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PubMed1998

A process approach to describing mathematics difficulties in girls with Turner syndrome.

OBJECTIVE: To expand on previous reports of mathematics difficulty in girls with Turner syndrome (TS). METHODS: Mathematics performance was examined by evaluating the types of errors made on mathematics achievement subtests by 29 girls with TS, 26 girls with fragile X syndrome (another genetic condition associated with mathematics difficulty), and 41 girls with neither disorder. Correlations between mathematics achievement scores and measures of IQ, attention, and visuospatial skills were also examined. RESULTS: Relatively low mathematics achievement was evident in girls with TS before 10 years of age, and a higher percentage of girls with TS made operation (57%) and alignment (48%) errors on a mathematics calculations test than did girls with fragile X syndrome (19% and 14%, respectively). No group differences were found for procedural or multiplication table errors. Girls with TS attempted more "unfamiliar" problems than did girls with fragile X syndrome or girls in the comparison group. Mathematics achievement scores in girls with TS were positively correlated with Judgment of Line Orientation and Wechsler Intelligence Scale for Children-Revised Third Factor scores; these correlations differed from those in the other groups. CONCLUSIONS: The qualitative group differences observed further support the concept of specificity of the TS phenotype and illustrate the importance of a process approach to assessment.

Adolescent↗
PubMed2002

Oncologic mathematics: evolution of a new specialty.

HYPOTHESIS: Mathematical methods and their derivatives have practical applications to oncology. They can be used to describe fundamental aspects of tumor behavior, such as loss of genetic stability, tumor growth, immunologic identity, genesis of diversity, and methods of prognosticating cancer. DATA SOURCES: Descriptive models and published literature in the fields of oncology and applied mathematics. DATA SYNTHESIS: Cancer does not conform to simple mathematical principles. Its irregular mode of carcinogenesis, erratic tumor growth, variable response to tumoricidal agents, and poorly understood metastatic patterns constitute highly variable clinical behavior. Defining this process requires an accurate understanding of the interactions between tumor cells and host tissues and ultimately determines prognosis. Applying time-tested and evolving mathematical methods to oncology may provide new tools with inherent advantages for the description of tumor behavior, selection of therapeutic modes, prediction of metastatic patterns, and providing an inclusive basis for prognostication. We term this combined field of research "oncologic mathematics." As surgeons, we have the unique opportunity to be active participants and assume leadership in research that affects selection of the optimal anticancer treatment for our patients. Mathematicians describe equations that define tumor growth and behavior, whereas surgeons actively deal with biological processes. Oncologic mathematics applies these principles to clinical settings. CONCLUSION: Experimentally testable, oncologic mathematics may provide a framework to determine clinical outcome on a patient-specific basis and increase the growing awareness that mathematical models help simplify seemingly complex and random tumor behavior.

Disease Progression↗
PubMed2006

Angiogenesis - understanding the mathematical challenge.

Biological mathematics is based on the development of mathematical descriptions of biological systems and behaviour. We are interested in developing mathematical models of capillary sprouting, and have adopted a novel approach to our modelling, in that the mathematics is based on the biochemistry underpinning cell behaviour. By considering the crucial steps of the angiogenic process, and through an understanding of the biochemistry involved, we successfully developed a preliminary model of angiogenesis. More importantly, our approach is applicable to many other areas of biological research. As mathematics remains a mystery to the majority of life scientists, we have aimed to describe our mathematical modelling strategy in biological terms. The assumptions and simplifications that form the basis of the modelling are explained, pinpointing the manner in which the different biological processes are linked via the mathematics. Examples of simulations using the mathematical model are shown, highlighting the success of our approach.

Angiopoietins↗
PubMed2006

Mathematical models and the experimental analysis of behavior.

The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make equally accurate predictions for a large body of data. In such cases, it is important to find and investigate situations for which the competing models make different predictions because, unless two models are actually mathematically equivalent, they are based on different assumptions about the psychological processes that underlie an observed behavior. Mathematical models developed in basic behavioral research have been used to predict and control behavior in applied settings, and they have guided research in other areas of psychology. A good mathematical model can provide a common framework for understanding what might otherwise appear to be diverse and unrelated behavioral phenomena. Because psychologists vary in their quantitative skills and in their tolerance for mathematical equations, it is important for those who develop mathematical models of behavior to find ways (such as verbal analogies, pictorial representations, or concrete examples) to communicate the key premises of their models to nonspecialists.

Humans↗
PubMed2006

The presence of mathematics and computer anxiety in nursing students and their effects on medication dosage calculations.

AIM: To determine if the presence of mathematical and computer anxiety in nursing students affects learning of dosage calculations. METHOD: The quasi-experimental study compared learning outcomes at differing levels of mathematical and computer anxiety when integrative and computer based learning approaches were used. Participants involved a cohort of second year nursing students (n=97). RESULTS: Mathematical anxiety exists in 20% (n=19) of the student nurse population, and 14% (n=13) experienced mathematical testing anxiety. Those students more anxious about mathematics and the testing of mathematics benefited from integrative learning to develop conditional knowledge (F(4,66)=2.52 at p<.05). Computer anxiety was present in 12% (n=11) of participants, with those reporting medium and high levels of computer anxiety performing less well than those with low levels (F(1,81)=3.98 at p<.05). CONCLUSION: Instructional strategies need to account for the presence of mathematical and computer anxiety when planning an educational program to develop competency in dosage calculations.

Analysis of Variance↗
PubMed1998

The effects of spatial visualization and students' sex on mathematical achievement.

Sex differences in mathematical achievement and spatial visualization skill were examined in a sample of 724 Norwegian sixth-grade students. Boys had significantly higher mean mathematics scores than girls. Significant sex differences favouring boys were found in the subsamples of most difficult tasks, but not in the subsamples of easiest tasks. No significant sex difference in spatial visualization was found. The hypothesis that boys' superior achievement in mathematics is due to a superior ability in spatial visualization was not supported. Although the effect of spatial visualization on mathematical achievement increased significantly up to a certain level of mathematics task difficulty, the hypothesis that the effect of spatial visualization on mathematical achievement increases with increasing task difficulty was not fully supported. With increasing mathematics task difficulty, it is hypothesized that boys, more than girls, will benefit from spatial visualization. This hypothesis was not supported by the present elementary school data.

Achievement↗
PubMedDate not supplied

Educational assessment of mathematics skills and abilities.

Mathematics assessments play a valuable role in identifying students' strengths and weaknesses and in developing and monitoring instructional practice. Over the last century, mathematics assessment has been refined as math content has changed as a result of curriculum reform. Today, researchers and practitioners use various assessment techniques to (a) identify students who have mathematics learning disabilities (LD), (b) target individual strengths and weaknesses across mathematics areas, (c) document the effects of mathematics instruction in a remedial or special program, (d) identify strategies that students employ during math activities, (e) conduct research about the characteristics of students with math LD, and (f) examine the technical characteristics of mathematics tests. This article provides an historical overview of the development of mathematics assessment and a description of specific strategies for conducting math evaluations.

Educational Measurement↗
PubMed1998

Mathematics preparation and professional development of deaf education teachers.

With the world increasingly dependent on mathematics and problem-solving skills, the poor mathematics performance of deaf and hard of hearing students is cause for concern. The present article focuses on the mathematics competency of teachers of deaf and hard of hearing students as a factor in this poor performance. As part of a larger study (Pagliaro, 1996, 1998a), deaf education teachers provided data on their postsecondary education and their professional development activities related to mathematics. Administrators were also questioned to investigate the schools' contribution to these activities. Results reveal an insufficient level of mathematics preparation among deaf education teachers, especially at the high school level. Few hold degrees in a mathematics-related field, and only a moderate number seek professional development in this discipline. Recommendations for improving the mathematics competencies of deaf education teachers are provided, with the objective of improving student performance.

Deafness↗
PubMed2006

Attitudes toward and approaches to learning first-year university mathematics.

This study examined the relationship for 180 undergraduate students enrolled in a first-year university calculus course between attitudes toward mathematics and approaches to learning mathematics using the Mathematics Attitude Scale and the Approaches to Learning Mathematics Questionnaire, respectively. Regression analyses indicated that scores for the Mathematics Attitude Scale were negatively related to scores for the Surface Approach and accounted for 10.4% of the variance and scores for the Mathematics Attitude Scale were positively related to scores for the Deep Approach to learning mathematics and accounted for 31.7% of the variance.

Adult↗
PubMed1990

Mathematics achievement of children in China and the United States.

First and fifth graders in Beijing and Chicago were given a battery of mathematics test. Whether tested with problems requiring solely computation or with ones requiring application of knowledge about mathematics, American children's performance was consistently inferior to that of Chinese children. Interviews with American children suggested that they like mathematics, believe they are doing well in mathematics, and do not perceive mathematics as a difficult subject. American children's poor performance appears to be attributable, in part, to low motivation for devoting more attention to mathematics. Low standards held by American parents for academic achievement and lower interest in teaching mathematics by American teachers appear to contribute to American children's poor performance.

Achievement↗
PubMed1993

Boys and girls who reason well mathematically.

Since 1971 the Study of Mathematically Precocious Youth (SMPY) at Johns Hopkins University has pioneered in discovery of and provision of educational help for 12-year-old boys and girls who reason better mathematically than 99% of other 12-year-olds. SMPY originated widespread searches for such youths and special academic classes for them outside the regular school system. A regional talent search, verbal as well as mathematical, now covers all 50 states of the USA, and many varied residential summer programmes are offered across the country. These have provided educational facilitation for many thousands, and have encouraged greater curricular flexibility in schools and better articulation of in-school with out-of-school learning experiences. From the first talent search conducted by SMPY in 1972, it became obvious that boys tend to score considerably higher than girls on the College Board Scholastic Aptitude Test-Mathematical (SAT-M), a test intended mainly for college-bound 17- and 18-year-olds. This difference was reported in 1974 but attracted little attention until a controversial report in 1980 stimulated research on sex differences in various aspects of mathematics. Here I describe a study of sex differences over 10 years on 14 College Board high school achievement tests, which are taken (three usually) by bright 17- and 18-year-olds seeking admission to the USA's selective colleges and universities. Among the high scores on the European history test the ratio of males to females was greatest, 6:1. The next most sex-differentiating test was physics, 2.9:1, followed by elementary-level mathematics (mainly algebra and geometry), 2.5:1. Other ratios favouring males were, in 1991, chemistry (2.4:1), American history (2.1:1), biology (1.8:1), precalculus mathematics (1.6:1), Latin (1.6:1), French (1.4:1), modern Hebrew (1.1:1) and German (1.02:1). Tests in which more females were high scorers were literature (1.26:1), English composition (1.05:1) and Spanish (1.01:1). The largest sex differences on other standardized tests, for mechanical reasoning and spatial rotation, favour males. There are even larger differences for self-reported evaluative attitudes, with the theoretical value high for boys and the aesthetic high for girls. Such value scores correlated strangely with scores on achievement and aptitude tests. By 12 or younger, bright boys and girls already show many of the cognitive sex differences found in 18-year-olds.

Adolescent↗
PubMed1976

Mathematics and the surgeon.

The surgeon uses elementary mathematics just as much as any other educated layman. In his professional life, however, much of the knowledge and skill on which he relies has had a mathematical strand in its development, possibly woven into the supporting disciplines such as physics, chemistry, biology, and bioengineering. The valves and limitations of mathematical models are examined briefly in the general medical field and particularly in relation to the surgeon. Arithmetic and statistics are usually regarded as the most immediately useful parts of mathematics. Examples are cited, however, of medical postgraduate work which uses other highly advanced mathematical techniques. The place of mathematics in postgraduate and postexperience teaching courses is touched on. The role of a mathematical consultant in the medical team is discussed.

Computers↗
PubMed1996

Tracer kinetic modelling of receptor data with mathematical metabolite correction.

Quantitation of metabolic processes with dynamic positron emission tomography (PET) and tracer kinetic modelling relies on the time course of authentic ligand in plasma, i.e. the input curve. The determination of the latter often requires the measurement of labelled metabolites, a laborious procedure. In this study we examined the possibility of mathematical metabolite correction, which might obviate the need for actual metabolite measurements. Mathematical metabolite correction was implemented by estimating the input curve together with kinetic tissue parameters. The general feasibility of the approach was evaluated in a Monte Carlo simulation using a two tissue compartment model. The method was then applied to a series of five human carbon-11 iomazenil PET studies. The measured cerebral tissue time-activity curves were fitted with a single tissue compartment model. For mathematical metabolite correction the input curve following the peak was approximated by a sum of three decaying exponentials, the amplitudes and characteristic half-times of which were then estimated by the fitting routine. In the simulation study the parameters used to generate synthetic tissue time-activity curves (K1-k4) were refitted with reasonable identifiability when using mathematical metabolite correction. Absolute quantitation of distribution volumes was found to be possible provided that the metabolite and the kinetic models are adequate. If the kinetic model is oversimplified, the linearity of the correlation between true and estimated distribution volumes is still maintained, although the linear regression becomes dependent on the input curve. These simulation results were confirmed when applying mathematical metabolite correction to the [11C]iomazenil study. Estimates of the distribution volume calculated with a measured input curve were linearly related to the estimates calculated using mathematical metabolite correction with correlation coefficients >0.990. However, the slope of the regression line displayed considerable variability among the subjects (0.33-0.95), demonstrating that absolute quantitation of the distribution volume was impaired. Mathematical metabolite correction is a feasible method and may prove useful in cases where actual metabolite data cannot be obtained. The potential for absolute quantitation seems limited, but the method allows the quantitative assessment of regional ratios of receptor measures.

Adult↗
PubMed2005

RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

Catheter Ablation↗
PubMed1981

Mathematic coupling of data: a common source of error.

The relationship between two variables may be mathematically coupled if either one or both variables are derived and/or calculated, and this can lead to erroneous results and invalid conclusions. The purpose of this report is to identify four types of mathematic coupling of data. Type 1 coupling involves directional changes in two variables which are mathematically coupled. Type 2 coupling is the functional relationship between two calculated variables which have one or more common component variables. Type 3, the most common type of mathematic coupling, is direct algebraic coupling between two variables, when one or more of the variables is derived and/or calculated. Type 4 is indirect coupling or physiologic coupling. The common problem in each type of mathematic coupling is that one variable either directly or indirectly contains the whole or components of the second variable. Statistical techniques, when properly applied to the relationship between the two variables, further obscure the underlying mathematic coupling, and tend to support the erroneous results. Recognition of mathematic coupling is imperative for correct data analysis and accurate interpretation.

Statistics as Topic↗
PubMed2003

Will the digital computer transform classical mathematics?

Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.

Artificial Intelligence↗
PubMed1996

Nuclear medicine and mathematics.

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently used in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: they are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new "allies" of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking.

Artificial Intelligence↗
PubMed2005

Finnish nurses' and nursing students' mathematical skills.

The health care environment requires that practitioners have sufficient mathematical skills to perform accurate, safe and effective medication administration. This is a highly responsible and nursing task, which is performed daily. In this study 364 nurses and 282 graduating nursing students in Finland completed the Medication Calculation Skills Test (MCS Test). According to the findings students lacked accurate mathematical skills, while nurses attained higher scores in the test. Nurses with an upper secondary school education managed better with the calculation problems than nurses with a lower basic education. Students who had an excellent mark (9-10) in mathematics, had studied mathematics longer at high school and were more satisfied with the amount of medication calculation instructions and scored higher in the MCS Test than others. The differences between the nurses' and students' mathematical skills were significant. The MCS Test could be used to measure one's own skills and to give information of the mathematical skill level for constructing a nursing curriculum or additional training for clinical practice.

Adult↗