Some errors in the learning of algebra suggest students have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing in order to analyze the students' capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process depending on the characteristics of the algebraic statements given. We designed a written questionnaire composed of eight closed algebraic statements expressed symbolically, which was administered to 55 students who had finished their compulsory education and that had some previous experience in problem posing. In our analysis of the data, we examine both syntactic and semantic structures of the problem posed. We note that in most cases students posed problems with syntactic structures different to those given. They did not include computations within variables, and changed the kinds of relationships connecting variables. Students easily posed problems for statements with additive structures. Other differences in the type of problems posed depend on the characteristics of the given statements.
We define the cohomology categorical groups of a complex of symmetric categorical groups, and we construct a long 2-exact sequence from an extension of complexes. As special cases, we obtain Ulbrich cohomology of Picard categories and the Hattori-Villamayor-Zelinsky sequences associated with a ring homomorphism. Applications to simplicial cohomology with coefficients in a symmetric categorical group, and to derivations of categorical groups are also discussed.
Abstract. If is a group, then the category of -graded categorical groups is equivalent to the category of categorical groups supplied with a coherent left-action from . In this paper we use this equivalence and the homotopy classification of graded categorical groups and their homomorphisms to develop a theory of extensions of categorical groups when a fixed group of operators is acting. For this kind of extensions we show a suitable Schreier's theory and a precise theorem of classification, including obstruction theory, which generalizes both known results when the group of operators is trivial (categorical group extensions theory) or when the involved categorical groups are discrete (equivariant group extensions theory).
The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact spaces and manifolds. The notion of exterior weak N-S-equivalences is given by exterior maps which induce isomorphisms on the k-th N-exterior homotopy groups π N k for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray localized by exterior weak N-S-equivalences is called the category of exterior N-Stypes. The existence of closed model structures in the category of exterior spaces permits to establish equivalences between homotopy categories obtained by dividing by exterior homotopy relations, and categories of fractions (localized categories) given by the inversion of classes of week equivalences. The family of neighbourhoods 'at infinity' of an exterior space can be interpreted as a global prospace and under the condition of first countable at infinity we can consider a global tower instead of a prospace. The objective of this paper is to use localized categories to find the connection between S-types of exterior spaces and S-types of global towers of spaces. The main result of this paper establishes an equivalence between the category of Stypes of rayed first countable exterior spaces and the category of S-types of global towers of pointed spaces. As a consequence of this result, categories of global towers of algebraic models localized up to weak equivalences can be used to give some algebraic models of S-types.The authors acknowledge the financial support given by the projects FOMENTA 2007/03 and MTM2007-65431.
Homotopy categorical groups of any pointed space are defined via the fundamental groupoid of iterated loop spaces. This notion allows, paralleling the group case, to introduce the notion of K-categorical groups K i R of any ring R. We also show the existence of a fundamental categorical crossed module associated to any fibre homotopy sequence and then, K 1 R and K 2 R are characterized, respectively, as the homotopy cokernel and kernel of the fundamental categorical crossed module associated to the fibre homotopy sequence F R dR G G BGLR qR G G BGLR + .As consequence, the 3th level of the Postnikov tower of the K-theory spectrum of R is classified by this categorical crossed module.
ObjectiveDescribe the design and implementation of an intervention to confront the abuse and disrespect of women during childbirth care in Mexico.MethodsTwo methodological strategies were contemplated. The first consisted of a review of conventional literature and gray literature for Latin America and the Caribbean, whose objective was to identify previous experiences in the design of interventions to address abuse and disrespect of women during delivery care. The second was design and implementation of the intervention in national level, it was carried out between 2014–2016.ResultsLiterature review: Only seven articles were identified in the category of interventions in Latin America; however, none of them contributed content or methodologies that could be used to design the training.Intervention designA 40 hour training workshop was designed for multidisciplinary health personnel [PSM] involved in obstetric care. The state head of the family violence program saw the facilitating team from a profile defined by the research team. The purpose was to train the facilitating team as replicators of the workshops, for which the training was divided into thematic contents [human rights, reproductive health, maternal death, clinical practice guidelines], and technical [group dynamics to favor personal reflection and the one related to the care provided to women who come for obstetric care].The Ministry of Health organized training in stages, to cover the 32 entities in the country.ConclusionSome needs have been identified: It will be necessary to involve the hospital authorities, middle and top managers of the entities, decision makers to state level to consolidate this initiative.
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