Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “MATHEMATICS”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10Linked to original sources

The wrath of math. Deficiencies of mathematical mastery in the school child.

Mastery of mathematics involves the interactions of multiple developmental pathways. Children with mathematics disabilities often experience profound feelings of intellectual inadequacy that can erode self-esteem and academic motivation. This article delineates 16 interactive subcomponents that students who underachieve in mathematics can encounter. The article also discusses assessment and management issues for children with mathematics disabilities.

Child↗

The mathematical and military sciences in Renaissance England.

The Renaissance saw the evolution of troop management, fortification and artillery into 'mathematical' sciences and those who practiced these tasks into 'mathematical practitioners'. These terms have been allowed to imply that these areas were deeply theoretical, whereas they varied from theoretical to simply numerical. Gunnery, in particular, tended towards the latter. Practitioners of the simpler mathematics, however, gained by being able to connect their action to the more impressive study of 'the mathematicks'. Future work must recognize more critically the distinction inherent in the term 'mathematical' when applied to the arts of the Renaissance.

England↗

Mathematical modeling and analysis in biochemical engineering: past accomplishments and future opportunities.

This is a personal commentary on the history and future prospects of mathematical modeling and analysis in biochemical engineering. Major transitions in these fields were driven by the appearance of the Aiba, Humphrey, and Millis text, Fredrickson's guidance on conceptualizing mathematical representations of cell populations, and Ramkrishna's development of the cybernetic modeling approach. The value of mathematical models to organize data, to consider interactions in complex systems in a rational way, to correct the conventional wisdom, and to understand essential qualitative features of biological systems has been clearly documented in prior research. The impact of this research in biotechnology discovery has so far been limited, but this will change in the future if we are adept in recognizing emerging opportunities and in integrating new concepts and tools into our research. Mathematical structures and methods, allied with extraordinary contemporary computing power, are essential to the emerging field of functional genomics. Important in this quest is a hierarchy of powerful modeling, analysis, and computational tools which can capture essential quantitative features of available experimental data and use these effectively for analysis and design of metabolism.

Animals↗

Comorbidity of mathematics and reading deficits: evidence for a genetic etiology.

In order to assess the genetic etiology of the comorbidity of reading and mathematics difficulties, data were ascertained from two samples: (1) 102 identical and 77 same-sex fraternal twin pairs in which at least one member of each pair is reading disabled and (2) 42 identical and 23 same-sex fraternal twin pairs in which at least one member is math disabled. Composite reading and mathematics performance data from each sample were fitted to the basic multiple regression model for the analysis of selected twin data and its bivariate extension. Resulting estimates of bivariate heritability and the genetic correlation between the reading and the mathematics performance measures suggest that the comorbidity between mathematics and reading difficulties is due in part to genetic influences.

Adolescent↗

Neural substrates of mathematical reasoning: a functional magnetic resonance imaging study of neocortical activation during performance of the necessary arithmetic operations test.

Brain activation was examined using functional magnetic resonance imaging during mathematical problem solving in 7 young healthy participants. Problems were selected from the Necessary Arithmetic Operations Test (NAOT; R. B. Ekstrom, J. W. French, H. H. Harman, & D. Dermen, 1976). Participants solved 3 types of problems: 2-operation problems requiring mathematical reasoning and text processing, 1-operation problems requiring text processing but minimal mathematical reasoning, and 0-operation problems requiring minimal text processing and controlling sensorimotor demands of the NAOT problems. Two-operation problems yielded major activations in bilateral frontal regions similar to those found in other problem-solving tasks, indicating that the processes mediated by these regions subserve many forms of reasoning. Findings suggest a dissociation in mathematical problem solving between reasoning, mediated by frontal cortex, and text processing, mediated by temporal cortex.

Adult↗

Maternal affection moderates the impact of psychological control on a child's mathematical performance.

This study investigated the extent to which mothers' psychological control predicts their children's mathematical performance during the children's transition from preschool to primary school over and above the impact of maternal affection and behavioral control. Also investigated was the extent to which maternal affection and behavioral control moderate the impact of mothers' psychological control. Children 5-6 years old at baseline (N=196) were followed up 6 times to measure their performance in mathematics over a 3-year period from preschool to 2nd grade. Mothers were asked to fill in a questionnaire measuring their parenting styles once every year over the 3-year period. A high level of psychological control exercised by mothers predicted their children's slow progress in mathematics. However, this impact was particularly evident among those children whose mothers reported a high level of affection. No evidence was found that children's mathematical performance had any effect on their mothers' parenting styles.

Adult↗

Preschool children's mathematical knowledge: The effect of teacher "math talk.".

This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year.

Achievement↗

Gender differences in mathematics performance: a meta-analysis.

Reviewers have consistently concluded that males perform better on mathematics tests than females do. To make a refined assessment of the magnitude of gender differences in mathematics performance, we performed a meta-analysis of 100 studies. They yielded 254 independent effect sizes, representing the testing of 3,175,188 Ss. Averaged over all effect sizes based on samples of the general population, d was -0.05, indicating that females outperformed males by only a negligible amount. For computation, d was -0.14 (the negative value indicating superior performance by females). For understanding of mathematical concepts, d was -0.03; for complex problem solving, d was 0.08. An examination of age trends indicated that girls showed a slight superiority in computation in elementary school and middle school. There were no gender differences in problem solving in elementary or middle school; differences favoring men emerged in high school (d = 0.29) and in college (d = 0.32). Gender differences were smallest and actually favored females in samples of the general population, grew larger with increasingly selective samples, and were largest for highly selected samples and samples of highly precocious persons. The magnitude of the gender difference has declined over the years; for studies published in 1973 or earlier d was 0.31, whereas it was 0.14 for studies published in 1974 or later. We conclude that gender differences in mathematics performance are small. Nonetheless, the lower performance of women in problem solving that is evident in high school requires attention.

Aptitude↗

Sex, handedness, mathematical ability, and biological causation.

An important part of Benbow's (1988) assertion that sex differences in mathematical ability are primarily due to biological factors is the link between a trait that is assumed to reflect differences in brain organization (left-handedness) and mathematical giftedness. It is shown that the link between mathematical giftedness and an increased prevalence of left-handedness is not convincing. However, Benbow's (1986) data do show a convincing link between strong right-handedness and the lack of mathematical giftedness, in agreement with Annett and Manning's (1990a, 1990b) recent work.

Aptitude↗

A new mathematical formula for predicting long bone length in early pregnancy.

OBJECTIVE: To propose new mathematical formulae to estimate fetal long bone biometry in early pregnancy and to establish their efficacy in comparison to previously constructed mathematical formulae. METHODS: A study population of 1960 singleton euploid fetuses was referred for transvaginal ultrasound examinations between 71 and 112 days of gestation prior to genetic amniocentesis. To determine the relationship between the biparietal diameter and long bone length, a sample group of 400 randomly chosen normal fetuses was evaluated. Regression equations were derived, then tested in the remaining 1560 control fetuses and compared with previously reported mathematical formulae by other authors. Mean absolute error, mean absolute percentage error and mean systematic error with their standard deviations were calculated. RESULTS: The relationships between femur or humerus length vs. biparietal diameter (BPD) and gestational age (GA) were, respectively: expected femur length = -16.92108 + 0.4569402 x BPD + 0.171617 x GA (P < 0.001) and expected humerus length = -16.28531 + 0.4283019 x BPD + 0.1696017 x GA (P < 0.001). The confidence intervals of the predicted values for different values of biparietal diameter and gestational age and confidence intervals for the regression coefficients, such as the distribution of the residuals, are given. All previous formulae obtained by transabdominal ultrasound demonstrated an overestimation of expected long bones measurements; this was reduced using different formulae obtained in early pregnancy. Using our mathematical formulae, the mean absolute percentage error and the mean systematic error in estimating femur and humerus length were very low (11.15% and -2.02%; 10.59% and -1.74%, respectively). CONCLUSIONS: The new ultrasonographic morphometric models derived from transvaginal measurements in early pregnancy show a good reliability in estimating fetal long bone length.

Female↗

Anxiety, cognitive style, and mathematics achievement.

This study examined the relationship among state and trait anxiety, cognitive style, and mathematics achievement. The Ss were 50 junior college students enrolled in a mathematics course. The results confirmed the hypothesis that high state anxiety would be associated with poor mathematics achievement; trait anxiety showed no significant relationship to achievement. The need to develop learning aids and strategies to counteract the possible debilitating effects of state anxiety in learning and mathematics assessment was discussed.

Achievement↗

Geometric problem solving related to differences in sex and mathematical interests.

Sex differences in Einstellung Effects were confounded by attitudinal factors. Hypothesizing that this was the case for spatial visualization and restructurization, we compared male and female college students' solutions of three elementary geometric problems. Used by Max Wertheimer to study productive thinking, they call for a Gestalt, spatial approach. In group administration to 86 calculus students, males did somewhat better than females, but the reverse held in classes where most women majored in mathematics. Individual administration to 200 Ss, balanced for sex and major, showed that female mathematics majors had more solutions than other females: e.g., 51 percent more compared to 26 percent sex differences. Four hints were available for restructuring each problem. The percentage needing all four hints was highest for male nonmathematics major and next highest for female mathematics majors (e.g., 75 and 23 percent, respectively). Embarrassment at needing hints in such "easy problems" and ego-involvement were factors. Thus, sex differences were less pronounced than differences related to mathematical abilities and interests and to task-and ego-concerns.

Adult↗

Math anxiety, mother's education, and the mathematics performance of adolescent boys and girls: evidence from the United States and Thailand.

In this study, I investigated the relationship of mathematics performance to math anxiety, mother's education, and gender. A secondary analysis was conducted using nationally representative samples of 13-year-old children in the United States (N = 4,091) and Thailand (N = 3,613) collected as a part of the Second International Mathematics Study (Garden, 1987). Separate ANOVAs (Math Anxiety x Mother's Education x Gender) were run within each country using a 40-item math performance test as the dependent variable. Math anxiety has an inverse relationship with mathematics performance in the United States (r = -.24) and in Thailand (r = -.14). The relationship between math anxiety and mathematics performance is significant in both countries after controlling for previous achievement, mother's education, and gender, although the data suggest that there is a three-way interaction between math anxiety, mother's education, and gender in Thailand.

Achievement↗

Do medical students with A-level mathematics have a better understanding of the principles behind evidence-based medicine?

With the advent of evidence-based medicine, medical students, doctors and other healthcare professionals are required to be more skilled in the interpretation and manipulation of numerical data. The authors observed that undergraduate students without A-level mathematics expressed concern as to their ability to cope with an epidemiology and biostatistics course. It was hypothesized that these anxieties reflected differences in attitudes to numerical manipulation rather than any real lack of competence. Mean exam performance scores were compared for 498 first-year medical students between 2000 and 2002 depending on whether the students did or did not have A-level mathematics. The data revealed no difference in performance. Students without mathematics A-level scored marginally worse (-1.1%, 95% CI -3.1% to 0.8%, p=0.20) but were no more likely to fail the exam (odds ratio=0.98, 95% CI 0.40 to 2.6, p=0.9). It is concluded that some students experience 'numerophobia'-- a perceived and, it is thought, disproportionate fear of numbers and simple mathematical manipulation. This may act as a psychological barrier for future evidence-based practitioners.

Adult↗

Mathematical constraints and the Tulving-Wiseman law: a rejoinder.

Hintzman (1991; 1992) has claimed that the reason data points approximate the recognition failure function discovered by Tulving and Wiseman (1975) is that they are mathematically constrained to do so, and the reason that a few data points do not approximate the function, but are exceptions to it, is that these data points are less subject to mathematical constraints. He has additionally argued that such exceptions are more likely with low levels of recall and strong underlying sources of positive covariance. We provide empirical evidence relevant to this mathematical model using 301 observations from a database of all relevant experimental conditions published between 1973 and 1992 (Nilsson & Gardiner, 1993). We conclude that mathematical constraints have only a minor influence on the function, not the causal role assigned to them in Hintzman's (1992) model. By our account, both the function and exceptions to it reflect a single psychological principle, the functional effectiveness of contextual cues.

Cues↗

Mathematical aspects of impedance imaging.

The mathematical problem of reconstructing the unknown variable conductivity of an isotropic medium from a knowledge of boundary currents and voltages is an active area of mathematical research. In terms of impedance imaging the analytical problem is essentially the question 'is there only one conductivity distribution which could have produced this set of measurements?' In mathematical parlance this is an 'identification problem' or 'inverse problem' for an unknown coefficient in an elliptic partial differential equation. Recent results have come close to settling the analytical problem. Kohn and Vogelius have shown that the piece-wise analytic conductivity distributions can be identified by boundary measurements and Sylvester and Uhlmann have shown that a smooth conductivity can be identified in the three-dimensional case and, provided the conductivity is close enough to uniformity, in the two-dimensional case also. The practical numerical problem of designing a numerical algorithm is far from completely understood. Mathematically the problem is one of solving a non-linear functional equation. A common numerical technique for tackling this type of problem is to employ the Newton-Raphson method. This approach is considered in this paper and compared with some of the algorithms appearing in the bioengineering literature. It is observed that, to varying degrees, these methods approximate the Newton-Raphson method.

Algorithms↗

Mathematical simulation and analysis of cellular metabolism and regulation.

MOTIVATION: A better understanding of the biological phenomena observed in cells requires the creation and analysis of mathematical models of cellular metabolism and physiology. The formulation and study of such models must also be simplified as far as possible to cope with the increasing complexity demanded and exponential accumulation of the metabolic reconstructions computed from sequenced genomes. RESULTS: A mathematical simulation workbench, DBsolve, has been developed to simplify the derivation and analysis of mathematical models. It combines: (i) derivation of large-scale mathematical models from metabolic reconstructions and other data sources; (ii) solving and parameter continuation of non-linear algebraic equations (NAEs), including metabolic control analysis; (iii) solving the non-linear stiff systems of ordinary differential equations (ODEs); (iv) bifurcation analysis of ODEs; (v) parameter fitting to experimental data or functional criteria based on constrained optimization. The workbench has been successfully used for dynamic metabolic modeling of some typical biochemical networks (Dolgacheva et al., Biochemistry (Moscow), 6, 1063-1068, 1996; Goldstein and Goryanin, Mol. Biol. (Moscow), 30, 976-983, 1996), including microbial glycolytic pathways, signal transduction pathways and receptor-ligand interactions. AVAILABILITY: DBsolve 5. 00 is freely available from http://websites.ntl.com/ approximately igor.goryanin. CONTACT: gzz78923@ggr.co.uk

Algorithms↗

The effects of measurement error on previously reported mathematical relationships between indicator organism density and swimming-associated illness: a quantitative estimate of the resulting bias.

Several recent epidemiological studies seeking associations between swimming in recreational waters contaminated with domestic sewage and increased illness among such swimmers have reported mathematical relationships relating indicator organism densities to illness among swimmers. Common to the design of all of these studies is the failure to adequately control for large amounts of measurement error contained in estimates of exposure, i.e. estimated indicator organism densities. The limited precision of current methods of indicator organism enumeration, coupled with temporal and spacial variation in indicator organism densities at the locations studied, are responsible for a substantial portion of this measurement error. The failure to control adequately for these sources of measurement error has resulted in a significant amount of bias being present in the mathematical relationships reported by these previously published epidemiological studies. In order to explore the magnitude and direction of this bias, computer simulations were conducted using data in which estimation of indicator organism density was obtained by the two most widely used techniques of enumeration: the Multiple Tube Fermentation Technique and the Membrane Filtration Technique. The results of the computer simulations show that the bias caused by this measurement error is non-differential causing the mathematical relationships between indicator organism density and swimming-associated illness reported in previous epidemiological studies to underestimate true risk by a minimum of approximately 14%, and that this underestimate could range as high as approximately 30 to 57%. This study also demonstrates that substantial reduction of this bias can be easily accomplished by incorporating a formal water quality sampling strategy, based on statistical principles of experimental design and analysis, into the design of future epidemiological studies seeking mathematical relationships between indicator organism density and swimming-associated illness.

Analysis of Variance↗