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This experiment examined the effect of experience with mathematics on the brain's processing of problems in basic mathematics. As predicted, subjects who were given such experience showed more right lateral eye movements while solving such problems than subjects without this experience. The educational implications of these results are discussed.
24 students, who participated in a summer session mathematics enrichment program, viewed subliminally presented messages. Prior to each class, the experimental group of 16 viewed a subliminally presented psychoanalytic merging message and the control group of 8 viewed a neutral message. After 20 sessions students were retested. Experimental students had higher mathematics scores than controls. These data are compared with results obtained by other investigators.
This study investigated in 40 young university women the possible relationships between levels of testosterone and specific measures of overall self-confidence and self-confidence in approaching mathematics. Correlations of -.43 and -.49 with each measure of self-confidence, respectively, and level of testosterone were found in the portion of the sample displaying normal ovulatory function. There was no correlation (r=.02) between the measures of mathematics and overall self-confidence. 19 women did not display normal ovulatory function. The only significant result for the full sample was a significant correlation of -.73 between scores on the Bem Sex Role Inventory Masculinity and overall self-confidence. The reasons for the high anovulatory percentage are not clear, nor are the associations which anovulation might have with either hormonal levels or the personality characteristics in question.
Using a manipulative approach in a mathematics course, this study was designed to assess attitudes toward mathematics of undergraduates in elementary education. A 20-item attitude rating administered as pre- and posttest to 95 students (7 men and 88 women) was used to assess the effect of the hands-on approach. A dependent t test indicated a statistically significant but very small change in their ratings.
Questions from a national mathematics test taken by over a 1,000 12- and 13-yr.-olds in the United Kingdom were perused for heavily loaded spatial and numerical items. Pupils' answers to the two types of item were examined, and those who answered well in one of the categories but poorly in the other were selected to form two groups, those high in spatial thinking but low in numerical thinking and those high in numerical thinking but low in spatial thinking to assess whether the approaches to solve the item used by each group were different. The two groups did indeed utilize different thinking strategies to solve the questions. For example, questions involving angle and volume, items thought to require a high spatial facility, were answered correctly by the predominantly numerical thinkers as often as by the predominantly spatial thinkers. This would indicate that one of the samples, i.e., numerical thinkers, used a different strategy than the other, i.e., spatial thinkers. This was verified by examination of students' work in the test booklets and personal interviews of them. Also, the same proportion of boys in each group was recorded, but a higher percentage of girls was recorded in the spatial group than in the numerical. This reflected the large number of boys who scored high on the spatial measures also doing moderately well on the numerical items and so, being moved out of the solely spatial group. Since the tests used by mathematics educators to assess learning are so heavily laden with linguistic/analytical rather than holistic/spatial types of questions, pupils high in spatial but low in numerical thinking face a severe handicap in schools.
To investigate the mathematics anxiety of 159 students in Grade 8 (M age = 14.3 yr.) in the United Arab Emirates a 28-item anxiety scale was administered. Analysis indicated some mathematics anxiety. Also, boys and girls scored significantly differently as boys had the higher mean.
The Mathematics Anxiety Rating Scale was developed in 1972 by Richardson and Suinn as a single construct measure. A shortened version, the Revised Mathematics Anxiety Scale (RMARS) was developed by Alexander and Martray in 1989. The latter scale was subjected to factor analysis using 357 senior undergraduates in education. Three main factors accounted for 73% of the variance, confirming the scale's multidimensional structure.
As a measure of mathematics anxiety, the Mathematics Anxiety Rating Scale (MARS) has been a major scale used for research and clinical studies since 1972. Despite the usefulness of the original scale, researchers have sought a shorter version of the scale partly to reduce the administration time of the original 98-item scale. This study created a shorter version of the MARS and provides reliability and validity information for the new version. The Cronbach alpha of .96 indicated high internal consistency, while the test-retest reliability for the MARS 30-item was .90 (p<.001). The validity data confirm that the MARS 30-item test is comparable to the original MARS 98-item scale.
This study assessed reliability and validity of the Approaches to earning Mathematics Questionnaire, for 218 university students. The study also identified the relationship between subscales. Internal consistency as Cronbach alpha was .77 for the Surface Approach to Learning scale and .88 for the Deep Approach to Learning scale. Principal components analysis yielded a two-factor solution accounting for only 34.6% of variance. The factors were interpreted as Surface Approach and Deep Approach to learning mathematics, as in Australia. The former subscale scores were negatively correlated -.2 with the latter subscale scores.
The Arabic translation of the Mathematics Teaching Efficacy Beliefs was completed by 144 undergraduate students (M age=20.6) in Jordan. The findings support the internal reliability of the Arabic translation of the Mathematics Teaching Efficacy Beliefs as well as its construct validity.
A mathematical model for describing the caloric response over time offers many important advantages over the commercially-available qualitatively-fitted curves that are now used by the clinician for evaluating caloric results. In this report advances in the development of a nonlinear least-squares mathematical model are discussed and the roles and derivations of fitting parameters and curve-derived indices are outlined. This model provides a rigorous and objective description of the caloric response in its entirety with four continuous parameters. These fitting parameters make it possible to 1) describe individual caloric responses precisely and uniquely, 2) compare pairs of individual caloric responses or groups of caloric responses statistically, 3) extract information not previously available, 4) quantify variability within the caloric response, and 5) model physical properties of the caloric stimulus and physiological variables affecting the caloric response. Results from this model are compared with the results from our earlier models and with traditional multiparameter caloric results.
In order to study metabolic modifications induced by short term fasting and their consequences on the uptake and intracellular fate of fatty acids iodine labelled in omega position, rats undergo a 36h fasting. Hearts are perfused in a Langendorff system with a glucose (11 mM) perfusion medium; [123I] hexadecenoic acid (IHA) is injected as a bolus. A comparison between time-activity curves p.i. demonstrates a much faster activity decrease for the hearts fasted animals. The intracellular analysis shows that short fasting did not significantly increase the myocardial uptake of fatty acids, but decreased the storage and increased the degradation of the fatty acids taken up. Mathematical analysis of the myocardial time-activity curves obtained by external detection provided results comparable to those of intracellular analysis. The coefficients of correlation between the values of the aqueous phases, organic phases and free fatty acids measured by intracellular analysis and calculated with the compartmental model are consistently higher than 0.97. Consequently, this experimental model combined with mathematical analysis of the time-course of myocardial radioactivity after 123IHA administration appears to be very promising method for studying the effects of drugs or variations of energy substrate availability on myocardial fatty-acid metabolism.
The study of relationships between mathematical properties of functions used to model lactation curves is usually limited to the evaluation of the goodness of fit. Problems related to the existence of different lactation curve shapes are usually neglected or solved drastically by considering shapes markedly different from the standard as biologically atypical. A deeper investigation could yield useful indications for developing technical tools aimed at modifying the lactation curve in a desirable fashion. Relationships between mathematical properties and lactation curve shapes were analyzed by fitting several common functions (Wood incomplete gamma, Wilmink's exponential, Ali and Schaeffer's polynomial regression, and fifth-order Legendre polynomials) to 229,518 test-day records belonging to 27,837 lactations of Italian Simmental cows. Among the best fits (adjusted r(2) higher than 0.75), the 3-parameter models (Wood and Wilmink) were able to detect 2 main groups of curve shape: standard and atypical. Five-parameter models (Ali and Schaeffer function and the Legendre polynomials) were able to recognize a larger number of curve shapes. The higher flexibility of 5-parameter models was accompanied by increased sensitivity to local random variation as evidenced by the bias in estimated test-day yields at the beginning and end of lactation (border effect). Meaning of parameters, range of their values and of their (co) variances are clearly different among groups of curves. Our results suggest that analysis based on comparisons between parameter values and (co)variances should be done carefully. Comparisons among parameter values and (co)variances could yield more robust, reliable, and easy to interpret results if performed within groups based on curve shape.
A mathematical model was used to estimate the efficacy of postmilking teat disinfection from observations in split-udder trials with natural exposure. Data were studied from an outbreak of Staphylococcus aureus IMI during a split-udder trial in a commercial herd with low SCC. The efficacy of postmilking teat disinfection was similar when calculated based on incidence density rates or on transmission rates of IMI in dipped and control quarters. If, however, first and subsequent S. aureus IMI in a cow were not assumed to be independent and were therefore treated separately in the models, the efficacy of post-milking teat disinfection was calculated as being higher with the modeling procedure. The analysis using mathematical modeling, which includes the effect of the number of existing IMI on the number of new IMI, is presented and discussed. This analysis also allows estimation of the basic reproduction ratio. The impact of postmilking teat disinfection on transmission of pathogens is quantified, and proposals for additional preventive measures can be generated. We concluded that efficacy estimations from split-udder trials, assuming quarters to be independent observations, might underestimate the effect of postmilking teat disinfectants on udder pathogens.
A mathematical model was developed that describes the effects of filter plugging on flow through 3 micron pore polycarbonate filters as a function of time, pressure, and cell concentration, both under stirring and nonstirring conditions. The mathematical constants for the model were derived from experimental data generated with a filtration apparatus, and were tested by using various concentrations of cells that are able to plug filter pores. A computer simulation program was written to test the model over a wide range of nonfilterable cell concentrations.
The present work is a mathematical model of the fluid filtration in the glomerular network occurring in snakes. The model is based on the differential form of Starling's hypothesis and takes into account the angioarchitecture of the network and the behaviour on the microrheology of blood with nucleated red cells. The model predicts the hemodynamics and the transvascular fluxes in each vascular segment within the network. The model is applied to a vascular network of the glomerulus of the garter snake. A value of 0.593 microns/(s.mmHg) was determined for the hydraulic conductivity of the glomerular capillaries using the geometrical data of the network together with experimental data for the pressures and the blood flow rate reported in the literature. The analysis shows that the local filtration rates cover a wide range. In some of the vascular segments, the filtration leads to such a high increase in colloid-osmotic pressure that the level of the transvascular hydrostatic pressure difference is reached. Mathematical simulations of the variation of the glomerular blood flow rate due to vasoactivity of preglomerular arterioles show the effect on the filtration rate and the hemorheologic parameters.
Eighty learners were randomly selected from 160 first-year nursing students enrolled in an urban community college nursing program in Ontario. They were subsequently divided into control and treatment groups to investigate the effects of different teaching methods on mathematics anxiety and the students' ability to accurately calculate fractional drug doses. The results obtained in this study indicated that there were no statistically significant differences between the control and treatment groups in either mathematics anxiety levels or in arithmetic test performance. These findings counter many of those found in previous investigations. Reasons for these discrepancies are provided along with recommendations for present practice and future research.
BACKGROUND: Several clinical trials investigating myopic excimer laser photorefractive keratectomy (PRK) report an initial change in refraction from myopia to hyperopia, followed by a gradual regression toward emmetropia and occasionally to recurrent myopia. We examined the effect of corneal shape on refraction following PRK for myopia using a mathematical model. METHODS: We calculated the volume of corneal tissue removed by PRK for -3.00-diopter (D) and -6.00-D corrections with ablation diameters of 5 mm and 6 mm. For all the operating algorithms, the central region of the cornea was considered spherical. Mathematical models were developed based on calculations of the apical radius of the ablated cornea and the final refraction for a range of corneal asphericities. Baker's equation was used to model corneal asphericity. RESULTS: The smaller both the ablation size and desired correction, the smaller the effect of corneal asphericity on the refractive outcome. While corneal asphericity can influence the immediate refraction after PRK, the maximum effect is unlikely to be greater than +0.75 D. CONCLUSIONS: Corneal asphericity marginally affects the initial outcome of PRK. The effect will probably be offset by the healing response of the cornea.