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The discussion of purity of method usually emphasizes the study of particular proofs of mathematical practice. A critique of this position questions the value of purity by claiming that "mathematical progress" depends essentially on the use of impure methods. This article shows that a more holistic perspective, focusing on how purity claims can operate in the construction of autonomous theories, allows us to identify a context where purity of method acquires value in mathematical practice. In particular, the relevance of such demands is shown in the case of Kronecker's and Dedekind's algebraic number theories. [ABSTRACT FROM AUTHOR]

This article addresses women's representation during the Colombian armed conflict by analyzing the coverage given by Colombia's longest-running news magazine Semana. The research work involved going through every number published by the magazine in its print edition between January 1995 and December 2014. In total, 873 numbers were studied, detecting 2,080 pieces of news regarding the Colombian armed conflict, all published in the Nation section. Each piece was systematically disaggregated to find out women's participation quantitatively and qualitatively, explore their representation within the news body, and determine the variety of roles with which they have been symbolized in Semana. The study applied the gender perspective in a cross-cutting manner to distinguish the social attributions, ideas, representations, and prescriptions constructed, taking as a reference sexual differentiation from agenda-setting analysis. In conclusion, the invisibility of women's social-political representation is based not only on the absence of news events or decision-making positions but also on what we have conceptualized as (in)visibility processes. Despite being actors of events, women remained irrelevant for society and media due to multiple strategies analyzed in the present work. [ABSTRACT FROM AUTHOR]

Control charts are widely used to monitor the quality of industrial processes. It is quite common to assume that the random variable associated to the quality characteristic has a Normal distribution, and the control limits are defined so that the probability of obtaining a false alarm is 0.0027. However, the quality characteristic could follow a different distribution in practice, and this fact could have an impact on the efficiency of the control chart. In this paper, a Monte Carlo simulation study is carried out to evaluate empirically the impact of the lack of the normality assumption on the control chart for the mean. Different probabilistic distributions are considered. In addition, under control and out of control processes are considered. The results derived from the simulation study suggest that control charts are an effective tool when the distribution of the quality characteristic is slightly asymmetric. However, a large number of samples or larger sample sizes are required to obtain similar results to the case of symmetric distributions. In the case of asymmetric distributions, it is necessary to increase the sample sizes to obtain acceptable results. Finally, control charts are not recommended under evident cases of non-normality. [ABSTRACT FROM AUTHOR]

The knowledge of Mathematics teachers has been a very prominent focus of attention in the last decades. However, it leaves aside one of the dimensions involved in the development of this type of knowledge, specifically the knowledge of Mathematics teacher educators. In this paper, we discuss a mathematics teacher educator's knowledge in the context of classes on Euclid's division algorithm theorem in a Number Theory course for prospective secondary teachers. Some indicators of this specialized knowledge of mathematics teacher educators are presented and discussed. El conocimiento de los profesores de matemáticas ha sido un foco de atención muy activo en las últimas décadas. Sin embargo, tales focos dejan de lado una de las dimensiones involucradas en el desarrollo de dicho conocimiento, específicamente el conocimiento del formador de profesores de matemáticas. En este artículo, discutimos el conocimiento de un formador en el contexto de un curso de Teoría de números, para futuros profesores de secundaria, al probar el teorema del algoritmo de división de Euclides. Se presentan y se discuten algunos indicadores de este conocimiento del formador. [ABSTRACT FROM AUTHOR]

Canon 1733 includes the concept of "mediation" in administrative procedures - as an activity entrusted to authorized persons, not as a specific legal framework. Canonical teaching on this matter is limited, and practical applications by specific organizations (even those cited in the canon itself) are likewise rare. This study offers a number of theoretical reflections on mediation and its appropriate application in practice. [ABSTRACT FROM AUTHOR]

The teaching of probability in basic primary school in Colombia is guided by the 1998 Basic Competence Standards (Estándares Básicos de Competencias), but different studies have shown that teaching stochastic thinking is of no greater importance in classroom. The development of probabilistic thinking is crucial for students to deal more effectively with decision making in mathematical or everyday life situations, to manage uncertainty appropriately, and to develop skills to look beyond the apparent, especially in the face of statistical information currently prevalent in the media. Based on the historical-cultural perspective and the critical dialectical approach, this work analyzes how, through the theoretical and methodological framework called Teaching Guiding Activities, a group of primary school teachers from the Cristóbal Colón Educational Institution in Medellín managed to make a disciplinary approach to Probability through games and collectively build pedagogical reflections on their work. The information was collected through interviews and training sessions. It is concluded that it is fundamental for teachers to strengthen their disciplinary knowledge about Probability, that their conceptions about chance are linked to beliefs of a mystical or divine nature, which interferes with the objectivity of teaching, and that they recognize that games are a potential strategy for teaching stochastic concepts. [ABSTRACT FROM AUTHOR]

Textbooks and courses in Abstract Algebra (or Modern Algebra) present and explain several kinds of algebraic structures --such as abelian groups, vector spaces, rings, ideals and fields-- as if these were "free constructions of the human spirit". Usually mathematicians treat these structures as defined and analyzed in terms of operations which are characterized by properties which are presented as if comming up from a theoretical and purely platonic vacuum of ideas, in spite that they have been obtained indeed by inference and abstraction from well know, concrete operations in subjects such as Euclidean Geometry, Number Theory and Real Analysis. No considerations are done in those books about the existence and knowledge of physical objects endowed with mutual linkages, which are faithful models (or examples) of such algebraic structures with their inner operations. This paper presents one of those models, consisting of a class of electrical objects, the so-called electrical quadrupoles, which may be mutually connected in parallel (representing an "addition" between them) or in series (representing a "product' between them). Analysing these systems and these electrical operations, it is shown here how to construct a model of several of the above mentioned algebraic structures. [ABSTRACT FROM AUTHOR]

Objective: to characterize the adipose tissue of 7 to 18 years old schoolchildren . Material and methods: descriptive, correlational, cross-sectional study. Population: 224.200 students from public and private schools from Caldas in 2007, represented by 1,139 students (538 women, 601 men) probabilistic random sample in five municipalities. Technique: anthropometric measurement observation. Analysis: average, standard deviation, correlations between variables, hypothesis testing and significance of the differences between means were calculated using the Statgraphics 5.1 plus program. Results: average fat percentages were higher than those in the international reference population. Highly significant differences (P<0.01) in fat percentage were found between genders being higher in women. The nutritional classification from the energy reserve for men showed deficit 11%, normal 86.5% and excess 2,5%; for women it showed deficit 11.9%, normal 84.3% and excess 3.8%. Taking 85 and 95 percentiles of the sum of fat folds of triceps and subescapular for age as overweight and obesity criterion , the values varied slightly: 7.7% and 10.8% overweight for men and women respectively, and 3.3% and 1.1% obesity. In fat percentage (⩾25% ⩾32% men and women) obesity was found in 13.2% men and 13.6% women. These values are closer to those reported in recent international studies. Conclusions: women had more adipose tissue in all age groups and the studied population had a greater fat percentage than the international reference population. [ABSTRACT FROM AUTHOR]

The construction of a numerical sequence requires an ordinal model of conceptual support that can be defined by the given relationships in a system of progressions. Taking into account the ordinal model of conceptual support leads us to a coherent conceptual/interpretative system which takes into consideration conceptions and beliefs regarding numerical sequencing that immediately takes us back to epistemological and didactic considerations. Epistemological approaches are confined to looking at the nature, origin and mode of existence of the natural number and elementary arithmetic, so that construction of the numerical sequence relies, at this point, on the conclusions that are drawn in regard to the said problem. [ABSTRACT FROM AUTHOR]

In this work, some recreational aspects related to the Fibonacci sequence, as well as other recursive sequences, are shown. Moreover, in order to provide an educational application, some games and tricks based in the properties of that sequence are proposed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to reject the structuralist pretension to conceive of theoretical models as isomorphic to real structures of the world. By means of a series of examples drawn from physics, I show that a phenomenon can be characterized in different ways, complementary and equivalent with each other, and such that none of them is more real or more fictive than the other ones. I defend that the isomorphism relation can be held only among algebraic structures, and, secondly, that nature cannot be defined extensionally, as it were a set of fixed and immutable elements. [ABSTRACT FROM AUTHOR]

Introduction: In the XVII Century, Fermat d/eveloped the first general method to determine the minimums and maximums, in the memory Methodus ad disquirendam maximan et miniman et de tangentibus linearum curvarum, being a purely algorithmic procedure with no demonstrative foundation at all, and in which Fermat introduces the adequality technique, previously used by Diofantus in the Alexandria School. The vague and laconic way in which Fermat showed the Methodus has generated some interpretations under infinitesimal calculus terms, and one of them says that in the Methodus sub lies the calculation of a derivation that equals zero. Objective: To make a detailed study of the way Fermat explains his maximums and minimums method in the Methodus and discusses the anachronism interpretations given by some experts about his method. Methods: Based on the texts mentioned in the bibliography we make a historical scrutiny with the main objective of studying and analyzing the method showed by Fermat. Results: The detailed study is made, the method is applied to obtain a minimum in the problem of the segment division and the interpretations given by some experts are analyzed under the current standards. These interpretations must be seen carefully, because they force the method showed by Fermat. [ABSTRACT FROM AUTHOR]

The object of this presentation consists of analyzing the knowledge that is put into play when the students need to give some validation of their productions. For it, we look for classes fragments on numerical interpretations in the first year of the basic education corresponding to data of an research project on the learning and the education of the numeration system directed by D. Lerner. It interests to us to reflect approaches of the impact on the infantile numerical learning that can get to have the validation processes, in which the students introduce themselves in the criteria search to settle down if their productions have been correct and about some educational interventions directed to install and to maintain such processes. [ABSTRACT FROM AUTHOR]