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Molecules (Basel, Switzerland) Jun 2023Since chemistry, materials science, and crystallography deal with three-dimensional structures, they use mathematics such as geometry and symmetry. In recent years, the...
Since chemistry, materials science, and crystallography deal with three-dimensional structures, they use mathematics such as geometry and symmetry. In recent years, the application of topology and mathematics to material design has yielded remarkable results. It can also be seen that differential geometry has been applied to various fields of chemistry for a relatively long time. There is also the possibility of using new mathematics, such as the crystal structure database, which represents big data, for computational chemistry (Hirshfeld surface analysis). On the other hand, group theory (space group and point group) is useful for crystal structures, including determining their electronic properties and the symmetries of molecules with relatively high symmetry. However, these strengths are not exhibited in the low-symmetry molecules that are actually handled. A new use of mathematics for chemical research is required that is suitable for the age when computational chemistry and artificial intelligence can be used.
Topics: Artificial Intelligence; Mathematics; Crystallography
PubMed: 37298985
DOI: 10.3390/molecules28114509 -
Psychological Research Jul 2022There is a notion that mathematical equations can be considered aesthetic objects. However, whereas some aesthetic experiences are triggered primarily by the sensory...
There is a notion that mathematical equations can be considered aesthetic objects. However, whereas some aesthetic experiences are triggered primarily by the sensory properties of objects, for mathematical equations aesthetic judgments extend beyond their sensory qualities and are also informed by semantics and knowledge. Therefore, to the extent that expertise in mathematics represents the accumulation of domain knowledge, it should influence aesthetic judgments of equations. In a between-groups study design involving university students who majored in mathematics (i.e., experts) or not (i.e., laypeople), we found support for the hypothesis that mathematics majors exhibit more agreement in their aesthetic judgments of equations-reflecting a greater degree of shared variance driven by formal training in the domain. Furthermore, their judgments were driven more strongly by familiarity and meaning than was the case for laypeople. These results suggest that expertise via advanced training in mathematics alters (and sharpens) aesthetic judgments of mathematical equations.
Topics: Esthetics; Humans; Judgment; Mathematics; Semantics
PubMed: 34495389
DOI: 10.1007/s00426-021-01592-5 -
Behavioral and Brain Functions : BBF Jul 2012Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population.... (Comparative Study)
Comparative Study
BACKGROUND
Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys' mathematics performance is more negatively affected by MA than girls' performance is. The aim of the current study was to measure girls' and boys' mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies.
METHODS
Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires.
RESULTS
No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys.
CONCLUSIONS
Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on 'online' mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because there is evidence that MA develops during the primary school years. Furthermore, our study showed no gender difference in mathematics performance, despite girls reporting higher levels of MA. These results might suggest that girls may have had the potential to perform better than boys in mathematics however their performance may have been attenuated by their higher levels of MA. Longitudinal research is needed to investigate the development of MA and its effect on mathematics performance.
Topics: Adolescent; Affective Symptoms; Anxiety; Child; Educational Measurement; Female; Humans; Male; Mathematics; Psychology, Adolescent; Psychology, Child; Regression Analysis; Sex Characteristics; Test Anxiety Scale; Test Taking Skills
PubMed: 22769743
DOI: 10.1186/1744-9081-8-33 -
Journal of Experimental Child Psychology Nov 2023Schoolchildren with better executive functioning skills achieve better mathematics results. It is less clear how inhibition, cognitive flexibility, and working memory...
Schoolchildren with better executive functioning skills achieve better mathematics results. It is less clear how inhibition, cognitive flexibility, and working memory combine to predict mathematics achievement and difficulty throughout primary and secondary school. This study aimed to find the best combination of executive function measures for predicting mathematical achievement in Grades 2, 6, and 10 and to test whether this combination predicts the probability of having mathematical difficulties across school grades even when fluid intelligence and processing speed were included in the models. A total of 426 students-141 2nd graders (72 girls), 143 6th graders (72 girls), and 142 10th graders (79 girls)-were cross-sectionally assessed with 12 executive tasks, one standardized mathematical task, and a standardized test of intelligence. Bayesian regression analyses found various combinations of executive predictors of mathematical achievement for each school grade spanning Grade 2 to measures of cognitive inhibition (negative priming) and cognitive flexibility (verbal fluency); Grade 6 to measures of inhibition: resistance to distractor interference (receptive attention), cognitive flexibility (local-global), and working memory (counting span); and Grade 10 to measures of inhibition: resistance to distractor interference (receptive attention) and prepotent response inhibition (stop signal) and working memory (reading span). Logistic regression showed that the executive models derived from the Bayesian analyses had a similar ability to classify students with mathematical difficulty and their peers with typical achievement to broader cognitive models that included fluid intelligence and processing speed. Measures of processing speed, cognitive flexibility (local-global), and prepotent response inhibition (stop signal) were the main risk factors in Grades 2, 6, and 10, respectively. Cognitive flexibility (verbal fluency) in Grade 2 and fluid intelligence, which was more stable in all three grades, acted as protective factors against mathematical difficulty. These findings inform practical considerations for establishing preventive and intervention proposals.
Topics: Female; Humans; Child; Executive Function; Bayes Theorem; Memory, Short-Term; Mathematics; Schools
PubMed: 37307647
DOI: 10.1016/j.jecp.2023.105715 -
Mathematical Biosciences and... Mar 2020
Topics: Biological Science Disciplines; Mathematics; Models, Theoretical
PubMed: 32987510
DOI: 10.3934/mbe.2020167 -
Cognitive Science Apr 2021Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological...
Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged an inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object-wise, could underlie diagram-based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions.
Topics: Adult; Humans; Mathematics
PubMed: 33873252
DOI: 10.1111/cogs.12959 -
Developmental Cognitive Neuroscience Apr 2018Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains... (Review)
Review
Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses on the learning of arithmetic, which is quintessential to mathematical development. The nascent body of brain imaging studies reveals that arithmetic recruits a large set of interconnected areas, including prefrontal, posterior parietal, occipito-temporal and hippocampal areas. This network undergoes developmental changes in its function, connectivity and structure, which are not yet fully understood. This network only partially overlaps with what has been found in adults, and clear differences are observed in the recruitment of the hippocampus, which are related to the development of arithmetic fact retrieval. Despite these emerging trends, the literature remains scattered, particularly in the context of atypical development. Acknowledging the distributed nature of the arithmetic network, future studies should focus on connectivity and analytic approaches that investigate patterns of brain activity, coupled with a careful design of the arithmetic tasks and assessments of arithmetic strategies. Such studies will produce a more comprehensive understanding of how the arithmetical brain unfolds, how it changes over time, and how it is impaired in atypical development.
Topics: Brain; Child; Female; Humans; Learning; Magnetic Resonance Imaging; Male; Mathematics; Neuroimaging
PubMed: 28566139
DOI: 10.1016/j.dcn.2017.05.002 -
International Journal of Environmental... Dec 2021Research suggests that integrated STEM activities can best support students in developing their mathematical and scientific understanding. On one hand, while science...
Research suggests that integrated STEM activities can best support students in developing their mathematical and scientific understanding. On one hand, while science provides mathematics with real-life authentic problems to investigate, mathematics provides science powerful tools to explore those problems. In line with this call, in this study, we designed an integrated lesson at the cross-section of proportional reasoning and added sugar present in food products to explore how added sugar provides students with a meaningful context to engage in proportional reasoning and how proportional reasoning helps students identify the quantity of added sugar present in different food products and provides students with a platform to initiate a conversation around quality of food products. Developed on the theoretical framework of Realistic Mathematics Education (RME), this lesson was remotely implemented on three middle school students. The result section highlights the design principle of the lesson that provided students with an opportunity to construct an understanding of both the disciplines through a mutual interaction.
Topics: Curriculum; Humans; Mathematics; Problem Solving; Students; Sugars
PubMed: 34886547
DOI: 10.3390/ijerph182312821 -
BMJ (Clinical Research Ed.) Mar 1996
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Bulletin of Mathematical Biology Oct 2023Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise...
Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise solutions in different ways. Using ubiquitous computing infrastructure, we provide a means to go one step further in using computers to understand complex models through instantaneous and interactive exploration. This ubiquitous infrastructure has enormous potential in education, outreach and research. Here, we present VisualPDE, an online, interactive solver for a broad class of 1D and 2D partial differential equation (PDE) systems. Abstract dynamical systems concepts such as symmetry-breaking instabilities, subcritical bifurcations and the role of initial data in multistable nonlinear models become much more intuitive when you can play with these models yourself, and immediately answer questions about how the system responds to changes in parameters, initial conditions, boundary conditions or even spatiotemporal forcing. Importantly, VisualPDE is freely available, open source and highly customisable. We give several examples in teaching, research and knowledge exchange, providing high-level discussions of how it may be employed in different settings. This includes designing web-based course materials structured around interactive simulations, or easily crafting specific simulations that can be shared with students or collaborators via a simple URL. We envisage VisualPDE becoming an invaluable resource for teaching and research in mathematical biology and beyond. We also hope that it inspires other efforts to make mathematics more interactive and accessible.
Topics: Humans; Models, Biological; Mathematical Concepts; Nonlinear Dynamics; Mathematics; Students
PubMed: 37823924
DOI: 10.1007/s11538-023-01218-4