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In this article, Action-Process-Object-Schema (APOS) theory is used to examine the themati-zation of the derivative Schema and the role played by the equilibration mechanisms evidenced by some advanced students while facing tasks designed to confront the equilibrium of their Schemas and obtain thematization evidence. This investigation contributes to the study of Schema thematization by focusing on the mechanisms involved when students need to perform Action on their derivative Schema. Results show evidenceson the role that accommodation and assimilation mechanisms play in students’ strategies when they re-equilibrate their Schema and evidence its thematization Which has not received previous attention., En este artículo se usa la teoría Acción-Proceso-Objeto-Esquema (APOE) para examinar la tematización del Esquema de derivada y el papel que juegan los mecanismos de equilibración de dicho Es-quema a través de la evidencia mostrada por estudiantes avanzados al enfrentar tareas diseñadas para con-frontar el equilibrio de sus Esquemas y obtener evidencia de su posible tematización. Esta investigación contribuye al estudio de la tematización de un Esquema al enfocarse en los mecanismos que pueden po-nerse en juegocuando los estudiantes requieren hacer Acciones sobre su Esquema de derivada. Los resul-tados del estudio muestran evidencias que hacen visible el papel que los mecanismos de acomodación y asimilación juegan en las estrategias de los estudiantes para re-equilibrar su Esquema y demostrar su te-matización. Algo que no ha recibido atención previa.

Los resultados de investigaciones relacionadas con el aprendizaje del concepto de derivada constatan que su comprensión resulta muy compleja y que una cantidad significativa de estudiantes solo logra una construcción parcial del concepto. Desde este contexto, en esta investigación presentamos un análisis exploratorio/confirmatorio en el que identificamos y caracterizamos, por medio de métodos de análisis mixtos, los distintos subniveles de desarrollo del esquema de derivada que alcanzaron estudiantes universitarios con instrucción previa en Cálculo Diferencial. Los resultados muestran la utilidad del uso de estos métodos que, en este estudio, permitieron identificar los 9 subniveles de desarrollo y caracterizar 5 de ellos en función de las variables dominantes y sus elementos matemáticos asociados., The results of the research related to the learning process of the derivative notion show that its understanding is very complex and that only a significant number of students acquire a partial comprehension of the concept. In this context, this research presents an exploratory/confirmatory analysis in which we identify and characterize, through mixed analysis methods, the different sub-levels of development of the derivative schema that university students previously instructed in Differential Calculus managed to reach. The results show how useful these methods are in this study, since they made it possible to identify the 9 sub-levels of development and to characterize 5 of them according to the dominant variables and their associated mathematical elements.

Premi Extraordinari de Doctorat concedit pels programes de doctorat de la UAB per curs acadèmic 2017-2018, El desarrollo de esta tesis doctoral tuvo como objetivo analizar el esquema de la derivada en estudiantes universitarios, con instrucción previa en Cálculo Diferencial, por medio de la identificación y caracterización de los subniveles de desarrollo del esquema, y la posible tematización del mismo. Con el propósito de identificar y caracterizar los subniveles de desarrollo se aplicó un cuestionario a 103 estudiantes universitarios. El cuestionario estaba compuesto por tres tareas que involucraban el uso de los elementos matemáticos que configuran el concepto de derivada en los modos de representación analítico y gráfico. Los protocolos de resolución del cuestionario fueron discretizados por medio de una escala dicotómica con el fin de construir un vector asociado a cada protocolo de resolución. Estos vectores permitieron el desarrollo de un Análisis de Clúster por medio del cual se identificaron distintos subniveles de desarrollo del esquema de la derivada. Asimismo, el Análisis de Clúster permitió dividir la matriz de datos en submatrices, una para cada subnivel Inter y Trans. Desde estas submatrices se caracterizaron los subniveles de desarrollo del esquema de la derivada por medio del Análisis Estadístico Descriptivo e Implicativo interpretando los resultados de estos análisis con el marco de la teoría APOE. A partir de la identificación y caracterización de estos subniveles, se seleccionó el subnivel de desarrollo Trans más avanzado y se entrevistó a 5 estudiantes de él, a fin de caracterizar la posible tematización del esquema de la derivada. Para la caracterización de la tematización del esquema de la derivada, se observaron las relaciones que los estudiantes establecen cuando se enfrentan al tratamiento de valores extremos, puntos de inflexión y puntos conflictivos en derivadas sucesivas de orden mayor a dos. Los resultados de esta investigación permitieron identificar y caracterizar tres subniveles de desarrollo del esquema de la derivada para cada uno de lo, The objective of the development of this doctoral thesis was to analyze the derivative schema, in university students with prior instruction in differential calculus, through the identification and characterization of the sub-levels of development schema and their possible thematization. In order to identify and characterize the sub-levels of development, a questionnaire was provided to 103 university students. The questionnaire consisted of three tasks involving that involved the use of mathematical elements that shape the derivative concept in the of analytical and graphical representation modes. The resolution protocols of the questionnaire were discretized by means of a dichotomous scale in order to construct a vector associated with each resolution protocol. These vectors allowed the development of a Cluster Analysis whereby different development sub-levels of the derivative schema were identified. Also, the Cluster Analysis allowed to partition the data matrix into submatrices, one for each sub-level: Inter and Trans. From these submatrices the sub-levels of development of the derivative schema were characterized by Descriptive and Implicative Statistical Analysis interpreting the results of these analyzes with the framework of the APOS theory. From the identification and characterization of these sub-levels, the most advanced Trans sub-level development was selected, and five students were interviewed within it in order to characterize the possible thematization of the derivative schema. For the characterization of thematization of derivative schema, we observed the relationships that students establish when they face the treatment of extreme values, inflection points and conflictive points in successive derivatives of an order higher than two were observed. The results of this research helped to identify and characterize three sub-levels of the development derivative schema for each Inter and Trans level, some of these sub-levels have already been identified

We present a large-scale effort of creating composite spectra of high-redshift SNe la and comparing them to low-redshift counterparts in an attempt to understand possible cosmic evolution of SNe la, which has major implications for studies of dark energy. Through the ESSENCE project, we have obtained 107 spectra of 88 high-redshift SNe la with excellent light-curve information. In addition, we have obtained 397 spectra of low-redshift SNe la through a multiple-decade effort at the Lick and Keck Observatories, and we have used 45 UV spectra obtained by HST and IUE. The low-redshift spectra act as a control sample when comparing to the ESSENCE spectra. In all instances, the ESSENCE and Lick composite spectra appear very similar. The addition of galaxy light to the Lick composite spectra allows an excellent match of the overall SED with the ESSENCE composite spectra, indicating that the high-redshift SNe are more contaminated with host galaxy light than their low-redshift counterparts. This is caused by observing objects at all redshifts with similar angular slit widths, which corresponds to different projected physical distances. After correcting for the galaxy light contamination, a few marginally significant differences in the spectra remain. We have estimated the systematic errors when using current spectral templates for K-corrections to be ∼0.02 mag. The variance in the composite spectra gives an estimate of the intrinsic variance in low-redshift maximum light SN spectra of ∼3% relative flux in the optical and growing toward the UV. The difference between the maximum light low-and high-redshift spectra constrains the evolution of SN spectral features between our samples to be <10% relative flux in the rest-frame optical. Currently, galaxy contamination and the small samples of rest-frame UV spectra at low and high redshifts are the limiting factors for future studies.

We describe the implementation and optimization of the ESSENCE supernova survey, which we have undertaken to measure the dark energy equation-of-state parameter, w = P/(pc 2). We present a method for optimizing the survey exposure times and cadence to maximize our sensitivity to w for a given fixed amount of telescope time. For our survey on the CTIO 4 m telescope, measuring the luminosity distances and redshifts for Supernovae at modest redshifts (z ≈ 0.5± 0.2) is optimal for determining w. We describe the data analysis pipeline based on using reliable and robust image subtraction to find Supernovae automatically and in nearly real time. Since making cosmological inferences with supernovae relies crucially on accurate measurement of their apparent brightnesses, we describe our efforts to establish a thorough calibration of the CTIO 4 m telescope's natural photometric system. In its first four years, ESSENCE has discovered and spectroscopically confirmed 102 Type Ia supernovae, at redshifts from 0.10 to 0.78, identified through an impartial, effective methodology for spectroscopic classification and redshift determination. We present the resulting light curves for all of the Type Ia Supernovae found by ESSENCE and used in our measurement of w, presented in a companion paper by Wood-Vasey and coworkers.

We present the results of spectroscopic observations of targets discovered during the first 2 years of the ESSENCE project. The goal of ESSENCE is to use a sample of ∼200 Type Ia supernovae (SNe la) at moderate redshifts (0.2 ≲ z ≲ 0.8) to place con