Cognitive science in the field: A preschool intervention durably enhances intuitive but not formal mathematics

Uncovering individualised treatment effects for educational trials

Large-scale Randomised Controlled Trials (RCTs) are widely regarded as "the gold standard" for testing the causal effects of school-based interventions. RCTs typically present the statistical significance of the average treatment effect (ATE), which captures the effect an intervention has had on average for a given population. However, key decisions in child health and education are often about individuals who may be very different from those averages. One way to identify heterogeneous treatment effects across different individuals, not captured by the ATE, is to conduct subgroup analyses. For example, free school meal (FSM) pupils as required for projects funded by the Education Endowment Foundation (EEF) in England. These subgroup analyses, as we demonstrate in 48 EEF-funded RCTs involving over 200,000 students, are usually not standardised across studies and offer flexible degrees of freedom to researchers, potentially leading to mixed, if not misleading, results. Here, we develop and deploy an alternative to ATE and subgroup analysis, a machine-learning and regression-based framework to predict individualised treatment effects (ITEs). ITEs could show where an intervention worked, for which individuals, and to what extent. Our findings have implications for decision-makers in fields like education, healthcare, law, and clinical practices concerning children and adolescents.

Every Newborn-Reach Up Early Education Intervention for All Children (EN-REACH)- a parent group intervention for school readiness in Bangladesh, Nepal, and Tanzania: study protocol for a cluster randomized controlled trial

BACKGROUND

Vulnerable children, including those with neuro-developmental delays and disabilities, often face barriers in accessing early primary education, thus hindering progress toward Sustainable Development Goal 4.2. Evidence-based interventions are essential to enhancing inclusivity and establishing sustainable implementation strategies to address this challenge. This study, Every Newborn-Reach up Early Education Intervention for All Children (EN-REACH), builds on the previous Every Newborn- Simplified Measurement Integrating Longitudinal Neurodevelopmental and Growth (EN-SMILING) observational cohort study. This paper provides the protocol for a cluster randomized controlled trial (cRCT) to evaluate the effectiveness of a parenting group intervention program for enhancing school readiness in Bangladesh, Nepal, and Tanzania, and an embedded process evaluation to inform scalability and feasibility.

METHODS

EN-REACH is a cRCT with at least 150 clusters to evaluate the impact of a parent training program led by trained parent-teacher facilitator pairs, focusing on children aged 4 ~ 6 years preparing for preschool. Approximately 500 participants from the EN-SMILING cohort at each site have been identified. A geographic information system will define ~ 50 clusters in each of the three countries, each with approximately ten parent-child dyads. Half the clusters will be randomly assigned to intervention and control groups. The primary outcome is "school readiness", assessed using the Measuring Early Learning Quality and Outcomes tool. Secondary outcomes include Intelligence Quotient, child functioning, growth, visual, and hearing assessments. Data will be collected at baseline, and post-intervention data following implementation of the parent group intervention sessions over approximately 5 months. Quantitative data on coverage and quality care, combined with qualitative insights from children, caregivers, facilitators, and stakeholders' perspectives, will be used to conduct a process evaluation applying the Reach, Effectiveness, Adoption, Implementation, and Maintenance (RE-AIM) framework.  DISCUSSION: This protocol details a trial focused on enhancing school readiness and cognitive abilities in young children, inclusive of those with disabilities, aiming to bridge gap from home to early primary education. EN-REACH aims to provide insights into the effectiveness and acceptability of a co-designed disability-inclusive school readiness program in three countries, potentially impacting national and global policies for all children, including those with disabilities.

TRIAL REGISTRATION

The trial was retrospectively registered on clinicaltrials.gov on 29 February 2024 (NCT06334627).

Divisive language

What language devises, it might divide. By exploring the relations among the core geometries of the physical world, the abstract geometry of Euclid, and language, I give new insight into both the persistence of core knowledge into adulthood and our access to it through language. My extension of Spelke's language argument has implications for pedagogy, philosophy, and artificial intelligence.

Response to commentaries on What Babies Know

Twenty-five commentaries raise questions concerning the origins of knowledge, the interplay of iconic and propositional representations in mental life, the architecture of numerical and social cognition, the sources of uniquely human cognitive capacities, and the borders among core knowledge, perception, and thought. They also propose new methods, drawn from the vibrant, interdisciplinary cognitive sciences, for addressing these questions and deepening understanding of infant minds.

Diversity of spatial activities and parents' spatial talk complexity predict preschoolers' gains in spatial skills

Children's spatial activities and parental spatial talk were measured to examine their associations with variability in preschoolers' spatial skills (N = 113, Mage = 4 years, 4 months; 51% female; 80% White, 11% Black, and 9% other). Parents who reported more diversity in daily spatial activities and used longer spatial talk utterances during a spatial activity had children with greater gains in spatial skills from ages 4 to 5 (β = .17 and β = .40, respectively). Importantly, this study is the first to move beyond frequency counts of spatial input and investigate the links among the diversity of children's daily spatial activities, as well as the complexity of parents' spatial language across different contexts, and preschoolers' gains in spatial skills, an important predictor of later STEM success.

A rationale for promoting cognitive science in teacher education: Deconstructing prevailing learning myths and advancing research-based practices

PURPOSE

Cognitive science is essential to designing, implementing, and evaluating instruction for enhancing student learning. However, there may not be sufficient focus on the principles of cognitive science, as some educators hold learning beliefs that may be considered cognitive myths.

PROCEDURES

This review article analyzes examples of five learning myths (learning styles, pure discovery learning, digital natives, extrinsic motivation, multitasking) and five research-based learning strategies (dual coding, direct instruction, summarization, retrieval practice, spacing). It details the research evidence for each to explain those misconceptions of learning and also those underutilized or misunderstood but effective strategies shown to benefit student learning.

CONCLUSION

Educational practices related to learning myths are widespread in education with potentially detrimental effects on student learning. We recommend that colleges of education be restructured to ensure greater emphasis on cognitive science in educator preparation programs to better promote research-based instructional strategies to meet students' learning needs.

Effects of a 3-factor field intervention on numerical and geometric knowledge in preschool children

The main aim of this study was to develop and test the effects of a field math intervention program on both number and geometry knowledge. The intervention was developed based on three basic skills previously associated with mathematical performance: symbolic number knowledge, mapping processes and spatial reasoning. The participants were 117 preschoolers from six schools in Cali and Bogotá. The children were assigned to an intervention group (N = 55) or a control group (N = 62). The intervention lasted 11 weeks with 3 sessions per week where the children participated in different game-based activities. Tests of numerical and geometric knowledge were administered before and after the intervention. The effects of the intervention were tested twice, immediately after the program ended and six months later. The results show that the children in the intervention group improved more than the control group in both number and geometry. The second posttest revealed a significant intervention effect for geometry, but not for numerical knowledge. The implications of these mixed patterns of results are discussed in the paper.

Individual risk attitudes arise from noise in neurocognitive magnitude representations

Humans are generally risk averse, preferring smaller certain over larger uncertain outcomes. Economic theories usually explain this by assuming concave utility functions. Here, we provide evidence that risk aversion can also arise from relative underestimation of larger monetary payoffs, a perceptual bias rooted in the noisy logarithmic coding of numerical magnitudes. We confirmed this with psychophysics and functional magnetic resonance imaging, by measuring behavioural and neural acuity of magnitude representations during a magnitude perception task and relating these measures to risk attitudes during separate risky financial decisions. Computational modelling indicated that participants use similar mental magnitude representations in both tasks, with correlated precision across perceptual and risky choices. Participants with more precise magnitude representations in parietal cortex showed less variable behaviour and less risk aversion. Our results highlight that at least some individual characteristics of economic behaviour can reflect capacity limitations in perceptual processing rather than processes that assign subjective values to monetary outcomes.

Précis of What Babies Know

Where does human knowledge begin? Research on human infants, children, adults, and nonhuman animals, using diverse methods from the cognitive, brain, and computational sciences, provides evidence for six early emerging, domain-specific systems of core knowledge. These automatic, unconscious systems are situated between perceptual systems and systems of explicit concepts and beliefs. They emerge early in infancy, guide children's learning, and function throughout life.

Early Stimulation and Enhanced Preschool: A Randomized Trial

OBJECTIVES

To estimate the impacts of 2 interventions, early stimulation (ES) for children aged <3 years and enhanced preschool (EP) for children aged 3+ years, and their interactions.

METHODS

In Odisha, India, 192 villages were randomly assigned to ES or to no ES. Within each village, about 8 mothers with children initially aged 7 to 16 months were enrolled, receiving ES or no ES accordingly (n = 1449). Subsequently, when children were aged ∼3 years, the villages were rerandomized to either EP at Anganwadi centers or no EP. This yielded 4 groups: (1) ES and EP, (2) only ES, (3) only EP, and (4) no intervention. Trained Anganwadi workers ran the EP. Primary outcomes, measured at baseline and follow-up after ∼1 year, were children's IQ (summarizing cognition, language, and executive functioning) and school readiness (SR). Secondary outcomes were home environments, caregivers' child-development knowledge. and preschool quality.

RESULTS

Fifteen months after ES ended, onlyES had a sustained benefit on IQ (0.18 SD, P <.04) and on SR (0.13 SD, P <.08). Only EP improved IQ (0.17 SD, P <.04) and SR (0.24 SD, P <.01). Receiving both interventions improved IQ (0.24 SD, P <.01) and SR (0.21 SD, P <.01). No statistically significant interactions between the 2 interventions were observed.

CONCLUSIONS

Both ES and EP increased IQ and SR. Only ES impacts were sustained for 15 months. Only EP resulted in considerable catch-up for children who did not receive only ES. The absence of significant complementarities should be investigated further because of its profound policy implications.

Interventions to promote development in the next 1000 days: A mapping review

The next 1000 days - the period from 2 to 5 years of age - has been highlighted as a key developmental stage in the life-course. A mapping review was conducted to categorize existing literature on interventions in the next 1000 days that promote key developmental outcomes, including publications between 1990 and July 2020. A total of 805 intervention studies were included for data extraction in the review. The number of intervention studies has increased substantially from 2010. Most interventions were from high-income countries, with few (5%) from low- and lower-middle-income countries. Interventions including typically developing children (n = 593, 74%) were mostly (80%) implemented in early childhood care and education (ECCE) settings, with 15% taking place in the home or with families and 5% in community or healthcare settings. Children's literacy and language outcomes were the target of 27% of these interventions, while 25% of interventions targeted early childhood development more holistically or targeted multiple developmental domains. Social-emotional development and social skills were the target of 15% of interventions, motor development 13%, numeracy 8% and cognitive development 8%. For children with any developmental delay, disability, disease or exposure (n = 212), interventions frequently targeted Autism Spectrum Disorder (24%), language or literacy delays (21%), developmental delays or disability more generally (20%); 16% targeted behavioral (or conduct) problems; and 5% targeted attention deficit hyperactivity disorder. Almost half (49%) took place in ECCE settings; 24% occurred in the home or with families, or in community (13%) and/or healthcare (14%) settings. This review highlights the need for more intervention research in low- and middle-income countries and for interventions supporting development in the next 1000 days. While the evidence base for interventions to promote development in this age group continues to expand, the most vulnerable children are not benefiting from this evidence.

Analyzing the misperception of exponential growth in graphs

Exponential growth is frequently underestimated, an error that can have a heavy social cost in the context of epidemics. To clarify its origins, we measured the human capacity (N = 521) to extrapolate linear and exponential trends in scatterplots. Four factors were manipulated: the function underlying the data (linear or exponential), the response modality (pointing or venturing a number), the scale on the y axis (linear or logarithmic), and the amount of noise in the data. While linear extrapolation was precise and largely unbiased, we observed a consistent underestimation of noisy exponential growth, present for both pointing and numerical responses. A biased ideal-observer model could explain these data as an occasional misperception of noisy exponential graphs as quadratic curves. Importantly, this underestimation bias was mitigated by participants' math knowledge, by using a logarithmic scale, and by presenting a noiseless exponential curve rather than a noisy data plot, thus suggesting concrete avenues for interventions.

Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study

Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.

Training spatial cognition enhances mathematical learning in a randomized study of 17,000 children

Spatial and mathematical abilities are strongly associated. Here, we analysed data from 17,648 children, aged 6-8 years, who performed 7 weeks of mathematical training together with randomly assigned spatial cognitive training with tasks demanding more spatial manipulation (mental rotation or tangram), maintenance of spatial information (a visuospatial working memory task) or spatial, non-verbal reasoning. We found that the type of cognitive training children performed had a significant impact on mathematical learning, with training of visuospatial working memory and reasoning being the most effective. This large, community-based study shows that spatial cognitive training can result in transfer to academic abilities, and that reasoning ability and maintenance of spatial information is relevant for mathematics learning in young children.

Teaching the Science in Neuroscience to Protect From Neuromyths: From Courses to Fieldwork

In recent decades, Cognitive Neuroscience has evolved from a rather arcane field trying to understand how the brain supports mental activities, to one that contributes to public policies. In this article, we focus on the contributions from Cognitive Neuroscience to Education. This line of research has produced a great deal of information that can potentially help in the transformation of Education, promoting interventions that help in several domains including literacy and math learning, social skills and science. The growth of the Neurosciences has also created a public demand for knowledge and a market for neuro-products to fulfill these demands, through books, booklets, courses, apps and websites. These products are not always based on scientific findings and coupled to the complexities of the scientific theories and evidence, have led to the propagation of misconceptions and the perpetuation of neuromyths. This is particularly harmful for educators because these misconceptions might make them abandon useful practices in favor of others not sustained by evidence. In order to bridge the gap between Education and Neuroscience, we have been conducting, since 2013, a set of activities that put educators and scientists to work together in research projects. The participation goes from discussing the research results of our projects to being part and deciding aspects of the field interventions. Another strategy consists of a course centered around the applications of Neuroscience to Education and their empirical and theoretical bases. These two strategies have to be compared to popularization efforts that just present Neuroscientific results. We show that the more the educators are involved in the discussion of the methodological bases of Neuroscientific knowledge, be it in the course or as part of a stay, the better they manage the underlying concepts. We argue that this is due to the understanding of scientific principles, which leads to a more profound comprehension of what the evidence can and cannot support, thus shielding teachers from the false allure of some commercial neuro-products. We discuss the three approaches and present our efforts to determine whether they lead to a strong understanding of the conceptual and empirical base of Neuroscience.

Perception of geometric sequences and numerosity both predict formal geometric competence in primary school children

While most animals have a sense of number, only humans have developed symbolic systems to describe and organize mathematical knowledge. Some studies suggest that human arithmetical knowledge may be rooted in an ancient mechanism dedicated to perceiving numerosity, but it is not known if formal geometry also relies on basic, non-symbolic mechanisms. Here we show that primary-school children who spontaneously detect and predict geometrical sequences (non-symbolic geometry) perform better in school-based geometry tests indexing formal geometric knowledge. Interestingly, numerosity discrimination thresholds also predicted and explained a specific portion of variance of formal geometrical scores. The relation between these two non-symbolic systems and formal geometry was not explained by age or verbal reasoning skills. Overall, the results are in line with the hypothesis that some human-specific, symbolic systems are rooted in non-symbolic mechanisms.

The numerator bias exists in millions of real-world comparisons

Fractions are crucial, from math and science education to daily activities, but they are hard. A puzzling aspect of fractions is that people over-rely on the numerator when comparing a pair of fractions. Previous work has considered this numerator bias mostly as a reasoning mishap. Still, in a vast amount of pairwise comparisons, across many real-world domains, not just education textbooks, we report a high prior probability that the larger fraction has the larger numerator, and, for a relevant case, we provide formal arguments why. The existence of such a regularity suggests that the numerator bias may reflect a rational adaptation that detects and exploits likely events. In a pair of visual-proportion tasks (discrete and continuous fractions), we confirm that the numerator bias in participants adapts to experimented regularities. Even though weak education and math abilities play a role, adaptation to informative priors outside the classroom poses a challenge to educators, learners, and decision-makers.

Approximate arithmetic training does not improve symbolic math in third and fourth grade children

BACKGROUND

Prior studies reported that practice playing an approximate arithmetic game improved symbolic math performance relative to active control groups in adults and preschool children (e.g. Park & Brannon, 2013, 2014; Park et al., 2016; Szkudlarek & Brannon, 2018). However, Szkudlarek, Park and Brannon (2021) recently failed to replicate those findings in adults. Here we test whether approximate arithmetic training yields benefits in elementary school children who have intermediate knowledge of arithmetic.

METHOD

We conducted a randomized controlled trial with a pre and post-test design to compare the effects of approximate arithmetic training and visuo-spatial working memory training on standardized math performance in third and fourth grade children.

RESULTS

We found that approximate arithmetic training did not yield any significant gains on standardized measures of symbolic math performance.

CONCLUSION

A Bayesian analysis supports the conclusion that approximate arithmetic provides no benefits for symbolic math performance.

Failure to replicate the benefit of approximate arithmetic training for symbolic arithmetic fluency in adults

Previous research reported that college students’ symbolic addition and subtraction fluency improved after training with non-symbolic, approximate addition and subtraction. These findings were widely interpreted as strong support for the hypothesis that the Approximate Number System (ANS) plays a causal role in symbolic mathematics, and that this relation holds into adulthood. Here we report four experiments that fail to find evidence for this causal relation. Experiment 1 examined whether the approximate arithmetic training effect exists within a shorter training period than originally reported (2 vs 6 days of training). Experiment 2 attempted to replicate and compare the approximate arithmetic training effect to a control training condition matched in working memory load. Experiments 3 and 4 replicated the original approximate arithmetic training experiments with a larger sample size. Across all four experiments (N = 318) approximate arithmetic training was no more effective at improving the arithmetic fluency of adults than training with control tasks. Results call into question any causal relationship between approximate, non-symbolic arithmetic and precise symbolic arithmetic.

Online Developmental Science to Foster Innovation, Access, and Impact

We propose that developmental cognitive science should invest in an online CRADLE, a Collaboration for Reproducible and Distributed Large-Scale Experiments that crowdsources data from families participating on the internet. Here, we discuss how the field can work together to further expand and unify current prototypes for the benefit of researchers, science, and society.

The balance of rigor and reality in developmental neuroscience

The balance realism and rigor in psychological research is essential to the development of rich and accurate theories about the developing brain. In the field of neuroimaging researchers have used predominantly controlled laboratory methods to decompose neural signals into meaningful functions but there is currently a push to integrate naturalistic conditions into neural measurement. Sometimes naturalistic methods are used to validate existing functional theories ecologically, and other times they are used in data-driven studies for exploration. This article assesses the value and risk of these approaches for understanding the developing brain.

Training nonsymbolic proportional reasoning in children and its effects on their symbolic math abilities

Our understanding of proportions can be both symbolic, as when doing calculations in school mathematics, or intuitive, as when folding a bed sheet in half. While an understanding of symbolic proportions is crucial for school mathematics, the cognitive foundations of this ability remain unclear. Here we implemented a computerized training game to test a causal link from intuitive (nonsymbolic) to symbolic proportional reasoning and other math abilities in 4th grade children. An experimental group was trained in nonsymbolic proportional reasoning (PR) with continuous extents, and an active control group was trained on a remarkably similar nonsymbolic magnitude comparison. We found that the experimental group improved at nonsymbolic PR across training sessions, showed near transfer to a paper-and-pencil nonsymbolic PR test, transfer to symbolic proportions, and far transfer to geometry. The active control group showed only a predicted far transfer to geometry. In a second experiment, these results were replicated with an independent cohort of children. Overall this study extends previous correlational evidence, suggesting a functional link between nonsymbolic PR on one hand and symbolic PR and geometry on the other.

Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics

The ability to intuitively and quickly compare the number of items in collections without counting is thought to rely on the Approximate Number System (ANS). To assess individual differences in the precision of peoples' ANS representations, researchers often use non-symbolic number comparison tasks in which participants quickly choose the numerically larger of two arrays of dots. However, some researchers debate whether this task actually measures the ability to discriminate approximate numbers or instead measures the ability to discriminate other continuous magnitude dimensions that are often confounded with number (e.g., the total surface area of the dots or the convex hull of the dot arrays). In this study, we used hierarchical linear models (HLMs) to predict 132 adults' accuracy on each trial of a non-symbolic number comparison task from a comprehensive set of trial-level characteristics (including numerosity ratio, surface area, convex hull, and temporal and spatial variations in presentation format) and participant-level controls (including cognitive abilities such as visual-short term memory, working memory, and math ability) in order to gain a more nuanced understanding of how individuals complete this task. Our results indicate that certain trial-level characteristics of the dot arrays contribute to our ability to compare numerosities, yet numerosity ratio, the critical marker of the ANS, remains a highly significant predictor of accuracy above and beyond trial-level characteristics and across individuals with varying levels of math ability and domain-general cognitive abilities.

Cognitive and Neural Effects of a Brief Nonsymbolic Approximate Arithmetic Training in Healthy First Grade Children

Recent studies with children and adults have shown that the abilities of the Approximate Number System (ANS), which operates from early infancy and allows estimating the number of elements in a set without symbols, are trainable and transferable to symbolic arithmetic abilities. Here we investigated the brain correlates of these training effects, which are currently unknown. We trained two Groups of first grade children, one in performing nonsymbolic additions with dot arrays (Addition-Group) and another one in performing color comparisons of the same arrays (Color-Group). The training program was computerized, throughout seven sessions and had a pretest-posttest design. To evaluate cognitive gains, we measured math skills before and after the training. To measure the brain changes, we used electroencephalogram (EEG) recordings in the first and the last training sessions. We explored the changes in N1 and P2p, which are two electrophysiological components sensitive to nonsymbolic numeric computations. A passive Control-Group receiving no intervention also had their math skills evaluated. We found that the two training Groups had similarly gain in math skills, suggesting no specific transfer of the nonsymbolic addition training to math skills at the behavioral level. In contrast, at the brain level, we found that only in the Addition-Group the P2p amplitude significantly increased across sessions. Notably, the gain in P2p amplitude positively correlated with the gain in math abilities. Together, our results showed that first graders rapidly gained in math skills by different interventions. However, number-related brain networks seem to be particularly sensitive to nonsymbolic arithmetic training.

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children (n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic training improves early informal, but not formal, math skills.

Intergenerational associations of the approximate number system in toddlers and their parents

From birth, humans are able to discriminate quantities using the approximate number system (ANS). However, previous methods have only been suitable to examine ANS functioning in infancy and older children. The goals of this study were twofold: first, to modify an existing method of assessing ANS functioning for toddlerhood; and second, to investigate individual differences in toddlers' ANS performance by examining correlations with their parents' ANS acuity. Using a preferential looking paradigm, we found that 1- to 3-year-olds (N = 46) looked significantly longer to numerically changing images compared to numerically constant ones suggesting that the paradigm is a suitable measure of ANS functioning in toddlerhood. Furthermore, we found a positive relation between toddlers' ANS performance and that of their parents (assessed using a non-symbolic number comparison task) independent of children's vocabulary or parents' perceived math ability or preference for math. These findings are consistent with a specific intergenerational transmission of the ANS. Statement of contribution What is already known on this subject? Past methods used to examine ANS functioning were only suitable for infants and older children. Little research has examined sources underlying individual difference in ANS acuity. What does this study add? We developed a preferential looking task to assess ANS functioning in toddlerhood. Individual differences in toddlers' ANS functioning are correlated with their parents' ANS acuity.