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Using a person-centered approach, we aimed to identify different executive functioning profiles to assess heterogeneity across individuals within the same school grade through latent profile analysis. A sample of 150 Grade 2 (7-8 years old), 150 Grade 6 (11-12 years old), and 150 Grade 10 (15-16 years old) children and adolescents were assessed on 11 different executive tasks representative of the three main executive functioning subcomponents (i.e., inhibition, cognitive flexibility, and working memory), fluid intelligence, processing speed, problem-solving, and reading comprehension. Three different executive functioning profiles of different patterns of interactions based on inhibition, cognitive flexibility, and working memory within and between grades were identified. Moreover, these profiles were differentially related to reading comprehension and mathematical achievement. Second, as expected, we did not find these profiles to be associated with sociodemographic variables such as chronological age or sex. Still, fluid intelligence and processing speed were differentially related to the different profiles at each grade. We also found that the executive functioning profiles interacted with each cognitive skill (i.e., fluid intelligence and processing speed) in predicting reading comprehension and math achievement. These findings provide valuable insights for developing preventive and intervention strategies in education.

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We investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods. We find that even a single effective topological neighbour suffices for significant order in a system with non-local topological interactions. We also explore topological information flow patterns and clustering dynamics using Hodge spectral entropy and mean Forman-Ricci curvature.

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The recent emergence of innovative learning spaces, Future Classroom Lab (FCL), provides educators the use of physical learning spaces (to research, interact, exchange, develop, create, and present) and diverse technological tools to work according to active methodologies. Learners become more active in the learning process with the introduction of innovative learning environments that enable the application of interdisciplinary STEAM methodology and foster the development of 21st century competences. This study aims to uncover the probable link between application active and gamified STEAM educational interventions in the FCL and Pre-Service Teachers' (PSTs) affective domain. The findings obtained showed statistically significant variations and, therefore, positive effects on the PSTs' affective domain (self-efficacy, attitude, and emotion) after performing the intervention. The sample consisted of a total of 54 PSTs enrolled in the second year of Primary Education. Limited studies regarding the affective domain in the FCL were found, which restricted the comparison with prior research. This study has several implications, such as the introduction of innovative educational proposals to PSTs at the university level and, consequently, the implementation of similar interventions in elementary schools. This research intended to reveal how the different variables work as a support system for students' learning process in mathematics and science disciplines.

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BACKGROUND: Problem-solving and learning in mathematics involves sensory perception and processing. Multisensory integration may contribute by enhancing sensory estimates. This study aims to assess if combining visual and somatosensory information improves elementary students' perimeter and area estimates. METHODS: 87 4th graders compared rectangles with respect to area or perimeter either solely using visual observation or additionally with somatosensory information. Three experiments targeted different task aspects. Statistical analyses tested success rates and response times. RESULTS: Contrary to expectations, adding somatosensory information did not boost success rates for area and perimeter comparison. Response time even increased with adding somatosensory information. Children's difficulty in accurately tracing figures negatively impacted the success rate of area comparisons. DISCUSSION: Results suggest visual observation alone suffices for accurately estimating and comparing area and perimeter of rectangles in 4th graders. IMPLICATIONS: Careful deliberation on the inclusion of somatosensory information in mathematical tasks concerning perimeter and area estimations of rectangles is recommended.

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Many studies have explored the relationship between metacognition and academic achievement in mathematics, but the results vary. In this study, meta-analysis was used to explore this relationship between metacognition and academic achievement in mathematics and influencing factors. According to the literature search, a total of 147 studies (1986-2024) and 338 independent samples met the inclusion criteria (n = 698,096). The results revealed metacognition was significantly positively correlated with academic achievement in mathematics, r = 0.32, 95 % CI [0.30, 0.34], Z = 28.49. Moreover, the moderating effects of age, domain, and culture were significant (p < 0.01). In conclusion, Metacognition is closely associated with academic achievement in mathematics but also that age, domain, and culture have a considerable impact on their relationship. More specifically, the degree of correlation between metacognition and academic achievement in mathematics was on the rise from preschool to high school, while it was lower in college. Compared with general field metacognition, mathematical metacognition is more closely linked to mathematics academic achievement. Lastly, compared with British and American countries, Chinese metacognition was more closely related to academic achievement in mathematics.

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We investigated the relations between self-reported math anxiety, task difficulty, and pupil dilation in adults and very young children during math tasks of varying difficulty levels. While task difficulty significantly influenced pupillary responses in both groups, the association between self-reported math anxiety and pupil dilation differed across age cohorts. The children exhibited resilience to the effects of math anxiety, hinting at additional influential factors such as formal math education experiences shaping their relations to mathematics and their impact on cognitive processes over time. Contrary to expectations, no significant association between self-reported math anxiety and pupil dilation during task anticipation was found in either group. In adults, math anxiety influenced pupil dilation exclusively during the initial phase of task processing indicating heightened cognitive load, but this influence diminished during sustained task processing. Theoretical implications emphasize the need for exploring individual differences, cognitive strategies, and the developmental trajectory of math anxiety in very young children.

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Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this "foundations crisis" was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went a step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal Mathematische Annalen.

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This study introduces a pioneering framework for modeling students' cognitive processes in mathematics education through Fuzzy Cognitive Maps (FCMs). By integrating key educational theories-Duval's Semiotic Representation Theory, Niss's Mathematical Competencies, Marton's Variation Theory, and the broad Engagement, Motivation, and Participation framework- the model offers a comprehensive and holistic understanding of students' cognitive landscapes. This research underscores the necessity of a multidimensional approach to capturing the intricate interplay of cognitive, affective, and behavioral factors in students' mathematical learning experiences. The novelty lies in its methodological innovation, employing FCMs to transcend traditional qualitative analyzes and facilitate quantitative insights into students' cognitive processes. This approach is particularly relevant in the current era dominated by digital learning environments and artificial intelligence, where real-time, automated analysis of student interactions is increasingly vital. The proposed FCM has been developed over the years with a data-driven approach; the concepts and relationships in it have been derived from the literature and refined by the author's experience in the field. Illustrated through case studies, the framework's utility is demonstrated in diverse contexts, highlighting how the quantitative data obtained are confirmed by qualitative approach: analyzing the impact of remote learning during the Covid-19 pandemic on student engagement and exploring Augmented Reality's role in enhancing mathematical conceptualization. These applications show the framework's adaptability and its potential to integrate new technologies in educational practices. However, the transition from qualitative to quantitative methodologies poses a challenge, given the prevalent use of qualitative approaches in mathematics education research. Additionally, the technological implementation of the FCM model in educational software presents practical hurdles, necessitating further development to ensure ease of integration and use in real-time educational settings. Future work will focus on bridging these methodological gaps and overcoming technological challenges to broaden the FCM model's applicability and enhance its contribution to advancing mathematics education.

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Many studies have reported poor school achievement in evening persons and general circadian fluctuations in cognition. The aim of this study was to analyze circadian fluctuations in a cross-sectional design and examine the effects of chronotype on situational emotions and intrinsic motivation. A cross-sectional survey study was conducted in three Turkish secondary schools with a total sample of 599 students (283 females and 316 males). Data were collected at the end of specific math lessons of the same grade level and content, using a form combining three scales. We found no gender-related differences in intrinsic motivation, while there were some differences in situational motivation. In math classes, female students exhibited higher level of interest, while boys scored higher on boredom. In addition, students who scored high on morning affect reported higher levels of interest, well-being, and less boredom. Students with higher stability (and lower fluctuations in mood and cognition during the day) reported a higher degree of enjoyment, perceived competence, perceived choice, and less pressure/tension in their math lessons. A positive association was observed between distinctness, interest, and well-being, while negative correlations existed between distinctness and boredom. This suggests that students with higher diurnal stability reported a higher level of interest, well-being, and a lower level of boredom. Additionally, the results of the analyses showed that morningness, distinctness, and eveningness were significant predictors of intrinsic motivation. Conversely, gender, time of application, morningness, and distinctness emerged as predictors for situational emotions in mathematics classes.

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Math development in children relies on several underlying cognitive functions, including executive functions (EF), working memory (WM), and visual-motor abilities, such as visual-motor integration (VMI). Understanding how these cognitive factors contribute to children's math performance is critical to supporting math learning and long-term math success. The present quasi-experimental waitlist control study (N = 28) aimed to (a) examine the unique contributions of EF, WM, and VMI to math abilities among children ages 5-8 years old with neurodevelopmental difficulties; (b) determine whether a math intervention (the Mathematics Interactive Learning Experience; MILE) that supports these cognitive processes was effective when modified to be delivered to small groups in a school setting, and (c) examine whether any participant characteristics, such as age or IQ, were correlated with post-intervention math score changes. At baseline, participants' math scores were significantly below the normative mean in all math content areas (ps < .01). EF, WM, and VMI were highly correlated with math ability; however, verbal WM was the only unique predictor of math ability in regressions analysis. Compared to a waitlist control group, children in the immediate MILE intervention group achieved significantly greater math gains overall. When all children who ultimately completed the intervention were considered together, significant improvement was observed in more than half of math content areas. Furthermore, at the individual level, 85.7% of participants showed reliable change in at least one math content area. Implications for supporting math learning in children with neurodevelopmental difficulties are discussed.

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More and more digital technologies are being integrated into school learning, and one strategy by policymakers to reinforce this trend is employing digital one-to-one approaches. For digital technologies to be fruitfully integrated into school-based learning scenarios, teachers and their anticipations are key. In our study, we want to explore how internal, external and technological factors affect the instructional anticipations of mathematics teachers in a digital one-to-one educational environment. Therefore, we employed a modified model of the Unified Theory of Acceptance and Use of Technology. Through our structural equation study, in which data from more than 900 mathematics teachers were analyzed, we identified that especially technological and external factors can predict mathematics teachers' instructional anticipations. Findings from our study could be particularly relevant for educational policymakers, informing them about the importance of factors or interventions related to educational technology implementation.

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Habituation, the reduction of responding to repetitive stimuli, is often conceptualized as a kind of attentional filter, amplifying salient signals at the expense of non-salient signals. No prior account has explicitly formalized filtering principles that can explain the major characteristics of habituation. In this paper, a simple probabilistic model is developed which permits analysis of the optimal filtering problem. This model exhibits the major characteristics of habituation, while also shedding light on other, relatively neglected, characteristics. These results demonstrate that habituation can be understood as a form of optimal filtering.

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Mathematical operations are cognitive actions we take to calculate relations among numbers. Arithmetic operations, addition, subtraction, multiplication, and division are elemental in education. Addition is the first one taught in school and is most popular in functional magnetic resonance imaging (fMRI) studies. Division, typically taught last is least studied with fMRI. fMRI meta-analyses show that arithmetic operations activate brain areas in parietal, cingulate and insular cortices for children and adults. Critically, no meta-analysis examines concordance across brain correlates of separate arithmetic operations in children and adults. We review and examine using quantitative meta-analyses data from fMRI articles that report brain coordinates separately for addition, subtraction, multiplication, and division in children and adults. Results show that arithmetic operations elicit common areas of concordance in fronto-parietal and cingulo-opercular networks in adults and children. Between operations differences are observed primarily for adults. Interestingly, higher within-group concordance, expressed in activation likelihood estimates, is found in brain areas associated with the cingulo-opercular network rather than the fronto-parietal network in children, areas also common between adults and children. Findings are discussed in relation to constructivist cognitive theory and practical directions for future research.

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All pharmacists are expected to accurately perform pharmaceutical calculations to ensure patient safety. In recent years, there have been trends in declining performance on the North American Pharmacist Licensure Examination related to calculations. Understanding the cause of this decline and determining methods to correct underlying issues could benefit pharmacy administration, faculty, students, and patients. The aims of this commentary are to present the factors impacting the students' pharmaceutical calculations abilities, discuss the consequences of declining math skills, and provide a call to action for scholarship of teaching and learning pertaining to calculations, as well as increased administrative support to rectify this challenge.

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Some students suffer from math anxiety and experience negative emotions in mathematics education. Children's math anxiety is negatively related to their math achievement, suggesting that math anxiety puts their math learning at risk. Several theoretical accounts have been proposed that help to explain this association between math anxiety and achievement. In the current study, we aimed to test predictions of two prominent theories, namely the disruption account and the reduced competency account, using a comprehensive and unifying approach. A sample of 6- to 8-year-olds (N = 163) answered a math anxiety questionnaire, solved a spatial task (mental rotation), and solved several arithmetic problems. After each arithmetic problem, they were asked how they solved the problem. Strategies were then classified into counting and higher-level mental strategies (including decomposition and retrieval), with higher-level strategies loading strongly on working memory resources. Analyses revealed a negative, albeit small, association between children's math anxiety and accuracy in solving arithmetic problems. In line with the disruption account, children's frequency of using higher-level mental strategies mediated this relation between math anxiety and arithmetic performance. Moreover, our results support the reduced competency account given that arithmetic performance was related to math anxiety, whereas mental rotation was only indirectly related to math anxiety. Overall, our findings corroborate both accounts, lending further support to the notion that these accounts might not be mutually exclusive. Our findings imply that interventions might be most effective when focusing on emotion regulation strategies and improving mathematical and spatial performance.

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Parents can be instrumental in promoting young children's early mathematics and literacy skills. However, differences in parents' beliefs can influence their behavior during parent-child interactions. We examined how parental beliefs about the fixedness of children's math and reading abilities shape their interactions with their 4- and 5-year-old children during an educational activity. Parental beliefs about children's abilities were manipulated using "articles" indicating that academic ability is fixed in one domain (e.g., math) but malleable in another (e.g., reading). We then investigated differences in parental unconstructive (performance-oriented and controlling) and constructive (mastery-oriented and autonomy-supportive) involvement across conditions. We also examined whether parent behavior differed depending on the type of educational material parents were told the activity tapped into. The results showed that parents who were induced to have a fixed mindset about reading took full control of the reading activity more often than those who were induced to have a growth mindset about reading, but not math. Parents did not differ in constructive involvement between mindset induction conditions in either domain. We also found that parent autonomy behavior in math differed depending on parents' general theory of intelligence beliefs. Overall, we found some evidence that parents' beliefs about the malleability of their children's ability in a specific domain affected their behaviors in that domain.

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Numerical cognition is a field that investigates the sociocultural, developmental, cognitive, and biological aspects of mathematical abilities. Recent findings in cognitive neuroscience suggest that cognitive skills are facilitated by distributed, transient, and dynamic networks in the brain, rather than isolated functional modules. Further, research on the bodily and evolutionary bases of cognition reveals that our cognitive skills harness capacities originally evolved for action and that cognition is best understood in conjunction with perceptuomotor capacities. Despite these insights, neural models of numerical cognition struggle to capture the relation between mathematical skills and perceptuomotor systems. One front to addressing this issue is to identify building block sensorimotor processes (BBPs) in the brain that support numerical skills and develop a new ontology connecting the sensorimotor system with mathematical cognition. BBPs here are identified as sensorimotor functions, associated with distributed networks in the brain, and are consistently identified as supporting different cognitive abilities. BBPs can be identified with new approaches to neuroimaging; by examining an array of sensorimotor and cognitive tasks in experimental designs, employing data-driven informatics approaches to identify sensorimotor networks supporting cognitive processes, and interpreting the results considering the evolutionary and bodily foundations of mathematical abilities. New empirical insights on the BBPs can eventually lead to a revamped embodied cognitive ontology in numerical cognition. Among other mathematical skills, numerical magnitude processing and its sensorimotor origins are discussed to substantiate the arguments presented. Additionally, an fMRI study design is provided to illustrate the application of the arguments presented in empirical research.

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Most research papers in psychology study the behaviour of a sample of participants. To characterise this sample, authors report various characteristics, frequently including the mean age and the associated standard deviation. However, based on reports from authors who publish in Acta Psychologica and from respondents on X/Twitter, the present paper shows that some authors use rounded-down ages whereas others don't, which lead to an uncertainty of 0.5 year in the average age. The results furthermore show that the authors tend to report the average age with two decimals precision, irrespective of the uncertainty of this average. I recommend that publications should explicitly mention how the average age is determined and report its value using a number of decimals that reflects its uncertainty.

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The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills necessitate a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of non-symbolic numerical quantity, then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. While it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.