María Burgos

María Burgos
University of Granada | UGR · Departamento de Didáctica de la Matemática

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89
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761
Citations
Citations since 2016
56 Research Items
502 Citations
2016201720182019202020212022020406080100120
2016201720182019202020212022020406080100120
2016201720182019202020212022020406080100120
2016201720182019202020212022020406080100120

Publications

Publications (89)
Article
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The paper aims to analyze how the different degrees of mathematical formalization can be worked in the study of probability at non-university educational levels. The model of algebraization levels for mathematical practices based on the onto-semiotic approach is applied to identify the different objects and processes involved in the resolution of a...
Article
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Para favorecer el aprendizaje de las matemáticas, el profesorado debe ser capaz de analizar, interpretar y evaluar la actividad matemática de sus estudiantes, tomando decisiones sobre la comprensión y dificultades que muestran al resolver tareas matemáticas. Esta competencia de análisis cognitivo permite, al docente, comprender los procesos de apre...
Article
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España) jgodino@ugr.es RESUMEN. Se analizan los diferentes grados de formalización matemática que pueden aplicarse en el estudio de la probabilidad en los niveles de educación no universitarios. Se aplica el modelo de niveles de algebrización de las prácticas matemáticas basado en el Enfoque Ontosemiótico para identificar los tipos de objetos y pro...
Article
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Los materiales curriculares constituyen un puente entre el currículo previsto y el implementado en el aula, mediando en el aprendizaje de los estudiantes. Por tanto, desde la investigación educativa se debe estudiar su grado de adecuación a los procesos de enseñanza planificados. Valorar la pertinencia de estos materiales requiere desarrollar instr...
Article
Poder valorar lo que ocurre en un proceso de enseñanza-aprendizaje es una de las competencias esenciales del profesor. Este con frecuencia debe analizar y seleccionar los materiales educativos que considera pertinentes para sus alumnos. Entre los recursos que están ganando presencia en diversas propuestas pedagógicas se incluyen los vídeos educativ...
Article
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Resumen Una lección de un libro de texto puede ser considerada como un proceso de instrucción potencial o planificado por el autor del libro, que sirve de apoyo al docente para diseñar e implementar un proceso de instrucción efectivo. Esto permite aplicar las herramientas de análisis didáctico del enfoque ontosemiótico del conocimiento y la instruc...
Article
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A textbook lesson can be considered as a potential or planned instructional process proposed by the author’s book, which can help the teacher to design and implement an effective instructional process. This permits the application of didactical analysis tools of the onto-semiotic approach to mathematical knowledge and instruction in order to assess...
Article
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In this work, we apply the criteria and indicators of didactic suitability to the analysis of the Peruvian secondary education curricular syllabus in probability. The research has a qualitative approach, and the methodology used is content analysis based on the Onto-Semiotic Approach (OSA) categories. The results show a given priority to classical...
Article
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Los libros de texto constituyen un importante recurso para el diseño instruccional. El docente debe ser capaz de analizar su idoneidad, identificar limitaciones y realizar adaptaciones que las solventen considerando las necesidades de sus estudiantes. En este trabajo se describe el diseño, implementación y resultados de una intervención formativa c...
Article
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Resumen Una lección de libro de texto describe el proceso instruccional previsto para el estudio de un contenido, por lo que constituye un recurso relevante para los docentes, que deberán ser críticos cuando decidan cómo emplearla en su planificación curricular. En este estudio se describen y analizan las reflexiones que hacen futuros maestros sobr...
Article
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El objetivo de este trabajo es construir una pauta de indicadores de idoneidad didáctica específicos para el tema de la proporcionalidad, que pueda servir de apoyo para el análisis y valoración de lecciones de libros de texto, y como recurso para la reflexión de los profesores sobre procesos de instrucción efectivamente implementados sobre proporci...
Chapter
We present a synthesis of the seminar content held on the Dialogue between Theories in Mathematics Education corresponding to the Onto-semiotic Approach (OSA) of mathematical knowledge and instruction module. In the first session we presented the research problems that OSA addresses, as well as the epistemological, ontological and semiotic principl...
Conference Paper
Full-text available
Beltrán-Pellicer, P., Burgos, M. y Giacomone, B. (2021). Análisis de vídeos educativos en línea por estudiantes de máster de secundaria. En Diago, P. D., Yáñez D. F., González-Astudillo, M. T. y Carrillo, D. (Eds.), Investigación en Educación Matemática XXIV (pp. 157 – 164). Valencia: SEIEM. Resumen Este trabajo se enmarca en una línea de investig...
Article
Full-text available
In order to foster the learning of mathematics, the teacher must be able to analyse and assess the students’ mathematical activity. The explicit recognition of objects and processes involved in mathematical practices is a competence that the teacher should develop. This cognitive analysis competence allows the teacher to understand the processes of...
Article
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En esta investigación, se describen los criterios que asumen, de manera implícita, un grupo de futuros maestros de primaria, cuando han de valorar la adecuación de la trayectoria didáctica planificada con el visionado de dos vídeos en un canal educativo para la enseñanza de un contenido concreto, el porcentaje en sexto curso de primaria. Se emplea...
Article
En este trabajo se describe el diseño, implementación y análisis retrospectivo de una acción formativa con estudiantes del grado de Educación Primaria, cuyo objetivo es evaluar el conocimiento sobre proporcionalidad y el grado de desarrollo de dos aspectos relevantes del conocimiento didáctico-matemático de dicho contenido: el análisis de objetos y...
Article
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Una crítica tradicional a la investigación científica en el campo educativo ha sido la desconexión con la práctica docente, motivada por el fraccionamiento de los problemas de investigación. Para resolver esta disociación, las investigaciones de diseño instruccional plantean problemáticas de tipo predictivo más próximas a dicha práctica, pero deben...
Article
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Background: Every teacher should be able to use curriculum materials to guide instructional design and make reasoned pedagogical decisions about the limitations these resources may have. Objectives: In this paper, we describe and analyse a formative intervention with prospective high school mathematics teachers, aimed at developing their compet...
Article
The notions of meaning and sense, which are closely related to understanding, play an essential role in educational processes in general and, therefore, in the teaching and learning of mathematics. However, the terms ‘meaning’ and ‘sense’ are unevenly used in the theory of language, semiotics, philosophy and psychology. After describing the main ch...
Article
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Teaching and learning Calculus concepts and procedures, particularly the definite integral concept, is a challenge to teachers and students in their academic careers. In order to develop an informed plan for improving instructional processes, it is necessary to pay attention to the nature and complexity of the mathematical features of the definite...
Article
Solving problems by different methods, identifying the knowledge put at stake in each case, and stating variants of the problems are fundamental aspects of the competence of analysis of mathematical knowledge for teaching. This paper reports on the design, implementation, and results of a formative intervention with primary education prospective te...
Article
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El diseño curricular de un contenido matemático en los diversos niveles educativos requiere considerar la diversidad de significados y su articulación progresiva, atendiendo a los grados de generalidad y formalización. En este trabajo se analizan los diversos significados de la proporcionalidad aplicando herramientas teóricas del Enfoque Ontosemiót...
Article
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RECME - Revista Colombiana de Matemática Educativa 5(2) En este trabajo se aborda el problema de la articulación de dos marcos teóricos usados en la investigación sobre la enseñanza y aprendizaje de las matemáticas: la teoría de la objetivación y el enfoque ontosemiótico del conocimiento y la instrucción matemáticos. Como primera aproximación al p...
Article
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In this paper, we describe the design, implementation and results of a formative intervention, meant to develop prospective primary school teachers’ competence in the analysis of the difficulties emerging in the resolution of proportionality tasks. Solving problems by different methods, identifying the knowledge put at stake in each problem and tak...
Article
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A pesar de los enormes esfuerzos de investigación que se vienen realizando, el problema de cómo enseñar las matemáticas y las ciencias sigue abierto. Decidir entre los modelos didácticos centrados en el profesor (enseñanza transmisiva) o centrados en el estudiante (aprendizaje indagativo) plantea un dilema para la práctica educativa. En este trabaj...
Article
Full-text available
A pesar de los enormes esfuerzos de investigación que se vienen realizando, el problema de cómo enseñar las matemáticas y las ciencias sigue abierto. Decidir entre los modelos didácticos centrados en el profesor (enseñanza transmisiva) o centrados en el estudiante (aprendizaje indagativo) plantea un dilema para la práctica educativa. En este trabaj...
Chapter
Despite the huge research efforts that have been made, the problem of how to teach mathematics and sciences remains open. Deciding between teacher-focused teaching models (transmissive teaching) or student-focused (inquiring learning) poses a dilemma for educational practice. In this paper we address this problem and propose a solution applying the...
Article
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The theory of didactic situations in mathematics postulates that learning is produced by adaptation to an antagonistic milieu, given the central role that this theory assigns to the adidactical situations (moments where the students’ autonomous production of knowledge takes place). However, the relevance of constructivist approaches is questioned b...
Article
Full-text available
Resumen El libro de texto es un recurso ampliamente usado en la práctica de la enseñanza y en consecuencia, es objeto de investigación educativa, aplicando diversas perspectivas teóricas. En este trabajo se ejemplifica el uso de las herramientas teóricas del Enfoque Ontosemiótico del conocimiento y la instrucción matemáticos para realizar el anális...
Article
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Aunque suele haber un consenso bastante generalizado en educación matemática a favor de los modelos de instrucción de tipo constructivista la cuestión de su pertinencia no deja de ser controvertida. Entre los modelos extremos centrados, bien en el estudiante o en el profesor, se pueden encontrar otros modelos de tipo mixto en los que ambos agentes...
Article
Full-text available
El libro de texto es un recurso ampliamente usado en la práctica de la enseñanza y en consecuencia, es objeto de investigación educativa, aplicando diversas perspectivas teóricas. En este trabajo se ejemplifica el uso de las herramientas teóricas del Enfoque Ontosemiótico del conocimiento y la instrucción matemáticos para realizar el análisis didác...
Article
Full-text available
Although there is a fairly generalized consensus in mathematics education in favour of constructivist-type instructional models, their pertinence is controversial. Between the extreme centered models, either on the student or on the teacher, we find other mixed type models, where both educational process agents play a leading role, depending on the...
Article
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Let $A$ and $B$ be C$^*$-algebras. A linear map $T:A\to B$ is said to be a $^*$-homomorphism at an element $z\in A$ if $a b^*=z$ in $A$ implies $T (a b^*) =T (a) T (b)^* =T(z)$, and $ c^* d=z$ in $A$ gives $T (c^* d) =T (c)^* T (d) =T(z).$ Assuming that $A$ is unital, we prove that every linear map $T: A\to B$ which is a $^*$-homomorphism at the un...
Article
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Proportional reasoning is often considered as an access route to early algebraic reasoning. In this paper, we show the analysis of the answers of a group of fifth grade students, who are faced for the first time with proportionality tasks, analyzing in detail the developed procedures, representations, arguments and evidences obtained about their ge...
Article
https://www.maa.org/press/periodicals/convergence/on-squares-rectangles-and-square-roots On Squares, Rectangles, and Square Roots The purpose of this article is to provide an example of how the history of mathematics, and the use of manipulative materials, can be used to explore the meaning and calculation of the square root with children in a six...
Article
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Resumen En este trabajo se describe el diseño e implementación de una acción formativa con estudiantes de un máster de profesorado de Educación Secundaria en España sobre el tema de proporcionalidad. El objetivo principal de la experiencia es explorar sus conocimientos iniciales y evaluar el grado de desarrollo de aspectos relevantes de la faceta e...
Chapter
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Este trabajo forma parte de un proyecto de investigación cuyo objetivo es diseñar, experimentar y evaluar intervenciones educativas que promuevan formas de razonamiento algebraico en los primeros niveles de educación primaria usando tareas de proporcionalidad. Se informa de la fase de evaluación de una experiencia realizada con un grupo de alumnos...
Article
The vast number of online educational videos available at the moment has generated an emerging area of research concerning their level of suitability. This study considers the epistemic quality of educational videos on mathematics, focusing on the specific content of directly proportional distributions. A qualitative study is used, based on the app...
Article
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Burgos, M., Godino, J. D., Giacomone, B., & Beltrán-Pellicer, P. (2018). Competencia de análisis epistémico de tareas de proporcionalidad de futuros profesores. ALME Acta Latinoamericana de Matemática Educativa, 31(1), 706-713. México: Comité Latinoamericano de Matemática Educativa A. C. En el marco de una investigación de diseño, basada en el mod...
Chapter
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Se realiza el análisis a priori de la resolución de una tarea de proporcionalidad por varios métodos, identificando los conocimientos puestos en juego e identificando los niveles de algebrización impli-cados. Además, se analizan las respuestas dadas a la tarea por una muestra de 33 estudiantes de un máster de formación de profesores de matemáticas...
Conference Paper
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Significados pragmáticos y configuraciones ontosemióticas en el estudio de la proporcionalidad. En J. M. Contreras, P. Arteaga, G. R. Cañadas, M. M. Gea, B. Giacomone y M. M. López-Martín (Eds.), Actas del Segundo Congreso International Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos. Disponible en, enfoqueontos...
Article
We prove that every weak-local triple derivation on a JB⁎-triple E (i.e. a linear map T:E→E such that for each ϕ∈E⁎ and each a∈E, there exists a triple derivation δa,ϕ:E→E, depending on ϕ and a, such that ϕT(a)=ϕδa,ϕ(a)) is a (continuous) triple derivation. We also prove that conditions (h1) {a,T(b),c}=0 for every a, b, c in E with a,c⊥b; (h2)P2(e)...
Article
The present paper is devoted to the study of linear maps preserving certain relations, such as the sharp partial order and the star partial order in semisimple Banach algebras and -algebras.
Article
The present paper is devoted to the study of the diamond partial order in general C*-algebras and the description of linearmaps preserving this partial order
Article
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In this paper we investigate the properties of minus partial order in unital rings. We generalize several results well known for matrices and bounded linear operators on Banach spaces. We also study linear maps preserving the minus partial order in unital semisimple Banach algebras with essential socle.
Article
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We study new classes of linear preservers between C$^*$-algebras and JB$^*$-triples. Let $E$ and $F$ be JB$^*$-triples with $\partial_{e} (E_1)$. We prove that every linear map $T:E\to F$ strongly preserving Brown-Pedersen quasi-invertible elements is a triple homomorphism. Among the consequences, we establish that, given two unital C$^*$-algebras...
Article
We present a generalized version of Hua’s theorem for Banach algebras, where the condition for all invertible is replaced by for all invertible . We also study linear preservers of inverses along an element, a concept introduced recently that extends some classical concepts of generalized invertibility.
Article
We prove that every (not necessarily linear nor continuous) 2-local triple homomorphism from a JBW$^*$-triple into a JB$^*$-triple is linear and a triple homomorphism. Consequently, every 2-local triple homomorphism from a von Neumann algebra (respectively, from a JBW$^*$-algebra) into a C$^*$-algebra (respectively, into a JB$^*$-algebra) is linear...
Article
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It is established that every (not necessarily linear) 2-local $^*$-homomorphism from a von Neumann algebra into a C$^*$-algebra is linear and a $^*$-homomorphism. In the setting of (not necessarily linear) 2-local $^*$-homomorphism from a compact C$^*$-algebra we prove that the same conclusion remains valid. We also prove that every 2-local Jordan...
Article
We study orthogonality preserving surjective linear maps from a unital C∗C∗-algebra with non-zero socle AA to a C∗C∗-algebra. In particular, we prove that, when AA has essential socle, every biorthogonality preserving surjective linear map T:A→BT:A→B is automatically bounded and a Jordan ∗∗-isomorphism multiplied by an invertible element.
Article
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In a first result we prove that every continuous local triple deriva-tion on a JB * -triple is a triple derivation. We also give an automatic continuity result, that is, we show that local triple derivations on a JB * -triple are con-tinuous even if not assumed a priori to be so. In particular every local triple derivation on a C * -algebra is a tr...
Data
In a first result we prove that every continuous local triple deriva-tion on a JB * -triple is a triple derivation. We also give an automatic continuity result, that is, we show that local triple derivations on a JB * -triple are con-tinuous even if not assumed a priori to be so. In particular every local triple derivation on a C * -algebra is a tr...
Article
Let A and B be unital complex algebras, assume that A is a semisimple Banach algebra with non-zero socle. We prove that under certain conditions every bijective linear map T: A → B, which preserves zero products, is an isomorphism multiplied by a central invertible element. Zero Jordan product preservers, and a more restrictive version of zero prod...
Article
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The aim of the present paper is to give approximate versions of Hua’s theorem and other related results for Banach algebras and C *-algebras. We also study linear maps approximately preserving the conorm between unital C *-algebras.
Article
Let A and B be C *-algebras. We investigate linear maps from A to B strongly preserving Moore-Penrose invertibility, where A is unital, and either it is linearly spanned by its projections, or has large socle, or has real rank zero (in this last case the map T is assumed to be bounded).
Article
Let A and B be Banach algebras. Assume that A is unital. We prove that an additive map T:A→BT:A→B strongly preserves Drazin (or equivalently group) invertibility, if and only if T is a Jordan triple homomorphism. When A and B are C∗-algebras, we characterize the linear maps strongly preserving generalized invertibility (in the Jordan systems’ sense...
Article
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We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras.
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Let Lip(X, B(H)) and lipα(X, B(H)) (0 < α < 1) be the big and little Banach *-algebras of B(H)-valued Lipschitz maps on X, respectively, where X is a compact metric space and B(H) is the C *-algebra of all bounded linear operators on a complex infinite-dimensional Hilbert space H. We prove that every linear bijective map that preserves zero product...
Article
We prove that every biorthogonality preserving linear surjection between two dual or compact C⁎-algebras or between two von Neumann algebras is automatically continuous.
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We prove that every biorthogonality preserving linear surjection from a weakly compact JB*'-triple containing no infinite-dimensional rank-one summands onto another JB'-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBW-triples containing no infinite-dimensional rank-one summa...
Article
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We characterize surjective linear maps that preserve the minimum modulus between unital semisimple Banach algebras, one of them is a unital C* -algebra having either real rank zero or essential socle. We also describe surjective linear maps on L (H), with H an infinitedimensional Hilbert space, preserving the essential minimum modulus. Results conc...
Article
We describe linear maps from a C∗-algebra onto another one preserving different spectral quantities such as the minimum modulus, the surjectivity modulus, and the reduced minimum modulus.
Article
Let A be a unital C*-algebra of real rank zero and B be a unital semisimple complex Banach algebra. We characterize linear maps from A onto B preserving different essential spectral sets and quantities such as the essential spectrum, the (left, right) essential spectrum, the Weyl spectrum, the index and the essential spectral radius.
Article
Let T:Lip0(X)→Lip0(Y) be a surjective map between pointed Lipschitz ∗-algebras, where X and Y are compact metric spaces. On the one hand, we prove that if T satisfies the non-symmetric norm ∗-multiplicativity condition: then T is of the form where η and τ are functions on Y such that η(Y)⊆{0,1} and , and is a base point preserving Lipschitz homeomo...
Article
We obtain a complete characterization of all orthogonality preserving operators from a JB *-algebra to a JB *-triple. If T : J → E is a bounded linear operator from a JB *-algebra (respectively, a C *-algebra) to a JB *-triple and h denotes the element T**(1), then T is orthogonality preserving, if and only if, T preserves zero-triple-products, if...
Article
Let A and B be unital C∗-algebras such that at least one of them is of real rank zero. We investigate surjective linear maps from A to B preserving the conorm, the (von Neumann) regularity, the generalized spectrum, and their essential versions. As a consequence, we recover results of Mbekhta, and Mbekhta and Šemrl for $\mathcal{L}(H)$ when H is an...
Article
Let A be a unital C*-algebra with non-zero socle (soc(A)). We introduce the essential conorm of an element a in A (denoted by γ e (a)), as the conorm of the element π(a), where π denotes the canonical projection of A onto A/[`(soc(A))]A/\overline{soc(A)}. It is established that for every von Neumann regular element a Î Aa{\in}A, γ e (a) = max {g(a...
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We study orthogonality preserving operators between C∗-algebras, JB∗-algebras and JB∗-triples. Let be an orthogonality preserving bounded linear operator from a C∗-algebra to a JB∗-triple satisfying that T∗∗(1)=d is a von Neumann regular element. Then , every element in T(A) and d operator commute in the JB∗-algebra , and there exists a triple homo...
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We generalize the theory of associative unitary normed algebras to the setting of noncommutative Jordan algebras. Special attention is devoted to the case of alternative algebras.
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We revise the notion of von Neumann regularity in JB*-triples by finding a new characterisation in terms of the range of the quadratic operator Q(a). We introduce the quadratic conorm of an element a in a JB*-triple as the minimum reduced modulus of the mapping Q(a). It is shown that the quadratic conorm of a coincides with the infimum of the squar...
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We prove that a complex Banach space X is a Hilbert space if (and only if) the Banach algebra (of all bounded linear operator on X) is unitary and there exists a conjugate-linear algebra involution • on satisfying T• = T−1 for every surjective linear isometry T on X. Appropriate variants for real spaces of the result just quoted are also proven. Mo...
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We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X h...
Article
We study unitary Banach algebras, as defined by M. L. Hansen and R. V. Kadison in 1996, as well as some related concepts like maximal or uniquely maximal Banach algebras. We show that a norm-unital Banach algebra is uniquely maximal if and only if it is unitary and has minimality of the equivalent norm. We prove that every unitary semisimple commut...
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In the present paper we continue to study the descent spectrum of an operator on a Banach space. We obtain that a Banach space X is finite-dimensional if and only if there exists a bounded operator T on X such that its commutant is formed by algebraic operators. We provide also an affirmative answer to a question of M.A. Kaashoek and D.C. Lay.

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