Volume VI. Number 2. October 2016

We present the second number of the sixth volume of the “Mathematical Thinking´´ Journal. It includes some papers framed in the different sections of the Journal. The articles cover a wide range of the Mathematics topics and its applications.

Title: Créditos editoriales, Índice de artículos y Editorial del Número 2 (Vol. VI)
Author: Equipo Editorial
Investigation This article outlines a methodology for quality control in the production of thematic cartography, doing an analysis of the indices of thematic quality from obtaining the confusion or error matrix.
Title: Análisis de Calidad Cartográfica mediante el estudio de la Matriz de Confusión
Author: José Manuel Sánchez Muñoz

This paper presents a review of multicriteria decision making methods and their mathematical formulation. Similarly, a methodology based on the sequential application of several decision methods is developed. As a specific example, it is applied to analysis of alternatives in planning stage design of facilities and infrastructures.
Title: Aplicación de métodos de decisión multicriterio discretos al análisis de alternativas en estudios informativos de infraestructuras de transporte
Authors: Belén Muñoz y Manuel G. Romana
Teaching Experiences From a discrete spiral, a development of a logarithmic spiral is proposed to students of Architecture and from this one, the goal is to get a loxodrome on the unit sphere, in an assignment included in a course of ‘Geometry of Curves and Surfaces’. The aim would be to motivate the student by means of relationships between each of the curves that appears in the assignment and Architecture (his main interest) and another fields like Art, History…
Title: Un trabajo con espirales
Authors: Diego Cano-Lasso, M. Carmen Escribano, J. Carlos Garro, J. Rojo, J. Tarrés y S. Victoria

This Study is aimed to analyze the links between Cooperative Learning and a set of relevant skills for the study of maths, and specifically Creativity. But it also analyzes the ability to think logically and mathematically, as well as to make critical judgments and communicate them. Two tests (one individual and another for a group) had been designed and conducted in five different groups, four of them from 4th year of secondary education, of which one is under cooperative learning, and the fifth from the first year of Baccalaureate, from the school of excellence. The results points to a higher ability to mathematical thinking, problem solving and critical judgment in the cooperative students than the others, but the excellence ones, in individual skills. However the cooperative students perform significantly better than any other in the group test. Furthermore, in creativity they score above the other groups, expect the excellence one.
Title: Creatividad y aprendizaje cooperativo: un pequeño estudio
Authors: Susana Merchán Rubira y José Samuel Rodríguez García

This work aims to achieve the first-year students of Fundamentals of Architecture degree face up the core subject of Affine and Projective Geometry from a non-traditional perspective, more in line with the interests that moved them to choose a degree in Architecture, in which the design and layout of urban and living spaces lead them to have an essentially geometric approach of the use of a space that should be useful, beautiful and sustainable, all at once. In order to accomplish that goal, we have relied on the most suitable part of the program for this purpose: the isometric transformations, taking them as the basis of a work in which Mathematics and Architecture come together in a common objective: the analysis of the infinite possibilities of Geometry when undertaking a design.
Title: Intervenciones Geométricas en Arquitectura
Author: Juana María Sánchez González

In the last years the Department of Applied Mathematics and Statistics of the San Pablo CEU University has made a firm intent of using free software, R in particular, for teaching Statistics. For this reason we have developed the rk.Teaching package in order to overcome the limitations of existing R graphical user interfaces and to free students of the technical and programming skills required to manage R. This article presents the main features of the package rk.Teaching and evaluates its use in practical classes of both face-to-face and on-line Statistics courses.
Title: Innovación en la docencia de Estadística con R y rk.Teaching
Author: Alfredo Sánchez Alberca
History of Mathematics This article aims to do a historical tour of the logical proofs of the existence of God with particular attention to the ontological argument.
Title: Lógica y Dios: la tentación de lo absoluto
Author: Danilo Magistrali

This paper offers teachers of Secondary Compulsory Education a glossary of the life and work of Andalusian mathematicians born between the fiftieth and twentieth century, with the objective of using the history of Mathematics as a methodological resource in the classroom. To provide data to be used as models in workshops and panels which can be treated with in the cultural weeks in their centers is also pretended.
Title: Algunos matemáticos andaluces nacidos entre los siglos XV y XIX
Author: Juan Núñez Valdés
Games and Mathematical Oddities First personal computers exist since last quarter of twentieth century. Also first electronic pocket calculators exist since that time. At present they are a common and accessible element. But the need to perform mathematical calculations accurately and quickly has been a constant throughout history solved with ingenious mechanical devices. The logarithmic slide rule, is a calculation tool that facilitates rapid and comfortable performing arithmetic operations. Its use was widespread since the mid-nineteenth century until the late twentieth century, when its use declined with the appearance of the first pocket calculators and personal computers. In the seventies of the last century its use gradually disappeared. In the last decades of the twentieth century there were hardly generations of engineers who use them. Its use has been relegated to museums, organizations, friends, and to specific applications within the basic teaching of mathematics. This article gives details of basic principles of operation of the slide rules. The resources available are also displayed today to start in handling the calculation rules. Finally, they attached to article two models of paper cut-out slide rules , so that the reader can build his own rule and practice with it.
Title: Reglas de Cálculo
Author: Santiago Higuera de Frutos

Statistics is present in most of the activities that take place around us. However, most people are not aware of that. The simple fact of turning the light on when we wake up (energy demand), the way traffic is managed in a city, the pricing data or the time we spend waiting a queue in a supermarket, are simple actions that are relevant to statistic techniques. In this paper, a reflection about some areas where statistics has been despised is presented. The ideas that we develope can be applied in high school education, not only in order to make contents more atractive to students but to avoid future misconceptions in adult life and contribute to create freer and more responsible individuals.
Title: Verdad, mentira y estadísticas
Author: Alejandro Galindo Alba
Mathematical Stories Along the course 2015-2016 the mathematical Workshop π-ensa celebrated the first Contest of Short Tales with mathematical content “π-ensa”. In this issue it is continued the publication of the awarded tales in this contest. All the information about the contest is included in the web page of the Workshop: http://innovacioneducativa.upm.es/museomatematicas/. This paper presents the second place awarded tale in the second level (Secondary students).
Title: La incógnita de las incógnitas
Author: Inés Pérez Teresa
Title: La voluntad de los números
Author: Raúl Ortega González
Crí­tics and Reviews A group of mathematics teachers of high school and college is writing some books for Secondary Education that are posted on the web. The intention is that these books can be used by the students for free. In this article we will explain what are their characteristics, advantages and the methodological ideas that are behind. We have wanted to make some quality books written by professors with great enthusiasm and extensive teaching experience.
Title: Marea Matemática
Authors: Adela Salvador Alcaide, Raquel Caro Carretero y María Merino Doncel
Interview Juan Antonio Cuesta is a Professor of Statistics in the Sciences Faculty of Cantabria University. He is responsible for the International Centre of Mathematical Meetings (CIEM) that belongs to Cantabria University. This institution promotes excellence in basic and applied mathematical investigation.
Title: Juan Antonio Cuesta: Director del CIEM
Author: Equipo Editorial


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