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Cadernos de Saude Publica Oct 2018
Topics: Brazil; Female; Humans; Mathematics; Science; Sexism; Women
PubMed: 30329000
DOI: 10.1590/0102-311X00173718 -
CBE Life Sciences Education Jun 2019Over the past two decades, science, technology, engineering, and mathematics (STEM) faculty have been striving to make their teaching practices more inclusive and...
Over the past two decades, science, technology, engineering, and mathematics (STEM) faculty have been striving to make their teaching practices more inclusive and welcoming to the variety of students who enter college. However, many STEM faculty, even those at teaching-focused institutions, have been educated in a traditional environment that emphasizes research and may not include classroom teaching. This can produce a deficit in training that leaves many STEM faculty feeling uncertain about inclusive teaching practices and their essential undergirding principles. This essay describes an online, evidence-based teaching guide ( https://lse.ascb.org/evidence-based-teaching-guides/inclusive-teaching ) intended to help fill this gap, serving as a resource for science faculty as they work to become more inclusive, particular with regard to differences in race, ethnicity, and gender. The guide describes the importance of developing self-awareness and empathy for students as a precursor to considering classroom practices. It also explores the role of classroom climate before turning to pedagogical choices that can support students' sense of belonging, competence, and interest in the course. Finally, the guide suggests that true inclusivity is a community effort and that instructors should leverage local and national networks to maximize student learning and inclusion. Each of these essential points is supported by summaries of and links to articles that can inform these choices. The guide also includes an instructor checklist that offers a concise summary of key points with actionable steps that can guide instructors as they work toward a more inclusive practice. We hope that the guide will provide value for both faculty who are just beginning to consider how to change their teaching practices and faculty seeking to enrich their current efforts.
Topics: Empathy; Engineering; Faculty; Humans; Mathematics; Metacognition; Science; Students; Teaching; Technology; Universities
PubMed: 31025917
DOI: 10.1187/cbe.19-01-0021 -
Physical Biology Jun 2019Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic... (Review)
Review
Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.
Topics: Computational Biology; Computer Simulation; Humans; Mathematics; Medical Oncology; Models, Biological; Models, Theoretical; Neoplasms; Single-Cell Analysis; Systems Biology
PubMed: 30991381
DOI: 10.1088/1478-3975/ab1a09 -
Physical Biology Jul 2023Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like,... (Review)
Review
Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.
Topics: Mathematics; Lens, Crystalline; Mitochondria; Physics
PubMed: 37290456
DOI: 10.1088/1478-3975/acdcdb -
Progress in Biophysics and Molecular... Oct 2016Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the... (Review)
Review
Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the rich interactions between physics and mathematics. These two disciplines share common principles of construction of concepts and of the proper objects of inquiry. Theory construction in physics relies on mathematical symmetries that preserve the key invariants observed and proposed by such theory; these invariants buttress the idea that the objects of physics are generic and thus interchangeable and they move along specific trajectories which are uniquely determined, in classical and relativistic physics. In contrast to physics, biology is a historical science that centers on the changes that organisms experience while undergoing ontogenesis and phylogenesis. Biological objects, namely organisms, are not generic but specific; they are individuals. The incessant changes they undergo represent the breaking of symmetries, and thus the opposite of symmetry conservation, a central component of physical theories. This instability corresponds to the changes of the environment and the phenotypes. Inspired by Galileo's principle of inertia, the "default state" of inert matter, we propose a "default state" for biological dynamics following Darwin's first principle, "descent with modification" that we transform into "proliferation with variation and motility" as a property that spans life, including cells in an organism. These dissimilarities between theories of the inert and of biology also apply to causality: biological causality is to be understood in relation to the distinctive role that constraints assume in this discipline. Consequently, the notion of cause will be reframed in a context where constraints to activity are seen as the core component of biological analyses. Finally, we assert that the radical materiality of life rules out distinctions such as "software vs. hardware."
Topics: Animals; Biology; Humans; Mathematics; Physics
PubMed: 27390105
DOI: 10.1016/j.pbiomolbio.2016.06.005 -
Cognitive Psychology Nov 2023Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural... (Review)
Review
Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural language also provide a basis for mathematics. To date, however, no theoretically rigorous investigation has been conducted to support such arguments. Therefore, this study uses a methodology based on theoretical linguistics to analyze the syntactic properties of mathematical expressions. Through a review of recent behavioral and neuroimaging studies on mathematical syntax, we report several inconsistencies with theoretical linguistics, such as the use of ternary structures. To address these, we propose that a syntactic category called Applicative plays a central role in analyzing mathematical expressions with seemingly ternary structures by combining binary structures. Besides basic arithmetic expressions, we also examine algebraic equations and complex expressions such as integral and differential calculi. This study is the first attempt at building a comprehensive framework for analyzing the syntactic structures of mathematical expressions.
Topics: Humans; Language; Linguistics; Mathematics
PubMed: 37748253
DOI: 10.1016/j.cogpsych.2023.101606 -
Biological Cybernetics Dec 2021Natural phenomena can be quantitatively described by means of mathematics, which is actually the only way of doing so. Physics is a convincing example of the...
Natural phenomena can be quantitatively described by means of mathematics, which is actually the only way of doing so. Physics is a convincing example of the mathematization of nature. This paper gives an answer to the question of how mathematization of nature is done and illustrates the answer. Here nature is to be taken in a wide sense, being a substantial object of study in, among others, large domains of biology, such as epidemiology and neurobiology, chemistry, and physics, the most outspoken example. It is argued that mathematization of natural phenomena needs appropriate core concepts that are intimately connected with the phenomena one wants to describe and explain mathematically. Second, there is a scale on and not beyond which a specific description holds. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis, which has meanwhile been confirmed on many occasions. Furthermore, a mathematical description can, as in physics, but need not be universally valid, as in biology. Finally, the history of science shows that only an intensive gauging of theory, i.e., mathematical description, by experiment leads to progress. That is, appropriate core concepts and appropriate scales are a necessary condition for mathematizing nature, and so is its verification by experiment.
Topics: Mathematics; Neurobiology; Physics
PubMed: 34837542
DOI: 10.1007/s00422-021-00914-5 -
Neuroscience and Biobehavioral Reviews Mar 2024Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying... (Review)
Review
Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.
Topics: Humans; Learning; Cognition; Brain; Mathematics; Neurobiology
PubMed: 38220032
DOI: 10.1016/j.neubiorev.2024.105545 -
Annals of the New York Academy of... Jul 2022In this paper, we discuss several largely undisputed claims about mathematics anxiety (MA) and propose where MA research should focus, including theoretical...
In this paper, we discuss several largely undisputed claims about mathematics anxiety (MA) and propose where MA research should focus, including theoretical clarifications on what MA is and what constitutes its opposite pole; discussion of construct validity, specifically relations between self-descriptive, neurophysiological, and cognitive measures; exploration of the discrepancy between state and trait MA and theoretical and practical consequences; discussion of the prevalence of MA and the need for establishing external criteria for estimating prevalence and a proposal for such criteria; exploration of the effects of MA in different groups, such as highly anxious and high math-performing individuals; classroom and policy applications of MA knowledge; the effects of MA outside educational settings; and the consequences of MA on mental health and well-being.
Topics: Anxiety; Anxiety Disorders; Humans; Mathematics
PubMed: 35322431
DOI: 10.1111/nyas.14770 -
Annals of the New York Academy of... Jul 2022Mathematics anxiety (MA) is negatively associated with mathematics performance. Although some aspects, such as mathematics self-concept (M self-concept), seem to...
Mathematics anxiety (MA) is negatively associated with mathematics performance. Although some aspects, such as mathematics self-concept (M self-concept), seem to modulate this association, the underlying mechanism is still unclear. In addition, the false gender stereotype that women are worse than men in mathematics can have a detrimental effect on women. The role that the endorsement of this stereotype (mathematics-gender stereotype (MGS) endorsement) can play may differ between men and women. In this study, we investigated how MA and mathematics self-concept relate to arithmetic performance when considering one's MGS endorsement and gender in a large sample (n = 923) of university students. Using a structural equation modeling approach, we found that MA and mathematics self-concept mediated the effect of MGS endorsement in both men and women. For women, MGS endorsement increased their MA level, while in men, it had the opposite effect (albeit weak). Specifically, in men, MGS endorsement influenced the level of the numerical components of MA, but, unlike women, it also positively influenced their mathematics self-concept. Moreover, men and women perceived the questions included in the considered instruments differently, implying that the scores obtained in these questionnaires may not be directly comparable between genders, which has even broader theoretical and methodological implications for MA research.
Topics: Anxiety; Anxiety Disorders; Female; Humans; Male; Mathematics; Self Concept; Stereotyping
PubMed: 35429357
DOI: 10.1111/nyas.14779