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PubMed1982

An application of mathematical programming concepts to behavioural research design.

More and more frequently, human factors specialists are being asked to design behavioural research and evaluation techniques that will be applied many times to many different systems, and not always by behavioural scientists. One way to meet the repeatability requirement is to base evaluation technique design on the concepts of mathematical optimisation (eg, linear programming). This paper presents a general model for the application of mathematical programming concepts to behavioural research design, and an example of the use of this approach to design a simulator certification programme for the Strategic Air Command (SAC).

Journal Article↗
PubMed2000

A structural model for predicting mathematics achievement: its relation with anxiety and self-concept in mathematics.

This study proposed and tested a model of mathematics achievement and its relations to antecedent and subsequent factors using structural equations modeling. A sample of elementary school students in Al-Ain school district (n = 394) completed an Arabic version of the Self-description Questionnaire as well as a questionnaire measuring their perception of the importance of mathematics, anxiety about it, and the amount of effort they exerted in studying. Mathematics grades were obtained from the official school records. Importance and effort were positively related to achievement which in turn had a positive path coefficient to self-concept and a negative path to anxiety. The hypothesized model explained 40%, 64%, and 73% of the variance in achievement, self-concept, and anxiety, respectively. The results can be interpreted as indicating that achievement is an important outcome and antecedent construct within the proposed model.

Achievement↗
PubMed2001

Psychometric characteristics of the conceptions of mathematics questionnaire.

This study describes the psychometric characteristics of the 19-item Conceptions of Mathematics Questionnaire for a total of 158 students (86 women and 72 men). The coefficient alpha of internal consistency reliability was .75. Principal components analysis with varimax rotation indicated a two-component solution could be extracted. The two theoretically meaningful dimensions were fragmented conceptions (alpha = .80) and cohesive conceptions (alpha = .80). The former entails seeing mathematics as number rules and formulae to be used to solve problems. Students who hold this conception use rote learning and memorization. In contrast, the latter entails seeing mathematics as a complex logical system for solving complex problems. Students with such a conception approach learning to attain, develop, and apply knowledge.

Adolescent↗
PubMed1993

Achievement-related expectancies, academic self-concept, and mathematics performance of academically underprepared adolescent students.

The relationship between achievement-related expectancies, academic self-concept, and mathematics performance of 191 academically underprepared adolescent students was examined. After the effects of prior academic achievement were controlled for, a significant main effect for academic self-concept was found; as expected, students with higher academic self-concept earned significantly higher mathematics grades. In addition, after the effects of prior achievement were controlled for, female students were found to earn significantly higher mathematics grades than did male students. A significant three-way (Sex x Ethnic Group x Achievement-Related Expectancies) interaction was also noted. Unlike in several previous studies, no significant racial differences in mathematics performance were found. These students had a similar socioeconomic status (SES), and the effects of prior academic achievement were controlled for, suggesting that racial and gender differences in mathematics achievement may be partially explained by prior schooling and SES background, as posited by Reyes and Stanic (1988).

Adolescent↗
PubMed2005

Combining reliability coefficients: toward reliability generalization of the conceptions of mathematics questionnaire.

The combined coefficient alpha from studies reporting the reliability of scores using the Conceptions of Mathematics Questionnaire were computed. Five studies comprising 898 participants were evaluated. A test of differences among the independent coefficients alpha was statistically significant (chi42= 10.38, p = .04) for the Fragmented and (chi42 = 11.58, p = .02) for the Cohesive subscales. Post hoc comparisons showed the difference (F129,299 = 1.50, p=.003) was between Australia and Nigeria for the former and (F155,157 = 1.54, p= .004) between South Africa and the United States for the latter alpha values. A one-way analysis of variance, testing for homogeneity among means within each subscale, indicated that these were homogeneous because the measure of the strength of association accounted for 10% of variability. As reliability coefficients were from homogeneous samples and alpha values were not different, the combined reliability is the best estimate of the population reliability for each subscale.

Australia↗
PubMed1991

Experimental testing of constructivism and related theories.

The purpose of this article is to show that experimental scientific methods can be applied to explain how the analytic mechanism of the left cerebral hemisphere and the synthetic mechanism of the right one create complex cognitive constructions like ontology and mathematics. Nominalism and ordinal mathematical concepts are related to the analytic left hemisphere while Platonism and cardinal mathematical concepts are related to the synthetic right one. Thus persons with a dominant left hemisphere tend to prefer nominalist ontology and have more aptitude for ordinal mathematics than for cardinal mathematics, while persons with a dominant right hemisphere tend to prefer platonist ontology and have more aptitude for cardinal mathematics than for ordinal mathematics. It is further explained how the Kantism temporal mode of perceiving experience can be related to the left hemisphere while the Kantian spatial mode of perceiving experience can be related to the right hemisphere. This relation can be tested experimentally, thus the Kantian source of constructivism, and through it constructivism itself, can be tested experimentally.

Attention↗
PubMed1984

Automatic aftereffects in two-choice reaction time: a mathematical representation of some concepts.

A mathematical model is developed to describe sequential effects in two-choice reaction time experiments with a short response-stimulus interval. Evidence is briefly discussed that in conditions with short response-stimulus intervals, automatic aftereffects dominate sequential effects, and the influence of subjective expectancy can be neglected. In these conditions the model premises three components of automatic aftereffects--facilitation, inhibition, and noise, with a common decay factor. Influence of response-stimulus interval and practice on sequential effects are examined and related to parameter changes in the proposed single-decay model. The decrease of automatic aftereffects with increasing response-stimulus interval is primarily ascribed to an increasing decay factor. The parameter representation of the model also clarifies the issue of the disappearance of automatic aftereffects with practice. It shows a gradual fading of inhibition in the initial stages of practice, together with a slower decrease of the facilitation effect. The single-decay model provides a satisfactory explanation for the processes involved in compatible two-choice reaction time with short response-stimulus interval.

Choice Behavior↗
PubMed1997

The effect of social comparison on mathematics self-concept.

Implicit in the frame of reference hypothesis is the assumption that social comparison is one of the causal determinants of self-concept. The present study of Norwegian sixth-grade elementary school students showed that students of low-, medium-, and high-achievement classes did not differ in mathematics self-concept. Mathematics self-concept was, however, significantly influenced by the students' within-classroom position in mathematics. The results support the frame of reference hypothesis, and the support was consistent over gender.

Achievement↗
PubMed1990

Athletic self-concept and mathematics achievement in girls.

Several researchers have suggested that girls' mathematics performance may be mediated by an assertive sex role or "masculine interest." The present study made the assumption that girls' athletic self-confidence reflects "masculine interest" so girls' test scores for perceived athletic competence would be related to their mathematics achievement scores. A total of 207 boys and girls in Grades 4, 5, and 6 were tested for their perceived athletic ability using the Athletic Competence subscale of Harter's 1985 Self-perception Profile, and these scores were correlated with their mathematics achievement as measured on the Metropolitan Achievement Test and term grades. A low but significant correlation with Athletic Competence scores was found for girls on both measures of mathematics achievement. Although boys scored higher on the Athletic Competence subscale, there were no sex differences on either measure of mathematics achievement. Results are discussed in terms of both sex-role theory and cognitive development.

Achievement↗
PubMedDate not supplied

[Mobile cardiac electrical center: a new concept and mathematical modeling].

A method for determination of the cardiac electric center on the basis of noninvasive multichannel measurements and multipole description of the cardioelectric potential is proposed. The method provides a more accurate and stable spatial location of the cardioelectric generator as compared to other methods (in particular, those based on minimization of the quadrupole potential). The position of the electric center is a useful characteristic for topical diagnosis of the electrophysiological state and function of the heart. Using mathematical models, the dependence of the position of the electric center, determined by the method presented, on the configuration and spatial position of the cardiogenerator is illustrated.

Algorithms↗
PubMedDate not supplied

The Triangle Technique: a new evidence-based educational tool for pediatric medication calculations.

Many nursing student verbalize an aversion to mathematical concepts and experience math anxiety whenever a mathematical problem is confronted. Since nurses confront mathematical problems on a daily basis, they must learn to feel comfortable with their ability to perform these calculations correctly. The Triangle Technique, a new educational tool available to nurse educators, incorporates evidence-based concepts within a graphic model using visual, auditory, and kinesthetic learning styles to demonstrate pediatric medication calculations of normal therapeutic ranges. The theoretical framework for the technique is presented, as is a pilot study examining the efficacy of the educational tool. Statistically significant results obtained by Pearson's product-moment correlation indicate that students are better able to calculate accurate pediatric therapeutic dosage ranges after participation in the educational intervention of learning the Triangle Technique.

Adult↗
PubMed1998

Self-reports of mathematics self-concept and educational outcomes: the roles of ego-dimensions and self-consciousness.

BACKGROUND: There is a need for research to (a) explore more fully the academic outcomes that follow from under-/over-rating of self-concept and (b) identify factors that predict the nature of self-reports of self-concept as well as under- and over-rating of this self-concept. AIMS: The study examines the link between students' self-appraisals of both mathematics self-concept and under-/over-rating of this self-concept and educational outcomes in mathematics such as achievement and motivation (future plans for mathematics). Ego-dimensions (ego-orientation and competence-valuation) and public self-consciousness were examined as two factors that might contribute to predicting these self-appraisals. SAMPLE: Findings are drawn from a sample of 382 male and female high school students ranging in age from 14 to 16 years. METHODS: Students responded to a questionnaire (at Time 1) that assessed self-concept, motivation orientation, competence-valuation, self-consciousness, and mathematics motivation. Teachers rated each student using a brief mathematics self-concept scale. RESULTS: Higher mathematics self-concept and over-rating of this self-concept were predictive of higher levels of mathematics motivation and later mathematics achievement (Time 2). Findings also indicate that ego-orientation and competence-valuation are positively associated with mathematics self-concept and over-rating, whilst public self-consciousness negatively predicts mathematics self-concept and is also associated with a tendency to under-rate oneself in this domain.

Achievement↗