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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 -
Journal of Experimental Child Psychology Aug 2023Identifying the underpinnings of mathematics proficiency is relevant for all societies. A growing literature supports a relation between executive function (EF) and... (Randomized Controlled Trial)
Randomized Controlled Trial
Identifying the underpinnings of mathematics proficiency is relevant for all societies. A growing literature supports a relation between executive function (EF) and mathematics across a wide age range, but causal links are not well understood. In the current study, typically developing preschool children (N = 104) were randomly assigned to one of four training conditions: EF, Number, EF + Number, or an active Control. They participated in three brief training sessions and pretest and posttest sessions measuring EF and mathematics skills. EF training improved EF skills on a task similar to the training but did not extend to an untrained EF task. In addition, the EF training improved number skills but not general mathematics skills. The EF + Number training improved number and general mathematics skills but not EF skills. The EF + Number training did not yield significantly greater benefits for EF and mathematics beyond other training conditions. Finally, differential training effects emerged, such that children with lower pretest EF skills had greater EF benefits on only the trained EF skill. In addition, children from lower versus higher socioeconomic households had greater gains in numerical skills following EF training. No training condition improved verbal knowledge, suggesting that results were specific to the targeted skills. These results extend prior findings on the effectiveness of improving EF and mathematical skills through short-term trainings during early childhood.
Topics: Humans; Child, Preschool; Executive Function; Mathematics
PubMed: 36948040
DOI: 10.1016/j.jecp.2023.105663 -
Brain, Behavior and Evolution 2024Neural exaptations represent descent via transitions to novel neural functions. A primary transition in human cognitive and neural evolution was from a predominantly... (Review)
Review
INTRODUCTION
Neural exaptations represent descent via transitions to novel neural functions. A primary transition in human cognitive and neural evolution was from a predominantly socially oriented primate brain to a brain that also instantiates and subserves science, technology, and engineering, all of which depend on mathematics. Upon what neural substrates and upon what evolved cognitive mechanisms did human capacities for science, technology, engineering, and mathematics (STEM), and especially its mathematical underpinnings, emerge? Previous theory focuses on roles for tools, language, and arithmetic in the cognitive origins of STEM, but none of these factors appears sufficient to support the transition.
METHODS
In this article, I describe and evaluate a novel hypothesis for the neural origins and substrates of STEM-based cognition: that they are based in human kinship systems and human maximizing of inclusive fitness.
RESULTS
The main evidence for this hypothesis is threefold. First, as demonstrated by anthropologists, human kinship systems exhibit complex mathematical and geometrical structures that function under sets of explicit rules, and such systems and rules pervade and organize all human cultures. Second, human kinship underlies the core algebraic mechanism of evolution, maximization of inclusive fitness, quantified as personal reproduction plus the sum of all effects on reproduction of others, each multiplied by their coefficient of relatedness to self. This is the only "natural" equation expected to be represented in the human brain. Third, functional imaging studies show that kinship-related cognition activates frontal-parietal regions that are also activated in STEM-related tasks. In turn, the decision-making that integrates kinship levels with costs and benefits from alternative behaviors has recently been shown to recruit the lateral septum, a hub region that combines internal (from the prefrontal cortex, amygdala, and other regions) and external information relevant to social behavior, using a dedicated subsystem of neurons specific to kinship.
CONCLUSIONS
Taken together, these lines of evidence suggest that kinship systems and kin-associated behaviors may represent exaptations for the origin of human STEM.
Topics: Animals; Humans; Biological Evolution; Brain; Cognition; Engineering; Mathematics; Science; Technology
PubMed: 38368855
DOI: 10.1159/000537908 -
Bio Systems Jul 2021This is a brief overview of Vladimir Voevodsky's (1966-2017) intellectual and professional biography, which is partly based on the author's personal memories....
This is a brief overview of Vladimir Voevodsky's (1966-2017) intellectual and professional biography, which is partly based on the author's personal memories. Voevodsky's biologically-motivated mathematical works are considered in the context of his research in the Algebraic Geometry and in the Univalent Foundations of mathematics. Some biographical details, which are important for understanding Voevodsky's achievements and his personality, are provided.
Topics: Biology; History, 20th Century; History, 21st Century; Mathematics; Russia
PubMed: 33746020
DOI: 10.1016/j.biosystems.2021.104407 -
Journal of Biomedical Informatics Jun 2022Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the... (Review)
Review
Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a "digitization" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the "shape" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics.
Topics: Data Analysis; Diagnostic Imaging
PubMed: 35508272
DOI: 10.1016/j.jbi.2022.104082 -
Cognition Aug 2022Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness,...
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows exponentially as the argument expands. When a mathematician encounters a proof, how does she come to believe it? Here we show that, under a cognitively-plausible belief formation mechanism combining deductive and abductive reasoning, belief in mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. To show this, we analyze an unusual dataset of forty-eight machine-aided proofs from the formalized reasoning system Coq, including major theorems ranging from ancient to 21st Century mathematics, along with five hand-constructed cases including Euclid, Apollonius, Hernstein's Topics in Algebra, and Andrew Wiles's proof of Fermat's Last Theorem. Our results bear both on recent work in the history and philosophy of mathematics on how we understand proofs, and on a question, basic to cognitive science, of how we justify complex beliefs.
Topics: Cognitive Science; Female; Humans; Mathematics; Philosophy; Problem Solving
PubMed: 35405458
DOI: 10.1016/j.cognition.2022.105120 -
Molecular Biology of the Cell Apr 2021In science, technology, engineering, and mathematics (STEM) fields, disabled people remain a significantly underrepresented part of the workforce. Recent data suggests...
In science, technology, engineering, and mathematics (STEM) fields, disabled people remain a significantly underrepresented part of the workforce. Recent data suggests that about 20% of undergraduates in the United States have disabilities, but representation in STEM fields is consistently lower than in the general population. Of those earning STEM degrees, only about 10% of undergraduates, 6% of graduate students, and 2% of doctoral students identify as disabled. This suggests that STEM fields have difficulty recruiting and retaining disabled students, which ultimately hurts the field, because disabled scientists bring unique problem-solving perspectives and input. This essay briefly explores the ways in which ableism-prejudice against disabled people based on the assumption that they are "less than" their nondisabled peers-in research contributes to the exclusion of disabled scientists and suggests ways in which the scientific community can improve accessibility and promote the inclusion of disabled scientists in academic science.
Topics: Engineering; Humans; Mathematics; Prejudice; Science; Students; Technology; United States
PubMed: 33793322
DOI: 10.1091/mbc.E20-09-0616 -
Journal of Experimental Child Psychology Feb 2022A robust association between young children's early mathematical proficiency and later academic achievement is well established. Less is known about the mechanisms...
A robust association between young children's early mathematical proficiency and later academic achievement is well established. Less is known about the mechanisms through which early mathematics skills may contribute to later mathematics and especially reading achievement. Using a parallel multiple mediator model, the current study investigated whether executive function (integration of working memory, inhibition, and cognitive flexibility) can explain the relations between early mathematics skills and elementary school mathematics and reading achievement. Data in this longitudinal study were collected from 243 children during the last year of early childhood education and care (kindergarten ages 5 and 6 years), 1 year later in first grade, and 5 years later when the children were in fifth grade. Background variables (maternal education, age, sex, and immigrant status), kindergarten baseline skills, and mediating effects of first-grade mathematics, phonological awareness, vocabulary, and possible omitted variables were controlled. Results showed that first-grade executive function mediated the effects of kindergarten mathematics on fifth-grade mathematics and on reading achievement. These findings suggest that executive function may work as a mechanism that may help to explain the frequently found strong association between children's early mathematics skills and later mathematics and reading achievement.
Topics: Achievement; Child; Child, Preschool; Executive Function; Humans; Longitudinal Studies; Mathematics; Reading
PubMed: 34655996
DOI: 10.1016/j.jecp.2021.105306 -
Zhonghua Yu Fang Yi Xue Za Zhi [Chinese... Apr 2021The interspecies transmission of pathogens among multiple hosts is a complex dynamic process, which poses a severe challenge to the reliability of the early warning... (Review)
Review
The interspecies transmission of pathogens among multiple hosts is a complex dynamic process, which poses a severe challenge to the reliability of the early warning system of zoonotic infectious diseases. By introducing the theories and methods of infectious disease ecology, this paper reviews and summarizes the study of the interaction among pathogens, hosts and environment through the dynamic mathematical model of environment-host-infectious diseases, and also includes research paradigm for quantifying the effects of environment on epidemic trends, vectors and pathogenic microorganisms. Taking the study of -type hemorrhagic fever with renal syndrome, also known as epidemic hemorrhagic fever, in China as an example, the application of mathematical model of infectious diseases in actual prediction and early warning of epidemic situation is introduced, and new monitoring indexes and early warning methods is further developed.
Topics: Animals; China; Humans; Mathematics; Models, Theoretical; Reproducibility of Results; Zoonoses
PubMed: 33858072
DOI: 10.3760/cma.j.cn112150-20201130-01407 -
Advances in Wound Care Jun 2021For over 30 years, there has been sustained interest in the development of mathematical models for investigating the complex mechanisms underlying each stage of the... (Review)
Review
For over 30 years, there has been sustained interest in the development of mathematical models for investigating the complex mechanisms underlying each stage of the wound healing process. Despite the immense associated challenges, such models have helped usher in a paradigm shift in wound healing research. In this article, we review contributions in the field that span epidermal, dermal, and corneal wound healing, and treatments of nonhealing wounds. The recent influence of mathematical models on biological experiments is detailed, with a focus on wound healing assays and fibroblast-populated collagen lattices. We provide an overview of the field of mathematical modeling of wound healing, highlighting key advances made in recent decades, and discuss how such models have contributed to the development of improved treatment strategies and/or an enhanced understanding of the tightly regulated steps that comprise the healing process. We detail some of the open problems in the field that could be addressed through a combination of theoretical and/or experimental approaches. To move the field forward, we need to have a common language between scientists to facilitate cross-collaboration, which we hope this review can support by highlighting progress to date.
Topics: Animals; Humans; Mathematics; Models, Theoretical; Wound Healing
PubMed: 32634070
DOI: 10.1089/wound.2019.1132