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PubMed1987

Mathematics classrooms in Japan, Taiwan, and the United States.

Observations were conducted in Chinese, Japanese, and American classrooms during mathematics classes. Activities in 20 representative classrooms were observed in each of 2 grades (1 and 5) and in each country. Some observations focused on individual children and others on the teachers. Large cross-cultural differences were found in many variables related to classroom structure and management. These differences paralleled differences in achievement in mathematics among the 3 countries. A number of these variables also were significantly related to average level of mathematics achievement within the American classrooms.

Achievement↗
PubMed1986

[Use of mathematical theory in experiments evaluating the protective properties of antimicrobial preparations].

Mathematical design of multifactorial experiments in investigation of protective properties of antimicrobial drugs provided acceleration of preclinical study of new antimicrobial drugs, increasing its level and decreasing its size and cost. The advantage of the experiment mathematical design in investigation and estimation of protective properties of antimicrobial drugs was shown on a model of doxycycline chemotherapy of experimental anthracic infection caused by the vaccinal strain of the causative agent in albino mice. Second order quasi-D-optimal plans for 3-, 4- and 5-factorial experiments are presented and variation ranges of the main factors affecting chemotherapeutic activity of antimicrobial drugs are recommended: daily doses of the antibiotic, the inoculum size, the time of chemotherapy initiation after inoculation and the period of the preventive treatment. The main advantages of the experiment mathematical design in preclinical chemotherapy, along with economic utilization of experimental animals, are the following: possible estimation of the effect of every of the active factors on drug protective properties, objective evaluation of protective activity of drugs under various regimens of their use and feasibility of developing optimal schemes for drug use.

Animals↗
PubMed1985

The coordination of arm movements: an experimentally confirmed mathematical model.

This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. Experimental observations of human subjects performing voluntary unconstrained movements in a horizontal plane are presented. They confirm the following predictions of the mathematical model: unconstrained point-to-point motions are approximately straight with bell-shaped tangential velocity profiles; curved motions (through an intermediate point or around an obstacle) have portions of low curvature joined by portions of high curvature; at points of high curvature, the tangential velocity is reduced; the durations of the low-curvature portions are approximately equal. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.

Arm↗
PubMed1980

[Flow rates in the isolated perfused rat liver by pulse labeling with radioactive substrates and mathematical analysis of the wash-out kinetics].

The multiple indicator dilution technique (Goresky and Bach) is critically evaluated and its application to the isolated, hemoglobin-free perfused rat liver is described. From the results of pulse labelling experiments using indicator substances for the total aqueous space of the liver ([3H]water and [14C]urea) an for the extracellular space ([14C]sucrose, [3H]-inulin and [3H]dextrane), it is concluded that the mathematical model of the liver in situ according to Goresky and Bach is sufficient to also describe the hemodynamics of the isolated liver perfused with a saline solution. The data indicate that the multiple indicator dilution technique in combination with the available mathematical basis is applicable to the study of transport across the liver cell membrane. The method, however, is restricted to compounds which are metabolized very slowly, such as D-lactate. A possible extension of this method to metabolic processes is discussed in view of pulse labelling experiments with [3H]-and [1-14C]L-lactate. Since the involvement of metabolism in the available mathematical model is not differentiated and the release of products is not taken into consideration, the method in its present state is not applicable to studies of metabolism. Moreover, even the parameters of transport derived by this technique are of limited value, when the transported compounds are rapidly metabolized by reversible reactions. Despite these uncertainties, the present data indicate that the transport of L-lactate is ten times faster than that of D-lactate.

Animals↗
PubMed1984

Mathematical models for ligand-receptor binding. Real sites, ghost sites.

In the basic life sciences the term "model" implies a physical, chemical, or molecular construct that provides a representation for the interpretation of experimental observations. To the statistician, however, a model is a mathematical expression for correlating data, which may or may not have roots in a molecular picture. With regard to ligand-receptor interactions, the mathematical model used plays a crucial role in extrapolations of binding measurements. Regardless of the statistical goodness of fit of data to an equation, the relationships of the parameters of a mathematical formalism to the molecular features of ligand-receptor complexes are generally very complex. Oversimplified interpretations of the molecular significance of the constants derived from binding measurements are unwarranted, unless one has independent information from molecular probes.

Kinetics↗
PubMed1978

Comparison of the performance of first-grade and mentally retarded students on the Peabody Mathematics Readiness Test.

The Peabody Mathematics Readiness Test was developed to assess mathematics readiness and identify children who would encounter difficulty in first-grade mathematics. In the present study, we compared performances of mentally retarded subjects and first-grade subjects on this test. Retarded subjects' mean scores were significantly lower than those of the nonretarded subjects on the drawing test; however, there were no significant differences between the mean scores of the groups on the other five subscales.

Adolescent↗
PubMed1980

A mathematical model for the curves of intrauterine growth.

Different mathematical models for a chart of intrauterine growth were tested attempting to employ uncomplicated curves. In this manner, a chart of foetal growth was elaborated by plotting the cube root of neonate weight against the gestational age. Two different regions can be clearly seen in this chart of growth. In the first one, until the 34th week of pregnancy, there is a linear relationship between the two variables. In the second region, for pregnancies above the 34th week, the curve has a quadratic equation, reaching the maximum between the 43rd and 44th week, decreasing posteriorly. The goodness of fit obtained by the present mathematical model is more satisfactory than that obtained by mathematical models with a single linear equation.

Anthropometry↗
PubMed1980

[Measurement of the specific electrical resistance of the blood (rho) and its determination mathematically in dogs].

The role of specific electric resistance of blood (rho) in determining systolic cardiac volume by impedance plethysmography is discussed. It is pointed out that the known five mathematical equations for rho estimation by the hematocrit (Hct) and the temperature (T0) differ from one another and are moreover good for humans, but not for experimental animals. A suitable equipment and technique for direct (in vitro) measurement of rho is suggested. The obtained results enabled to deduce a mathematical dependence, allowing to determine the specific electric resistance of blood (rho) in dogs with sufficient accuracy, on the basis of the hematocrit and the temperature. The adequacy of this mathematical dependence for determination of rho in dogs has been confirmed by control studies.

Animals↗
PubMed1995

Motivation and mathematics achievement: a comparative study of Asian-American, Caucasian-American, and east Asian high school students.

This study examined the motivation and mathematics achievement of Asian-American, Caucasian-American, and East Asian students. Subjects were 304 Asian-American, 1,958 Caucasian-American, 1,475 Chinese (Taiwan), and 1,120 Japanese eleventh graders (mean age = 17.6 years). Students were given a curriculum-based mathematics test and a questionnaire. Mathematics scores of the Asian-American students were higher than those of Caucasian-American students but lower than those of Chinese and Japanese students. Factors associated with the achievement of Asian-American and East Asian students included having parents and peers who hold high standards, believing that the road to success is through effort, having positive attitudes about achievement, studying diligently, and facing less interference with their schoolwork from jobs and informal peer interactions. Contrary to the popular belief that Asian-American students' high achievement necessarily takes a psychological toll,they were found not to report a greater frequency of maladjustive symptoms than Caucasian-American students.

Acculturation↗
PubMedDate not supplied

Mathematical models of disease transmission: a precious tool for the study of sexually transmitted diseases.

This paper is an introduction to the mathematical epidemiology of sexually transmitted diseases (STDs) and its application to public health. After a brief introduction to transmission dynamics models, the construction of a deterministic compartmental mathematical model of HIV transmission in a population is described. As a background to STD transmission dynamics, basic reproductive rate, intergroup mixing, rate of partner change, and duration of infectivity are discussed. Use of the models illustrates the effect of sexual mixing (proportionate to highly assortative), of preventive intervention campaigns, and of HIV-chlamydia interaction on HIV prevalence in the different population groups. In particular, planned prevention campaigns can benefit the targeted intervention group but surprisingly can be disadvantageous for the general population. Through examples, mathematical models are shown to be helpful in our understanding of disease transmission, in interpretation of observed trends, in planning of prevention strategies, and in guiding data collection.

Adult↗
PubMed1998

Population dynamics of tuberculosis treatment: mathematical models of the roles of non-compliance and bacterial heterogeneity in the evolution of drug resistance.

SETTING: Patient non-compliance and/or spatial heterogeneity in drug concentration or effectiveness may contribute to the emergence of drug resistance during multiple-drug chemotherapy of tuberculosis. OBJECTIVE: Using mathematical models of mycobacterial population dynamics under antimicrobial treatment, to assess the effects of non-compliance, heterogeneity and other factors on the success of treatment. DESIGN: A mathematical model is used to generate predictions about the ascent of drug resistance in treated hosts with non-compliance and/or a 'protected compartment' of bacteria where only one drug is active; simulations of a more realistic version of this model take into account random mutation, and different assumptions about the size of, and growth rate of bacteria in, the protected compartment. RESULTS: The existence of a protected compartment can increase the likelihood of resistance to the single drug active in that compartment, but only if bacteria resistant to that drug can grow in the protected compartment or if the host is non-adherent to the treatment regimen. However, the protected compartment may also slow the ascent of bacteria resistant to drugs not active in it (e.g. isoniazid) by providing a reservoir of non-selected mycobacteria. The model predicts that relative rates of killing are more important than mutation rates in determining the order in which resistant mutants ascend. Model predictions, in combination with data about drug resistance patterns, suggest that non-compliance, but not heterogeneity, is an important cause of treatment failure. CONCLUSION: Patterns of acquired drug resistance may be used to infer processes of selection during treatment; mathematical models can aid in generating predictions about the relative impacts of treatment parameters in the evolution of resistance, and eventually in suggesting improved treatment protocols.

Antitubercular Agents↗
PubMed2006

The mathematical model of insulin desorption from the bioactive, fibrous artificial store.

The aim of this study was to study insulin desorption from fibrous insulin artificial store in vitro as well as in vivo, with the intention to define a mathematical model that would describe this process. Release profile of cylindrical fibrous matrixes for various insulin concentrations, desorption temperatures, time periods, and pH were presented. Change of insulin concentration in the fibers and the effect of insulin release were discussed. This model was also used to predict the optimal conditions of the release process. Possibility of predicting the effect of the fibrous store design parameters (fibre radius, amount of bonded insulin, fiber type) on the resulting insulin release rate was the major advantage of this mathematical model. Also, taking all the relevant conditions regarding these experiments into consideration, by the application of mathematical model, the diffusion coefficient during insulin release was determined.

Insulin↗
PubMed2005

Magnetic resonance imaging and mathematical modeling of progressive formalin fixation of the human brain.

The temporal magnetic resonance (MR) appearance of human brain tissue during formalin fixation was measured and modeled using a diffusion mathematical model of formalin fixation. Coronal MR images of three human brains before formalin fixation and at multiple time points thereafter were acquired. T1 relaxation, T2 relaxation, water apparent diffusion coefficient (ADC), and proton density (PD) maps were calculated. The size of a light "formalin band" region, visible in T1 weighted images, was compared to a mathematical model of diffusive mass transfer of formalin into the brain. T1 relaxation, T2 relaxation, and PD all decreased, in both gray and white matter, as formalin fixation progressed. The ADC remained more or less constant. The location of the inner boundary of the formalin band followed a time course consistent with the steepest formalin concentration gradient in the mathematical model. Based on the diffusion model, the brain is not completely saturated in formalin until after 14.8 weeks of formalin immersion and, based on the observed changes in T1, T2, and PD, fixation is not complete until after 5.4 weeks. During fixation, the ongoing attenuation of T1 relaxation, T2 relaxation, and PD must be taken into consideration when performing postmortem MRI studies.

Brain↗
PubMed2001

Analysis of the infection system of human T-cell leukaemia virus type I based on a mathematical epidemic model.

Human T-cell leukaemia virus type I (HTLV-I) is a retrovirus that causes adult T-cell leukaemia (ATL). HTLV-I has existed in Japanese people for thousands of years. In order to prevent an epidemic of HTLV-I, it is important to explain the infection system by a mathematical approach. By considering the main infection routes in Japan, that is: (i) mother-to-child transmission; (ii) male (husband)-to-female (wife) transmission; and (iii) female (wife)-to-male (husband) transmission, a mathematical model for describing the time-dependent change of the infection proportion can be constructed. An upper bound of the present infection rate per year in male-to-female transmission and that in female-to-male transmission is given by the model, and theoretical results related to HTLV-I infection are also deduced from the mathematical model. A simulation study based on the present model demonstrates the theoretical results relating to the HTLV-I infection.

Computer Simulation↗
PubMed1998

Cognitive and Metacognitive Abilities Involved in the Solution of Mathematical Word Problems: Validation of a Comprehensive Model.

With this investigation we tried to validate an economic model of the cognitive and metacognitive abilities involved in Mathematical Word Problems. From the literature we chose seven abilities: text comprehension, problem representation, problem categorization, solution estimate, planning the solution, procedure self-evaluation, calculus self-evaluation. In order to measure these abilities, we devised a series of mathematical word problems (partitioned problem) where, for each ability, subjects have to answer a multiple choice question. A hierarchical regression model with only five variables (excluding solution estimate and calculus self-evaluation) explained more than 50% of the variance of the solution scores of the Partitioned Problems, and 40% of the variance of the solution of a series of problems presented with only the text. The model was validated with five different samples of subjects of different school grade and with a bootstrap procedure. Furthermore the relationship of the variables was tested using a path analysis. The discrimination validity of three different levels of problem solving efficiency give further support to the validity of the model. The model obtained may be utilized in order to devise practical instruments for the analysis of mathematical word problem difficulties. Copyright 1998 Academic Press.

Journal Article↗
PubMed1999

Self-Efficacy, Motivation Constructs, and Mathematics Performance of Entering Middle School Students.

The objectives of this study were to determine the influence of various motivation variables on task-specific mathematics performance and to explore whether these variables change during the first year of middle school (N = 273). Students' task-specific self-efficacy was the only motivation variable to predict performance and did so both at start and end of year. There were no differences in anxiety, self-concept, or self-efficacy for self-regulation between start and end of year, but, by end of year, students described mathematics as less valuable and reported lower effort and persistence. Gifted students had stronger mathematics self-concept beliefs, and they had more accurate and less overconfident self-efficacy beliefs than did regular education students. There were no gender differences in any of the motivation constructs. Copyright 1999 Academic Press.

Journal Article↗
PubMed2000

Motivational Beliefs, Study Strategies, and Mathematics Attainment in High- and Low-Achieving Chinese Secondary School Students.

In order to examine the relationship between cognitive and motivational variables and their relationship to mathematics attainment, Hong Kong-Chinese students enrolled in schools for high-, average-, and low-achievers completed questionnaires in Year 10 and in Year 11. Low-achievers perceived academic learning as being less useful over time and reported spending less time studying in Year 10 than in Year 11 but high- and low-achievers did not differ on their use of self-regulated learning strategies. Performance on the public examination in mathematics was predicted by prior achievement and Self-Concept of Mathematics Ability. Results underscore the importance of considering cultural beliefs systems and educational systems in models of academic motivation. Copyright 2000 Academic Press.

Journal Article↗
PubMed1999

Sex Differences in Mathematical Abilities: Commentary on the Math-Fact Retrieval Hypothesis.

The hypothesis that a male advantage in speed of math-fact retrieval underlies the sex difference, favoring males, in mathematical abilities is unique and provocative. However, the hypothesis does not provide an explanation for the male advantage in mathematical domains, such as geometry, that do not require arithmetic, nor does it accommodate the sex differences in social and occupational interests that contribute to the sex difference in mathematical achievement. An alternative hypothesis focusing on the sex difference in three-dimensional spatial cognition is favored over the math-fact retrieval hypothesis. Copyright 1999 Academic Press.

Journal Article↗