Papers by Fernando Barrera-Mora
Resumen. En este artículo se documenta cómo el uso de tecnologías digitales en el proceso de reso... more Resumen. En este artículo se documenta cómo el uso de tecnologías digitales en el proceso de resolución de problemas puede apoyar a los estudiantes en el desarrollo de competencias matemáticas, lo cual será entendido en este trabajo como el desarrollo de elementos propios del pensamiento matemático tales como: representar información, identificar relaciones entre datos e incógnitas o hipótesis y conclusiones, resolver casos particulares; explorar e identificar patrones, formular conjeturas, presentar justificaciones y comunicar resultados. Se argumenta que el carácter dinámico de las representaciones que se pueden construir con un software como Cabri-Geometry o Geogebra y la disponibilidad de herramientas de medida son factores que favorecen el desarrollo de competencias matemáticas.
A triple of rational integers (a, b, c) is called a Pythagorean Triple (PT) if a + b = c. When th... more A triple of rational integers (a, b, c) is called a Pythagorean Triple (PT) if a + b = c. When the condition gcd(a, b, c) = 1 (coprime integers) is required, the triple is called a Primitive Pythagorean Triple (PPT). It is well known that the PPTs, over the rational integers, are parameterized by the map (m,n)→ (m − n, 2mn,m + n), where m > n ≥ 1, gcd(m,n) = 1 and n + m is odd. Along the same lines, Kubota [2] has characterized the PTs in a unique factorization domain (UFD). On another direction, M. Q. Zhan et al. [4] have estudied the set of 3× 3 matrices that preserve Pythagorean triples. The aim of this project is to characterize the 3 × 3 matrices with entries in a UFD that preserve PTs, that is, if A is a 3 × 3 matrix with entries in a UFD, Y = (a, b, c) is a PT, we would like to know the conditions under which AY t is again a PT. We are also interested in finding the fixed points of a matrix preserving PTs over a UFD. Research on the above question is appropiate for student...
La resolucion de ecuaciones cuadraticas y cubicas se considera un proceso algebraico por excelenc... more La resolucion de ecuaciones cuadraticas y cubicas se considera un proceso algebraico por excelencia, sin embargo, el uso de ideas geometricas puede ser de utilidad para lograr un entendimiento mas profitndo de los conceptos, metodos y procesos que se utilizan al resolverlas. En el presente articulo se muestra una forma de establecer conexiones entre ideas geometricas y algebraicas para resolver ecuaciones cuadraticas y de esto se obtienen dos aspectos adicionales que pueden ayudar a los estudiantes a profundizar en el entendimiento del tema: Se muestra un metodo geometrico para resolver cuadraticas y se encuentra la conexion geometrica entre los metodos para resolver cuadraticas y cubicas.
Si A es una matriz n × n, entonces existe unúnico polinomio de mínimo grado, mónico m(x) que sati... more Si A es una matriz n × n, entonces existe unúnico polinomio de mínimo grado, mónico m(x) que satisface: m(A) = 0. Si f (x) es otro polinomio tal que f (A) = 0, entonces m(x) divide a f (x). deg (m(x)) ≤ n. DEMOSTRACIÓN Existencia: sea {Y 1 ,. .. , Y n } una base de R n , existe h i (x) polinomio tal que h i (A)Y i = 0, defina g(x) := h 1 (x) • • • h n (x), entonces g(A) = 0. La segunda parte se prueba usando el algoritmo de la división. Esta parte implica la unicidad.
Pädi Boletín Científico de Ciencias Básicas e Ingenierías del ICBI, 2021
En este artículo se caracteriza una perspectiva de la resolución de problemas como aproximación d... more En este artículo se caracteriza una perspectiva de la resolución de problemas como aproximación didáctica. Particularmente se identifican aquellos aspectos de una comunidad de aprendizaje que favorecen el desarrollo de un aprendizaje con entendimiento, a partir de las contribuciones de diversos matemáticos y educadores matemáticos, entre los que se encuentran George Polya, Paul Halmos, Jaques Hadamard, Alan Schoenfeld, James Hiebert y Richard Lesh.
Abstract: I.M. Isaacs has proven a very interesting theorem concerning solv-ability of polynomial... more Abstract: I.M. Isaacs has proven a very interesting theorem concerning solv-ability of polynomials by real radicals. His result deals with an irreducible polynomial over the field of rational numbers which has a real radical element and splits in R. In this note we present a short proof of a generalization of Isaacs Theorem. AMS Subject Classification: 12E10, 12F99
Abstract: What are the fundamental features that characterize a research framework in mathematics... more Abstract: What are the fundamental features that characterize a research framework in mathematics education? What types of questions are important to ask in order to contrast and evaluate the potential associated with different frameworks? What vision of mathematics is endorsed or appears as important in particular perspectives? What types of tasks are used to promote learning within those perspectives? What instructional environments favor students learning under those frameworks? These questions were used as a guide to examine three important conceptual frameworks widely used in research and practice in mathematics education: Problem-solving, representations and visualization, and models-modeling perspectives.
The Mathematics Enthusiast, 2013
In this paper we document and discuss how the use of digital technologies in problem solving acti... more In this paper we document and discuss how the use of digital technologies in problem solving activities can help students to develop mathematical competences; particularly, we analyze the characteristics of reasoning that students develop as a result of using Cabri Geometry software in problem solving. We argue that the dynamical nature of representations constructed with Cabri, and the availability of measure tools integrated to it are important elements that enhance students' ability to think mathematically and foster the implementation of several heuristic strategies in problem solving processes.
PÄDI Boletín Científico de Ciencias Básicas e Ingenierías del ICBI, Jul 5, 2015
PÄDI Boletín Científico de Ciencias Básicas e Ingenierías del ICBI, Jul 5, 2014
<jats:p>En este ensayo se discute una caracterización del entendimiento en términos de la c... more <jats:p>En este ensayo se discute una caracterización del entendimiento en términos de la construcción de relaciones o conexiones robustas entre los nuevos conocimientos y aquellos que se conocen de forma previa. Además, se describen cinco elementos que pueden ser útiles en la identificación de un salón de clase en el que se promueve el entendimiento o en la selección de aquellas acciones didácticas que un profesor debería llevar a cabo si busca que sus estudiantes construyan una comprensión conceptual de las ideas matemáticas.</jats:p>
Journal of Pure and Applied Algebra, 1991
What types of activities should professional development programs include to revise and extend hi... more What types of activities should professional development programs include to revise and extend high school teachers’ mathematical and pedagogical knowledge? We propose a route to engage high school teachers in an inquiry approach to reflect on their current practice and to construct hypothetical learning trajectories that can eventually guide or orient the development of their lessons. In this report, we focus on the activities that were worked within a professional community that include the participation of mathematicians, mathematics educators and doctoral students.
Recently, it has been considered important to reflect on the coincidences between the mathematica... more Recently, it has been considered important to reflect on the coincidences between the mathematical thinking of the “School of Mathematics ” and the “Discipline of Mathematics”. It is widely accepted that a professional mathematician has naturally developed reasoning abilities that are essential to his practice. Such reasoning abilities are considered central to student F. HITT, F. BARRERA-MORA and M. CAMACHO-MACHÍN 94 learning at different educational levels. While the problem is not entirely
A weight is placed on the top of a rectangular rigid ideal table with four legs, each leg is plac... more A weight is placed on the top of a rectangular rigid ideal table with four legs, each leg is placed at each vertex of the rectangular table. It is assumed that the legs do not bend when the weight is added. The reactions are computed by assuming the table is supported on a beam, introducing two new beam parameters and minimizing a deflection function of the new parameters. A physical experiment is performed in the lab and the reactions on each leg are provided. The experimental results match the theoretical ones obtained by the proposed model. Geometrical interpretations of the results are given.
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Papers by Fernando Barrera-Mora