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.

Eye tracking technology is a high-potential tool for different mathematic cognition research areas. Moreover, there is a dire need for more studies that provide detailed information on the quality of registered eye data. This study aimed to illustrate the applicability of eye tracking in the examination of mathematical cognition, focusing specifically on primary school students completing a computerized mental arithmetic task. Results suggested that the eye tracking device effectively captured high-quality eye movement data when primary school children engaged in this specific task. Furthermore, significant negative correlations have been found between task performance and number of eye fixations. Finally, eye movements distinctions between \"Areas of Interest\" have been found, indicating different visual tracking associated with different components of arithmetic calculations. This study underscores the extensive possibilities for future research employing eye tracking devices during computerized calculation tasks as assessment tools to explore the complex visual and cognitive processes.

This study delves into special class of generalized p-trigonometric functions, examining their connection to the established counterparts like p-cosine and p-sine functions. We here explore the new class of functions called the p-versine, p-coversine, p-haversine, and p-hacovercosine, by providing comprehensive definitions and properties. Grounded in the characteristics of p-cosine and p-sine functions, the newly proposed functions offer unique mathematical insights. Our work contributes towards a thorough understanding of these new special functions, showcasing their potential applications in diverse scientific domains, from mathematical analysis to physics and engineering. This paper contributes as a valuable resource for future applied mathematics researchers, engaging with these new mathematical functions, enhancing the ability to model complex patterns from diverse real-world applications.

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 factors impacting 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.

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 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.

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.

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.

Design-based STEM learning is believed to be an effective cross-disciplinary strategy for promoting children\'s cognitive development. Yet, its impact on executive functions, particularly for disadvantaged children, still need to be explored. This study investigated the effects of short-term intensive design-based STEM learning on executive function among left-behind children. Sixty-one Grade 4 students from a school dedicated to the left-behind children in China were sampled and randomly assigned to an experimental group (10.70 ± 0.47 years old, n = 30) or a control group (10.77 ± 0.43 years old, n = 31). The experimental group underwent a two-week design-based STEM training program, while the control group participated in a 2-week STEM-related reading program. Both groups were assessed with the brain activation from 4 brain regions of interest using functional near-infrared spectroscopy (fNIRS) and behavioral measures during a Stroop task before and after the training. Analysis disclosed: (i) a significant within-group time effect in the experimental group, with posttest brain activation in Brodmann Area 10 and 46 being notably lower during neutral and word conditions; (ii) a significant between-group difference at posttest, with the experimental group showing considerably lower brain activation in Brodmann Area 10 and Brodmann Area 46 than the control group; and (iii) a significant task effect in brain activity among the three conditions of the Stroop task. These findings indicated that this STEM learning effectively enhanced executive function in left-behind children. The discrepancy between the non-significant differences in behavioral performance and the significant ones in brain activation implies a compensatory mechanism in brain activation. This study enriches current theories about the impact of Science, Technology, Engineering, and Mathematics (STEM) learning on children\'s executive function development, providing biological evidence and valuable insights for educational curriculum design and assessment.

OBJECTIVE: Peer relationships during adolescence play an important role in shaping academic outcomes. The present study examined friend influences on emotions towards math, as well as the role of temperament in these influences.
METHODS: The sample consisted of 350 Finnish students (mean age 13.29 years; 64% girls) who were involved in stable friendship dyads from fall to spring of Grade 7.
METHODS: In this two-wave study, information on adolescents\' temperament (i.e., negative emotionality, extraversion, effortful control) and on seven emotions towards math (i.e., enjoyment, hope, pride, anger, anxiety, shame, hopelessness, and boredom) was collected during grade 7. The data were analysed using longitudinal actor-partner interdependence models.
RESULTS: The results showed that friends resembled each other in all the investigated math-related emotions. Furthermore, over and above these initial similarities, friends mutually influenced each other\'s math-related enjoyment and anger towards math. Students characterized by higher negative emotionality also influenced their friends with lower levels of negative emotionality towards an increase in math-related anger and a lack of effortful control made adolescents more susceptible to friend influence over math-related shame and anxiety.
CONCLUSIONS: Our findings demonstrate that friends influence each other over time in math-related enjoyment and frustration. Furthermore, high negative emotionality may make adolescents more influential over their friends\' math-related anger and a lack of effortful control may make adolescents more susceptible to friend influence over math-related shame and anxiety. Thus, the current findings have implications for how peer relations may impact individual outcomes in mathematics, for better or worse.