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.
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.
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.
Spatial skills are critical for learning in STEM areas and are affected by spatial anxiety and working memory. Prior work also showed that there are interaction effects between spatial anxiety and verbal working memory (WM) on spatial skills, such that the negative relation between spatial anxiety and spatial skills is stronger among higher- than lower-verbal WM children. To date, this interaction effect has not been found for visuospatial WM. However, a recent meta-analysis showed that both verbal WM and visuospatial WM are impaired by anxiety to a similar extent. The current study hypothesized that visuospatial WM interacts with spatial anxiety on spatial skills and that this interaction effect gets stronger as age increases. We investigated spatial anxiety, visuospatial WM, and two spatial skills (mental transformation and mental rotation) in 402 U.S. children in first to fourth grades. We found a significant three-way interaction of spatial anxiety, visuospatial WM, and grade level on mental transformation skill: only fourth-graders with high visuospatial WM showed a significant relation between spatial anxiety and lower mental transformation skills, whereas low-visuospatial WM fourth-graders and children in Grades 1 to 3 did not show this relation. However, this effect was not significant for children’s mental rotation skills. We discuss the results in terms of age-related differences in visuospatial WM and strategy use, as well as differences between the mental transformation and mental rotation tasks. Our findings indicate that the interaction effect between spatial anxiety and working memory on spatial skills extends beyond verbal WM to visuospatial WM and becomes more pronounced as children's age increases.
Evidence of positive associations between the frequency of home math activities and preschool children’s math skills is mixed, and the operationalization of home math activities varies across studies. We test whether home math activities can be grouped by activity factors based on the math subdomain they target (i.e., counting and cardinality, comparison, number identification, addition and subtraction, and patterning) and examine associations between these activity factors and child math skills. Data were collected from 78 parents and their four-year-old children in the United States. Parents completed a home math activities survey, and children completed math assessments. Confirmatory Factor Analyses (CFA) indicated a well-fitting model with the five activity factors (one factor per subdomain) and a sixth factor for activities that could incorporate multiple subdomains. Structural Equation Modeling (SEM) analyses indicated positive associations between activity factors and child math skills for counting and cardinality, comparison, addition and subtraction, and patterning, but not for number identification. Results reveal that this model is appropriate for older four-year-old children closer to the beginning of kindergarten but is not appropriate for younger four-year-old children. This study suggests the possibility of operationalizing home math activities by activity factors based on math subdomains.
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.
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.
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.
When children first learn to count, what do they understand about the structure of the count system? The present study investigated English-speaking children’s ability to generalize the rules that structure their count list to novel contexts. A total of N = 86 children (3;0 – 6;11) completed a battery of tasks aimed at measuring their understanding of the English count list: they counted as high as they could, and were asked to generate successors to English numbers (e.g., “Fifty-seven: what comes next?”). Next, they were introduced to novel decade terms, and were asked to generate successors to numbers containing those terms (e.g., “Blicky-seven: what comes next?”). Children’s ability to generate successors was predicted by their counting ability, and a sizeable subset of children were able to generate successors both for novel numbers and for English numbers outside their productive count range. These data suggest that emerging counters can use their understanding of the structure of the English count list to generate successors to unfamiliar numbers.
Math and executive functioning (EF) skills are thought to be tightly linked in early childhood. To facilitate our understanding of this link in early childhood, here we present a meta-analysis of over 1,000 different correlation values between EF and math measures in early childhood (4-6yrs). The overall average EF-Math relation was r = .350, 95% CI [.338, .361]. We then examined whether the strength of the EF-Math relation in this age-range depends on measurement factors, socio-economic status (SES), and the nature and direction of longitudinal relations. [1] Overall achievement measures of EF and math generally led to higher estimates of the EF-Math relation relative to measures of isolated EF subprocesses or specific math skills, though this may be due more to measurement than developmental factors. [2] EF measures using numerical stimuli inflate estimates of the EF-Math association by roughly 40%. [3] Low SES samples showed the strongest average EF-Math associations. [4] Longitudinal associations that do not adjust for Time-1 measurement of the outcome variable lead to inflated (as much as 120%) estimates of directional associations. After making this adjustment, we found [5a] significant, albeit reduced bidirectional relations between EF and math, and [5b] that math is a stronger predictor of future change in EF than the reverse. In sum, the results of this work contribute to theoretical models of the interaction between EF and math in early childhood, as well as to practical attempts to foster growth in children’s EF and math skills, whether in the lab, classroom or living room.
Early math experiences predict children’s later math abilities and beliefs. However, less is known about longer-term associations between early childhood math experiences and adult math outcomes. The present study examined emerging adults’ earliest memories of mathematics and reading experiences, asking whether characteristics of their early learning memories differ across domains of learning and relate to their adulthood math achievement and beliefs. Undergraduate students (n = 161, MAge = 19.6 years) described their earliest memories of math and reading, then completed measures of their math anxiety, math task value, and math achievement. Our results reveal significant domain differences in participants’ age during their earliest memories, the level of social interaction, and their overall rating of the experience. Emerging adults with more positive memories of their earliest math experiences had lower math anxiety, higher math task value, and higher math achievement. Our results provide additional evidence of the long-term associations between early math experiences and later math outcomes and underscore the need to promote early math experiences that are positive and engaging for young children.
Improving early mathematical competence is a major priority worldwide; thus, assessing early math abilities is critical. Although various international standardized instruments serve this purpose, their usage in underdeveloped countries is prohibitive due to their resource-intensive requirements. In this report, we explore the development of the “Test de Pensamiento Matemático" (TPM, Test of Preschool Mathematics), which is an automated, game-based, digital instrument for assessing early math abilities in 4-to-6-year-old children in accordance with international curricular standards. A confirmatory factor analysis shows an optimal fit for two dimensions: numerical thinking and visuospatial reasoning. By drawing on technology, the TPM can be applied to large groups of children, so it becomes an efficient tool for assessing performance, monitoring learning improvements, and screening children who need additional support to develop their math abilities at the same pace with their peers.
This study aims to present the psychometric properties of the Polish language version of the Mathematical Resilience Scale (MRS; Kooken et al., 2016), established in a sample of 443 adults. We confirmed the first-order three-factor structure (Value, Struggle, Growth) with the second-order factor (Total Mathematical Resilience) of the MRS and its measurement invariance across gender and field of study and profession. We also confirmed the validity of the scale: negative correlations were found between MRS scores and math anxiety, math avoidance, intellectual helplessness in mathematics; positive correlations were found between MRS scores, mathematical achievement, math learning motivation; no relationship or weak correlations were found between MRS scores, intellectual helplessness in Polish language, Polish language grades obtained in high school. Finally, we observed gender and study and profession differences in some of the MRS scores. However, further research is needed on the nature of mathematical resilience, especially to establish its relationship with general resilience.
Using data from the Trends in International Mathematics and Science Study (TIMSS), this study examines the student and school characteristics that contribute to students’ mathematics performance in early elementary school in Chile. Previous research has separately analyzed the association of student and school factors with mathematics performance. This study uses multilevel modeling analyses to account for those factors together and understand variability within and between schools. The sample in this study was 6,322 fourth grade students from 169 schools. The students’ mean age was 10.07 (SD = 0.50); 49.6% were girls. The results from this study show that student characteristics, such as the home mathematics environment, helped explain the variation between schools more than within schools. These findings highlight the importance of considering contextual factors, such as parent–child math interactions, when developing education policy and intervention to foster students’ mathematics skills.
Book Review of "Numerical Cognition and the Epistemology of Arithmetic" by Markus Pantsar Authors Valeria Giardino Institut Jean Nicod, CNRS, Paris, France Abstract No abstract available. PDF HTML XML Article info Impact Citations How to Cite License Published at 14. March 2025 https://doi.org/10.5964/jnc.16325 Issue: Vol. 11 (2025) Section: Book Reviews Share: Giardino, V. (2025). Book Review of "Numerical Cognition and the Epistemology of Arithmetic" by Markus Pantsar. Journal of Numerical Cognition, 11, 1-3. https://doi.org/10.5964/jnc.16325 More Citation Formats ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Download Citation Endnote/Zotero/Mendeley (RIS) BibTeX This work is licensed under a Creative Commons Attribution (CC BY) 4.0 International License. PlumX Dimensions Views: Total Abstract PDF HTML XML 7 1 2 3 1
Previous research has investigated the Spatial Numerical Associations of Response Codes (SNARC) effect as a measure of spatial number coding in relation to mathematics (Cipora et al., 2020, https://doi.org/10.1111/nyas.14355). An issue that arises if one wants to correlate mathematical performance with the SNARC effect, is how individual differences in the SNARC effect are measured. Specific design choices might have an impact on the size of the SNARC effect as an individual difference measure. In the present study we investigated two design choices that have previously been neglected as possible determinants of the size of the SNARC effect as obtained in the parity judgment task. The first determinant that we investigated is mapping order. The odd-even left-right response assignments can be congruent (even-right and odd-left) or incongruent (even-left and odd-right) in terms of linguistic markedness (MARC effect: markedness association of response codes) and might be presented in two different orders (congruent first or incongruent first) possibly affecting the size of the SNARC effect. A second possible determinant is task instruction. Instructions can emphasize parity (judge numbers as odd or even) or emphasize two categories (classify numbers as 1-3-7-9 versus 2-4-6-8) as the basis for responding, perhaps requiring different levels of semantic processing. To investigate the potential impact of these variables, this study used a 2x2 between subject design, resulting in four conditions to verify the effect of mapping order and instructions. The results show that the SNARC effect is not influenced by mapping order or by the nature of the instructions, revealing the parity judgment SNARC effect as a robust marker of spatial number coding useful for individual difference research.
Although numbers are universal, there are great differences between languages and cultures in terms of how they are represented. Numerical notation can influence number processing. Two well-known types of notational systems are sign-value, such as the Roman numeral system, and place-value systems, such as the Indo-Arabic numeral system. What is involved in learning each system? Here we report a study that investigated adults’ abilities to implicitly learn an artificially created sign-value or place-value system. We asked if they could perform symbolic comparison and ordering tasks using the novel symbol system. We found adults could learn the ordinal meaning of symbols within either system and were able to extend the system to symbols not encountered during training. There was a relative advantage of the sign-value system over the place-value system for expressions encountered during the training, but also for expressions that had not previously been encountered. These results shed light on how easily the structure of place-value and sign-value systems can be learned.
Math learning in early childhood is critical for later success, as it is predictive of mathematical and academic achievement through adolescence. Therefore, developing engaging and effective methods for early math instruction are important. Math games are a common method for teaching math in a way that is motivating and engaging for young children and are often used in early childhood classrooms. However, research on what games are effective and who can benefit from playing them often focuses on single elements or contexts of gameplay, and there is little research summarizing the effects of math games on children’s learning. The current systematic review presents research on the impact of math games on preschool through third grade children’s math development, examining what game contexts, types, and content areas are effective for math learning, who can learn from games, and what features of math games effectively promote learning in early childhood. Themes in the literature include the impact of game design factors, math outcomes studied, and dosage of gameplay for learning through games. The review reveals that future research is needed to compare the effects of gameplay across contexts and to examine additional factors influencing children’s learning from games.
Background: An important source for the difficulties that students face with comprehending fractions is the natural number bias (NNB). The NNB 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). Recently, it was shown cross-sectionally that the NNB may affect students’ state anxiety responses on a fraction arithmetic task (i.e., anxiety experienced during a fraction arithmetic task). Aim: The current longitudinal study examines, for the first time, the role of the natural number bias in the longitudinal development of fraction state anxiety. Sample: In total, 334 fifth and sixth graders were included in the study. Specific attention was given to two subgroups of learners, low performers with and without an NNB. Methods: Students’ fraction arithmetic performance and fraction state anxiety were measured in the beginning and end of the same school year. Results: The findings reveal that, in students with a clear NNB, a decrease in NNB answers (sign of overcoming the NNB misconception) co-occurred with an increase in fraction state anxiety. Conclusions: The present study concludes that a better understanding of a mathematical topic does not necessarily lead to a decrease in mathematics anxiety experienced while solving a task within the same topic. The present study has the implication that in mathematics anxiety research, especially in intervention studies, the qualitative different profiles of students should be taken into account. Special attention should be given to misconceptions, as increases in anxiety may occur while overcoming a misconception.
