The relations between growth mindset, motivational beliefs, and career interest in math intensive fields in informal STEM youth programs.

Past research has shown that growth mindset and motivational beliefs have an important role in math and science career interest in adolescence. Drawing on situated expectancy-value theory (SEVT), this study extends these findings by investigating the role of parental motivational beliefs (e.g., expectancy beliefs, utility values) and parent growth mindset in math on adolescent career interest in math-intensive fields (e.g., mathematics, computer science, statistics, and engineering; MCSE) through adolescent motivational beliefs in math. Structural equation modeling was used to test the hypothesized model using data from 290 adolescents (201 girls, 69.3%; Mage = 15.20), who participate in informal STEM (science, technology, engineering, mathematics) youth programs, and their parents (162 parents, 87.7% female) in the United Kingdom and the United States. As hypothesized, adolescent expectancy beliefs, utility values, and growth mindset in math had a significant direct effect on MCSE career interest. Further, there was a significant indirect effect of parental expectancy beliefs in math on MCSE career interest through adolescents' expectancy beliefs. Similarly, there was a significant indirect effect from parental utility values in math to MCSE career interest through adolescents' utility values. The findings suggest that parents' math motivational beliefs play a critical role in adolescent math motivational beliefs and their career interest in math-intensive fields.

Soft super-continuity and soft delta-closed graphs.

Introducing a strong form of soft continuity between soft topological spaces is significant because it can contribute to our growing understanding of soft topological spaces and their features, provide a basis for creating new mathematical tools and methods, and have significant applications in various fields. In this paper, we define soft super-continuity as a new form of soft mapping. We present various characterizations of this soft concept. Also, we show that soft super-continuity lies strictly between soft continuity and soft complete continuity and that soft super-continuity is a strong form of soft δ-continuity. In addition, we give some sufficient conditions for the equivalence between soft super-continuity and other related concepts. Moreover, we characterize soft semi-regularity in terms of super-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and products by soft super-continuity. In addition to these, we study the relationship between soft super-continuity and soft δ-continuity with their analogous notions in general topology. Finally, we give several sufficient conditions on a soft mapping to have a soft δ-closed graph.

Torsion affects the calculation of DNA twisting number.

The topological properties of DNA have long been a focal point in biophysics. In the 1970s, White proposed that the topology of closed DNA double helix follows White's formula: Lk=Wr+Tw. However, there has been controversy in the calculation of DNA twisting number, partly due to discrepancies in the definition of torsion in differential geometry. In this paper, we delved into a detailed study of torsion, revealing that the calculation of DNA twisting number should use the curve's geodesic torsion. Furthermore, we found that the discrepancy in DNA twisting numbers calculated using different torsion is N. This study elucidated the impact of torsion on the calculation of DNA twisting numbers, aiming to resolve controversies in the calculation of DNA topology and provided accurate computational methods and theoretical foundations for related research.

Developing a predictive science of the biosphere requires the integration of scientific cultures.

Increasing the speed of scientific progress is urgently needed to address the many challenges associated with the biosphere in the Anthropocene. Consequently, the critical question becomes: How can science most rapidly progress to address large, complex global problems? We suggest that the lag in the development of a more predictive science of the biosphere is not only because the biosphere is so much more complex, or because we do not have enough data, or are not doing enough experiments, but, in large part, because of unresolved tension between the three dominant scientific cultures that pervade the research community. We introduce and explain the concept of the three scientific cultures and present a novel analysis of their characteristics, supported by examples and a formal mathematical definition/representation of what this means and implies. The three cultures operate, to varying degrees, across all of science. However, within the biosciences, and in contrast to some of the other sciences, they remain relatively more separated, and their lack of integration has hindered their potential power and insight. Our solution to accelerating a broader, predictive science of the biosphere is to enhance integration of scientific cultures. The process of integration-Scientific Transculturalism-recognizes that the push for interdisciplinary research, in general, is just not enough. Unless these cultures of science are formally appreciated and their thinking iteratively integrated into scientific discovery and advancement, there will continue to be numerous significant challenges that will increasingly limit forecasting and prediction efforts.

The concept of optimal planning of a linearly oriented segment of the 5G network.

In the article, the extreme problem of finding the optimal placement plan of 5G base stations at certain points within a linear area of finite length is set. A fundamental feature of the author's formulation of the extreme problem is that it takes into account not only the points of potential placement of base stations but also the possibility of selecting instances of stations to be placed at a specific point from a defined excess set, as well as the aspect of inseparable interaction of placed 5G base stations within the framework of SON. The formulation of this extreme problem is brought to the form of a specific combinatorial model. The article proposes an adapted branch-and-bounds method, which allows the process of synthesis of the architecture of a linearly oriented segment of a 5G network to select the best options for the placement of base stations for further evaluation of the received placement plans in the metric of defined performance indicators. As the final stage of the synthesis of the optimal plan of a linearly oriented wireless network segment based on the sequence of the best placements, it is proposed to expand the parametric space of the design task due to the specific technical parameters characteristic of the 5G platform. The article presents a numerical example of solving an instance of the corresponding extremal problem. It is shown that the presented mathematical apparatus allows for the formation of a set of optimal placements taking into account the size of the non-coverage of the target area. To calculate this characteristic parameter, both exact and two approximate approaches are formalized. The results of the experiment showed that for high-dimensional problems, the approximate approach allows for reducing the computational complexity of implementing the adapted branch-and-bounds method by more than six times, with a slight loss of accuracy of the optimal solution. The structure of the article includes Section 1 (introduction and state-of-the-art), Section 2 (statement of the research, proposed models and methods devoted to the research topic), Section 3 (numerical experiment and analysis of results), and Section 4 (conclusions and further research).

How syllabi relate to outcomes in higher education: A study of syllabi learner-centeredness and grade inequities in STEM.

Fostering equity in undergraduate science, technology, engineering, and mathematics (STEM) programs can be accomplished by incorporating learner-centered pedagogies, resulting in the closing of opportunity gaps (defined here as the difference in grades earned by minoritized and non-minoritized students). We assessed STEM courses that exhibit small and large opportunity gaps at a minority-serving, research-intensive university, and evaluated the degree to which their syllabi are learner-centered, according to a previously validated rubric. We specifically chose syllabi as they are often the first interaction students have with a course, establish expectations for course policies and practices, and serve as a proxy for the course environment. We found STEM courses with more learner-centered syllabi had smaller opportunity gaps. The syllabus rubric factor that most correlated with smaller gaps was Power and Control, which reflects Student's Role, Outside Resources, and Syllabus Focus. This work highlights the importance of course syllabi as a tool for instructors to create more inclusive classroom environments.

Theoretical and mathematical codynamics of nonlinear tuberculosis and COVID-19 model pertaining to fractional calculus and probabilistic approach.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel virus known as coronavirus 2 (SARS-CoV-2) that affects the pulmonary structure and results in the coronavirus illness 2019 (COVID-19). Tuberculosis (TB) and COVID-19 codynamics have been documented in numerous nations. Understanding the complexities of codynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of TB and COVID-19 in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Sensitivity analysis and bifurcation of the submodel are also investigated with system parameters. Furthermore, existence and uniqueness results are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system's long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical technique, power-law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of TB and COVID-19 minimizes the propagation of the codynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in TB and COVID-19 co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level.

Inhibitory control mediates the association between body mass index and math performance in children: A cross-sectional study.

BACKGROUND: Overweight and obesity affect more than 18% of children and adolescents in the world. Obesity-related associations with brain morphology might be associated with reduced efficiency of inhibitory control. This association highlights a possible mechanism by which obesity impacts intelligence and academic achievement. Prior work indicates a mediating effect of inhibitory control on the relationship between body mass index (BMI) and intelligence and academic achievement. However, although obesity is associated with impaired math performance, we do not know whether inhibitory control also mediates the relationship between BMI and math performance. This study tests the hypothesis that inhibitory control statistically mediates the relationship between BMI and math performance. METHODS: 161 children (9 to 13 years old, 80 female) participated in the present study. We evaluated BMI; math performance, in a test composed of 20 arithmetic equations of the type x = (a × b) - c; and inhibitory control through the Flanker test. We carried out Spearman correlation tests, hierarchical multiple linear regression, and tested the confidence of the model where inhibitory control statistically mediates the indirect association between BMI and math performance. Mediation analysis in this cross-sectional study aimed to improve understanding of indirect relationships and offer insights into possible causal connections. RESULTS: Better math performance and lower BMI were associated with greater accuracy on the inhibitory control test and greater accuracy on the inhibitory control test was associated with better performance on math test. We found an indirect association between higher BMI in children and impairments in math performance, that was mediated by inhibitory control (a: -0.008, p = 0.025; b: 7.10, p = 0.0004; c: 0.05, p = 0.592; c': 0.11, p = 0.238; Indirect Effect: -0.0599, 95% CI: -0.13, -0.005). CONCLUSIONS: An indirect association between higher body mass indices in children and impairments in math performance was detected, through the impact that BMI has on inhibitory control.

Improving mental arithmetic ability of primary school students with schema teaching method: An experimental study.

Skillful utilization of mental arithmetic can significantly improve students' mathematical computation ability. However, it was observed that primary school students often resort to reiterating the process of written arithmetic in their minds during mental arithmetic, which is not conducive to their numerical ability improvement. This paper devises a set of graphic teaching aids for primary school students' mental arithmetic improvement based on mental arithmetic strategies, schema theory, and working memory. To validate the effectiveness of schema teaching in enhancing mental arithmetic ability among primary school students, a controlled experiment was conducted with two groups of third-grade students randomly selected from a primary school in Jingshan City. The results, obtained through descriptive statistical analysis and the multitrait-multimethod approach (MTMM), indicated that the experimental group (n = 52) demonstrated significant improvements in speed, accuracy, and stability in mental addition and subtraction after a 14-day instruction period in schema teaching. This study offers a potent mental arithmetic teaching strategy for elementary mathematics education, which can lead to a comprehensive enhancement of students' mental calculation abilities. It also holds promise for inspiring innovative teaching methodologies in primary and secondary mathematics education in the future.

The power of digital story in early mathematics education: Innovative approaches for children with intellectual disabilities.

This study explored the effectiveness of digital story interventions in improving early math skills in kindergarten children with mild intellectual disabilities. Digital stories are multimedia narratives that combine text, images, and audio to enhance learning experience. This experimental study used a pretest-posttest control group design. The intervention group consisted of 15 children who participated in an 8-week digital story intervention targeting early math skills. A matched control group was used to control for sex differences. Data were collected through the TEMA-3 test scores and teacher and child feedback. Post-intervention, the experimental group showed significant improvements in TEMA-3 test scores compared to the control group. Teachers and children reported a positive perception of the intervention's social validity, highlighting enhanced engagement and understanding of math concepts. This study demonstrated that digital story-based education is a promising approach for improving early math skills in children with mild intellectual disabilities. These findings suggest potential implications for integrating digital storytelling into special education curricula and highlight avenues for future research in this field.

Evolutionary graph theory beyond pairwise interactions: Higher-order network motifs shape times to fixation in structured populations.

To design population topologies that can accelerate rates of solution discovery in directed evolution problems or for evolutionary optimization applications, we must first systematically understand how population structure shapes evolutionary outcome. Using the mathematical formalism of evolutionary graph theory, recent studies have shown how to topologically build networks of population interaction that increase probabilities of fixation of beneficial mutations, at the expense, however, of longer fixation times, which can slow down rates of evolution, under elevated mutation rate. Here we find that moving beyond dyadic interactions in population graphs is fundamental to explain the trade-offs between probabilities and times to fixation of new mutants in the population. We show that higher-order motifs, and in particular three-node structures, allow the tuning of times to fixation, without changes in probabilities of fixation. This gives a near-continuous control over achieving solutions that allow for a wide range of times to fixation. We apply our algorithms and analytic results to two evolutionary optimization problems and show that the rate of solution discovery can be tuned near continuously by adjusting the higher-order topology of the population. We show that the effects of population structure on the rate of evolution critically depend on the optimization landscape and find that decelerators, with longer times to fixation of new mutants, are able to reach the optimal solutions faster than accelerators in complex solution spaces. Our results highlight that no one population topology fits all optimization applications, and we provide analytic and computational tools that allow for the design of networks suitable for each specific task.

Finger counting, finger number gesturing, and basic numerical skills: A cross-sectional study in 3- to 5-year-olds.

Recent evidence suggests that using finger-based strategies is beneficial for the acquisition of basic numerical skills. There are basically two finger-based strategies to be distinguished: (a) finger counting (i.e., extending single fingers successively) and (b) finger number gesturing (i.e., extending fingers simultaneously to represent magnitudes). In this study, we investigated both spontaneous and prompted finger counting and finger number gesturing as well as their contribution to basic numerical skills in 3- to 5-year-olds (N = 156). Results revealed that only 6% of children spontaneously used their fingers for counting when asked to name a specific number of animals, whereas 59% applied finger number gesturing to show their age. This indicates that the spontaneous use of finger-based strategies depends heavily on the specific context. Moreover, children performed significantly better in prompted finger counting than in finger number gesturing, suggesting that both strategies build on each other. Finally, both prompted finger counting and finger number gesturing significantly and individually predicted counting, cardinal number knowledge, and basic arithmetic. These results indicate that finger counting and finger number gesturing follow and positively relate to numerical development.

Adaptive Lifting Index (aLI) for Real-Time Instrumental Biomechanical Risk Assessment: Concepts, Mathematics, and First Experimental Results.

When performing lifting tasks at work, the Lifting Index (LI) is widely used to prevent work-related low-back disorders, but it presents criticalities pertaining to measurement accuracy and precision. Wearable sensor networks, such as sensorized insoles and inertial measurement units, could improve biomechanical risk assessment by enabling the computation of an adaptive LI (aLI) that changes over time in relation to the actual method of carrying out lifting. This study aims to illustrate the concepts and mathematics underlying aLI computation and compare aLI calculations in real-time using wearable sensors and force platforms with the LI estimated with the standard method used by ergonomists and occupational health and safety technicians. To reach this aim, 10 participants performed six lifting tasks under two risk conditions. The results show us that the aLI value rapidly converges towards the reference value in all tasks, suggesting a promising use of adaptive algorithms and instrumental tools for biomechanical risk assessment.

Exploring the utility of Geometric Morphometrics to analyse prehistoric hand stencils.

Hand stencils are a remarkable graphic expression in Prehistoric rock art, dating back to 42 ka BP. Although these stencils provide direct impressions of the artists' hands, the characterization of their biological profile (i.e., biological sex and age) is very challenging. Previous studies have attempted this analysis with traditional morphometrics (TM), whereas little research has been undertaken using Geometric Morphometrics (GM), a method widely used in other disciplines but only tentatively employed in rock art studies. However, the large variation in relative finger position in archaeological hands poses the question of whether these representations can be examined through GM, or, in contrast, if this creates an unmanageable error in the results. To address this issue, a 2D hand scans sample of 70 living individuals (F = 35; M = 35) has been collected in three standardized positions (n = 210) and digitized with 32 2D conventional landmarks. Results show that the intra-individual distance (mean Procrustes distance between Pos. 1-2 = 0.132; 2-3 = 0.191; 1-3 = 0.292) is larger than the inter-individual distance (mean in 1 = 0.122; 2 = 0.142; 3 = 0.165). Finally, it has been demonstrated that the relative finger positions, as well as the inclusion of all hand parts in the analysis, have an overshadowing effect on other variables potentially involved in the morphometric variability of the hand, such as biological sex.

Developmental associations of fundamental motor skills and executive functions in preschoolers - The role of the physical activity and the effects on early numeracy.

BACKGROUND: Physical activity, fundamental motor skills, executive functions and early numeracy have shown to be related, but very little is known about the developmental relations of these factors. PROCEDURE: We followed 317 children (3-6 years) over two years. Fundamental motor skills and executive functions (inhibition+switching, updating) were measured at all time points (T1, T2, T3) and physical activity at T1 and early numeracy at T3. MAIN FINDINGS: Children with better fundamental motor skills at T1 developed slower in inhibition and switching. Fundamental motor skills developed faster in children who had better initial inhibition and switching ability. Vigorous physical activity at T1 was associated with a weaker initial inhibition and switching. The initial level and the developmental rate of updating were related to better early numeracy skills. CONCLUSIONS: Findings indicate that fundamental motor skills and executive functions are developmentally related, and updating is an important predictor for early numeracy in preschoolers.

Electrophysiological correlates of symbolic numerical order processing.

Determining if a sequence of numbers is ordered or not is one of the fundamental aspects of numerical processing linked to concurrent and future arithmetic skills. While some studies have explored the neural underpinnings of order processing using functional magnetic resonance imaging, our understanding of electrophysiological correlates is comparatively limited. To address this gap, we used a three-item symbolic numerical order verification task (with Arabic numerals from 1 to 9) to study event-related potentials (ERPs) in 73 adult participants in an exploratory approach. We presented three-item sequences and manipulated their order (ordered vs. unordered) as well as their inter-item numerical distance (one vs. two). Participants had to determine if a presented sequence was ordered or not. They also completed a speeded arithmetic fluency test, which measured their arithmetic skills. Our results revealed a significant mean amplitude difference in the grand average ERP waveform between ordered and unordered sequences in a time window of 500-750 ms at left anterior-frontal, left parietal, and central electrodes. We also identified distance-related amplitude differences for both ordered and unordered sequences. While unordered sequences showed an effect in the time window of 500-750 ms at electrode clusters around anterior-frontal and right-frontal regions, ordered sequences differed in an earlier time window (190-275 ms) in frontal and right parieto-occipital regions. Only the mean amplitude difference between ordered and unordered sequences showed an association with arithmetic fluency at the left anterior-frontal electrode. While the earlier time window for ordered sequences is consistent with a more automated and efficient processing of ordered sequential items, distance-related differences in unordered sequences occur later in time.

Eyes on the Future: Inspiring Latino Middle School Youth to Pursue Careers in STEM Through Early Interactive Science Programming.

BACKGROUND: Given the need for a diverse health care workforce, efforts must be made early in their education to support underrepresented minorities in medicine and the science, technology, engineering, and mathematics (STEM) fields. METHODS: The Eyes on the Future program introduces underrepresented minority 8th grade students to science and medicine via interactive science-based programming and mentorship by medical and graduate students. Program impact was evaluated using pre- and post-program surveys. RESULTS: Of 25 participating students, 24 and 22 responded to pre- and post-program surveys, respectively. Students showed strong interest in science concepts and STEM careers, with high, positively correlated, and statistically similar pre- and post-program survey responses. DISCUSSION: The Eyes on the Future program was well-received and represents a step towards addressing barriers to STEM careers faced by underrepresented minority students.

Ferryman between two cultures: The calling of a historian of science.

In well-established disciplines like history it is not common to find professionals who admit that they are driven by a "calling" or who say they have a "mission" to fulfill. In emerging disciplines, however, the situation is different: in order to gain recognition these new disciplines need highly driven practitioners, who's calling enables them to overcome opposition or neglect from the side of the established disciplines. A clear example of such a practitioner with a mission in an emerging field of knowledge is the Dutch historian of science Eduard Jan Dijksterhuis (1892-1965). His career as a mathematics teacher, historical scholar, and public intellectual was marked by the desire to re-integrate science and mathematics in culture in general. Dijksterhuis regarded the history of science as a major instrument to bring about this ideal. His magnum opus, The Mechanization of the World Picture (first published in 1950 in Dutch; translated into English in 1961), was the culmination of a lifetime of writing in the service of a cultural vision that can still inspire our own generation.

The notorious man-in-the-street: Hermann Weyl and the problem of knowledge.

Hermann Weyl's philosophical reflections remain a topic of considerable interest in the history and philosophy of science. In particular, Weyl's commitment to a form of idealism, as it pertains to his reading of Husserl and Fichte, has garnered much discussion. However, much less attention has been given to Weyl's later, and at that only partial, turn towards a form of empiricism (i.e. from the late 1920s onward). This lack of focus on Weyl's later philosophy has tended to obscure some of the most significant lessons that Weyl sought to draw from his decades of research in the foundations of mathematics and physics. In this paper, I develop some aspects of what I will term as Weyl's 'modest' empiricism. I will argue that Weyl's turn toward empiricism can be read in the context of a development of Helmholtz's epistemological program and his unique form of 'Kantianism'. The hope is that this reading will not only provide a better understanding of Weyl's later thought, especially his (1954) criticism of Cassirer, but that it may also provide the basis for a novel 'Weylian' account of the mathematization of nature underwriting the group-theoretic methodology of parts of modern physics.

When intuitive Bayesians need to be good readers: The problem-wording effect on Bayesian reasoning.

Are humans intuitive Bayesians? It depends. People seem to be Bayesians when updating probabilities from experience but not when acquiring probabilities from descriptions (i.e., Bayesian textbook problems). Decades of research on textbook problems have focused on how the format of the statistical information (e.g., the natural frequency effect) affects such reasoning. However, it pays much less attention to the wording of these problems. Mathematical problem-solving literature indicates that wording is critical for performance. Wording effects (the wording varied across the problems and manipulations) can also have far-reaching consequences. These may have confounded between-format comparisons and moderated within-format variability in prior research. Therefore, across seven experiments (N = 4909), we investigated the impact of the wording of medical screening problems and statistical formats on Bayesian reasoning in a general adult population. Participants generated more Bayesian answers with natural frequencies than with single-event probabilities, but only with the improved wording. The improved wording of the natural frequencies consistently led to more Bayesian answers than the natural frequencies with standard wording. The improved wording effect occurred mainly due to a more efficient description of the statistical information-cueing required mathematical operations, an unambiguous association of numbers with their reference class and verbal simplification. The wording effect extends the current theoretical explanations of Bayesian reasoning and bears methodological and practical implications. Ultimately, even intuitive Bayesians must be good readers when solving Bayesian textbook problems.