Influence of quantities representation in solving word problems in the worksheet environment

Hemos llevado a cabo una experimentación en la que pretendíamos observar las consecuencias de enseñar a resolver problemas de manera algebraica en el entorno de la hoja de cálculo a un grupo de estudiantes de primer curso de secundaria que no habían sido introducidos previamente en el mundo del álgebra. En este artículo ofreceremos ejemplos de fenómenos de anclaje en las formas de resolver propias de la aritmética por parte de algunos alumnos cuando resolvían en la hoja de cálculo. Mostraremos cómo estas resoluciones aritméticas se veían influidas por la enseñanza y el entorno dando lugar a: (1) la imposibilidad de introducir una fórmula en una celda que no hubiera sido etiquetada previamente con un nombre propio del espacio semiótico en que se ofrecía el problema; y (2) la aparición de resoluciones con características aritméticas en las que se operaba con lo desconocido.We have carried out an experiment in which we intended to observe the consequences of teaching the algebraic way of solving problems in the spreadsheet environment to a group of secondary school freshmen that had not been previously entered into the realm of algebra. In this paper, we will offer examples of anchoring phenomena in arithmetical methods by some students when solving problems in the spreadsheet. We will show how these arithmetic resolutions were influenced by the teaching sequence and the environment resulting in: (1) the inability to enter a formula in a cell that had not previously been labelled with a name proper to the semiotic space in which the problem has been offered; (2) the emergence of resolutions with arithmetical characteristics in which students operated with the unknown

Hacia profesores artificiales en la resolución algebraica de problemas verbales

Presentamos los fundamentos del diseño de un sistema tutorial inteligente para la enseñanza y aprendizaje de la resolución de problemas verbales aritmético-algebraicos. El programa resultante admite resoluciones aritméticas y algebraicas, establece la validez de las acciones atendiendo a las restricciones del problema y puede generar ayudas a demanda, tras identificar la línea de resolución que se está siguiendo. El sistema es capaz de determinar parte de las características del estudiante como resolutor con respecto al modelo de competencia. Con este fin usamos la idea de esquema conceptual. De esta forma podemos clasificar las acciones de los estudiantes cuando resuelven problemas verbales de más de una etapa mediante un criterio que tiene en cuenta la tarea y las decisiones que se toman. Para finalizar, ofrecemos líneas futuras y preguntas de investigación que quedan abiertas

On the Measurement of Privacy as an Attacker's Estimation Error

A wide variety of privacy metrics have been proposed in the literature to evaluate the level of protection offered by privacy enhancing-technologies. Most of these metrics are specific to concrete systems and adversarial models, and are difficult to generalize or translate to other contexts. Furthermore, a better understanding of the relationships between the different privacy metrics is needed to enable more grounded and systematic approach to measuring privacy, as well as to assist systems designers in selecting the most appropriate metric for a given application. In this work we propose a theoretical framework for privacy-preserving systems, endowed with a general definition of privacy in terms of the estimation error incurred by an attacker who aims to disclose the private information that the system is designed to conceal. We show that our framework permits interpreting and comparing a number of well-known metrics under a common perspective. The arguments behind these interpretations are based on fundamental results related to the theories of information, probability and Bayes decision.Comment: This paper has 18 pages and 17 figure

Cophenetic metrics for phylogenetic trees, after Sokal and Rohlf

Phylogenetic tree comparison metrics are an important tool in the study of evolution, and hence the definition of such metrics is an interesting problem in phylogenetics. In a paper in Taxon fifty years ago, Sokal and Rohlf proposed to measure quantitatively the difference between a pair of phylogenetic trees by first encoding them by means of their half-matrices of cophenetic values, and then comparing these matrices. This idea has been used several times since then to define dissimilarity measures between phylogenetic trees but, to our knowledge, no proper metric on weighted phylogenetic trees with nested taxa based on this idea has been formally defined and studied yet. Actually, the cophenetic values of pairs of different taxa alone are not enough to single out phylogenetic trees with weighted arcs or nested taxa. In this paper we define a family of cophenetic metrics that compare phylogenetic trees on a same set of taxa by encoding them by means of their vectors of cophenetic values of pairs of taxa and depths of single taxa, and then computing the $L^p$ norm of the difference of the corresponding vectors. Then, we study, either analytically or numerically, some of their basic properties: neighbors, diameter, distribution, and their rank correlation with each other and with other metrics.Comment: The "authors' cut" of a paper published in BMC Bioinformatics 14:3 (2013). 46 page

Formas de construir nombres y referirse a las cantidades en las actuaciones de alumnos de Secundaria al resolver problemas verbales en el entorno de la hoja de cálculo

Presentamos parte de los resultados de un proyecto de investigación que pretende identificar qué características de la hoja de cálculo obstaculizan y cuáles promueven la evolución hacia un pensamiento algebraico. Concretamente, mostramos resultados relacionados con los nombres que los estudiantes construyen para las cantidades y las formas de referirse a ellas cuando resuelven problemas verbales. El grupo de estudiantes observado cursaba primero de secundaria, no había recibido instrucción previamente en la resolución de problemas utilizando el lenguaje del álgebra y se les enseñó a resolverlos en el entorno de la hoja de cálculo

Shall I post this now? Optimized, delay-based privacy protection in social networks

The final publication is available at Springer via http://dx.doi.org/10.1007/s10115-016-1010-4Despite the several advantages commonly attributed to social networks such as easiness and immediacy to communicate with acquaintances and friends, significant privacy threats provoked by unexperienced or even irresponsible users recklessly publishing sensitive material are also noticeable. Yet, a different, but equally significant privacy risk might arise from social networks profiling the online activity of their users based on the timestamp of the interactions between the former and the latter. In order to thwart this last type of commonly neglected attacks, this paper proposes an optimized deferral mechanism for messages in online social networks. Such solution suggests intelligently delaying certain messages posted by end users in social networks in a way that the observed online activity profile generated by the attacker does not reveal any time-based sensitive information, while preserving the usability of the system. Experimental results as well as a proposed architecture implementing this approach demonstrate the suitability and feasibility of our mechanism.Peer ReviewedPostprint (author's final draft