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[A method for teaching mathematics].

This paper reports on an experience in teaching mathematics in a graduate course in public health, intermingled with reflections and concepts. Students enrolled in such courses generally feel uneasy about learning mathematics. Without underrating the usual obstacles and even affinities in developing abstractions, the results suggest that a major portion of the difficulties derives not from mathematics itself, but from an oppressive experience in the past. Difficulties also relate to the construction of space in the classroom. Such a perspective involves understanding experiments and life experiences in which the subjects are involved. In short, the work focuses on how to transmit mathematics in the development of a pedagogical approach.

Education, Graduate↗
PubMed2003

Integer/linear mathematical programming models: a tool for allocating healthcare resources.

In today's environment, the demand for efficient healthcare resource allocation is increasing. As new technologies become available, allocation decisions become more complex and tools to assist decision makers in determining efficient allocations of healthcare resources are encouraged. Mathematical programs have multiple properties that are desirable for healthcare decision makers such as the simultaneous consideration of multiple constraints and a built-in sensitivity analysis. These models have been well researched and are considered invaluable in other industries. Mathematical programming has also become increasingly visible in facilitating the allocation of healthcare resources in the health services research sector. However, the use of mathematical programming tools has been limited in economic evaluations of new technologies. Budget allocations, such as formulary, drug development, and pricing decisions may benefit greatly from the use of mathematical programs. As an increasing number of expensive new technologies become available and pressure grows to contain healthcare costs, these tools may help guide a more efficient allocation of resources for technologies under budgetary and other constraints.

Decision Making↗
PubMed2004

Correlations among handedness, eyedness, monocular shifts from binocular focal point, and nonverbal intelligence in university mathematics students.

Relationships among hand preference, nonverbal intelligence, and the monocular shifts of binocular focal point were studied in 33 men and 12 women university mathematics students. Ocular dominance was assessed with the Miles test. The monocular shift of binocular focal point for each eye was assessed with a modified Miles test. Hand preference was assessed on the Edinburg Handedness Inventory. Nonverbal intelligence was assessed with Cattell's Culture Fair Intelligence Test. In a prior study, the percentage of left-eye preference had been reported to be greater for mathematics students than for nonmathematics students. In the present study there were positive correlations between hand preference and the sum of the monocular shifts of two eyes. In addition, there was a negative correlation between nonverbal intelligence and the sum of the monocular shifts of two eyes. As these resultssuggest that the sum of the monocular shifts of two eyes may be related to mathematical ability and nonverbal intelligence, further research with a larger sample including non-mathematics students is needed.

Adolescent↗
PubMed1997

Mathematics achievement and attitudes of senior secondary-school students in Transkei, South Africa.

In a study of mathematics achievement and attitudes toward mathematics, a sample of 266 Standard 10 (Grade 12) students (98 boys and 168 girls) from 10 senior secondary schools in the Umtata district of Transkei, South Africa, were administered a mathematics achievement test and an attitude questionnaire. Contrary to other studies analysis showed no significant relationship between students' scores on measures of mathematics achievement and attitudes.

Achievement↗
PubMed2004

A study orientation questionnaire in mathematics for use in a tertiary environment.

The Study Orientation Questionnaire in Mathematics Tertiary is being developed as a diagnostic measure for South African lecturers and counselors to help students improve their orientation toward the study of mathematics. In this pilot study subjects were freshman black students registered for the Five-year Study Programme in the School of Engineering at the University of Pretoria. During the first phase of the standardisation in 2000, 33 students (28 men; 5 women, M age=19.6, SD=.9) were assessed, and in 2001, 40 students (27 men, 13 women, M age=19.2, SD=.9). In 2002 the questionnaire was administered to 51 students (39 men, 12 women, M age= 19.1, SD= .9). Analysis showed satisfactory reliability coefficients and item-field correlations. Step-wise linear regression in 2001 indicated that a combination of two fields, namely, Information Processing and Problem-solving Behaviour in mathematics, contributed significantly (R2=46.9%) to predicting achievement in calculus. In 2002 one field, Mathematics Confidence, contributed significantly (R2= 25.2%) to that prediction.

Adult↗
PubMed2005

Mathematical background and attitudes toward statistics in a sample of Spanish college students.

To examine the relation of mathematical background and initial attitudes toward statistics of Spanish college students in social sciences the Survey of Attitudes Toward Statistics was given to 827 students. Multivariate analyses tested the effects of two indicators of mathematical background (amount of exposure and achievement in previous courses) on the four subscales. Analysis suggested grades in previous courses are more related to initial attitudes toward statistics than the number of mathematics courses taken. Mathematical background was related with students' affective responses to statistics but not with their valuing of statistics. Implications of possible research are discussed.

Adolescent↗
PubMed2005

Mathematics beliefs and achievement of adolescent students in Japan: results from the TIMSS 1999 assessment.

A recent study (1) of undergraduate students in a precalculus course indicated that they expressed slightly positive attitudes toward mathematics. It is important, however, to examine relationships between students' initial attitudes and achievement outcomes. The present purpose was to assess the relationship between self-beliefs and mathematics achievement for a large national sample of students from the TIMSS 1999 international sample (eighth graders) from Japan. Several significant relationships between mathematics beliefs and test scores were noted. In addition, the overall multiple regression equation that assessed the joint significance of the complete set of self-belief variables was significant (F7.65 = 159.48, p < .001) and explained 20.6% of the variance in mathematics achievement test scores.

Achievement↗
PubMed2005

The effects of stating problems in bilingual students' first and second languages on solving mathematical word problems.

Researchers have suggested that among bilinguals, solving word problems in mathematics is influenced by linguistic factors (K. Durkin & B. Shire, 1991; L. Verschaffel, B. Greer, & E. De Corte, 2000). Others have suggested that students exhibit a strong tendency to exclude real-world constraints in solving mathematics word problems (L. Verschaffel, E. De Corte, & S. Lasure, 1994). In the present study, the authors explored the effects of stating word problems in either Filipino or English on how Filipino-English bilingual students solved word problems in which the solution required the application of real-world knowledge. The authors asked bilingual students to solve word problems in either their first or second language. For some of the word problems, real-life constraints prevented straightforward application of mathematical procedures. The authors analyzed the students' solutions to determine whether the language of the word problems affected the tendency to apply real-life constraints in the solution. Results showed that the bilingual students (a) rarely considered real-life constraints in their solutions, (b) were more successful in understanding and solving word problems that were stated in their first language, and (c) were more likely to experience failure in finding a solution to problems stated in their second language. The results are discussed in terms of the relationship between linguistic and mathematical problem-solving processes among bilinguals.

Adolescent↗
PubMed1984

Do baccalaureate students possess basic mathematics proficiency?

Since 1979, over 700 junior level baccalaureate nursing students at the Intercollegiate Center for Nursing Education (ICNE) in Spokane, Washington, have had their basic mathematical skills tested, using a teacher constructed examination. The "Mathematics Proficiency Exam" utilized evaluates the nursing student's ability to add, subtract, multiply, and divide whole numbers, fractions, decimals, and percentages. Ratios, proportions, and problems are also included in the exam. The results of the testing have been surprising. From 9% to 38% of each student group tested have been unable to pass all parts of the examination at the 70% level. These findings have led the ICNE to require basic mathematical proficiency via the "Mathematics Proficiency Exam," developed by the authors, as a criterion for admission to the upper division nursing major. Subsequently, competence in medication calculation skills has been required within the first clinical course at the ICNE via a second teacher-constructed examination.

Achievement↗
PubMed2006

A self-paced course in pharmaceutical mathematics using web-based databases.

OBJECTIVE: To transform a pharmaceutical mathematics course to a self-paced instructional format using Web-accessed databases for student practice and examination preparation. DESIGN: The existing pharmaceutical mathematics course was modified from a lecture style with midsemester and final examinations to a self-paced format in which students had multiple opportunities to complete online, nongraded self-assessments as well as in-class module examinations. ASSESSMENT: Grades and course evaluations were compared between students taking the class in lecture format with midsemester and final examinations and students taking the class in the self-paced instructional format. The number of times it took students to pass examinations was also analyzed. CONCLUSIONS: Based on instructor assessment and student feedback, the course succeeded in giving students who were proficient in pharmaceutical mathematics a chance to progress quickly and students who were less skillful the opportunity to receive instruction at their own pace and develop mathematical competence.

Computer-Assisted Instruction↗
PubMed1999

Music training and mathematics achievement.

Iowa Tests of Basic Skills (ITBS) mathematics scores of eighth graders who had received music instruction were compared according to whether the students were given private lessons. Comparisons also were made between students whose lessons were on the keyboard versus other music lessons. Analyses indicated that students who had private lessons for two or more years performed significantly better on the composite mathematics portion of the ITBS than did students who did not have private lessons. In addition, students who received lessons on the keyboard had significantly higher ITBS mathematics scores than did students whose lessons did not involve the keyboard. These results are discussed in relation to previous research on music training and mathematics achievement.

Achievement↗
PubMed2000

[Estimate of fetal long bone length in early pregnancy: comparison between mathematical formulae].

BACKGROUND: The aim of this study was to determine the efficacy of different mathematical formulae described in the literature and to propose new mathematical formulae to estimate fetal long bones biometry in early pregnancy. METHODS: In 1481 singleton euploid fetuses a transvaginal ultrasound examination was performed between 9 and 16 week's gestation. To determine the relationship between the biparietal diameter and long bone lengths, a sample group of 100 randomly chosen normal fetuses was evaluated by regression equations. The equations derived were then tested in the remaining 1381 control fetuses and the mean absolute percentage error and the mean systematic error with their standard deviations were compared with previously reported mathematical formulae by other authors. RESULTS: All previous formulae described in literature when applied to our population revealed an overestimation of expected long bones measurements. Using our mathematical formulae, the mean absolute percentage error and the mean systematic error were 11.5% and 1% in estimating femur and 10.9% and 0.8% in estimating humerus length, respectively. CONCLUSIONS: These newly derived ultrasound morphometric formulae could be proposed as reliable models in estimating fetal long bone lengths in early pregnancy.

Anthropometry↗
PubMed1975

The influence of fibre shape in lung deposition-mathematical estimates.

Inhaled fibres deposit by sedimentation, diffusion, impaction, and interception in airways of the respiratory system. Long straight fibres may exhibit periodic motiion with ordered orientation in those airways having laminar flow. We assume that irregular fibres are randomly oriented in airways. Mathematical models based on respiratory system architecture, respiratory airflow, and mathematical expressions for deposition mechanisms have been developed to predict deposition in respiratory compartments of fibres in ordered orientation and of various fibre confirgurations in random orientations. The size and shape characteristics of chamber aerosols generated with U.I.C.C. asbestos specimens have been determined. Combinations of the chamber aerosol data with mathematical estimates of deposition suggest that fibre shape as well as size influences the magnitude of deposition in pulmonary spaces. For size distributions such as those of the U.I.C.C. asbestos chamber aerosols, the mathematical models predict pulmonary spaces deposition for straight fibres in ordered orientation about twice as great as for irregular fibres in random orientation.

Aerosols↗
PubMed1991

The mathematical description of structures.

Any mathematical description of structures should start from a precisely stated definition of the concept of "structure". Unfortunately no universally accepted definition of this type exists. All that can be said is that the concept of "structure" is changing together with the modern physico-mathematical thought, so that different 'points of view' on the problem of the mathematical description of structures can be distinguished. The aim of this paper is to compare the explicative and predictive power of these different 'viewpoints' without entering into historical detail, in order to critically examine the limits and powers of the mathematical tools available today.

Classification↗
PubMed1986

Evaluation of mathematic models to assess platelet kinetics.

Twelve mathematic methods used to calculate the mean platelet survival time were compared by determining the "goodness of fit" of the models to the platelet survival curves of 15 reference subjects and 54 patients. Platelets were labeled with [111In]oxine. The linear (LN), exponential, weighted mean, multiple hit (MH), Dornhorst (DH), Meuleman (ML), alpha order (AO), and polynomial (PO) mathematic models were investigated. The goodness of fit for the exponential model was determined by the nonlinear least squares method (EP), and also by the linear least squares method on logarithmically transformed data (EX) as is recommended. The modified weighted mean (MWM) and the usual weighted mean method (WM) obtained with these exponential models were tested. The Dornhorst (DH10) and Meuleman (ML10) models, where the potential age-dependent platelet survival times were kept constant at 10 days, were also evaluated. The goodness of fit results, expressed as % s.d. indicated that the LN (5.2%), EX (5.0%), EP (4.4%), WM (3.7%), DH10 (3.7%), and ML10 (3.7%) models all fitted the data significantly worse than the MWM, MH, DH, ML, AO, and PO models (range 3.2-3.3%). The mean platelet survival time determined with the MH model differed significantly from the results with the DH, ML, and AO models. The results of mean platelet survival time calculated with different mathematic models cannot, therefore, be compared directly. The models that fitted the platelet survival curve well varied slightly in sensitivity to noise as is indicated by the coefficient of variation of the mean platelet survival time estimates for the reference subjects (range 7.9-12.0%). Fitting data to at least two mathematic models has definite advantages. Data on which the calculations are based are probably invalid if the following are true: (a) if the mean platelet survival time estimated with the alpha order model is shorter than that estimated with the EP, MWM, or MH models, or (b) the mean platelet survival time estimated with either the DH, ML, AO, or PO models, is longer than the LN, MWM, or MH estimate of the mean platelet survival time. We conclude that the mean platelet survival time can be reliably estimated by fitting the data to either the MWM method (if limited computing facilities are available) or the MH model. Confidence in the result will be increased if considered in conjunction with the finding obtained with one other model; in those cases where the platelet survival time is very short, the alpha order model is recommended.(ABSTRACT TRUNCATED AT 400 WORDS)

Blood Platelets↗
PubMed1986

Sex role orientation, level of cognitive development and mathematics performance in late adolescence.

Sex differences in mathematics performance are found in late adolescence. This study investigates the effects of psychological sex role orientation (BSRI: masculine, feminine, undifferentiated, androgynous) and level of cognitive development (concrete, formal) on performance in mathematics. ANOVA analysis (N = 69; 18 males, 51 females) revealed significant effects for level of cognitive development and for masculine by feminine sex role orientation interaction. Subjects whose BSRI masculine and feminine scores were either both low or both high scored significantly lower on the mathematics test than subjects whose scores on either masculine or feminine scales were high. This indicates lower mathematics performance for androgynous and undifferentiated subjects. This result is hypothesized to be a function of the particular age level of these subjects and their concomitant overconcern with appropriate sex role development.

Achievement↗
PubMed1980

The use of a mathematical model in rhinomanometry.

The authors consider the mathematical model proposed by the Swedish Group (Broms et al.). This model permits the pressure gradient-flow recording as obtained from anterior or posterior rhinomanometry to be converted into a mathematical formula. The model was tested for its mathematical, statistical, and clinical utility with 32 normal test subjects. It is the conviction of the authors, although not totally without reservation, that this is the best mathematical model in existence.

Adolescent↗
PubMed1997

Effects of cognitive ability and affect on school mathematics performance and feelings of difficulty.

Research on cognitive ability and affect has indicated that both of them may function at various levels of generality (LG). This study aimed to investigate the possible effects of LG on school mathematics performance and related feelings of difficulty. Two hundred forty-three students of seventh, eighth, and ninth grades of both genders participated in the study. They were tested with cognitive ability tasks, affective questionnaires, and two school mathematics batteries. The difficulty of each of the school mathematics task was also rated on a 4-point scale. The two school mathematics batteries and affective questionnaires were re-administered 1 year after the first testing. Rates of difficulty were also taken. Path analysis showed that performance was mainly influenced by cognitive ability factors, whereas feelings of difficulty were influenced by performance, cognitive ability, and affective factors. The long-term relations between cognitive and affective factors are discussed.

Adolescent↗