Month: March 2025

One of the challenges in mathematics is to find the area under a curve when the usual methods of integration are not feasible. There are various approaches to deal with this problem, most of them relying on Newton-Cotes formulas, but they have some drawbacks and errors. This article presents a different method that uses Bézier interpolation to approximate the curve and calculate the area. This method has the advantage of being accurate and general, meaning that it can handle any kind of curve, even those that come from experimental data that may be irregular or noisy.

Título: The use of Bézier interpolation for numerical integration of uneven data Autor: Stefan T Orszulik

An explicit formula which characterizes the pairs of integers that are relatively prime is obtained. It doesn’t require the knowledge of the prime factors of the arguments, what allows to construct other explicit formulas for the Euler’s totient function and the Prime counting function.

Título: Explicit formulas for the Euler’s phi function and the counting of primes Autor: Carlos Mañas Bastidas

For the last decades, digital tools have acquired a fundamental role in education. Consequently, this work evaluates the incorporation of the RStudio® Cloud program as a suitable teaching tool for the teaching of mathematics, specifically, for the statistics block.

As a result, it was found that the program is a feasible learning platform for the secondary education stage, since it allows the integration of the different competency and curricular profiles. In addition, together with the interest and positive assessment of the students, it is worth highlighting their ability to integrate the program and perform the proposed tasks.

Título: RStudio® Cloud as didactic tool for teaching statistics in high school Autor: Francisco López-Martínez & Antonio Ramón López-Martínez

The aim of this article is to gather information about the knowledge that 6 to 8-year-old students have regarding partiality in non-binary situations through the presentation of the story Where is he? Based on the reading of the story, two exploratory activities were conducted to evaluate the students’ level of understanding of partiality and the quantifiers related to it: ‘nothing’, ‘something’, ‘quite a bit’, and ‘a lot’. The results seem to indicate that children of these ages have a good command of using these terms in non-binary contexts.

Additionally, the story can also be used to review the first five ordinal numbers and to establish a one-to-one correspondence between different levels of fun and various facial expressions of laughter.

Título: Where is it? A story for the study of fuzzy thinking in primary education Autor: Queralt Viladevall, Ángel Alsina & Joan Carles Ferrer-Comalat

The use of virtual platforms has transformed the teaching of mathematics in university education, promoting pedagogical innovation and improving the interaction between teachers and students. This study aims to analyze how virtual platforms contribute to the teaching of mathematics in the university setting, focusing on the teaching experiences at the Universidad Simón Bolívar, El Litoral campus, in the state of La Guaira, Venezuela, and the innovative pedagogical strategies that are used. Through a qualitative approach, based on semi-structured interviews and participant observation, the attitudes of five teachers towards the use of virtual platforms are examined, as well as the difficulties they face when integrating them into their teaching.

The results indicate that, although virtual platforms allow for more interactive and collaborative learning, many teachers face obstacles such as a lack of technological training and resistance to change in their pedagogical practices. Despite these barriers, teachers who adopt a proactive approach use the platforms to offer interactive resources, encourage collaboration between students, and provide personalized feedback. In this context, the research draws on key pedagogical approaches, such as social constructivism and connectivism, to understand how technology can enhance interaction and collaborative learning in mathematics.

The study highlights the need for ongoing training for teachers and strong institutional support to overcome technological difficulties. Finally, recommendations are proposed to improve the integration of virtual platforms in mathematics teaching, with the aim of optimizing learning and making mathematics education at university more accessible.

Título: Educational innovation in mathematics through the use of virtual platforms: Teaching experiences in university education Autor: María C Urbano

Mathematics with its versatility has been applied to solve problems that emanate from biological sciences or social sciences, among other sciences. Currently, mathematics is helping to achieve sustainable scenarios between nature and anthropogenic activities. This work briefly mentions how mathematical modeling has been used to understand the effects of tourism on the environment.

Título: Mathematical modeling to understand the effects of tourists on the environment Autor: Osvaldo Osuna & José Geiser Villavicencio-Pulido

This paper presents a problem related to Geometry and Probability Theory from the point of view of a dialogue between teachers and students, both peculiar.

Título: A story of triangles and probability Fiction with a touch of Lakatos and Sanderson Autor: Dionisio Pérez

An academic investigation by this author on the didactic budgets of a sample of students, enrolled in a master’s degree for secondary education teachers, has confirmed certain forms, classic and routine, used in the transmission of physical-mathematical knowledge specific to the educational level noted. The generally observed features coincide in excessively formalistic physical-mathematical conceptions and, almost always, very far from the circumstantial models of human natural reality.

This article proposes, instead, a teaching practice for teachers that bases the symbolic syntax used on three of the main components of human understanding: space, time and matter/causation. Constituents, all three, of the principle of sufficient reason of knowable realities.

Título: Steps toward naturalized physical-mathematical knowledge Autor: José Vico Martín

A short story is presented, aimed to children between 9 and 12 years old, in which basic arithmetic operations are carried out, while, for its resolution, a creative exercise of imagination is requested.

Título: Math-adventures at the farm: challenges Autor: Osvaldo Osuna y Berenice Reyes-Herrera

This article presents the review of the book: “It’s not too late! Together towards learning”. Being a teacher in higher education is a demanding profession. The dizzying pace of changes in our society requires a successful and rapid response to the training needs of citizens who must integrate into the world of work in the 21st century. It is necessary to conceive, design and deliver good training proposals, which consider and integrate the demands and characteristics that define the current context and in turn can be projected into the future; form true learning communities, with true citizen and social commitment, in which each student develops their abilities to understand new concepts with a critical spirit and application to the real environment.

Teachers from the Polytechnic University of Madrid, in collaboration with international teaching staff, share reflections and experiences around the question of how to promote the learning of higher education students, mostly in Engineering, promoting their leading role in the process. The result shows different real examples of specific educational actions, with an impact on improving educational quality.

Título: It’s not too late yet! Together towards learning Autor: Equipo editorial

Written in informative key, where there are no formulas and everything is explained with words, using analogies and illustrative examples instead, Cuando menos es más is intended to show that engineering and math may conform an excellent binomial to carry out more efficient designs in any field of science and technology.

Título: When less is more Autor: Alberto Donoso Bellón