Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “MATHEMATICS”

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 703 records · Page 39Linked to original sources
PubMed1991

Making connections in mathematics.

Math textbooks, which usually represent the mathematics curriculum, seem to be linked to the poor math performance of U.S. students. The major shortcomings of math textbooks are described in this article; then an alternative perspective is offered (the sameness analysis), along with research conducted with students with learning disabilities and at-risk students. The article then presents a detailed illustration of the sameness analysis--how to teach the addition-subtraction and multiplication-division relationships and their interrelationships in the context of solving word problems in mathematics.

Child↗
PubMedDate not supplied

Mathematics instruction for secondary students with learning disabilities.

Secondary students with learning disabilities generally make inadequate progress in mathematics. Their achievement is often limited by a variety of factors, including prior low achievement, low expectations for success, and inadequate instruction. This article will discuss techniques that have been demonstrated to be effective with secondary students who have learning disabilities in mathematics.

Achievement↗
PubMed2001

Benchmarking to the world's best in mathematics. Quality control in curriculum and instruction among the top performers in the TIMSS.

UNLABELLED: This article describes the education quality control systems (for mathematics) used by those countries that performed best on the Third International Mathematics and Science Study (TIMSS). Enforced quality control measures are defined as "decision points"--where adherence to the curriculum and instruction system can be reinforced. Most decision points involve stakes for the student, teacher, or school. They involve potential consequences for failure to adhere to the system and to follow the program at a reasonable pace. Generally, countries with more decision points perform better on the TIMSS. When the number of decision points and TIMSS test scores are adjusted for country wealth, the relationship between the degree of (enforced) quality control and student achievement appears to be positive and exponential. CONCLUSION: The more (enforced) quality control measures employed in an education system, the greater is students' academic achievement.

Benchmarking↗
PubMed1989

Mathematical analysis of first metatarsal osteotomies.

The mathematical analysis of most first metatarsal osteotomy corrections for metatarsus primus varus is presented and interpreted with respect to metatarsal lengthening or shortening and changes in clinical reference angles (e.g., intermetatarsal or angle of declination). The critical parameters for each osteotomy such as location and angles of cuts and amount of displacement are defined and their theoretical effects on the final correction determined. Although exactitude in surgical methodology and an absolute prediction of final clinical results are impossible at the present time, even guidelines as to the potential effectiveness of various surgical techniques and quantitative methods for subsequent evaluation are lacking. This mathematical analysis can provide guidelines for prospective choices and a basis for retrospective interpretation as well as represent a critical component for biomechanical calculations.

Humans↗
PubMedDate not supplied

Utilization of mathematical processing of retinal images with use of adaptive contrast control (ACC) method to detect quantity of vascular endings.

PURPOSE: The authors investigated whether the method of mathematical processing of retinal images with the use of a computer can be used to evaluate ocular background figures of patients with physiologic retinal findings. This method is based on identification of vascular endings in an examined retinal area. When the authors mention vascular endings, they do not refer to factual endings, but recognizable vascular endings; there are no endings in a vascular system. METHODS: Adaptive contrast control (ACC) method was used to determine a number of vascular endings. The method is based on mathematical processing of a digitized retina picture with the use of a computer. On a digitized retinal picture, the vascular system is identified with the use of the conditional erosion methodology, and the number of vascular endings is then determined. The ACC method was used to process a file of retinal pictures of 38 patients (76 eyes) with physiologic retinal findings. RESULTS: Based on the results of statistical analysis, the authors detected that the number of vascular endings showed a normal curve (Gaussian distribution, p=0.05). A tight correlation between quantities of vascular endings in the right and the left eyes was also detected, which means that the quantity of vascular endings in the right and the left eyes is in a very close correlation (p=0.05). CONCLUSIONS: The authors highlight that the curve of the number of vascular endings of patients with physiologic retinal findings shows a Gaussian distribution.

Adolescent↗
PubMed1994

Mathematical model application to the kinetic study of tumor markers.

In order to overcome the inefficient cutoff criterion in the management of neoplastic patients after therapy, in follow-up, in recurrence and in monitoring treatment, we have analysed some mathematical models to evaluate serial determinations of tumor markers, with the aim to ascertain the radicality of surgery or the presence of recurrences. Since a tracer study of the biological system of tumor markers is impossible, some information, such as rate factor and half-life, is obtained by determination of the marker after radical treatment. In steady state with two or more samples in time it is possible with adequate statistical models to establish a significant increase in the marker. In recurrence, if it is true that the secretion rate of the marker by a tumor is proportional to tumor mass, then increasing concentrations of the tumor marker would be a phenotypic expression of tumor growth. Therefore some mathematical models are proposed to evaluate the kinetics of tumor growth.

Biomarkers, Tumor↗
PubMed1983

On-line digitizing: useful mathematical techniques.

A mathematical and computational approach to some of the common problems found in writing digitizing programs for cephalometric analysis is described. The paper is aimed at those with access to a microcomputer and digitizer, some knowledge of the BASIC computer language and simple mathematics but little experience of writing digitizing programs.

Cephalometry↗
PubMed2002

Mathematical model to predict individual survival for patients with renal cell carcinoma.

PURPOSE: To develop a multivariate model and mathematical formula capable of calculating personalized survival for renal cell carcinoma (RCC) patients with clinically available variables. PATIENTS AND METHODS: A total of 477 patients out of 661 undergoing nephrectomy at the University of California Los Angeles between 1989 and 1999 were eligible for evaluation and formed the analyzed cohort for this retrospective study. Time to death was the primary end point assessed. Univariate analysis for 14 to 20 variables was conducted, followed by a multivariate Cox analysis. The variables that provided independent information as to the time of death for metastatic and nonmetastatic patients were coded and incorporated into a function based on the Nadas equation principle. RESULTS: For nonmetastatic patients, the significant variables in the multivariate analysis were Fuhrman's grade and Eastern Cooperative Oncology Group performance status. For the metastatic patients, Fuhrman's grade, 1997 classification T stage, number of symptoms, nodal involvement, and immunotherapy were independent predictors for survival. These variables, based on the Cox multivariate regression model, were implanted into an exponential Nadas equation. The expected survival predicted by use of the Nadas equations faithfully describes the actual survival based on Kaplan-Meier curves. CONCLUSION: We have developed mathematical equations for estimating survival after radical nephrectomy for RCC. The resulting formulas are capable of better tailoring survival estimates for a specific patient and are based on widely accepted clinical prognostic variables. On validation with external data, this type of representation can be used as a tool for the determination of personalized prognosis and may be useful for patient education and counseling.

Carcinoma, Renal Cell↗
PubMed2002

A minimal mathematical model of calcium homeostasis.

A mathematical model of calcium homeostasis is presented in which the controlling factors are the plasma concentrations of calcium, PTH, and calcitriol, and the effector organs are the parathyroids, bone, kidney, and intestine. Other factors can be added as the need arises. The model is aimed at simulating what happens in a single individual, but its parameters and variables were adjusted to the corresponding published average values. Simulations of published observations in humans undergoing the infusion of calcium or its chelators are presented. With a single exception, these simulations provided a good fit to the data. The response of the system to extrinsic perturbations was characterized by simulating chronic infusions of calcium, PTH, and calcitriol. Finally, the steady state response to perturbations in some of its parameters (the secretory mass of the parathyroids and the affinity and/or sensitivity of the calcium, PTH, and calcitriol receptors) and to renal failure were also investigated in an attempt to analyze the pathogenesis of clinical hypo- or hypercalcemias. In its present form the model cannot be used to base clinical decisions in individual cases. However, it requires modest computational resources, and clinicians with a modest mathematical background can manipulate it. It is a useful tool for the analysis of general mechanisms of the diseases of calcium metabolism and for the design of clinical experiments aimed at characterizing these diseases. The model can also be the core of future autoadaptive extensions to be used in individual patients.

Calcitriol↗
PubMed2004

Failure of mathematical indices to accurately assess insulin resistance in lean, overweight, or obese women with polycystic ovary syndrome.

Insulin resistance is a common metabolic feature of polycystic ovary syndrome (PCOS). In this study, we examined the validity of the mathematical indices [the quantitative insulin sensitivity check index (QUICKI) and the homeostasis model of assessment (HOMA)] that calculate insulin sensitivity and their correlation to glucose utilization with the insulin infusion rate in 40 mU/m(2).min by the euglycemic clamp (M) in women with PCOS. We studied 59 women with PCOS (20 lean, 16 overweight, and 23 obese subjects). Euglycemic clamp testing was performed, and QUICKI, HOMA, total testosterone, fasting insulin, fasting glucose, and glucose-to-insulin ratio were estimated. No difference was found in testosterone and glucose levels among the three groups. Lean or overweight women compared with obese women differed in insulin levels, glucose-to-insulin ratio, QUICKI, and HOMA (P < 0.01). No statistical difference was found between lean and overweight women in the above parameters. M differed when lean women were compared with overweight (P < 0.002) or obese women (P < 0.0001); however, no statistical difference was observed between overweight and obese women. No significant correlation was found between M and QUICKI or HOMA. We conclude that mathematical indices should be applied with caution in different insulin-resistant populations and should not be considered a priori equivalent to the euglycemic clamp technique.

Adult↗
PubMed2004

Application of a new mathematical method for the estimation of the mean surface area to calculate the percolation threshold of lobenzarit disodium [correction of dissodium] salt in controlled release matrices.

One of the practical handicaps for the application of the percolation theory to estimate the percolation threshold of drugs in controlled release systems is the fact that the dissolution studies must be carried out so that only one surface of the tablet is exposed to the dissolution medium. The aim of this work is to estimate the percolation threshold of the antiarthritic drug lobenzarit dissodium (LBD) in inert matrices prepared with the excipients Ethocel((R)) 100 and Eudragit((R)) RS-PO (10-75% w/w). Release assays were performed using the paddle method. The whole surface of the tablets was exposed to the dissolution medium. For the first time, a new mathematical method is developed to transform the amount of drug released in amount released per surface area in order to calculate the percolation thershold of LBD. The mathematical method proposed allows to calculate, using a new equation, the evolution of the mean surface area (O((t))). The new method was validated and three novel results were achieved: A constant value of (O((t))) at critical time (theta) in the matrices (O((theta))=1.272 cm(2)); a linear relationship between initial surface area (O((0))) and critical time; and a linear relationship between O((t)) and time. Employing the values of O((t)), it was possible to calculate for the first time, the percolation threshold (p(c1)) for LBD in Ethocel((R)) 100 (p(c1)=0.280+/-0.102) and Eudragit((R)) RS-PO (p(c1)=0.344+/-0.07) matrices.

Delayed-Action Preparations↗
PubMed1993

Using cell replication data in mathematical modeling in carcinogenesis.

Risk estimation involves the application of quantitative models of dose versus response to carcinogenicity data. Recent advances in biology, computing, and mathematics have led to the application of mathematically complicated, mechanistically based models of carcinogenesis to the estimation of risks. This paper focuses on two aspects of this application, distinguishing between models using available data and the development of new models to keep pace with research developments.

Animals↗
PubMed2001

Teaching mathematics to students with mild-to-moderate mental retardation: a review of the literature.

A systematic search of the literature from 1989 through 1998 was conducted to identify and analyze mathematics interventions for students with mild-to-moderate mental retardation. We found that the focus of instruction has shifted from basic skills instruction to computation and problem-solving instruction. Techniques such as constant-time delay, peer tutoring, time trials, and direct instruction proved beneficial in improving mathematics skills. Further, students with mental retardation learned to employ cognitive strategies successfully when these techniques were included. Although this information is promising, we recommend that further studies be conducted in secondary schools and in inclusive settings.

Adolescent↗
PubMed2006

Improving mathematics teaching and learning experiences for hard of hearing students with wireless technology-enhanced classrooms.

Hard of hearing students usually face more difficulties at school than other students. A classroom environment with wireless technology was implemented to explore whether wireless technology could enhance mathematics learning and teaching activities for a hearing teacher and her 7 hard of hearing students in a Taiwan junior high school. Experiments showed that the highly interactive communication through the wireless network increased student participation in learning activities. Students demonstrated more responses to the teacher and fewer distraction behaviors. Fewer mistakes were made in in-class course work because Tablet PCs provided students scaffolds. Students stated that the environment with wireless technology was desirable and said that they hoped to continue using the environment to learn mathematics.

Education of Persons with Hearing Disabilities↗
PubMed1999

Etiology of covariation between reading and mathematics performance: a twin study.

The etiology of the observed relationship between reading and mathematics performance was examined by analyzing data from samples of same-sex twin pairs tested in the Colorado Learning Disabilities Research Center. Bivariate phenotypic and genetic structural equation models were fitted to data from 526 twin pairs selected for reading deficits (290 identical and 236 same-sex fraternal) and 355 control pairs (220 identical and 135 same-sex fraternal). Subtests of the Peabody Individual Achievement Test (PIAT; Reading Recognition, Reading Comprehension, and Spelling) were used as measures of reading performance, and scores from the Wechsler Intelligence Scale for Children-Revised (WISC-R) or Wechsler Adult Intelligence Scale-Revised (WAIS-R) Arithmetic subtest, the Wide Range Achievement Test Arithmetic subtest, and the PIAT Math subtest were used as indices for mathematics performance. The results of these confirmatory factor analyses indicate that genetic and environmental covariances between reading and math latent factors do not differ significantly for twin pairs in the proband and control groups. Estimates of heritability for reading performance in the proband and control samples were 0.81 and 0.69, respectively, and those for math performance were 0.88 and 0.67, respectively. Moreover, genetic influences accounted for 83% of the covariation between the reading and math factors in the proband group and for 58% of the covariation between these two latent variables in the control group; in contrast, shared environmental influences did not contribute significantly to the relationship between the reading and math latent factors nor to their independent variation.

Achievement↗
PubMed2006

Transformations of mathematical and stimulus functions.

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel formula-to-graph tests and 10 novel graph-to-formula tests. Seven of the 8 participants showed substantial improvement in identifying formula-to-graph relations; however, in the test of novel graph-to-formula relations, participants tended to select equations in their factored form. Next, we manipulated contextual cues in the form of rules regarding mathematical preferences. First, we informed participants that standard forms of equations were preferred over factored forms. In a subsequent test of 10 additional novel graph-to-formula relations, participants shifted their selections to favor equations in their standard form. This preference reversed during 10 more tests when financial reward was made contingent on correct identification of formulas in factored form. Formula preferences and transformation of novel mathematical and stimulus functions are discussed.

Adult↗
PubMedDate not supplied

Mathematical modeling of phosphorus losses from land application of hog and cattle manure.

Mathematical models may provide a means to estimate phosphorus (P) losses from land application of manure. Phosphorus losses typically occur during brief episodes of runoff and erosion. Models must be able to simulate P losses during these episodes by representing the basic chemical, physical, and biological processes by which these losses occur. The mathematical model ecosys combines dynamic distributed flow of solutes and nonsolutes through runoff and erosion with convective-dispersive transport of solutes, and both biologically and thermodynamically driven transformations between solutes and nonsolutes. This model was tested against P lost in runoff, erosion, and leachate measured during 90 min of controlled rainfall at 65 mm h(-1) on soils from six sites at which different rates of manure had been applied over the previous 3 to 6 yr. Transport and transformation kinetics in the model enabled it to simulate changes of dissolved inorganic phosphorus (DIP) in runoff from >1.0 to <0.05 mg L(-1) and changes of total phosphorus (TP) in sediment from 15 to 3 mg L(-1) measured during controlled rainfall on soils with diverse P contents. Results from 60-yr model runs using these kinetics with different application rates of cattle manure indicated that (i) a positive interaction exists between annual rainfall and application rate on P losses and (ii) rates greater than 30 Mg ha(-1) yr(-1) would cause TP concentrations in water leaving the site to rise above acceptable limits. The interaction between rainfall and rate suggests that P losses from manure application at any site should be assessed under the upper range of likely rainfall intensities.

Agriculture↗
PubMed2005

Sex differences in line judgment: relation to mathematics preparation and strategy use.

This study explored visuospatial ability using a new group-administered task, the Judgment of Line Angle and Position-15 test (JLAP-15). We investigated how this task relates to the Vandenberg Mental Rotation Test and whether the sex difference in performance could be explained by the number of prior mathematics courses or strategy used. Undergraduates (n=86 men and 112 women) completed the two tests and reported their strategies. Men had higher scores than women on both tests (d=1.04 for JLAP-15 and 1.10 for the Vandenberg Mental Rotation Test), with a significant intertask correlation of .41. Regression analyses indicated that strategy type, number of mathematics courses completed, and sex were significant predictors of performance on the JLAP-15 but only accounted for 21% of the variance.

Adult↗