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At least 19 recordsLinked to original sources
PubMedDate not supplied

A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties.

Mathematical competencies of 180 children were examined at 4 points between 2nd and 3rd grades (age range between 7 and 9 years). Children were initially classified into one of 4 groups: math difficulties but normal reading (MD only), math and reading difficulties (MD-RD), reading difficulties but normal math (RD only), and normal achievement in math and reading (NA). The groups did not differ significantly in rate of development. However, at the end of 3rd grade the MD only group performed better than the MD-RD group in problem solving but not in calculation. The NA and RD only groups performed better than the MD-RD group in most areas. Deficiencies in fact mastery and calculation fluency, in particular, are defining features of MD, with or without RD.

Aptitude↗
PubMed1996

Sex and mathematical background as predictors of anxiety and self-efficacy in mathematics.

Anxiety and self-efficacy in mathematics as a function of sex and mathematical background were investigated. This study employed an ex post facto 2 x 2 factorial design in which sex and mathematical background were classification variables. It was predicted that men would report lower anxiety scores and higher self-efficacy scores than women and that students with a high mathematical background would report lower anxiety scores and higher self-efficacy scores than those with a low background in mathematics. An interaction between sex and mathematical background was also predicted. 51 subjects were given the revised Mathematics Anxiety Scale and the Mathematics Self-efficacy Scale. Results supported the hypotheses with respect to background in mathematics for anxiety in mathematics, and all of the hypotheses were supported for self-efficacy in mathematics.

Adolescent↗
PubMed1996

Mathematical calculation ability and mathematical anxiety of baccalaureate nursing students.

Accurate mathematical calculations are a critical skill that nurses must demonstrate in order to safely administer medications. This study was designed to investigate differences in mathematical calculation ability and mathematical anxiety for a group of baccalaureate nursing students (n = 56) and a group of undergraduate students majoring in fields other than nursing (n = 56). Results showed the nursing students had significantly lower mathematical skills test performance than the non-nursing students. No group differences were found for mathematical anxiety. These results are consistent with previous findings that indicate that nursing students are seriously deficient in mathematical skills. The greater deficiency in mathematical skills performance noted in the nursing group indicates that nursing education must consider more selective admission requirements related to mathematics. Mathematical calculation skills must be evaluated early in the program of study and educational opportunities to increase mathematical proficiency must be planned throughout the nursing program.

Adult↗
PubMed1997

Developmental differences in addition strategies: a comparison of mathematically disabled and mathematically normal children.

BACKGROUND: Several studies concerned with task-specific strategies in addition have suggested that, when compared with the performance of mathematically normal peers (MN pupils), the performance of mathematically disabled pupils (MD pupils) is characterised by frequent use of inefficient problem-solving strategies. These studies, however, have focused more or less exclusively on single age-groups and on the youngest age-groups in particular. What characterises strategy use, as this develops year by year during the primary school stage, has not been adequately studied. AIMS: The major purpose of the present study was to investigate the character and extent of differences between the MD pupils and the MN pupils as reflected in the use of task-specific strategies for solving elementary addition problems as the pupils move up through primary school, i.e., from grade 1 to grade 7. Particular concern was with the variability within the groups of MD pupils, especially in light of the general literature showing substantial heterogeneity in the performance characteristics of the mathematically less able children. SAMPLE: The sample included 32 MD pupils in grade 1, 33 MD pupils in grade 3, 36 MD pupils in grade 5 and a corresponding number of MN pupils in each of the grades. METHODS: The pupils were asked to solve 28 single-digit addition problems on two different occasions separated by an interval of two years. The task-specific strategies used by the pupils were recorded on a 'trial-by-trial basis' and were classified as defined single variants of backup strategies and retrieval strategies, respectively. RESULTS: The pattern of development as it emerged in a longitudinal perspective in the present study showed the mathematically disabled pupils as being characterised by: (a) use of backup strategies only, (b) use of the most primary backup strategies, (c) small degree of variation in the use of strategy variants and, (d) limited degree of change in the use of strategies from year to year throughout the primary school. CONCLUSIONS: Compared with the mathematically normal pupils, the mathematically disabled exhibited a divergent pattern of development, with unexpectedly little variability within the group itself.

Age Factors↗
PubMedDate not supplied

[Interactive determination of the parameters of mathematical models in planning radiotherapy of malignant tumors. 3. Method of local adjustment of the parameters of mathematical models (examples of application)].

To increase the accuracy of calculation of tolerance doses of the likelihood of radiation-induced complications in normal organs and tissues by using mathematical models, the author has developed a method for local mathematical model parameter adjustment (LMMPA) which included analysis of the structure of a mathematical model, systematization of clinical information and its goal-oriented use to determine the parameters of a model. The necessity of developing the LMMPA method stemmed from the complexity of the body exposed to radiation a system and from the quest for taking into account the impact of the system on the values of mathematical models. LMMPA may be regarded as the extension of determination of the parameters of mathematical models or as the interactive determination of their parameters that describing radiation exposures of complex biological systems. Different aspects of using of LMMPA are indicated how to apply it to the determination of tolerance doses for connective tissue, lung tissue, and the brain by using the Ellis and LQ models. The extended LMMPA is shown how to determine the parameters of a mathematical models for calculation of the likelihood of radiation-induced complications in the lung tissue.

Brain↗
PubMed2001

Does using an instrument make you mathematical? Mathematical practitioners of the 17th century.

Gaining an insight into what it meant to be a mathematical practitioner in the 17th century is difficult. People who thought themselves mathematical included navigators, sundial makers and book-keepers. For some, the simple use of instruments was construed as mathematical; for others, this was merely a 'showing of tricks'. One profession reliant on mathematics was land surveying. An analysis of this profession throws up many interesting questions about what it meant to be mathematical in early modern England.

Equipment and Supplies↗
PubMed1996

Perceptions of mathematics ability versus actual mathematics performance: Canadian and Hong Kong Chinese children.

This study compared levels of mathematics achievement between Canadian and Hong Kong Chinese children and explored the relations between perceptions of children's competence and mathematics achievement. The Canadian sample was made up of 125 4th-grade children who were randomly selected from five schools in Calgary. A comparative sample of 128 children was drawn from five Chinese-speaking schools in Hong Kong. Parents, teachers and children rated children's competence and a mathematics achievement test was given to the children. Hong Kong Chinese children outperformed their Canadian peers in the mathematics test. However, ratings of children's scholastic/mathematical abilities by Canadian respondents were significantly higher than those by Hong Kong Chinese informants. The Harter Self-Perception Profile Scale revealed that the aspects of themselves considered most important for sense of general self-worth were for Canadian children: physical appearance and social acceptance, for Hong Kong children: behavioural conduct and scholastic competence. Discussion centres on the contributions that expectations and evaluations of competence and self-worth make to the large difference in the mean levels of mathematics achievement between children in the two cultures.

Achievement↗
PubMed1982

The measurement of mathematics anxiety: the Mathematics Anxiety Rating Scale for Adolescents--MARS-A.

Describes the Mathematics Anxiety Rating Scale for Adolescents (MARS-A). Normative data on over 1,200 junior high and senior high students are reported. In addition, psychometric data that relate to reliability and construct validity for the MARS-A scale are discussed. Two factors were identified in the scale, a factor of numerical anxiety that appeared in 91% of the items and a factor of mathematics test anxiety that appeared in the remaining items. Results that show the association between high mathematics anxiety scale scores and low grade average in mathematics courses are reported on two samples of students.

Adolescent↗
PubMed2001

[Do cover stories of mathematical word problems influence analogical transfer in mathematics?].

In 3 experiments, we examined the effect of cover stories of mathematical word problems on analogical transfer and its interaction with the problem solvers' mathematical performance. In a first step, the principles for solving mathematical source problems were illustrated with cover stories that were either appropriate or inappropriate for the respective problem's deep structure. Subsequently, participants' performance on a target problem was measured. Results of study 1 showed that analogical transfer was influenced by the source problem's cover story. In the second experiment, this effect was more pronounced for participants with high (versus low) mathematical performance. Using some critical sentences, study 3 provided evidence that the cover stories already influenced the encoding of the target problem. The results are discussed within the framework of content-based accounts of analogical transfer emphasizing the importance of cover stories for understanding the problems' deep structure.

Adult↗
PubMedDate not supplied

[The interactive determination of the mathematical model parameters for the planning of the radiation therapy of malignant tumors. 2. A method of adjusting the mathematical model parameters for calculating the tolerance doses and probabilities of the occurrence of radiation complications in body organs and tissues].

To enhance the accuracy of calculation of tolerance doses, adequate doses and the likelihood of radiation complications in normal organs and tissues, a method has been developed for local model parameter adjustment (LMPA) by using mathematical models. It includes the analysis of the structure of a mathematical model, the systematization of clinical data and their goal-oriented use for model adjustment. The necessity of developing a new research line (LMPA) is determined by the complexity of the irradiated organism as a system and by the attempts to take into account the impact of the system on the parameters of mathematical models. LMPA can be considered to generalize determination of the parameters of mathematical models or their directed (interactive) determination. The strategy of using LMPA, which is based on the preset radiation treatment protocol and its respective dosage distributions in normal organs and tissues, is described. The efficiency of LMPA is shown to depend on the volume and relevance of clinical data that the radiological therapist has at his disposal.

Computer Simulation↗
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↗
PubMed1977

Cyclic kinetics and mathematical expression of the primary immune response to soluble antigen. VII. The conveyer hypothesis and its mathematical expression.

The conveyer hypothesis is based on the fact that because of clone predetermination, antibody production takes place in an organism without the presence of antigen as a result of natural cell differentiation. Soluble antigen is an analogue of a specific mitogen which gives rise to reproduction mainly of cells carrying on their surface the immunoglobulin receptors to the given antigen. The mathematical model of the conveyer hypothesis takes into account the initial conditions, among them the background level of antibody-producing cells before injection of a soluble antigen, migration of precursor cells in the draining lymphoid organ, and the rate of precursor differentiation, including the rate of the change of the immunoglobulin receptor number on the cell surface. Changes of antigen concentration in blood determine the intensity of precursor proliferation. Comparison of real experiments (intraperitoneal injections of capsular antigen of Pasteurella pestis into inbred mice) with calculations done on the basis of the developed mathematical model shows a definite qualitative resemblance with the kinetics of antibody-producing cells and free antibodies as well as with the decrease of free antigen concentration in blood. In spite of some differences between model experiments and real experiments the conveyer hypothesis and its mathematical model appear suitable for describing the primary immune response of mice immunized with low doses of capsular antigen of Pasteurella pestis.

Animals↗
PubMed1991

Mathematical model of antiviral immune response regulation. II. Mathematical formalization of the modelled processes. Imitation of acute course of hepatitis B.

The mathematical formalization of the conceptual model for antiviral immune response regulation described in the preceding report was carried out. The mathematical model is presented as a system of 30 ordinary nonlinear differential equations with delays. The algorithm for numerical integration of the mathematical model is based on Gear's methods of variable step and variable order. Initial conditions and parameters, as well as intervals of plausible values for them, were chosen for adaptation of the model for description of acute hepatitis B.

Acute Disease↗
PubMed1983

Mathematical immunogenetics I. Mathematics as language.

This paper summarizes approaches to developing mathematics that can act as a language for immunogenetics. The need for this has been documented by showing inadequacies of the standard symbolism. Apparent distinctions in symbolizing and conceptualizing factors involved in immunogenetics are seen to disappear in the mathematical models presented here. One model, a three-fold Boolean matrix factorization, subsumes all approaches to the idea of specificity and yet is general enough to incorporate data beyond that found only in a reaction matrix.

Antibody Specificity↗
PubMed2002

A preliminary study of achievement, attitudes toward success in mathematics, and mathematics anxiety with technology-based instruction in brief calculus.

This study was designed to compare achievement, attitudes toward success in mathematics, and mathematics anxiety of college students taught brief calculus using a graphic calculator, with the achievement and attitudes and anxiety of students taught using the computer algebra system Maple, using a technology based text book. 50 men and 50 women, students in three classes at a large public university in the southwestern United States, participated. Students' achievement in brief calculus was measured by performance on a teacher-made achievement test given at the end of the study. Analysis of variance showed no significant difference in achievement between the groups. To measure change in attitudes and anxiety, responses to paper-and-pencil inventories indicated significant differences in favor of students using the computer.

Adolescent↗
PubMedDate not supplied

[Interactive determination of the parameters of mathematical models for planning radiotherapy of malignant tumors. I. Mathematical models for calculating dose tolerance, adequate doses and the likelihood of development of radiation complications in normal organs and tissues].

Mathematical models for calculating tolerance doses, adequate doses and the likelihood of radiation complications in the body's normal tissues are considered. To determine the parameters of these models that describe the outcomes of radiation exposure of complicated biological systems, a method of local adjustment of the parameters of the models has been developed, which will be described in parts 2 and 3 of the proposed paper. In part 1 (the present paper), particular emphasis is laid on the inclusion of an important parameter, such as a volume, into Ellis and LQ models. A mathematical model is presented for calculating the likelihood of a radiation complication in the tissue, which is the basis for deriving a formula to calculate an adequate uniform tissue radiation dose that is equivalent to the nonuniform tissue distribution of a dose in terms of the likelihood of radiation complications.

Humans↗