The Calculating Brain.

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.

Gender and circadian preferences influence emotions and motivation in secondary mathematics classrooms.

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.

A new ontology for numerical cognition: Integrating evolutionary, embodied, and data informatics approaches.

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.

The bias and precision of reporting the average age of human participants.

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.

Quantitative evaluation of a theoretical-conceptual model based on affective and socio-behavioral dimensions to explain the academic performance of mathematics students.

Objective: There is evidence that suggests that affective dimensions, personality traits, as well as students' cooperative interpersonal interactions, are an important element in the students learning process. In this work we propose a theoretical model, based on evidence, that shows the direct and indirect relationships between these factors and academic performance in mathematics courses, in undergraduate and school students. Methods: To understand the type of relationships between these variables, the PANAS psychometric test of positive and negative affect, the BIG FIVE personality test and the economic decision game DUPLES GAME were applied. The study sample was 130 students between 17 and 22 years of age from undergraduate and school (M ± SD = 20.1 ± 3.99). Results: From a path analysis, statistically significant relationships were found, for example, a direct relationship between neuroticism and positive affect, which in turn is related to academic performance. We also found a direct relationship between neuroticism and negative affect, extraversion and positive affect. This allows us to propose that some of the independent variables of the model directly and indirectly influence the academic performance of students in the subject of mathematics. Conclusion: Positive affect and negative affect directly affect academic performance in mathematics, neuroticism has a direct impact on negative affect and extraversion direct impact on positive affect. Consequently, there are direct and indirect relationships between personality traits and affective dimensions, which affect the academic performance of mathematics students.

Counting on Change: Conquering Challenges in Teaching Pharmaceutical Calculations.

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.

Add, subtract and multiply: Meta-analyses of brain correlates of arithmetic operations in children and adults.

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.

Uncovering mathematics teachers' instructional anticipations in a digital one-to-one environment: A modified UTAUT study.

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.

Habituation as optimal filtering.

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.

Mathematics anxiety and math achievement in primary school children: Testing different theoretical accounts.

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.

The role of parents' ability mindsets in parent-child interactions during math and reading activities.

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.

Math Abilities Among Children with Neurodevelopmental Difficulties: Understanding Cognitive Factors and Evaluating a Pilot Intervention.

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.

Drug-target interaction prediction using knowledge graph embedding.

The prediction of drug-target interactions (DTIs) is a critical phase in the sustainable drug development process, especially when the research focus is to capitalize on the repositioning of existing drugs. Computational approaches to predicting DTIs can provide important insights into drug mechanisms of action. However, current methods for predicting DTIs based on the structural information of the knowledge graph may suffer from the sparseness and incompleteness of the knowledge graph and neglect the latent type information of the knowledge graph. In this paper, we propose TTModel, a knowledge graph embedding model for DTI prediction. By exploiting biomedical text and type information, TTModel can learn latent text semantics and type information to improve the performance of representation learning. Comprehensive experiments on two public datasets demonstrate that our model outperforms the state-of-the-art methods significantly on the task of DTI prediction.

The Treatment Selection for a 36-Year-Old Woman With Stress Urinary Incontinence Using a Discrete Mathematical Approach: A Case Report.

This case report describes the treatment selection process for a 36-year-old woman with stress urinary incontinence (SUI) and an overactive bladder (OAB) who desired pregnancy. The patient had comorbidities of hypertension and type 2 diabetes, which required consideration to improve her quality of life and reproductive health. A recently developed decision support tool using a discrete mathematical approach was used to select a treatment method tailored to the patient's individual situation. The analysis determined that vaginal erbium laser (VEL) treatment (Renovalase SP Dynamis Fotona d.o.o, Ljubljana, Slovenia) was the most suitable for this patient. VEL treatment significantly improved both SUI and OAB and changing antihypertensive medication eliminated nocturia. This case suggests the potential application of graph theory in treatment selection for SUI patients.

Navigating Treatment Choices for Stress and Urgency Urinary Incontinence Using Graph Theory in Discrete Mathematics.

In this study, we propose a method for navigating the choice of treatment for stress urinary incontinence (SUI) and urgency urinary incontinence (UUI) using graph theory in discrete mathematics. Our previous study accumulated data from 150 patients who underwent tension-free vaginal tape (TVT), transobturator tape (TOT), and vaginal non-ablation Erbium YAG laser (VEL) surgeries between 2014 and 2016. Network diagrams were created using this data. The treatments TVT, TOT, and VEL, along with patient characteristics (1-hour pad test: 1-hrPadTest, Overactive Bladder Symptom Score: OABSS), were represented as nodes and edges in the network diagram. We then employed a heuristic function to select the optimal treatment method for the patients with SUI and UUI. This process enables medical professionals to easily navigate the data for patients with both SUI and UUI concerns by calculating the shortest path connecting the 1-hrPadTest and OABSS. These results, which are consistent with those of previous studies, suggest that VEL is the optimal treatment. Unlike previous studies that employed statistical knowledge that is challenging for patients to understand, our study aids patients in visually comprehending and developing a customized treatment plan. This approach introduces a novel perspective for clinical decision-making in the treatment of urinary incontinence. To the best of our knowledge, this is the first study to apply discrete mathematics to patient decision-making for urinary incontinence treatment.

Learners' Spontaneous Gesture Before a Math Lesson Predicts the Efficacy of Seeing Versus Doing Gesture During the Lesson.

Gestures-hand movements that accompany speech and express ideas-can help children learn how to solve problems, flexibly generalize learning to novel problem-solving contexts, and retain what they have learned. But does it matter who is doing the gesturing? We know that producing gesture leads to better comprehension of a message than watching someone else produce gesture. But we do not know how producing versus observing gesture impacts deeper learning outcomes such as generalization and retention across time. Moreover, not all children benefit equally from gesture instruction, suggesting that there are individual differences that may play a role in who learns from gesture. Here, we consider two factors that might impact whether gesture leads to learning, generalization, and retention after mathematical instruction: (1) whether children see gesture or do gesture and (2) whether a child spontaneously gestures before instruction when explaining their problem-solving reasoning. For children who spontaneously gestured before instruction, both doing and seeing gesture led to better generalization and retention of the knowledge gained than a comparison manipulative action. For children who did not spontaneously gesture before instruction, doing gesture was less effective than the comparison action for learning, generalization, and retention. Importantly, this learning deficit was specific to gesture, as these children did benefit from doing the comparison manipulative action. Our findings are the first evidence that a child's use of a particular representational format for communication (gesture) directly predicts that child's propensity to learn from using the same representational format.

Multiscale homogenization for dual porosity time-dependent Darcy-Brinkman/Darcy coupling and its application to the lymph node.

We study the coupling between time-dependent Darcy-Brinkman and the Darcy equations at the microscale subjected to inhomogeneous body forces and initial conditions to describe a double porosity problem. We derive the homogenized governing equations for this problem using the asymptotic homogenization technique, and as macroscopic results, we obtain a coupling between two Darcy equations, one of which with memory effects, with mass exchange between phases. The memory effects are a consequence of considering the time dependence in the Darcy-Brinkman equation, and they allow us to study in more detail the role of time in the problem under consideration. After the formulation of the model, we solve it in a simplified setting and we use it to describe the movement of fluid within a vascularized lymph node.

How teachers make connections among ideas in mathematics instruction.

Conceptual understanding involves understanding connections among ideas within a domain. In this chapter, we consider how teachers support students in learning about connections among ideas in mathematics. We review research focusing on teachers' connection making in mathematics classrooms, and we consider several dimensions of variability in that connection making. Across three corpora of lessons that varied in students' grade levels (first grade to college), cultural settings (United States and China), and mathematics content, we found that all teachers produced linking episodes, but the frequency with which they did so varied substantially, raising new questions about the sources and consequences of that variability. Teachers of first-grade students in China routinely engaged their students in co-constructing links; teachers of middle schoolers and college students in the United States typically explained links to students. Linking episodes targeted many different types of connections, including connections between representations, connections between principles and exemplars, connections between procedures and concepts, and connections between concepts and real-world instantiations. Across all three corpora, teachers expressed linked ideas multimodally in a majority of linking episodes. Based on the findings, we present several hypotheses about how teacher behaviors may support students' understanding of connections among ideas, and we suggest directions for future work.