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PubMed1998

[Novel mathematical approach to determination of antibiotics concentration by agar diffusion method. Analysis of graphical, table and mathematical options of relative biological activity estimation].

Several varieties of relative biological activity estimation are comparatively analyzed and illustrated by an example of tylosin. For visual demonstration the estimates with the equation of a straight line are represented graphically. It is concluded that the design equations in the State Pharmacopeia XI (USSR) should be respectively replaced. The advantages of the variety for the biological activity estimation with the one-point intercept form of the equation of a straight line are illustrated by particular examples.

Agar↗
PubMedDate not supplied

Mathematics education and students with learning disabilities: introduction to the special series.

The prevalence of students with mathematics learning disabilities has triggered an interest among special education researchers and practitioners in developing an understanding of the needs of this group of students, and in identifying effective instructional programming to foster their mathematical performance during the school years and into adulthood. Research into the characteristics of students with mathematics learning disabilities is being approached from different perspectives, including developmental, neurological and neuropsychological, and educational. This diversity helps us develop a broader understanding of students' learning needs and difficulties. Special education assessment practices encompass a variety of approaches, including norm-referenced, criterion-referenced, and nonstandardized procedures, depending on the specific assessment questions professionals seek to answer. Students' mathematical knowledge and conceptual understanding must be examined to determine their strengths and weaknesses, curriculum-based progress, and use of cognitive strategies to arrive at mathematical solutions. Research findings have identified empirically validated interventions for teaching mathematics curricula to students with mathematics learning disabilities. Research studies have been grounded in behavioral theory and cognitive psychology, with an emergent interest in the constructivist approach. Although research studies have focused primarily on computational performance, more work is being conducted in the areas of story-problem solving and technology. These areas as well as other math curricular skills require further study. Additionally, the needs of adults with math LD have spurred educators to examine the elementary and secondary math curricula and determine ways to infuse them with life skills instruction accordingly. As the field of mathematics special education continues to evolve, special educators must remain cognizant of the developments in and influences on the field of mathematics education. Reform efforts have shaped the field significantly since the 1950s, contributing to the curriculum offered in mathematics textbooks and the pedagogical practices taught in higher education courses. Mathematics educators continue to search for a better understanding of how children learn mathematics; this process is shaped by the prevailing theoretical orientations and research methodologies. This special series in mathematics special education provides readers with information about the characteristics of students with mathematics learning disabilities, assessment procedures, mathematics programming, teacher preparation, and future directions for the field. The series originated as a result of discussions with Dr. Lee Wiederholt and Dr. Judith K. Voress, who saw a need for the compilation of recent research and best practices in mathematics special education. I thank them for their support of and thoughtful insights about the development of this series. I also appreciate the support of Dr. George Hynd and his editorial assistant, Kathryn Black, in finalizing the details for publication. Finally, I am most appreciative of the authors' contributions to this series; their work continues to significantly influence the development of the field of mathematics special education and programming for students with mathematics learning disabilities.

Adolescent↗
PubMed2004

Familial aggregation patterns in mathematical ability.

Mathematical talent is an asset in modern society both at an individual and a societal level. Environmental factors such as quality of mathematics education undoubtedly affect an individual's performance, and there is some evidence that genetic factors also may play a role. The current study was performed to investigate the feasibility of undertaking genetics studies on mathematical ability. Because the etiology of low ability in mathematics is likely to be multifactorial and heterogeneous, we evaluated families ascertained through a proband with high mathematical performance in grade 7 on the SAT to eliminate, to some degree, adverse environmental factors. Families of sex-matched probands, selected for high verbal performance on the SAT, served as the comparison group. We evaluated a number of proxy measures for their usefulness in the study of clustering of mathematical talent. Given the difficulty of testing mathematics performance across developmental ages, especially with the added complexity of decreasing exposure to formal mathematics concepts post schooling, we also devised a semiquantitative scale that incorporated educational, occupational, and avocational information as a surrogate for an academic mathematics measure. Whereas several proxy measures showed no evidence of a genetic basis, we found that the semiquantitative scale of mathematical talent showed strong evidence of a genetic basis, with a differential response as a function of the performance measure used to select the proband. This observation suggests that there may be a genetic basis to specific mathematical talent, and that specific, as opposed to proxy, investigative measures that are designed to measure such talent in family members could be of benefit for this purpose.

Aptitude↗
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↗
PubMed2003

Mathematics deficits in adolescents with bipolar I disorder.

OBJECTIVE: This study examined mathematical ability in adolescents with bipolar I disorder, compared to adolescents with major depressive disorder and psychiatrically healthy comparison subjects. METHOD: Participants (N=119) included adolescents in remission from bipolar disorder (N=44) or major depressive disorder (N=30), as well as comparison subjects (N=45) with no psychiatric history. Participants were assessed with the following measures: the Wide-Range Achievement Test, Revised 2 (WRAT-R2), Peabody Individual Achievement Test, Bay Area Functional Performance Evaluation Task-Oriented Assessment (functional mathematics subtest), Test of Nonverbal Intellegence-2, and a self-report of mathematics performance. RESULTS: WRAT-R2 and Peabody Individual Achievement Test scores for spelling, mathematics, and reading revealed that adolescents with bipolar disorder had significantly lower achievement in mathematics, compared to subjects with major depressive disorder and comparison subjects. Results for the Test of Nonverbal Intellegence-2 were not significantly different between groups. Adolescents with bipolar disorder took significantly longer to complete the Bay Area Functional Performance Evaluation mathematics task. Significantly fewer adolescents with bipolar disorder (9%) reported above-average mathematics performance, compared with the other groups. CONCLUSIONS: Adolescents with remitted bipolar disorder have a specific profile of mathematics difficulties that differentiates them from both adolescents with unipolar depression and psychiatrically healthy comparison subjects. These mathematics deficits may not derive simply from more global deficits in nonverbal intelligence or executive functioning, but may be associated with neuroanatomical abnormalities that result in cognitive deficits, including a slowed response time. These deficits suggest the need for specialized assessment of mathematics as part of a comprehensive clinical follow-up treatment plan.

Adolescent↗
PubMed2005

Cognitive skills in mathematical problem solving in Grade 3.

BACKGROUND: Research on the relationship between cognitive skills and mathematical problem solving is usually conducted on adults or on participants with acquired deficits associated with brain injury (e.g.Cipolotti, 1995; Cohen, Dehaene, & Verstichel, 1994; McCloskey, 1992). AIMS: In these studies we wanted to make a contribution to the field of children's mathematical problem solving. The first aim of this study was to investigate whether mathematical problem solving in children is merely determined by semantic elaboration, as hypothesized in some of the models of adult processing (semantic hypothesis). In addition, we aimed to investigate whether there is a continuum from very good to very poor mathematical problem solving among children with mathematical learning disabilities showing immature cognitive skills (maturational lag hypothesis). SAMPLE: The participants were 376 third graders and 107 second graders. METHOD: The internal structure of the data was analysed with a principal components analysis. In addition, two MANOVA were conducted to compare children with learning disabilities or problems with age-matched and performance-matched subjects. RESULTS: Two components, a semantic and a non-semantic one, were needed to account for an adequate fit of the dataset. In addition, children with mathematical learning disabilities had less-developed cognitive skills compared with peers without learning disabilities, but they did not differ from younger children on seven of the nine cognitive skills. CONCLUSIONS: This study highlighted that children's mathematical problem solving is not determined by one general component. The picture is more complex, since two mathematics components were found. In addition, although our findings point in the direction of the maturational lag hypothesis it may be important to assess the different cognitive skills and especially assess the number system knowledge, since it seems below average in children with mathematical learning disabilities, compared with the knowledge of younger children with comparable skills in mathematics.

Child↗
PubMed2006

Relationship between students' self-assessment of their capabilities and their teachers' judgments of students' capabilities in mathematics problem-solving.

The study examined the judgments made by four seventh-grade mathematics teachers of their 107 students' competence in solving mathematics problems. Simultaneously, the 107 students made self-efficacy judgments about their capability in solving mathematics problems. The two sets of judgments were tested for predicting students' mathematics performance. Also, students' prior mathematics achievement was studied for its influence on both teachers' and students' judgments and students' mathematics performance. Teachers were asked to make judgments of each student for every mathematics problem solved. Results were consistent with prior research indicating that students' mathematics self-efficacy beliefs were highly predictive of their performance. Path analysis indicated that the mathematics teachers' judgments were also highly predictive of students' performance and self-efficacy. In turn, these variables predicted students' postperformance judgments. Combining students' self-efficacy judgments and teachers' judgments of students increased predictiveness for students' mathematics performance. Educational implications were also discussed.

Achievement↗
PubMed1995

Psychovegetative syndrome diagnosis: an automated psychophysiological investigation and mathematical modeling approach.

1. INTRODUCTION. The main purpose of our work was to create the informational expert system of psychovegetative syndrome diagnosis by applying clinical data and estimating the functioning of the central and peripheral part of regulatory apparatus of the human organism, taking into consideration parallel and consecutive sensory, motor, associative, emotional drive systems, and internal body state. We used automatized psychophysiological investigation and mathematical models. For this purpose the following principal tasks have been prepared: the creation of database of quantifiable estimation patient state; the definition and automation of psychophysiological investigation; mathematical modeling of vegetative functions using a non-invasive sample and its connection with real psychophysiological experiment; mathematical modeling of organisms inner medium homeostasis; and the creation of an informational-expert system of psychovegetative syndrome diagnosis. 2. DATABASE OF ESTIMATION OF PATIENTS STATE. The medical records of the DB "PATIENT" contain data on patient psychic and somatoneurological status. 3. AUTOMATED PSYCHOPHYSIOLOGICAL INVESTIGATION. Psychophysiological investigation enables estimation of the functioning of several subsystems of the human organism and establishes an interrelationship between them by means of electrophysiological data and performance parameters. The study of psychophysiological provision of behavior by psychophysiological investigation enables us to get information about adaptational mechanisms of the patient under certain environmental loads. By means of special mathematical provision, the mathematical elaboration of biosignals as performance parameters has been realized; also realized were the formation of received parameters in the database, the estimation of separated parameters in the view of informativity, and the establishment of diagnostic patterns. 4. MATHEMATICAL MODELS FOR ESTIMATION INTERNAL BODY STATE. The proposed mathematical models allow investigation of homeostatic regulation in various intensities of the metabolic processes and external load. This approach in mathematical models allows us to characterize the relations between the central and peripheral parts of the regulatory mechanisms, using non-invasive samples under psychophysiological investigation and the simulation of different surroundings for brain cells functioning. 5. INFORMATION-EXPERT SYSTEM. Proceeding from the principle of psychoneural unity, we characterized the functioning mechanisms of CNS by means of automatized EEG analysis, visually evoked potential analysis, estimated psychic status, and the characteristics of neural system biochemical processes received by mathematical modeling. By using the indices of the viscero-vegetative and somatolocomotor system (as well as parameters received by automatized analysis of ECG), the EEG respiratory signal--from mathematical models of vegetative functions decision support system applied in estimation of a peripheral block of the regulatory system--is reflected in diagnosis of certain syndromes. The informational expert system, proceeding from the functioning of the human organism's regulatory apparatus, diagnosed psychovegetative syndrome and described the mechanisms of its development. 6. CONCLUSION. The informational expert system enables estimation of the functioning of a human organism as a whole and can be introduced in the sphere of practical medicine and professional orientation as well as in laboratories of experimental psychology and neurosciences.

Brain↗
PubMed2005

Mathematical skills in Prader-Willi Syndrome.

OBJECTIVES: This paper investigates mathematical skills in Prader-Willi Syndrome (PWS), a pathological condition because of congenital alterations of chromosome pair 15. The following questions were addressed: (1) Are mathematical skills in PWS relatively more impaired with respect to other cognitive functions (as has been repeatedly but anecdotally reported)?; and (2) What is the nature of the mathematical impairment? METHODS: The first study employed the Wechsler Adult Intelligence Scale (WAIS) and an extensive battery of cognitive tasks for which norms are known. Both batteries include a mathematical section. The second study used a theoretically motivated series of mathematical tasks specifically designed to individually assess the different cognitive components underlying mathematical skills. RESULTS: Mathematical skills were found to be the most impaired cognitive abilities together with short-term memory capacity. No specific mathematical domain was seen to be unaffected in PWS participants. The clearest deficits observed concern 'syntactic' processes in number transcoding, multiplication, number facts retrieval and calculation procedures. CONCLUSION: Failure of mathematical skills is the most distinctive feature in the cognitive profile of PWS. However, to determine whether this is indeed a specific pattern of performance related to PWS, results must be compared with those obtained with patients manifesting other genetic disorders.

Adolescent↗
PubMedDate not supplied

Mathematical thinking in second-grade children with different forms of LD.

Based on their performance on a standardized achievement test, second-grade children (N = 49) were classified as having mathematics difficulties with normal reading achievement (MD only), both mathematics and reading difficulties (MD/RD), reading difficulties with normal mathematics achievement (RD only) and normal mathematics and reading achievement (NA). Each child was given a series of tasks so that we might assess their thinking across four areas of mathematics: number facts, story problems, place value, and written calculation. Children with MD/RD performed significantly worse than NA children in most areas of mathematical thinking, whereas children with MD only performed worse than NA children only on complex story problems. The MD-only group outperformed the MD/RD group on story problems and written calculation. No significant differences were found between the RD-only and NA groups on any of the tasks. The results suggested that among children with mathematics difficulties, the MD/RD subgroup is distinct from the MD-only subgroup, with the former being characterized by pervasive deficiencies in mathematical thinking and the latter by more specific deficits in problem solving.

Aptitude Tests↗
PubMedDate not supplied

Discrete mathematics in deaf education: a survey of teachers' knowledge and use.

The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world-oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.

Child↗
PubMedDate not supplied

[On the founders of the Institute of Mathematics and Physics, University of Bahia].

The reduced number of female students of mathematics at the University of Bahia School of Philosophy (Faculdade de Filosofia, Universidade da Bahia - FF/UBa) is quite surprising. To date, they are concentrated in areas traditionally viewed as feminine whereas men predominate in the mathematical fields. I have examined interview data from a few women who graduated in mathematics and went on to teach at the University of Bahia School of Mathematics (Faculdade de Filosofia - FF) and at the Institute of Mathematics and Physics (Instituto de Matemática e Física - IMF), where they were soon to outnumber men and constitute the majority of the mathematics teaching staff. In this study, I have investigated the course of their careers over time: from their early student days, through their time as teaching assistants and professors, and finally as founders of the Institute of Mathematics and Physics, in 1960. Special reference is made to Martha Maria de Souza Dantas, organizer of the I Brazilian Conference on Mathematics Teaching, an event which has provided the groundwork for what was to become the Institute (IMF); and to Arlete Cerqueira Lima, the mastermind behind its creation.

Brazil↗
PubMed1996

Thoughts about judging dialysis treatment: mathematics and measurements, mirrors in the mind.

This article considers the contributions of the urea kinetic parameters, , Kt/V and nPCR, to beliefs about judging dialysis treatment. The values calculated from any set of data depend on the model (eg, 1 pool, 2 pool, or so forth) and the mathematics used to derive the values. Yet, the medical community debates the value of Kt/V at which patients should be treated even as they debate the mathematics by which Kt/V should be calculated. The resulting ambiguities about proper targets and methods may actually frustrate large-scale clinical quality enhancement initiatives. The casual use of mathematical models can mislead unwary clinicians and compromise quality enhancement. For example, the observation that a high Kt/V is associated with a high nPCR leads to the widespread belief that improving Kt/V must substantially improve nutritional status. The association, however, results mainly, if not solely, from mathematical coupling rather than biological cause and effect. The misguided belief could contribute to ineffective treatment of malnourished patients. Complicated mathematical models are useful tools for describing and evaluating evolving concepts about the physical properties of dialysis and for estimating the effects of new therapies. However, the changing nature of concepts, and therefore the mathematical models designed to support them, makes clinical care ideas that attempt to shoehorn old concepts into new equations. It is the result of the dialysis treatment, not the mathematical path by which it is achieved, that is associated with improved patient health. Consequently, clinical care should be guided by simple measurements that reflect the outcome of the treatment, not by mathematical parameters.

Humans↗