Volume X. Number 1. April 2020

We are experiencing a strange period due to the confinement by the COVID 19. We wanted to comment on how it is affecting the scientific world, mathematics, teaching…This number of “Mathematical Thinking” Journal, presents some articles about different aspects related to Mathematics, not only from a formal o theoretical point of view but Maths applied to different areas such as engineering or physics.

Title: Créditos editoriales, Índice de artículos y Editorial del Número 1 (Vol. X)
Author: Equipo Editorial
Investigation This article discusses the importance of building a model that studies the effect of temperature on Aonidiella aurantii and its natural enemy Aphytis Mellinus that is parabolic rather than linear. The studies of other authors use linear models that do not fit the facts and are not adequate, since it makes no sense to adjust with a straight line, or with a power function y=a·Tb, which are increasing, when the temperature behaviour at which the number of days begins to grow is first decreasing and then increasing. This article analyses other adjustments, verifying that the best adjustment is through a polynomial function of the second degree.
Title: Modelo matemático para estudiar el efecto de la temperatura en las poblaciones de Aonidiella aurantii y de Aphytis Mellinus
Authors: Alfonso Garmendia y Adela Salvador
Teaching Experiences This paper makes a statistical study of the mathematical errors of the students of a High School in Mexico, by means of a written evaluation elaborated and applied to a sample of students. With the information collected and with the help of descriptive statistics, those typical mistakes that students frequently make were detected. Once this was done, strategies for better learning were implemented, insisting on those aspects that generated the most difficulties, with the objective of overcoming the errors detected. Consequently, a second written evaluation was applied to the sample of students, to then apply the t of Student statistical test and match the data collected. The objective was to compare the learning results of the group of students before and after receiving the training focused on the most frequent errors.
Title: Errores frecuentes en el área de matemáticas, un análisis estadístico con alumnos de bachillerato
Author: Pablo Sánchez Madrigal

One of the didactic strategies that most contributes to discovery learning in the process of teaching and learning of mathematical contents at the initial and middle levels, is the work with concrete or manipulative material. This work allows students to transit through mental processes of comparison, analysis, synthesis, abstraction, generalization, etc., conducive to the formation of new concepts and / or the formulation of new propositions. In this way, the potential offered by the use of polygonal tessellations can be exploited, in order to deduce in an elegant, motivating and creative way the formulations and / or demonstrations of new theorems. […]
Title: Formulaciones y demostraciones de los teoremas de los catetos y de la altura mediante teselaciones poligonales
Authors: José Enrique Martínez Serra, Marco Vinicio Vásquez Bernal, Arelys García Chávez y Ramiro Infante Roblejo
Stories In this work we present a simple introduction of the Special Relativity theory without formulae, suitable for being explained to high school students. Using this framework we are able to prove graphically the time dilation and length contraction.
Title: Enseñando Relatividad Especial gráficamente
Authors: Daniel de la Fuente Benito, José Antonio Sánchez Pelegrín y Alfonso Zamora Saiz

Euclid wrote a land surveying treatise entitled On the Division of Figures that was lost in the many vicissitudes through which the Library of Alexandria crossed. We have news of this work thanks to Proclo (Vth century d.C.). It has been possible to be recovered after a long journey through some Arabic manuscripts, geometry texts from the 12th and 13th centuries and translations into Latin and other languages from Arabic, from the 16th to the 19th centuries. This allowed Raymond Clare Archibald to publish a reconstruction of the cited text in 1915.
Title: El largo Viaje de “Sobre la División de las Figuras”
Author: Juan Tarrés Freixenet

In this paper we overview how the mathematization of the knowledge in the XVI and XVII centuries demanded from mathematics a sudden evolution to cope with the needs of the new science. The classical mathematics from Greek and Hellenistic period with its geometric focus, its reluctance to use infinites and its inability to deal with curves other than conics were unable to satisfy the challenge.
Title: El Problema de las Curvas y el Nacimiento del Cálculo
Author: Román Ceano
Games and Mathematical Oddities The Fermat´s Principle (Least Time Principle) serves to develop a mechanical model, which can be exemplified in the proposed exercise, in which the mathematics of Snell´s law of optics is compared to the idealized physical problem.
Title: Un principio de mínimo para socorrer a un bañista en apuros
Author: Rosa M. Herrera

This article shows a curious way in which combinatorial numbers can behave giving rise to a curious new concept (order of combinatorial number). In addition to the order, the sum, the binomial and some interesting prime numbers using this concept are analyzed.
Title: Curiosidad del número combinatorio(concepto de orden)
Author: Juan Patricio Ondo Ona Ayetebe
Mathematical Stories This paper shows the story that the architect Rafael Rivera, creator of the Gulliver Park in Valencia, tells young children teach them how to propose and carry out a project, in this case, of a playground.
Title: La historia de Gulliver
Author: Rafael Rivera

This story is intended to begin in an entertaining way and from a didactic point of view the beginning of the study of complex numbers.
Title: El origen de los números complejos
Author: Miguel Oscar Almarales Milán
Critics and Reviews This article presents a review of the film “Gifted´´ directed by Marc Webb. The film is about a girl with special abilities for mathematics who along with her uncle tries to overcome the difficulty in comprehending the reality of the social, personal, sentimental and family environment that surrounds her which prevents a “normal´´ development of her childhood.
Title: Informe sobre la película “Un Don Excepcional”
Author: José Manuel Sánchez Muñoz
Interviews María Medina is a researcher and professor at the Universidad de Granada. She is living in Rome and her researching is based on Partial differential equations.
Title: María Medina: “Historia de una investigadora en matemáticas que (sobre)vive lejos de casa”
Author: Susana Merchán Rubira


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