we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children's difficulties learning symbolic arithmetic, and they suggest ways to enhance children's engagement with formal mathematics.

Understanding the complexities of mathematical cognition: A multi-level framework.

Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.

Positive impact of sleep on recall of multiplication facts.

This study tested the hypothesis that learning complex multiplication problems (e.g. 8 × 23 = 184) prior to sleep would benefit recall in adult participants compared with learning the problems prior to a period of wakefulness. This study used a within-participant design where all participants learnt complex multiplication problems in two conditions separated by one week. In one condition, learning was before bed (sleep learning condition) and in the other condition learning was in the morning (wake learning condition). In each condition, recall was tested approximately 10.5 h later. Data were collected online from 77 participants. In the subset of the sample with greater than or equal to 60% accuracy at the initial learning session (n = 37), the sleep learning condition participants had better recall compared with the wake learning condition. This equated to a moderate effect size, Cohen's d = 0.51. Regardless of initial levels of learning (n = 70) the same beneficial effect of sleep on recall was found with a small effect size, Cohen's d = 0.33. This study has identified a beneficial effect of learning prior to sleep on recall of complex multiplication problems compared with learning these problems during the daytime. Future research should explore whether similar effects are observed with children learning simple multiplication facts.

Learning artificial number symbols with ordinal and magnitude information.

The question of how numerical symbols gain semantic meaning is a key focus of mathematical cognition research. Some have suggested that symbols gain meaning from magnitude information, by being mapped onto the approximate number system, whereas others have suggested symbols gain meaning from their ordinal relations to other symbols. Here we used an artificial symbol learning paradigm to investigate the effects of magnitude and ordinal information on number symbol learning. Across two experiments, we found that after either magnitude or ordinal training, adults successfully learned novel symbols and were able to infer their ordinal and magnitude meanings. Furthermore, adults were able to make relatively accurate judgements about, and map between, the novel symbols and non-symbolic quantities (dot arrays). Although both ordinal and magnitude training was sufficient to attach meaning to the symbols, we found beneficial effects on the ability to learn and make numerical judgements about novel symbols when combining small amounts of magnitude information for a symbol subset with ordinal information about the whole set. These results suggest that a combination of magnitude and ordinal information is a plausible account of the symbol learning process.

Higher level domain specific skills in mathematics; The relationship between algebra, geometry, executive function skills and mathematics achievement.

Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms.

Substitution and sameness: two components of a relational conception of the equals sign.

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 here that, in addition to these two conceptions, the notion of substitution is also an important part of a sophisticated understanding of mathematical equivalence. We provide evidence from a cross-cultural study in which English and Chinese children were asked to rate the "cleverness" of operational, sameness, and substitutive definitions of the equals sign. A principal components analysis revealed that the substitutive items were distinct from the sameness items. Furthermore, Chinese children rated the substitutive items as 'sort of clever' or 'very clever', whereas English children rated them as not so clever, suggesting that the notion of substitution develops differently across the two countries. Implications for developmental models of children's understanding of equivalence are discussed.

Etiology of persistent mathematics difficulties from childhood to adolescence following very preterm birth.

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 adolescents were assessed at age 11-15 years. Mathematics achievement was assessed using the Wechsler Individual Achievement Test-II. Specific mathematics skills and general cognitive skills were assessed using standardized and experimental tests. VP adolescents had poorer mathematics achievement than term-born adolescents (-10.95 points; 95% CI -16.18, -5.73) and poorer number fact knowledge, understanding of arithmetic concepts, written arithmetic, counting, reading and writing large numbers, and algebra. Between-group differences in mathematics skills were no longer significant when working memory and visuospatial skills were controlled for (p's >0.05), with the exception of writing large numbers and conceptual understanding of arithmetic. In a previous study, 83 of the VP adolescents and 49 of the term-born adolescents were assessed at age 8-10 years using measures of the same skills. Amongst these, the between-group difference in mathematics achievement remained stable over time. This study extends findings of a persistent deficit in mathematics achievement among VP children over the primary and secondary school years, and provides evidence of a deficit in factual, procedural and conceptual mathematics skills and in higher order mathematical operations among VP adolescents. We provide further evidence that VP children's mathematics difficulties are driven by deficits in domain-general rather than domain-specific cognitive skills.