Evaluación del desempeño profesional de docentes de matemática

Evaluar el desempeño profesional de los docentes de secundaria no es una tarea fácil, en especial cuando no se cuenta con instrumentos psicométricos cuyos resultados muestren evidencias de validez. Una de las aristas de evaluar la labor docente es quién o quiénes emiten criterios para fundamentar los juicios a los que se llegan en la evaluación. Con la presente evaluación se recabó la opinión del estudiantado que asistía a lecciones de séptimo año de tres colegios nocturnos, sobre el desempeño profesional de sus educadores de Matemática desde dos perspectivas: el perfil docente y la forma en cómo realizan la medición pedagógica los profesores. Se visualiza la evaluación del desempeño docente como el principal insumo que tiene el profesor para retroalimentar su quehacer educativo, es decir, ella más que un mecanismo de control o de calificación del profesorado, debe servir como estímulo para incentivar los procesos de autoevaluación

Desarrollo en la prueba nacional de bachillerato de matemática: una necesidad

Los programas de Matemática aprobados en el 2012 por el Consejo Superior de Educación para la primaria y secundaria cambiaron la forma en cómo se venía realizando la mediación pedagógica en las aulas costarricenses. Los procesos de enseñanza y aprendizaje ahora se deben caracterizar por la presencia de una metodología basada en la resolución de problemas, desde la cual se hace un llamado por estimular en los estudiantes el desarrollo de una serie de habilidades matemáticas generales y específicas. Ante este escenario, la prueba nacional de bachillerato de Matemática debe ser congruente con la nueva propuesta curricular, por lo que se propone en ella la incorporación de ítems de desarrollo, con el objeto que en la prueba se evalúe de forma más pertinente el constructo de competencia matemática, el cual es punto de partida en los nuevos programas. Incluir ítems de desarrollo en la prueba de bachillerato no es una tarea fácil, pues se deben establecer los lineamientos y las condiciones en el sistema educativo para que los resultados de ella sean válidos y confiables; en especial, en lo referente a su calificación, por lo es necesario crear una guía de codificación de las respuestas de los estudiantes que regule el procedimiento para la asignación de las calificaciones a los ítems de desarrollo

Competencias de los docentes de matemática según criterio estudiantil

La educación basada en competencias es una propuesta para eliminar de los procesos educativos la distancia entre teoría y práctica, con ella se pretende que la utilidad de los conocimientos para la vida se encuentre siempre presente en el acto educativo. Ante el bajo rendimiento estudiantil en Matemática, es necesario analizar los factores que lo impactan en forma directa e indirecta, uno de ellos es la formación profesional de los profesores y las competencias que deben tener o desarrollar estos para llevar a cabo una labor educativa de calidad. En esta investigación se precisaron 12 competencias profesionales que deben tener los docentes en la asignatura de Matemática a la hora de impartir clases de secundaria, según criterio del estudiantado. A partir del grado de importancia que le confirieron los estudiantes a estas competencias, se predijo la calificación del desempeño profesional docente

Modeling the AC Electrokinetic Behavior of Semiconducting Spheres

We study theoretically the dielectrophoresis and electrorotation of a semiconducting microsphere immersed in an aqueous electrolyte. To this end, the particle polarizability is calculated from first principles for arbitrary thickness of the Debye layers in liquid and semiconductor. We show that the polarizability dispersion arises from the combination of two relaxation interfacial phenomena: charging of the electrical double layer and the Maxwell–Wagner relaxation. We also calculate the particle polarizability in the limit of thin electrical double layers, which greatly simplifies the analytical calculations. Finally, we show the model predictions for two relevant materials (ZnO and doped silicon) and discuss the limits of validity of the thin double layer approximation

Dipolophoresis and Travelling-Wave Dipolophoresis of Metal Microparticles

We study theoretically and numerically the electrokinetic behavior of metal microparticles immersed in aqueous electrolytes. We consider small particles subjected to non-homogeneous ac electric fields and we describe their motion as arising from the combination of electrical forces (dielectrophoresis) and the electroosmotic flows on the particle surface (induced-charge electrophoresis). The net particle motion is known as dipolophoresis. We also study the particle motion induced by travelling electric fields. We find analytical expressions for the dielectrophoresis and induced-charge electrophoresis of metal spheres and we compare them with numerical solutions. This validates our numerical method, which we also use to study the dipolophoresis of metal cylinders.Spanish Research Agency MCI under contract PGC2018-099217-B-I00

Length Uncertainty in a Gravity's Rainbow Formalism

It is commonly accepted that the combination of quantum mechanics and general relativity gives rise to the emergence of a minimum uncertainty both in space and time. The arguments that support this conclusion are mainly based on perturbative approaches to the quantization, in which the gravitational interactions of the matter content are described as corrections to a classical background. In a recent paper, we analyzed the existence of a minimum time uncertainty in the framework of doubly special relativity. In this framework, the standard definition of the energy-momentum of particles is modified appealing to possible quantum gravitational effects, which are not necessarily perturbative. Demanding that this modification be completed into a canonical transformation determines the implementation of doubly special relativity in position space and leads to spacetime coordinates that depend on the energy-momentum of the particle. In the present work, we extend our analysis to the quantum length uncertainty. We show that, in generic cases, there actually exists a limit in the spatial resolution, both when the quantum evolution is described in terms of the auxiliary time corresponding to the Minkowski background or in terms of the physical time. These two kinds of evolutions can be understood as corresponding to perturbative and non-perturbative descriptions, respectively. This result contrasts with that found for the time uncertainty, which can be made to vanish in all models with unbounded physical energy if one adheres to a non-perturbative quantization.Comment: 12 pages, accepted for publication in Physical Review

Quantum Time Uncertainty in a Gravity's Rainbow Formalism

The existence of a minimum time uncertainty is usually argued to be a consequence of the combination of quantum mechanics and general relativity. Most of the studies that point to this result are nonetheless based on perturbative quantization approaches, in which the effect of matter on the geometry is regarded as a correction to a classical background. In this paper, we consider rainbow spacetimes constructed from doubly special relativity by using a modification of the proposals of Magueijo and Smolin. In these models, gravitational effects are incorporated (at least to a certain extent) in the definition of the energy-momentum of particles without adhering to a perturbative treatment of the back reaction. In this context, we derive and compare the expressions of the time uncertainty in quantizations that use as evolution parameter either the background or the rainbow time coordinates. These two possibilities can be regarded as corresponding to perturbative and non-perturbative quantization schemes, respectively. We show that, while a non-vanishing time uncertainty is generically unavoidable in a perturbative framework, an infinite time resolution can in fact be achieved in a non-perturbative quantization for the whole family of doubly special relativity theories with unbounded physical energy.Comment: 8 pages, accepted for publication in Physical Review

Linear and algebraic structures in function sequence spaces

Historically, many mathematicians of all ages have been attracted and fascinated by the existence of large algebraic structures that satisfy certain properties that, a priori, contradict the mathematical intuition. The aim of the present Dissertation is the study of the lineability of certain families of sequences of functions with very specific properties. The Dissertation is divided in 6 chapters, where Chapters 1, 2 and 3 focus on introducing the basic notation and main terminology of the theory of Lineability and modes of convergence that will be used along this Dissertation. In Chapter 4 we begin with the study of the algebraic size of two families of sequences of functions with different modes of convergence in the closed unit interval [0, 1]: convergence in measure but pointwise almost everywhere and pointwise but not uniform convergence. In Chapter 5 we focus our attention on the setting of (Lebesgue) integrable functions. We start with sequences of integrable functions with different modes of convergence in comparison to the L1-convergence, and finish the chapter with the algebraic size of the family of unbounded, continuous and integrable functions on [0, +∞) and sequences of them. Finally, in Chapter 6 we turn into the setting of series of functions, obtaining positive results about the linear and algebraic size of the family of sequences of functions whose series converges absolutely and uniformly but does not verify the hypothesis of the Weierstrass M-test.Hist´oricamente han sido muchos los matem´aticos de todas las ´epocas que se han sentido atra´ıdos y fascinados por la existencia de grandes estructuras algebraicas que satisfacen ciertas propiedades que, a priori, pueden contradecir a la intuici´on matem´atica. El objetivo de la presente Memoria es el estudio de la lineabilidad de diversas familias de sucesiones de funciones con propiedades muy espec´ıficas. La Memoria se divide en 6 cap´ıtulos, donde los Cap´ıtulos 1, 2 y 3 se centran en introducir la notaci´on b´asica y la terminolog´ıa principal de la teor´ıa de la Lineabilidad y de los modos de convergencia que usaremos a lo largo de esta Memoria. En el Cap´ıtulo 4 comenzamos el estudio del tama˜no algebraico de dos familias de sucesiones de funciones con distintos modos de convergencia en el intervalo unidad cerrado [0, 1]: convergencia en medida pero no puntual en casi todo y convergencia puntual pero no uniforme. En el Cap´ıtulo 5 centramos nuestra atenci´on en el marco de las funciones integrables (Lebesgue). Comenzamos con sucesiones de funciones integrables y distintos modos de convergencia en comparaci´on con la convergencia en norma L1, y finalizamos el cap´ıtulo con el tama˜no algebraico de las familias de funciones no acotadas, continuas e integrables en [0, +∞), y las sucesiones de ellas. Finalmente, en el Cap´ıtulo 6 trabajamos en el ´ambito de las series de funciones, obteniendo resultados positivos sobre el tama˜no lineal y algebraico de la familia de sucesiones de funciones cuya serie asociada converge uniformemente pero no verifica las hip´otesis del Criterio M de Weierstrass

Canonical Realizations of Doubly Special Relativity

Doubly Special Relativity is usually formulated in momentum space, providing the explicit nonlinear action of the Lorentz transformations that incorporates the deformation of boosts. Various proposals have appeared in the literature for the associated realization in position space. While some are based on noncommutative geometries, others respect the compatibility of the spacetime coordinates. Among the latter, there exist several proposals that invoke in different ways the completion of the Lorentz transformations into canonical ones in phase space. In this paper, the relationship between all these canonical proposals is clarified, showing that in fact they are equivalent. The generalized uncertainty principles emerging from these canonical realizations are also discussed in detail, studying the possibility of reaching regimes where the behavior of suitable position and momentum variables is classical, and explaining how one can reconstruct a canonical realization of doubly special relativity starting just from a basic set of commutators. In addition, the extension to general relativity is considered, investigating the kind of gravity's rainbow that arises from this canonical realization and comparing it with the gravity's rainbow formalism put forward by Magueijo and Smolin, which was obtained from a commutative but noncanonical realization in position space.Comment: 18 pages, accepted for publication in International Journal of Modern Physics