Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Concepts”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47Linked to original sources
PubMed2003

Cognitive representation of negative numbers.

To understand negative numbers, must we refer to positive number representations (the phylogenetic hypothesis), or do we acquire a negative mental number line (the ontogenetic hypothesis)? In the experiment reported here, participants made lateralized button responses to indicate the larger of two digits from the range -9 to 9. Digit pairs were displayed spatially congruent or incongruent with either a phylogenetic or an ontogenetic mental number line. The pattern of decision latencies suggests that negative numbers become associated with left space, thus supporting the ontogenetic view.

Adult↗
PubMed1990

Using logistic regression in perinatal epidemiology: an introduction for clinical researchers. Part 2: The logistic regression equation.

In Part 1 basic concepts were introduced as a preparation for an introductory explanation of logistic regression. Logistic regression is a statistical modelling technique, designed for the estimation of the simultaneous effects of predictors on the risk of a certain dichotomous outcome variable where each effect is estimated while adjusting for the effect of the other factors considered. The basic concepts--odds, odds ratio, confounding and interaction--were introduced in such a way that they naturally lead to the concept of logistic regression. In Part 2 the concepts are 'translated' into simple equations. By studying these equations the equivalence between such mathematical expressions and the underlying clinical assessment of risk will become clear.

Female↗
PubMed1995

Representation and reasoning in early numerical development: counting, conservation, and comparisons between sets.

The first experiment examined the developmental relation between counting and number conservation in the 3-6-year-old age range. Results indicated extended developments in both children's counting and their conservation reasoning, and a close relation between the 2. Only the oldest children gave evidence of conserving, and they also differentiated appropriately between conservation and control problems in their use of counting. The second and third experiments extended the finding that children below 6 years of age do not conserve to conditions in which counting was precluded. These results provide evidence of protracted developments in young children's understanding of relational aspects of number.

Child↗
PubMedDate not supplied

Development of numerical estimation in young children.

Two experiments examined kindergartners', first graders', and second graders' numerical estimation, the internal representations that gave rise to the estimates, and the general hypothesis that developmental sequences within a domain tend to repeat themselves in new contexts. Development of estimation in this age range on 0-to-100 number lines followed the pattern observed previously with older children on 0-to-1,000 lines. Between kindergarten and second grade (6 and 8 years), patterns of estimates progressed from consistently logarithmic to a mixture of logarithmic and linear to a primarily linear pattern. Individual differences in number-line estimation correlated strongly with math achievement test scores, improved estimation accuracy proved attributable to increased linearity of estimates, and exposure to relevant experience tended to improve estimation accuracy.

Child↗
PubMed1993

Children's understanding of number words.

This research notes gives details of an atypical response to a 'give a number' task by a 34-month-old child. The child clearly demonstrated that he understood the word 'two' to refer to an object rather than to a quantity. This incident offers support to Fuson's (1988) theory of the functionally specific initial acquisition of number word meanings and suggests that Gelman & Meck's (1983) 'principles first' account of the development of counting gives insufficient weight to the role of language and social interaction in the development of early number understanding. The incident also shows that our knowledge of this area of development would benefit from a greater emphasis on longitudinal studies, studies of social context and studies of individual differences in the processes of acquisition.

Child Development↗
PubMed2000

Maximum-likelihood approach to strain imaging using ultrasound

A maximum-likelihood (ML) strategy for strain estimation is presented as a framework for designing and evaluating bioelasticity imaging systems. Concepts from continuum mechanics, signal analysis, and acoustic scattering are combined to develop a mathematical model of the ultrasonic waveforms used to form strain images. The model includes three-dimensional (3-D) object motion described by affine transformations, Rayleigh scattering from random media, and 3-D system response functions. The likelihood function for these waveforms is derived to express the Fisher information matrix and variance bounds for displacement and strain estimation. The ML estimator is a generalized cross correlator for pre- and post-compression echo waveforms that is realized by waveform warping and filtering prior to cross correlation and peak detection. Experiments involving soft tissuelike media show the ML estimator approaches the Cramer-Rao error bound for small scaling deformations: at 5 MHz and 1.2% compression, the predicted lower bound for displacement errors is 4.4 microns and the measured standard deviation is 5.7 microns.

Journal Article↗
PubMed2000

A comparison of critical velocity estimates to actual velocities in predicting simulated rowing performance.

The most accurate critical velocity (CV) estimate for the prediction of velocity during a simulated 2,000-m rowing race and the relationship to aerobic power were studied. Sixteen male rowers completed randomized maximal exertion trials (200, 400, 600, 800, 1,000, and 1,200 m), a maximal oxygen consumption (VO(2)max) on a Concept II rowing machine, and an actual 2,000-m simulated rowing race. Three mathematical models were applied to 4 rowing distance combinations producing 12 CV estimates. Seven of the 12 possible CV estimates were not significantly different from actual 2,000-m velocity. Comparison of the 3 CV models using all 6 trial distances revealed that the nonlinear model produced a CV estimate lower than the 2 linear CV models. CV was significantly correlated to VO(2)max (r = 0.91) and the mean velocity achieved during the 2,000-m simulated rowing race (r = 0.97). VO(2)max was significantly correlated to 2,000-m simulated rowing race velocity (r = 0.93).

Adult↗
PubMed1978

Thinking.

Explore the source record for details and available documents.

Concept Formation↗
PubMed1996

Categorical relations in shape perception.

Many researchers have proposed that objects are perceived as structural descriptions, which specify the configuration of an object's features (or parts) in terms of their categorical relations to one another. Others have proposed that objects are perceived as views, which specify the configuration of an object's features in terms of their coordinates, in particular 2D views. This paper presents five experiments testing these competing accounts of the perception of the configuration of an object's features. Subjects learned to recognize a set of target objects and were tested for their ability to distinguish them from various distractors that differed either in their categorical relations or their coordinates. Subjects were consistently more likely to confuse both 2D and 3D objects that were similar in their parts' relations to each other than to confuse objects similar in their parts' coordinates (in any reference frame). This effect persisted when subjects were allowed to view the objects as long as they wished and when they were explicitly trained to distinguish them from the distractors. These findings suggest that we perceive an object's features in terms of their categorical relations to one another. A preliminary model of the findings is presented.

Attention↗
PubMed2005

A critical history of individual and collective ethics in the lineage of Lellouch and Schwartz.

The notions of individual and collective ethics were first explicitly defined in the biostatistical literature in 1971 to motivate a mathematical solution to a posed ethical dilemma. This paper reviews key antecedents to these concepts and traces explicit references to them over time, primarily in the biostatistical literature. Following a historical exposition of these texts, a critical thematic analysis shows the following: the normative force of these concepts has not been adequately argued. Individual and collective ethics do not solve the problem of how to use accumulating data to inform ethical action. The notions of the "individual" and the "collective" are too vague to prompt clear moral imperatives, especially in difficult cases. These concepts have not been successfully linked to a standard ethical framework. Finally, the paper concludes with the observation that a systematic, comprehensive ethical framework must be identified to fulfill the intuitions behind individual and collective ethics.

Bioethics↗
PubMed2005

Threats to group value, domain-specific self-esteem and intergroup discrimination amongst minimal and national groups.

The research reported in this investigation sought to examine the self-esteem hypothesis (SEH) using measures of domain-specific and public collective self-esteem (CSE). Two studies were conducted. Each tested both propositions of the SEH. The first study revealed that minimal group members (a) experienced an increase in that domain of self-esteem judged to be relatively more important to the in-group, following the display of in-group favouritism and (b) that minimal group members with low public CSE (and who thus believed that the in-group was negatively evaluated by the out-group) showed enhanced levels of in-group favouritism. The second study, which utilized the members of real social categories (i.e. New Zealanders and Australians) and negative outcome allocations (i.e. white noise) revealed identical findings. The theoretical implications of these results are discussed.

Adult↗
PubMed2005

Toxicity assessment of environmentally relevant pollutant mixtures using a heuristic model.

In this study, 9 chemicals were chosen from a recent report on surface water concentrations of a variety of xenobiotics to test the hypothesis that the toxicity of chemical mixtures could be estimated using a model based on the toxicity of the individual chemicals. Concentration-response curves for the endpoints of lifespan, growth rate, and fecundity were generated for each chemical experimentally using the crustacean, Daphnia magna. From this data, a mathematical model for the combined toxicity of these chemicals was generated that merged the concepts of concentration addition and independent joint action. Toxicity of a mixture was modeled at various levels at which the ratio of the chemicals within the mixture was maintained at that reported for median detected environmental levels. Toxicity of the mixture was then determined experimentally and compared to model predictions. The model accurately predicted the most sensitive endpoint, as well as the lowest toxic effect level of the mixture. Results demonstrated that, for this mixture of chemicals, toxicity was not influenced significantly by interactions among the chemicals and a single constituent dominated toxicity. According to model predictions and experimental results, the median detected environmental concentrations of chemicals constituting this mixture provided no margin of safety.

Animals↗
PubMed1990

Beginning kindergarteners' perception of number.

97 children in 5 kindergarten classes when tested for perceptions of number could begin counting and 9 counted to 30, 84 counted a set of 6 correctly but when the blocks were covered 33 could say there were 6. 57 showed 1:1 correspondence but some had to count to decide. 14 showed conservation of number, but 94 recognized two sets were unequal and which one was larger. 30 pointed to the third car, but 24 could state an ordinal name for a target. Clearly the children varied greatly.

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↗
PubMed1990

The perceptual interaction of graphical attributes: configurality, stimulus homogeneity, and object integration.

Researchers have proposed that graphical efficacy may be determined, in part, by the nature of the perceptual interactions that exist between attributes used to create graphical displays. One extreme type of interaction is integrality, in which two or more physical dimensions are represented as a single psychological dimension in the observer. An alternative type of interaction is configurality, in which a global emergent dimension is available to the observer in addition to the component attributes. Thirteen stimulus sets, each composed of attributes commonly used in the design of graphs, were submitted to the performance-based diagnostics of integrality and configurality. Analyses suggest a continuum of configurality among the present stimulus sets, with little evidence for integral graphical attributes. The configural pattern of results was more common when two identical dimensions were paired (homogeneous stimuli) than when two different dimensions were paired (heterogeneous stimuli). However, there was no evidence that pairs of dimensions belonging to a single object (object integration) were any more configural than dimensions belonging to different objects. Object integration was, however, consistently related to inefficient performance in tasks requiring the filtering of one of two component dimensions.

Adult↗
PubMed1998

Geometric considerations in anterior dental aesthetics: restorative principles.

While aesthetics is traditionally regarded as an artistic concept, quantifiable scientific principles are used in its development. Dental aesthetics are governed by mathematical parameters that, when applied by the clinician and laboratory technician, can achieve restorations with a unique aesthetic appearance. These geometric laws should not be viewed as immutable, but as useful guidelines for the fabrication sequence. This article demonstrates a series of geometric principles for the anterior maxillary dentition that can be utilized in the development of aesthetic restorations.

Age Factors↗