María J. Beltrán Meneu

• Doctor
• Professor at Jaume I University

The behaviour of the generalized Hilbert operator associated with a positive finite Borel measure $$\mu $$ μ on [0, 1) is investigated when it acts on weighted Banach spaces of holomorphic functions on the unit disc defined by sup-norms and on Korenblum type growth Banach spaces. It is studied when the operator is well defined, bounded and compact....

Este trabajo registra rasgos diferenciadores de talento matemático en estudiantes de primero y segundo de ESO que resuelven una prueba de acceso a un programa de estímulo del talento matemático. Se comparan los estudiantes admitidos en el programa y los no admitidos, centrando el análisis en la resolución de un problema de generalización que involu...

Let μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} be a positive finite Borel measure on [0, 1). Cesàro-type operators Cμ\documentclass[12pt]{min...

The behaviour of the generalized Hilbert operator associated with a positive finite Borel measure $\mu$ on $[0,1)$ is investigated when it acts on weighted Banach spaces of holomorphic functions on the unit disc defined by sup-norms and on Korenblum type growth Banach spaces. It is studied when the operator is well defined, bounded and compact. To...

El periodo de prácticas es fundamental en la formación del futuro personal docente, ya que permite que el estudiantado entre en contacto con la realidad de su futura profesión y adquiera conocimientos, competencias y estrategias metodológicas que contribuyan a su desarrollo formativo y a forjar su identidad profesional. El modelo de prácticum en al...

Let µ be a positive finite Borel measure on [0, 1). Cesàro-type operators Cµ when acting on weighted spaces of holomorphic functions are investigated. In the case of bounded holo-morphic functions on the unit disc we prove that Cµ is continuous if and only if it is compact. In the case of weighted Banach spaces of holomorphic function defined by ge...

Given an affine symbol $$\varphi $$ φ and a multiplier w , we focus on the weighted composition operator $$C_{w, \varphi }$$ C w , φ acting on the spaces Exp and $$Exp^0$$ E x p 0 of entire functions of exponential and of infraexponential type, respectively. We characterize the continuity of the operator and, for w the product of a polynomial by an...

Presentamos parte de un proyecto de investigación que tiene como objetivo general, analizar la progresión en el pensamiento algebraico de estudiantes de Educación Primaria al resolver una secuencia de problemas de patrones geométricos. Para ello, es necesario analizar las distintas estrategias que emplean los estudiantes al resolver este tipo de pr...

Actas de las Jornadas Internacionales de Investigación y Práctica Docente en Alta Capacidad Matemática, celebradas virtualmente en la Universidad de la Rioja, en Noviembre de 2020

Resumen Presentamos un estudio comparativo de las estrategias empleadas por estudiantes medios y superdotados de los últimos cursos de Educación Primaria al resolver problemas de patrones geométricos. El análisis nos ha permitido descubrir las diferencias existentes entre ambos grupos e identificar algunas características diferenciadoras de la alta...

Our study is focused on the dynamics of weighted composition operators defined on a locally convex space $E\hookrightarrow (C(X),\tau_p)$ with $X$ being a topological Hausdorff space containing at least two different points and such that the evaluations $\{\delta_x:\ x\in X\}$ are linearly independent in $E'$. We prove, when $X$ is compact and $E$...

We study the dynamics of the weighted composition operator Cw,φ on weighted Banach spaces of entire functions. We characterize the continuity and compactness of the operator and, in the case of affine symbols φ(z)=az+b,a,b∈C, and exponential weights, we analyze when the operator is power bounded, (uniformly) mean ergodic and hypercyclic. Continuous...

Our study is focused on the dynamics of weighted composition operators defined on a locally convex space E↪(C(X),τp) with X being a topological Hausdorff space containing at least two different points and such that the evaluations {δx:x∈X} are linearly independent in E′. We prove, when X is compact and E is a Banach space containing a nowhere vanis...

Our study is focused on the dynamics of weighted composition operators defined on a locally convex space $E\hookrightarrow (C(X),\tau_p)$ with $X$ being a topological Hausdorff space containing at least two different points and such that the evaluations $\{\delta_x:\ x\in X\}$ are linearly independent in $E'$. We prove, when $X$ is compact and $E$...

We describe and analyse the strategies used by students in primary grades 4, 5 and 6 to solve linear and affine geometric pattern problems. Based on two problems posed in a teaching experiment, we have identified several profiles of strategies used by students to solve the problems. We consider the profiles of students who were good geometric patte...

We analyze the solutions given by secondary school mathematically gifted students to a collaborative task designed to promote the development of students’ competence of visualization. Each student was provided with two different orthogonal projections of a set of buildings made of cubes and other verbal data, and they were asked to place the buildi...

ABSTRACT. There are numerous studies that support the interest of starting the development of algebraic thinking in Primary School. In this paper, we present a part of a research project aimed to explore the processes of solution of geometric pattern problems by students in Primary grades 4th to 6th. We analyze the behavior of students who were adm...

RESUMEN. El objetivo de esta comunicación es presentar la secuencia de actividades empleada con un estudiante superdotado de 9 años, que había finalizado 4º de Educación Primaria, con el fin de explorar los problemas de patrones geométricos como una posible forma de introducir y trabajar el pre-álgebra con estudiantes de Educación Primaria con alta...

The aim of this work is to evaluate the design of the subject ICT as a teaching resource in science and mathematics taught in the Bachelor's Degree in Primary Education of the Universitat de València, during the academic courses 2013-14 and 2014-15. The analysis is based on the works of the students and their responses to a questionnaire. The purpo...

Algebraic thinking allows students operating with variables and unknowns without needing formal symbolic alphanumeric expressions, and it enhances the mathematical abilities of students, particularly of mathematically gifted students (gifted students hereafter). Geometric pattern problems (gp problems hereafter) are a context adequate to develop al...

Resumen En este capítulo presentamos los resultados obtenidos en una investigación de diseño en la que hemos diseñado y puesto en práctica una secuencia de enseñanza para iniciar en álgebra, mediante problemas de patrones geométricos, a estudiantes con altas capacidades matemáticas. Hemos experimentado la secuencia diseñada con un estudiante superd...

Spatial Visualization in Primary School Students.

Introduction to generalization in primary school students.

In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students’ difficulties when treating eige...

We present a teaching unit aimed to introduce students to algebra and solution of linear equations through geometric pattern problems. We analyse the answers, to the teaching unit, made by a 9-years-old mathematically gifted student in grade 5. We have classified his answers in several styles of strategies of use of graphical information and differ...

Presentamos una unidad de enseiianza para introducir el algebra a estudiantes de Educaci6n Primaria mediante problemas de patrones geometricos. La unidad esta dividida en tres partes, cada una relacionada con un objetivo didactico diferente: iniciaci6n a la generalizaci6n, para aprender a generalizar relaciones empiricas; introducci6n de conceptos...

In this workshop, through specific examples, we propose the attendees to "create" their own problems so that they fit specific research needs. The process for the design is based on reviewing the appropriate bibliography, consulting databases and programs addressed to talent, selecting related problems and modifying their components. Participants i...

En este trabajo analizamos la transmisión de información entre dos estudiantes de alta capacidad matemática mientras resuelven, a través de videoconferencia, una tarea cooperativa de visualización. Las categorías que más afloraron en el análisis del discurso fueron informar, demandar información, sugerir, parafrasear y confirmar. Los indicadores qu...

La forma de usar la visualización ayuda a caracterizar a los estudiantes con talento matemático (Ramírez, 2012). Los investigadores adoptan varios puntos de vista para analizar esta relación (Ryu y otros, 2007). Entendiendo la visualización como "el tipo de razonamiento basado en el uso de elementos visuales o espaciales, tanto mentales como físico...

Let φ be a self-map of the unit disc of the complex plane and let ψ be a holomorphic function on . We investigate the mean ergodicity and power boundedness of the weighted composition operator with symbol φ and multiplier ψ on the space . We obtain necessary and sufficient conditions on the symbol φ and on the multiplier ψ which characterize when t...

To promote learning of mathematically gifted (mg) children, teachers should pose them challenging tasks (Diezmann & Watters, 2001). Grouping mg students together to solve problems in collaborative teams is not always possible in schools, but virtual environments allow such interactions. Researchers have reported benefits for mg students of collabor...

Mathematics preservice teachers' (ps-teachers hereafter) training has to include the evaluation of students' outcomes, grounded on specialized mathematical content knowledge and noticing of students' thinking. Geometric pattern problems (gp-problems hereafter) offer students contexts where they may start handling literal symbols in meaningful ways....

En este trabajo se presenta un ejemplo de cómo introducir conceptos básicos de Álgebra Lineal en un primer curso de Ingeniería a partir del modelo de color RGB basado en la síntesis aditiva de los tres colores de luz primarios rojo, verde y azul. Utilizando este modelo se pretende establecer una conexión entre la obtención de colores por adición y...

Given a symbol $\varphi,$ i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator $C_{\varphi}(f)=f\circ\varphi$ defined on the Banach spaces of holomorphic functions $A(\mathbb{D})$ and $H^{\infty}(\mathbb{D})$. We obtain different conditions on the symbol $\varphi$ which characterize when the composition operator i...

We report here a case study of two pairs of mg students (12-15 years old), living in different cities. We analyse the interactions of each pair while collaboratively solving a task by communicating in real-time via Skype.

We study the integration operator, the differentiation operator and more general differential operators on radial Fréchet or (LB) Hörmander algebras of entire functions. We analyze when these operators are power bounded, hypercyclic and (uniformly) mean ergodic.

We investigate the dynamical behavior of the operators of differentiation and integration and the Hardy operator on weighted Banach spaces of entire functions defined by integral norms. In particular we analyze when they are hypercyclic, chaotic, power bounded, and (uniformly) mean ergodic. Moreover, we estimate the norms of the operators and study...

We study the operators of differentiation and of integration and the Hardy operator on weighted Banach spaces of entire functions. We estimate the norm of the operators, study the spectrum, and analyze when they are surjective, power bounded, hypercyclic, and (uniformly) mean ergodic.

Given a decreasing sequence of weights V on a Banach space X, we consider the weighted inductive limits of spaces of entire functions V H(X) and V H 0(X). We prove that V H(X) is the strong dual of a Fréchet space F for a particular class of sequence of weights, and we study some conditions to ensure that the equality V H 0(X)′′ = V H(X) holds. The...

Given a decreasing family of continuous weights on a Banach space X, we consider the weighted inductive limits of spaces of entire functions VH(X)VH(X) and VH0(X)VH0(X). Motivated by recent research by D. Carando and P. Sevilla-Peris on weighted Fréchet algebras of entire functions on Banach spaces, we determine conditions on the family of weights...