Journal of Numerical Cognition

Unbounded Number Line Estimation as a Mechanism Linking Spatial Skills and Mathematical Performance in Adults

Felix Ayesu, Darcy Hallett, Nicole Eddy — Thu, 15 Oct 2026 00:00:00 +0000

Spatial skills are robustly associated with mathematical performance, yet the cognitive mechanisms underlying this relationship in adults remain poorly understood. The present research examined whether unbounded number line estimation mediates the association between spatial skills and mathematical performance in adults. Ninety (90) undergraduate students completed measures of spatial visualization, mental rotation, algebra, fractions, arithmetic, and unbounded number line estimation. Results indicated that spatial skills significantly predicted mathematical performance and that unbounded number line estimation indirectly mediated this relationship across all three mathematical domains. These findings extend spatial representation theory to adulthood, suggesting that stronger spatial skills may support the construction of more precise internal representations of numerical magnitude, which in turn facilitate mathematical proficiency.

Frequently Cited but Seldomly Actually Measured: The Mathematical Cast of Mind

Michaela A. Meier, Anna Ehrengruber, Stephan E. Vogel, Roland H. Grabner — Tue, 13 Oct 2026 00:00:00 +0000

Understanding the sources of individual differences in mathematical abilities is considered essential by both researchers and society alike. Almost 50 years ago, the Russian psychologist V.A. Krutetskii proposed the concept of a mathematical cast of mind (MCOM), which he described as a predisposition to perceive the world through ‘mathematical eyes’. This MCOM should be particularly evident in gifted individuals, enabling them to acquire mathematical knowledge more rapidly and to achieve higher levels of mathematical performance. Although Krutetskii's concept is often referred to in models of mathematical giftedness, empirical attempts to measure it have been limited. The aim of this study is to identify specific tasks that capture aspects of the MCOM and to determine whether these tasks contribute to an MCOM factor that is associated with mathematical achievement above and beyond verbal and figural intelligence. To this end, 82 university students worked on tasks that measure the MCOM components of obtaining mathematical information, processing of mathematical information, and motivational tendencies. The results of an exploratory factor analysis showed a three-factor structure in line with theoretical components of MCOM but not a single factor of MCOM. From the three components, only motivational tendencies was a significant predictor of mathematical achievement. Obtaining mathematical information, in contrast, showed negative correlations with the other two factors and did not significantly predict individual differences in mathematical competence. These findings provide further insights into the concept of MCOM and if it can be measured reliably to eventually predict individual differences in mathematics.

Developmental Differences in Classifiers of Low and High Mathematics Performance: A Classification and Regression Tree Analysis

Fri, 25 Sep 2026 00:00:00 +0000

Background: Given the contribution of domain-general and domain-specific skills to children’s mathematics performance and the importance of children’s early mathematical skills for future success, it is imperative to determine and compare the predictive skills that classify children’s mathematical performance. Previous efforts examining classifiers of mathematics performance have focused on development within a year (e.g., preschool; Purpura et al., 2017) or general predictive relations (e.g., Jordan et al., 2002). The question remains whether the classifiers of low and high mathematics performance differ across multiple years. Method: The current study used data from a longitudinal project that assessed children on a number of academic and behavioral measures across four time points spanning preschool and kindergarten. The analytic sample for this study consisted of 322 children (T1 Mage = 4.81 years; SD = 0.30; 50.6% female) from three cohorts. Results: Prior mathematics performance was the most consistent classifier for low and high mathematics performance at the end of kindergarten. Broad school readiness at the beginning of preschool was also a consistent classifier of low and high mathematics at the end of kindergarten. A consistent classifier of only low mathematics performance at the end of kindergarten was behavioral self-regulation skills in the spring of preschool. Further, reading skills at the beginning of kindergarten were a consistent classifier of only high mathematics performance. Conclusion: Findings can guide researchers and educators in identifying the important skills at different developmental periods in early schooling to support children at risk of low mathematics performance or those with exceptionally high mathematics performance.

Effect of Socioeconomic Environment on Understanding and Producing Mathematical Vocabulary in Preschool Children

Anne Lafay, Sonia Angonin, Carole Berger — Tue, 08 Sep 2026 00:00:00 +0000

We investigated the development of mathematical vocabulary understanding in young French children aged 3 to 6 years old as a function of the socioeconomic environment. A total of 306 French children were administered two tasks, respectively assessing their understanding and production of French mathematical vocabulary. The results showed differences in understanding and production of mathematical vocabulary between children in preschool/kindergarten Grade Levels 1 (3-4 yo), 2 (4-5 yo), and 3 (5-6 yo). Children from REP+ (“Réseau d’Education Prioritaire”) schools (that concerned neighborhoods or isolated sectors with the greatest concentrations of social difficulties) understood and produced less numerous mathematical terms than those from regular schools, whatever the grade level. Theoretical and practical contributions for teaching are discussed. Despite the measures as a priority education policy organized by the government in REP+ schools, the school fails to reduce the impact of social inequalities on mathematical vocabulary. Efficient intervention is therefore needed.

A Theoretical Position Statement on Mechanism Underlying Numerical Cognition

Ilse E. J. I. Coolen — Tue, 21 Jul 2026 00:00:00 +0000

This theoretical statement addresses the lack of a homogenous understanding of what constitutes a "mechanism" in studies in numerical cognition. Despite the increasing focus on mechanisms in the field, ambiguity exists in how mechanisms are defined and interpreted. To address this, I propose a conceptual framework that outlines three levels of mechanisms: micro-, relational, and macro-level, that each correspond to different levels of mechanisms to understand associations in the research field of numerical cognition. The micro-level mechanisms refer to a process-oriented perspective. The relational level refers to a perspective with a focus on underlying associations between variables, and finally the macro-level mechanisms refer to theory-oriented perspectives. I hope that this framework will serve as a starting point for future dialogue, providing clarity and promoting consistency in the conceptualisation of mechanisms in the field.

Math Anxiety and Financial Literacy: The Role of Math Avoidance

Allie Tung, Dominic J. Gibson — Thu, 09 Jul 2026 00:00:00 +0000

Math anxiety is a pervasive phenomenon that negatively impacts individuals’ ability to perform mathematical tasks, yet its implications for functioning in a society where math is often helpful if not necessary remain underexplored. This study examines the relations between math anxiety, financial anxiety, and financial literacy in a nationally representative sample of young adults in the U.S. (n = 393). As math anxiety and financial anxiety have previously been linked to avoidance of mathematical and financial content, we also examined the role of avoidance in their relations to financial literacy. Consistent with prior research, math anxiety, financial anxiety, and gender were related to financial literacy. Further analysis revealed that math-anxious individuals and women showed a greater tendency to avoid responding to financial literacy questions. These findings clarify the negative association between math and financial anxiety and financial literacy, suggesting that a tendency to avoid financial content may help explain the link between math anxiety and financial literacy. This study contributes to a broader understanding of the implications of math anxiety for young people’s educational and financial lives and offers insight into the mechanisms that underlie these relations. Insights for interventions targeting math anxiety and their potential for boosting financial literacy are discussed.

Parents’ and Teachers’ Practices, Beliefs, and Communication of Early Mathematics Learning

Thu, 09 Jul 2026 00:00:00 +0000

Prior research showed that US parents engage children in numeracy versus spatial or pattern activities more frequently, and that children receive more literacy versus numeracy instruction. We examined Hong Kong parents’ and teachers’ frequency of engaging children in learning activities, their beliefs about the fixedness of math ability, and frequency of school-home communication about children’s learning across learning domains. A total of 154 parents (68.8% women; 96.1% Chinese) and 89 teachers (80.9% women; 89.9% Chinese) of kindergarten children completed an online survey. We found that (a) both parents and teachers engaged children in numeracy versus pattern activities more frequently; (b) parents’ and teachers’ fixedness beliefs about math ability did not predict their frequency of providing math activities; (c) compared to math, parents and teachers engaged children in language activities more frequently, and ethics and aesthetics activities less frequently; (d) teachers versus parents were more likely to report school-home communication. The findings extend prior research on home math environments and reveal ways in which parents and teachers can strengthen children’s math learning.

Math Structure Biases Attention During Arithmetic Problem Solving: A Webcam Eye-Tracking Study

Puyuan Zhang, Aaron Wong, Caitlin Mills, Erin Ottmar — Thu, 18 Jun 2026 00:00:00 +0000

Using lab-based eye-trackers, previous studies have demonstrated that visual presentation, such as positions of high-order operators (HOOs) and presence of superfluous brackets, influences gaze behaviors during arithmetic problem solving (e.g., Egorova et al., 2024). The current study explored the feasibility of moving eye-tracking arithmetic problem solving studies online by replicating Egorova et al.’s (2024) study using a webcam-based eye-tracker (i.e., WebGazer). Furthermore, we examined whether the proportion of gazes on the HOO over time, a gaze measure that was not analyzed in Egorova et al. (2024) but commonly used in WebGazer studies, can suggest participants’ online problem solving strategies. We analyzed gaze data from 119 college students who mentally evaluated simple arithmetic expressions where the HOO appeared in left, center, or right positions with or without superfluous brackets. Replicating Egorova et al.’s (2024) findings, participants registered their first gaze on the HOO faster when the HOO was on the left compared to on the right (a left-to-right tendency), and slower when brackets were present compared to absent around the center HOO (center brackets effects). Nevertheless, the online gaze data did not replicate the gaze difference in left versus center HOO positions. Furthermore, results of the proportion of gazes on the HOO over time confirmed the left-to-right tendency and further indicated that superfluous brackets guide gaze behaviors in both early and late stages of evaluations. Based on these findings, we discuss the feasibility and cautions of using WebGazer in online eye-tracking arithmetic problem solving studies.

Optimizing the 0-100 Number Line Estimation Task: Scale Reduction and Its Implications for Elementary Mathematical Cognition

Kamal Chawla, Julie L. Booth, Christina Areizaga Barbieri — Fri, 08 May 2026 00:00:00 +0000

We investigate the optimal number of items for the 0-100 number line estimation task used in research on children’s mathematical cognition and learning. In this paper, we reanalyzed data involving N = 234 students, applying an Item Response Theory- Graded Response Model to identify items with high discrimination parameters (> 1.0), iteratively reducing the 23-item scale by including items with discrimination values close to 1.0 until the reduced scale produced comparable scores to the original. Our analysis identified a reduced scale of 15 items that maintained strong correlations with–and produced consistent patterns of developmental change and predictive capability compared to–the original scale. Our findings demonstrate that a reduced 0-100 number line estimation task can effectively measure numerical magnitude understanding (accuracy and linearity of estimates) from kindergarten through third grade while saving time and resources.

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

Maëlle Neveu, Christian Monseur, Laurence Rousselle — Wed, 29 Apr 2026 00:00:00 +0000

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.