Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Educational Documentation and its Contribution to Educational Policy. 'La documentación educativa y su contribución a la política educativa'.

Debido a que en la segunda mitad del siglo XX se produjo un incremento importante en el numero de instituciones y personas que se dedican de manera profesional a la investigación en todos los campos de conocimiento, fue necesario un desarrollo de mejores herramientas para sistematizar la información de las investigaciones y hacerla más accesible. Es por eso que surgen las bases de datos o bancos de datos. El texto se centra en la definición, tipos, características, planeación, diseño y desarrollo de estas bases de datos.

La sabiduría como competencia gerencial

Aunque el concepto de sabiduría ha sido ampliamente estudiado por expertos de áreas como la filosofía, la religión y la psicología, aún enfrenta limitaciones en cuanto a su definición y evaluación. Por esto, el presente trabajo tiene como objetivo, formular una definición del concepto de sabiduría que permita realizar una propuesta de evaluación del concepto como competencia en los gerentes. Para esto, se realizó un análisis documental de tipo cualitativo. De esta manera, se analizaron diversos textos sobre la historia, las definiciones y las metodologías para evaluar tanto la sabiduría como las competencias; diferenciando la sabiduría de otros constructos y analizando la diferencia entre las competencias generales y las gerenciales para posteriormente, definir la sabiduría como una competencia gerencial. Como resultado de este análisis se generó un prototipo de prueba denominado SAPIENS-O, a través del cuál se busca evaluar la sabiduría como competencia gerencial. Como alcances del instrumento se pueden identificar la posibilidad de medir la sabiduría como competencia en los gerentes, la posibilidad de dar un nuevo panorama a las dificultades teóricas y empíricas sobre la sabiduría y la posibilidad de facilitar el estudio de la sabiduría en ambientes reales, más específicamente en ambientes organizacionales.

La influencia de factores educativos y familiares sobre el aprendizaje de una segunda lengua, y los efectos sobre la inteligencia y cognición

Actualmente, la investigación científica acerca de la influencia de los factores educativos y familiares en el aprendizaje de una segunda lengua (L2) es limitada. En comparación, los efectos que tiene la L2 en la inteligencia y cognición han sido más estudiados. Por esta razón, el artículo presenta una revisión de la literatura empírica existente que relaciona lo mencionado anteriormente, ampliando así la temática del bilingüismo. Se buscaron artículos en cuatro bases de datos (PSICODOC, ISI Web of knowledge y SCOPUS), usando palabras claves específicas, en el periodo de 1990 hasta el 2012. De 79 artículos encontrados, 34 cumplieron con los criterios de inclusión para la revisión. Asimismo, se tuvieron en cuenta dos libros, de los cuales se revisó un capítulo por cada uno según los mismos criterios. En conjunto, los resultados arrojaron importantes datos teóricos y de investigación que relacionan el éxito en el aprendizaje de una L2 con la inteligencia y cognición, según la influencia de los factores educativos y familiares. En conclusión, se identificaron más factores educativos que familiares; lo cual a concepto de la autora evidencia la limitada investigación que se ha hecho sobre los factores familiares en el bilingüismo actualmente.

Development, implementation and application of electronic structural descriptors to the analysis of the chemical bonding, aromaticity and chemical reactivity

En la literatura sobre mecànica quàntica és freqüent trobar descriptors basats en la densitat de parells o la densitat electrònica, amb un èxit divers segons les aplicacions que atenyin. Per tal de que tingui sentit químic un descriptor ha de donar la definició d'un àtom en una molècula, o ésser capaç d'identificar regions de l'espai molecular associades amb algun concepte químic (com pot ser un parell solitari o zona d'enllaç, entre d'altres). En aquesta línia, s'han proposat diversos esquemes de partició: la teoria d'àtoms en molècules (AIM), la funció de localització electrònica (ELF), les cel·les de Voroni, els àtoms de Hirshfeld, els àtoms difusos, etc. L'objectiu d'aquesta tesi és explorar descriptors de la densitat basats en particions de l'espai molecular del tipus AIM, ELF o àtoms difusos, analitzar els descriptors existents amb diferents nivells de teoria, proposar nous descriptors d'aromaticitat, així com estudiar l'habilitat de totes aquestes eines per discernir entre diferents mecanismes de reacció.

Museums and quality, from the concept of the museum that carries out functions to the museum that provides services

Quality management Self-evaluation of the organisation Citizens/customers satisfaction Impact on society evaluation Key performance evaluation Good practices comparison (Benchmarking) Continuous improvement In professional environments, when quality assessment of museums is discussed, one immediately thinks of the honourableness of the directors and curators, the erudition and specialisation of knowledge, the diversity of the gathered material and study of the collections, the collections conservation methods and environmental control, the regularity and notoriety of the exhibitions and artists, the building’s architecture and site, the recreation of environments, the museographic equipment design. We admit that the roles and attributes listed above can contribute to the definition of a specificity of museological good practice within a hierarchised functional perspective (the museum functions) and for the classification of museums according to a scale, validated between peers, based on “installed” appreciation criteria, enforced from above downwards, according to the “prestige” of the products and of those who conceive them, but that say nothing about the effective satisfaction of the citizen/customers and the real impact on society. There is a lack of evaluation instruments that would give us a return of all that the museum is and represents in contemporary society, focused on being and on the relation with the other, in detriment of the ostentatious possession and of the doing in order to meet one’s duties. But it is only possible to evaluate something by measurement and comparison, on the basis of well defined criteria, from a common grid, implicating all of the actors in the self-evaluation, in the definition of the aims to fulfil and in the obtaining of results.

The use of a language eliciting procedure as a tool in the establishment of teaching goals

This paper reviews a study to examine the feasibility of using elicited language samples as a basis for planning language instruction and as a measure of progress in language development.

Interpretation of recommended risk terms: differences between doctors and lay people

Objectives: To examine doctors' (Experiment 1) and doctors' and lay people's (Experiment 2) interpretations of two sets of recommended verbal labels for conveying information about side effects incidence rates. Method: Both studies used a controlled empirical methodology in which participants were presented with a hypothetical, but realistic, scenario involving a prescribed medication that was said to be associated with either mild or severe side effects. The probability of each side effect was described using one of the five descriptors advocated by the European Union (Experiment 1) or one of the six descriptors advocated in Calman's risk scale (Experiment 2), and study participants were required to estimate (numerically) the probability of each side effect occurring. Key findings: Experiment 1 showed that the doctors significantly overestimated the risk of side effects occurring when interpreting the five EU descriptors, compared with the assigned probability ranges. Experiment 2 showed that both groups significantly overestimated risk when given the six Calman descriptors, although the degree of overestimation was not as great for the doctors as for the lay people. Conclusion: On the basis of our findings, we argue that we are still a long way from achieving a standardised language of risk for use by both professionals and the general public, although there might be more potential for use of standardised terms among professionals. In the meantime, the EU and other regulatory bodies and health professionals should be very cautious about advocating the use of particular verbal labels for describing medication side effects.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Empirical mode decomposition: a novel technique for the study of tremor time series

Tremor is a clinical feature characterized by oscillations of a part of the body. The detection and study of tremor is an important step in investigations seeking to explain underlying control strategies of the central nervous system under natural (or physiological) and pathological conditions. It is well established that tremorous activity is composed of deterministic and stochastic components. For this reason, the use of digital signal processing techniques (DSP) which take into account the nonlinearity and nonstationarity of such signals may bring new information into the signal analysis which is often obscured by traditional linear techniques (e.g. Fourier analysis). In this context, this paper introduces the application of the empirical mode decomposition (EMD) and Hilbert spectrum (HS), which are relatively new DSP techniques for the analysis of nonlinear and nonstationary time-series, for the study of tremor. Our results, obtained from the analysis of experimental signals collected from 31 patients with different neurological conditions, showed that the EMD could automatically decompose acquired signals into basic components, called intrinsic mode functions (IMFs), representing tremorous and voluntary activity. The identification of a physical meaning for IMFs in the context of tremor analysis suggests an alternative and new way of detecting tremorous activity. These results may be relevant for those applications requiring automatic detection of tremor. Furthermore, the energy of IMFs was visualized as a function of time and frequency by means of the HS. This analysis showed that the variation of energy of tremorous and voluntary activity could be distinguished and characterized on the HS. Such results may be relevant for those applications aiming to identify neurological disorders. In general, both the HS and EMD demonstrated to be very useful to perform objective analysis of any kind of tremor and can therefore be potentially used to perform functional assessment.

Controls of carbon dioxide concentrations and fluxes above central London

Eddy-covariance measurements of carbon dioxide fluxes were taken semi-continuously between October 2006 and May 2008 at 190 m height in central London (UK) to quantify emissions and study their controls. Inner London, with a population of 8.2 million (~5000 inhabitants per km2) is heavily built up with 8% vegetation cover within the central boroughs. CO2 emissions were found to be mainly controlled by fossil fuel combustion (e.g. traffic, commercial and domestic heating). The measurement period allowed investigation of both diurnal patterns and seasonal trends. Diurnal averages of CO2 fluxes were found to be highly correlated to traffic. However changes in heating-related natural gas consumption and, to a lesser extent, photosynthetic activity that controlled the seasonal variability. Despite measurements being taken at ca. 22 times the mean building height, coupling with street level was adequate, especially during daytime. Night-time saw a higher occurrence of stable or neutral stratification, especially in autumn and winter, which resulted in data loss in post-processing. No significant difference was found between the annual estimate of net exchange of CO2 for the expected measurement footprint and the values derived from the National Atmospheric Emissions Inventory (NAEI), with daytime fluxes differing by only 3%. This agreement with NAEI data also supported the use of the simple flux footprint model which was applied to the London site; this also suggests that individual roughness elements did not significantly affect the measurements due to the large ratio of measurement height to mean building height.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

Cholesterol reduction using manufactured foods high in monounsaturated fatty acids: a randomized crossover study

In two separate studies, the cholesterol-lowering efficacy of a diet high in monounsaturated fatty acids (MUFA) was evaluated by means of a randomized crossover trial. In both studies subjects were randomized to receive either a high-MUFA diet or the control diet first, which they followed for a period of 8 weeks; following a washout period of 4–6 weeks they were transferred onto the opposing diet for a further period of 8 weeks. In one study subjects were healthy middle-aged men (n 30), and in the other they were young men (n 23) with a family history of CHD recruited from two centres (Guildford and Dublin). The two studies were conducted over the same time period using identical foods and study designs. Subjects consumed 38% energy as fat, with 18% energy as MUFA and 10% as saturated fatty acids (MUFA diet), or 13% energy as MUFA and 16% as saturated fatty acids (control diet). The polyunsaturated fatty acid content of each diet was 7%. The diets were achieved by providing subjects with manufactured foods such as spreads, ‘ready meals’, biscuits, puddings and breads, which, apart from their fatty acid compositions, were identical for both diets. Subjects were blind to which of the diets they were following on both arms of the study. Weight changes on the diets were less than 1 kg. In the groups combined (n 53) mean total and LDL-cholesterol levels were significantly lower at the end of the MUFA diet than the control diet by 0×29 (SD 0×61) mmol/l (P,0×001) and 0×38 (SD 0×64) mmol/l (P, 0×0001) respectively. In middle-aged men these differences were due to a mean reduction in LDL-cholesterol of ¹11 (SD 12) % on the MUFA diet with no change on the control diet (¹1×1 (SD 10) %). In young men the differences were due to an increase in LDL-cholesterol concentration on the control diet of þ6×2 (SD 13) % and a decrease on the MUFA diet of ¹7×8 (SD 20) %. Differences in the responses of middle-aged and young men to the two diets did not appear to be due to differences in their habitual baseline diets which were generally similar, but appeared to reflect the lower baseline cholesterol concentrations in the younger men. There was a moderately strong and statistically significant inverse correlation between the change in LDLcholesterol concentration on each diet and the baseline fasting LDL-cholesterol concentration (r¹0×49; P,0×0005). In conclusion, diets in which saturated fat is partially replaced by MUFA can achieve significant reductions in total and LDL-cholesterol concentrations, even when total fat and energy intakes are maintained. The dietary approach used to alter fatty acid intakes would be appropriate for achieving reductions in saturated fat intakes in whole populations.