Journal of Numerical Cognition

Linking Sensorimotor Skills and Finger Use to Arithmetic Development: A Latent Growth Modeling Approach

2026-04-29T00:28:06+00:00

Although finger sensorimotor skills, such as finger gnosia and fine motor skills (FMS), are crucial for arithmetic development, the processes underlying this relationship remain poorly understood. This study examined the functionalist hypothesis by investigating longitudinal associations between finger sensorimotor skills, finger-based strategies, and arithmetic developmental trajectories. The predictive value of developmental changes in sensorimotor skills on arithmetic development and the possible mediating role of finger use in this relationship were also explored. Seventy-four 6-year-old children were assessed four times between the beginning of Grade 1 and the end of Grade 2. At each assessment time point, participants completed tasks evaluating their general cognitive abilities, arithmetic skills, finger gnosia and FMS. Using latent growth modelling, researchers found that the variance in the intercept of finger gnosia was a key predictor of arithmetic development, even when fluid reasoning was controlled for. Conversely, neither the variance of the FMS intercept nor its slope significantly predicted arithmetic development. Latent growth modelling failed to show that effective finger use during calculation was a predictor of the development of arithmetic skills. The present findings do not provide evidence that the relationship between finger gnosia and arithmetic is kinesthetic in nature in this developmental time window.

Implementing Schema Instruction to Support Young Children With Word Problems: A Systematic Review

2026-03-31T00:25:15+00:00

When young children are presented with mathematics word problems, they are asked to decode words, understand text, think critically, and perform calculations. Word problems are interdisciplinary and are known to be difficult for children across all grade levels. Schema instruction, in which children learn to solve word problems according to underlying concepts, has been identified as an evidence-based practice. Still, more attention needs to be devoted to how schema instruction impacts young children. We conducted a systematic search of experimental studies that implemented schema instruction with children in kindergarten, Grade 1, or Grade 2. In May of 2023, we conducted searches of three databases. To be included, studies had to be experimental (i.e., randomized-controlled trials, quasi-experiments, or single-case design) and peer reviewed or dissertations. Moreover, studies had to measure the impact of schema instruction on the word-problem performance of children in kindergarten, Grade 1, or Grade 2. Ultimately, we identified and included 13 studies with participants in Grades 1 and 2 (n ~ 2,100). Overall, schema instruction positively impacted word-problem outcomes. Common instructional components included: (a) systematic and explicit instruction on word-problem schemas; (b) diagrams, meta-equations, and gesturing; (c) the use of a problem-solving heuristic; (d) inclusion of numberless or intact story problems and isolated practice with identifying schemas; (e) explicit instruction on mathematics and word-problem specific vocabulary; (f) incorporating concrete or virtual manipulatives and a fact fluency component; and (g) the inclusion of a self-monitoring behavior component.

Exploring Cognitive Predictors: Examining Varied Impact on Early Number Skills in a Longitudinal Study

2026-03-19T01:27:42+00:00

This longitudinal study investigates the role of domain-general cognitive abilities in predicting domain-specific numerical abilities across early school years. Using von Aster and Shalev's four-step developmental model of numerical cognition (2007) and Ackerman's general theory of skill acquisition (1988), we examined how cognitive abilities (e.g., phonological processing, verbal working memory) contribute to children's counting knowledge, digit magnitude comparison, and number line estimation from kindergarten through second grade. The sample comprised 296 children (50.3% girls), who began participation at approximately six years (M_age = 6.7 years). Findings highlight the influence of domain-general cognitive functions throughout early numerical development. Specifically, phonological processes and processing speed significantly predict prior to formal education, while verbal working memory and nonverbal logical reasoning become more important after starting formal education. While the importance of certain domain-general abilities increases over time, others decline. Our results align with both von Aster and Shalev's (2007) model (positing that cognitive demands increase when learning new, more complex numerical abilities) and with Ackerman's (1988) theory (suggesting that reliance on cognitive abilities decreases as skills become more automated). Together, these frameworks complement each other, offering a comprehensive understanding of how cognitive abilities support numerical development. Our study highlights the important role of early cognitive abilities in forming the foundation for successively more complex numerical skills. While each framework provides valuable insights, integrating them may better capture the complexities of early numerical development. These findings emphasize the varying roles of domain-general cognitive abilities and the nuanced trajectories depicted by these theoretical models.

Longitudinal Predictors of Conceptual Understanding of Arithmetic Principles

2026-03-19T01:27:44+00:00

A bidirectional relationship between conceptual and procedural understanding in the development of arithmetic skills has often been reported. We investigated whether domain-specific longitudinal predictors of procedural arithmetic performance at the beginning of primary school also predict conceptual understanding two years later. We assessed conceptual and procedural understanding of arithmetic and mathematical reasoning in 195 UK children (mean age 8 years 2 months) in Year 3. Conceptual understanding was defined as children’s understanding of principles underlying arithmetic procedures. Performance on a speeded arithmetic task was taken as an indicator of children’s procedural understanding of arithmetic. The same children had been assessed in Year 1 on potential cognitive and numerical predictors including number transcoding, symbolic and non-symbolic magnitude comparison, arithmetic performance, verbal and visuo-spatial working memory, and non-verbal reasoning. A structural equation model including arithmetic performance, number transcoding and non-verbal cognitive skills measured in Year 1 predicted 33% of the variance in conceptual understanding in Year 3. Arithmetic performance and number transcoding in Year 1 were also significant longitudinal predictors of both procedural arithmetic understanding and mathematical reasoning in Year 3. When we ran a second structural equation model without arithmetic performance in Year 1, number transcoding and non-verbal cognitive skills remained the only significant longitudinal predictors of conceptual understanding in Year 3. Our study highlights substantial similarities as well as some differences in the longitudinal predictors of conceptual versus procedural understanding of arithmetic in early primary school.

Developing an Understanding of Repeating Patterning

2026-03-19T01:27:43+00:00

Patterning knowledge encompasses the ability to notice and use predictable sequences, and identifying, extending, and describing patterns in objects and numbers are core to mathematical thinking. Identifying the pattern rule (e.g., the unit of repeat) is often considered an indicator of patterning understanding. The goal of the current paper is to consider potential operationalizations of repeating patterning understanding, as well as expand the toolkit for measuring repeating patterning understanding. The Early Patterning Assessment (EPA) is a research instrument that can be given online or in person, using mostly selected-response items. Across four rounds of data collection in the U.S. (n = 244) and one study in Türkiye (formerly known as Turkey) (n = 107), the repeating patterning measure was a reliable measure for 4-7-year-old children, with scores increasing with age. It was also easier and faster to administer than past assessments that used constructed response items. IRT Rasch models were used to assess construct validity and identify the difficulty level of different types of items, within a Construct Modeling Approach (Wilson, 2023). Complete the pattern was the easiest task, and explicitly identifying the unit of repeat was the most difficult task. We considered three potential indicators of repeating patterning understanding and suggest operationalizing children’s understanding of repeating patterns as demonstrating spontaneous use of correct procedures across multiple tasks and pattern units.

The Evolved System for Conceptual Understanding: Implications for Mathematical Development

2026-03-19T01:27:43+00:00

The relative importance of knowledge of discrete facts (e.g., 12 + 5 = 17) or abstract concepts (e.g., mathematical equality) is debated and contributes to the math wars; the different assumptions and approaches of mathematics educators and cognitive scientists who study mathematical learning. Stepping back and approaching the issue using the properties of the controlled semantic cognition system could move the debate forward. The system supports conceptual learning across domains, and represents concepts as common properties of related experiences or things. These properties can be generalized across exemplars, contexts, and time and can be expressed across modalities. The concepts emerge slowly through statistical learning and will be shaped by the frequency and variety of exposures to experiences and things that share common features. The properties of the system help to explain why the ways in which math problems are presented (e.g., in textbooks) lead to conceptual understandings or misunderstandings; why repeated and varied (e.g., different surface structure) solving of problems that tap the same concept are required for concept learning; and, why mathematical concepts can be expressed through gesture, language, or visually. The approach has implications for improving children’s mathematical development.

Children’s Early Math Problem-Solving: The Role of Parent Numeracy Practices, Numeracy Expectations, and Math Attitudes

2025-12-19T07:17:16+00:00

This study allows for the examination of associations between components of the home mathematics environment – including parents’ formal numeracy practices, math attitudes, and numeracy expectations – and children’s development of math problem solving skills following the transition into formal school. Sixty-six children from three schools in the Southeastern United States were assessed six times across kindergarten and first grade using a battery of academic and cognitive measures – including a task that evaluated children’s strategy use and accuracy while solving basic arithmetic problems. Parents reported the frequency with which they engaged in formal numeracy practices in the home, their attitudes towards mathematics, and their numeracy expectations for their child. Results from growth curve models, controlling for parents’ education and children’s working memory, revealed that neither parents’ numeracy practices nor their expectations accounted for differences in children’s development, but that children with parents who held more negative views towards math entered kindergarten with lower math problem-solving skills (both accuracy and strategy use) than their peers. However, children who entered kindergarten with lower skills demonstrated greater improvement in their scores over the course of the two years. Findings highlight the importance of examining aspects of the home mathematics environment other than numeracy practices – such as parents’ math attitudes – as they relate to children’s mathematical development.

Untangling the Visual Coherence Effect of Numerosity Perception Throughout Development With Drift Diffusion Model

2025-12-19T07:09:37+00:00

Understanding how non-numerical visual features systematically distort numerosity perception holds promise for unveiling the processes that give rise to our visual number sense. Recent studies show that increasing visual coherence systematically increases perceived numerosity, with this effect strengthening over development (DeWind et al., 2020; Qu, Bonner, et al., 2024; Qu et al., 2022). Here, we investigate the cognitive mechanisms underlying the coherence illusion from a view of perceptual decision processes. Specifically, we applied a drift diffusion model (DDM) to a previously described dataset from participants aged 5-30 tested in an ordinal numerical comparison task with color entropy systematically manipulated (Qu et al., 2022). By jointly modeling choice data and response times, we decomposed numerical discrimination performance into distinct decision components: the speed of numerical evidence accumulation (drift rate), the amount of evidence required for a decision (boundary separation), and the response bias reflecting a prior tendency of selecting one side over the other. We found that color coherence affected only the drift rate but not response bias or boundary separation, demonstrating that color coherence distorts numerical calculation through biased accumulation of evidence of quantity. Moreover, the impact of coherence on the drift rate coefficient increased with age as quantitative information is accumulated more efficiently over development. Our results offer a framework for understanding how numerical illusions arise from perceptual decision-making dynamics.

When Anxiety Grows With Knowledge: The Role of the Natural Number Bias

2025-11-27T07:41:56+00:00

An important source for the difficulties students face with fractions is the natural number bias (NNB), which refers to the phenomenon of applying natural number properties in fraction tasks, even when this is inappropriate (e.g., 1/4+1/3 = 2/7). The present longitudinal study investigates whether this misconception is related to the development of mathematics state anxiety in the domain of fractions. The results indicated that, when a group of students with a clear NNB profile (n = 38) improved their fraction arithmetic understanding they showed an increase in state anxiety measured after the fraction arithmetic task. These results complement previous research by showing that a clear misconception, namely the natural number bias, might influence the development of students’ fraction state anxiety. Importantly, the increase in fraction state anxiety in the low-performing NNB group is not a characteristic of low performing students in general, as a significant decrease in fraction state anxiety was found in low-performing students without signs of the NNB (n = 37). The study highlights the importance of looking at different subgroups of students, as different developmental patterns can be found within qualitatively different groups of students.

How Different Negative Emotions Affect Young and Older Adults’ Arithmetic Performance in Addition and Multiplication Problems?

2025-11-27T07:41:10+00:00

We examined how different types of negative emotional states (anger, disgust, sadness) influence arithmetic performance, and whether this influence is modulated by the types of arithmetic operations and moderated by adults’ age. Younger and older adults verified addition and multiplication problems that were superimposed on emotionally negative (angry, disgust, sad) or neutral images. Emotionally negative images were matched on both arousal and valence. We found that different negative emotional stimuli had different effects on arithmetic performance. We also found that these effects differed for addition and multiplication problems, and were moderated by participants’ age. More specifically: (a) younger adults were more impaired by sad stimuli than older adults while solving addition problems; (b) older adults but not younger adults solved multiplication problems more slowly following disgust and sad stimuli than emotionally neutral stimuli and (c) anger stimuli did not affect younger and older adults’ performance while solving addition and multiplication problems. These findings shed important lights on how different negative emotional stimuli influence arithmetic performance and how this influence changes with age during adulthood.