Open Access
Aprender matemáticas: ¿qué enseñan los niños con discapacidad intelectual a los maestros en formación?
(Universidad de Zaragoza, 2019-05-14) Cogolludo, José Ignacio; García Catalán, Olga Raquel; Gil Clemente, Elena; Lizasoain Iriso, María Inmaculada; Millán Gasca, Ana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
La actitud con la que los maestros de Primaria afrontan su tarea como profesores de matemáticas tiene más que ver con sus experiencias previas como alumnos de la disciplina que con los contenidos que han aprendido durante las asignaturas de didáctica de las matemáticas en los Grados de Educación. Esta cuestión tiene un impacto sobre la instrucción matemática posterior de los niños, que se amplifica en el caso de los que tienen necesidades educativas especiales y conduce a emprender vías poco eficaces. Nuestro objetivo es trasladar a los estudiantes prácticas positivas, en forma de experiencia, llevadas a cabo con niños con discapacidad intelectual que puedan iluminarles sobre la forma de aprender de cualquier niño. Prácticas basadas por una parte en un enfoque histórico que propone una integración de aritmética y geometría elementales y por otra parte en el modelo desarrollado en Singapur para la resolución de problemas.
Open Access
Teoría de Clifford en el anillo de Burnside
(Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, 1995) Lizasoain Iriso, María Inmaculada; Ochoa Lezaun, Gustavo; Matemáticas; Matematika
Open Access
Orness for real m-dimensional interval-valued OWA operators and its application to determine a good partition
(Taylor & Francis, 2019) Miguel Turullols, Laura de; Paternain Dallo, Daniel; Lizasoain Iriso, María Inmaculada; Ochoa Lezaun, Gustavo; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA1
Ordered Weighted Averaging (OWA) operators are a profusely applied class of averaging aggregation functions, i.e. operators that always yield a value between the minimum and the maximum of the inputs. The orness measure was introduced to classify the behavior of the OWA operators depending on the weight vectors. Defining a suitable orness measure is an arduous task when we deal with OWA operators defined over more intricate spaces, such us intervals or lattices. In this work we propose a suitable definition for the orness measure to classify OWA operators defined on the set of m-dimensional intervals taking real values in [0, 1]. The orness measure is applied to decide which is the best partition of a continuous range that should be divided into four linguistic labels. This example shows the good behavior of the proposed orness measure.
Open Access
Orness measurements for lattice m-dimensional interval-valued OWA operators
(Elsevier, 2018) Miguel Turullols, Laura de; Paternain Dallo, Daniel; Lizasoain Iriso, María Inmaculada; Ochoa Lezaun, Gustavo; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks. The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggegating functions, which obviously give diferent results in the aggregation of the same set of data. In this paper, some possible classifications of OWA operators are suggested when they are de ned on m-dimensional intervals taking values on a complete lattice satisfying certain local conditions. A first classification is obtained by means of a quantitative orness measure that gives the proximity of each OWA to the OR operator. In the case in which the lattice is finite, another classification is obtained by means of a qualitative orness measure. In the present paper, several theoretical results are obtained in order to perform this qualitative value for each OWA operator.
Open Access
The interval-valued Choquet integral based on admissible permutations
(IEEE, 2018) Paternain Dallo, Daniel; Miguel Turullols, Laura de; Ochoa Lezaun, Gustavo; Lizasoain Iriso, María Inmaculada; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Aggregation or fusion of interval data is not a trivial task, since the necessity of arranging data arises in many aggregation functions, such as OWA operators or the Choquet integral. Some arranging procedures have been given to solve this problem, but they need certain parameters to be set. In order to solve this problem, in this work we propose the concept of an admissible permutation of intervals. Based on this concept, which avoids any parameter selection, we propose a new approach for the interval-valued Choquet integral that takes into account every possible permutation fitting to the considered ordinal structure of data. Finally, a consensus among all the permutations is constructed.
Open Access
Orness for idempotent aggregation functions
(MDPI, 2017) Legarreta, Leire; Lizasoain Iriso, María Inmaculada; Mardones Pérez, Iraide; Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Matemáticas
Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the orness—a measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition.
Open Access
Geometrical aggregation of finite fuzzy sets
(Elsevier, 2018) Campión Arrastia, María Jesús; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Lizasoain Iriso, María Inmaculada; Raventós Pujol, Armajac; Valero, Óscar; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE; Estadística, Informática y Matemáticas
A fuzzy set on a finite universe can be interpreted as a vector in a unit cube. This gives rise to a huge variety of approaches in order to aggregate finite fuzzy sets or to modify a given one. We analyze several geometrical methods and discuss possible applications in a multidisciplinary setting.
Open Access
Achieving transfer from mathematics learning
(MDPI, 2023) Orón, José Víctor; Lizasoain Iriso, María Inmaculada; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
The question of transfer is a special challenge in mathematics teaching because the wide range and fragmentation of the curricula have in many cases fostered an instrumental understanding, which makes transfer difficult for the students. Although promoting a relational learning has been a huge step forward in achieving transfer, understanding usually remains at the technical level of learning. Fostering critical thinking and metacognition raises learning to the psychological level, as students are encouraged to analyse their own thinking. Despite this, our hypothesis is that transfer will only be achieved when students are helped to reach a personal dimension, being encouraged to discover their own way of approaching the global reality of their lives beyond the subject. Learning, for instance, the greatest common divisor should be an opportunity to discover that, as numbers can be presented by their prime factors, people can be recognised by their features and interests. As such, looking for the greatest common divisor should not differ from discovering common interests with friends. Integrating specific and general learning will make transfer no longer unattainable. Personalising learning means discovering how one specific learning impacts on the personal way of understanding reality (oneself, others, and world), thus making transfer natural.
Open Access
El reto de acercarse al alumnado con discapacidad intelectual abre un nuevo enfoque en la enseñanza de las matemáticas para todo el alumnado
(Gobierno de Navarra / Nafarroako Gobernua, 2024) Lizasoain Iriso, María Inmaculada; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
La preocupación internacional por el tema de la formación matemática de los futuros docentes ha ido creciendo en los últimos años. Algunos estudios (Gellert, U., 2005) constatan que esta formación resulta más efectiva cuando en la universidad se aprenden las cosas de una forma semejante a la que sería deseable como práctica escolar. Con el fin de diseñar propuestas concretas para la formación inicial y continua de los maestros en forma de talleres, que fueran fácilmente trasladables a las aulas escolares, la Universidad Pública de Navarra (UPNA) coordinó el proyecto ANFoMAM (Aprender de los niños para formar a los maestros en el área de Matemáticas), en el que participaron otras tres universidades europeas (Universidad de Zaragoza, Universidad Roma Tre y Universidad de Burdeos) y dos instituciones que trabajan "a pie de calle", una de ellas con docentes de todas las etapas de enseñanza obligatoria (ToKalon, en Italia) y la otra con niños y niñas con Síndrome de Down (Sesdown en Zaragoza, España)
Open Access
La educación centrada en el encuentro como forma singular de innovación
(Universidad de Navarra, 2022) Orón Semper, José Víctor; Lizasoain Iriso, María Inmaculada; Institute for Advanced Materials and Mathematics - INAMAT2
Antes de hablar de innovación educativa, necesitamos determinar qué entendemos por perfeccionar tanto el acto educativo como el proceso de crecimiento de las personas involucradas en él. Inspirados por la forma de entender el desarrollo personal de Leonardo Polo y Erik Erikson, entre otros autores, analizamos los requisitos antropológicos y psicológicos necesarios para que emerja la novedad tanto en cada acto educativo como en los actores que participan en él. Encontramos que la novedad emerge en el interior de cada acto educativo cuando la competencia se pone al servicio de la transformación del mundo en aras del encuentro interpersonal