The concept of finite limit of a function at one point as explained by students of non-compulsory secondary education

We review various educational studies of the mathematical concept of limit of a function at a point that indicate how colloquial uses of the terms “to approach,” “to tend toward,” “to reach,” “to exceed” and “limit” influence students’ conceptions of these terms. We then present the results of an exploratory study of this question performed with Spanish students in non-compulsory secondary education and analyze the responses they provide to justify the truth or falsity of statements related to the different characteristics of the concept of finite limit of a function at a point when they use these terms. Finally, we organize their answers according to the kinds of arguments made. Using the response profiles detected, we discuss the influence of everyday usage on the students’ arguments

Competencias para una educación matemática innovadora

Reflexión sobre el significado y el papel de la noción de competencia matemáticas en las actuales directrices curriculares internacionales

From Sustainable Finances to Faithful Investing: A moral proposal according to the Catholic Social Thought

Finance is an element of economic life that can contribute to shaping a more humane, equitable and sustainable world; and finance oriented by reference to ESG criteria represents an encouraging step forward at the service of the Common Good. In this article we contrast finance from ESG criteria with Faithful Investing, more specifically, with the tradition of Catholic Social Thought (CST) and its criteria for ethical, responsible, and sustainable investing decisions. Therefore, we try to go beyond, opening a path towards a more explicit way of acting in financial markets from a moral option rooted in religion: Faithful Investing. The paper begins by delimiting differences among ambits of reality in the field of meta-financial investing options. So, the first section, using a Logical-symbolic notation, presents a triple thesis that serves as a framework for the rest of the paper. From it, the concept of Faithful Investing is demarcated, by contrasting it with other related concepts: ESG, SRI, and EI. After underlining the relevance of the moral dimension of financial activity, and after presenting in depth the principles of the CST, the paper presents the point of view of this tradition about finance. We conclude the paper by showing some empirical evidence of how Faithful Investing is not only attractive as a good moral option, but it is also, because of profitable portfolios, well diversified and with persistent and sustainable returns over time

Determinants of Land Use/Cover Change in the Iberian Peninsula (1990–2012) at Municipal Level

This work analyzes the determinants associated with main land use/cover changes in the Iberian Peninsula during the 1990–2012 period using a decision tree model. Our main objective is to identify broad-scale patterns that associate the characteristics of geographic areas with the dominant land use/cover change process based on CORINE Land Cover (Coordination of Information on the Environment) and defined in a previously published work. Biophysical, structural and socioeconomic variables were considered as potentially explanatory of the dominant change process at municipal scale. The resulting model allowed identification of a common pattern in Portugal and Spain (urbanization being highly associated to areas already densely populated in the previous period), but also some diverging ones. In particular, dominant trends in Portuguese territory appear to be highly determined by wildfire occurrence. In contrast, Spanish municipalities showed more diverse patterns, usually associated to biophysical determinants like average forest productivity or average terrain slopeS

Escaping Trauma thougth a Dreamworld: fantasy and the Evasion of Pain in Jane Yolen's "Briar Rose" and John Boyne's "The boy in the Striped Pyjamas"

Fiction has always been part of human beings, accompanying them even in the most difficult situations of life. In fact, certain victims of acute trauma may tend to mask and evade the pain they suffer by creating their own fictional world as a means of escaping from reality. This has become a recurrent theme In contemporary literature, as in the cases of Jane Yolen's Briar Rose and John Boyne's The Boy in the Striped Pyjamas, whose characters would respectively block a traumatic memory by replacing it with a fantasy or stubbornly refuse to see the painful reality in front of their eyes choosing over it a less harsh fictional alternative. Through the analysis of these two books, this article will compare and contrast these two different ways to deny a traumatic reality and will highlight the necessity to recover those repressed memories not only to work through past traumas, but to give voice and pay homage to those overcome by them.La ficción siempre ha formado parte del ser humano, acompañándole en las situaciones más difíciles de la vida. De hecho, algunas víctimas de grave trauma psicológico pueden enmascarar y evadir el dolor que sufren creando su propio mundo de ficción para escapar de la realidad. Esto se ha convertido en un tema recurrente en la literatura contemporánea, como en Briar Rose, de Jane Yolen y The Boy in the Striped Pyjamas de John Boyne, cuyos protagonistas, respectivamente, bloquearán una memoria traumática sustituyéndola por una fantasía o se negarán obstinadamente a ver la dolorosa realidad, optando por otra imaginaria y menos dura. A través del análisis de estos dos libros, el presente artículo comparará y contrastará estas dos formas diferentes de negar una realidad traumática y enfatizará la necesidad de recuperar la memoria reprimida, no sólo para superar traumas del pasado, sino para dar voz y homenajear a aquellos que fueron devastados por ellos

Concepciones sobre límite finito de una función en un punto: estudio a partir de gráficas

Este estudio se centra en las concepciones individuales de estudiantes de bachillerato acerca de límite finito de una función en un punto al emplear una definición personal para justificar la existencia o no de límite de funciones proporcionadas mediante sus gráficas. Analizamos los argumentos proporcionados por los estudiantes a cada una de las gráficas, en primer lugar, sin tener en cuenta la definición personal correspondiente, dando lugar a significados parciales del concepto; en segundo lugar, valorando la coherencia entre los argumentos y su definición personal asociada evaluando la capacidad de argumentar deductivamente a partir de definiciones. Entre los resultados, destacamos la persistencia de concepciones erróneas como identificación del límite como imagen, como el valor de la abscisa x, la no alcanzabilidad o no rebasabilidad y caracterizamos tres grados de coherencia entre argumento y definición; uso adecuado de condiciones necesarias y/o suficientes, uso inadecuado de condiciones necesarias y/o suficientes, y uso inadecuado de condiciones no necesarias ni suficientes

Significados puestos de manifiesto por estudiantes de bachillerato respecto al concepto de límite finito de una función en un punto. Estudio exploratorio

En este trabajo resumimos un estudio empírico llevado a cabo con estudiantes de bachillerato con la intención de explorar y describir los distintos significados vinculados al concepto de límite que los estudiantes pueden poner de manifiesto al abordar tareas que involucran la relación entre varios sistemas de representación. Describimos algunos aspectos del lenguaje utilizado por los escolares en sus interpretaciones, profundizando en las concepciones intuitivas a las que dan lugar, seguido de la exploración del manejo de otros sistemas de representación por parte de los escolares como el simbólico a la hora de interpretar gráficas de funciones

Inverse Modeling Problems in Task Enrichment for STEM Courses

Problem solving is considered as one of the most important topics in STEM (science, technology, engineering, and mathematics) education, and this is especially relevant when problems require modeling skills in order to be solved. Also, it should be noted that in many branches of science and technology, typical problems are posed in an inverse form. Then, combining both characteristics, the so-called inverse modeling problems deserve to be studied deeply, particularly in their potential for task enrichment. For those reasons, since 2016, a research project was carried out, by using inverse modeling problems to develop prospective teacher’s task enrichment skills. The results of this experience that took place in 2017 showed nine different groups of proposals where only few participants were very creative, whereas many others posed trivial problems or simply imitated examples analyzed previously. After that, a new research design was proposed during 2018 and implemented during the first months of 2019, with the aim of avoiding—or at least attenuating—those difficulties observed in the previous fieldwork. The new results showed interesting differences and few similarities when compared with the other experience. In this chapter, both experiences are analyzed, and lastly, findings and final conclusions are reported

Taller: límite en el estudio del movimiento

En este taller vamos a explorar los modos en que el movimiento puede interpretarse según cuáles sean los diversos conjuntos numéricos que modelen las magnitudes físicas espacio y tiempo. Tomamos en consideración tres tipos esenciales de modelos: El discreto (Números decimales con un número acotado de cifras decimales significativas, incluyendo los números naturales), el denso (números racionales, del cual destaca el subconjunto denso de los números decimales exactos) y el continuo (Números reales). Cada uno de estos modelos provee al movimiento resultante de unas propiedades deducidas de manera lógica y que pueden, o no, contradecir la observación empírica del fenómeno real