Inma Lizasoain - Academia.edu (original) (raw)
Papers by Inma Lizasoain
Education Sciences
The question of transfer is a special challenge in mathematics teaching because the wide range an... more 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, lo...
In this paper, we present a new format for mathematical workshops for pre-service teachers (PSTs)... more In this paper, we present a new format for mathematical workshops for pre-service teachers (PSTs) that seek to bring their university mathematical training closer to the school classroom reality while addressing issues such as confidence and their previous experiences of maths at school. The aim is to provide the participants with a group lived experience in order to change both their beliefs about the nature of mathematics and their attitude towards teaching it. The results of the implementation of an initial version of the workshops in a pilot phase of the project are presented here.
Estudios sobre Educación
Antes de hablar de innovación educativa, necesitamos determinar qué entendemos por perfeccionar t... more 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.
In this paper the number of isomorphism classes of the right transversals of the symmetric group ... more In this paper the number of isomorphism classes of the right transversals of the symmetric group Σ_n-1 in the symmetric group Σ_n is calculated. This result together with the techniques employed along the paper may be used to go forward in the study and classification of the subgroups with a certain number of isomorphism classes of transversals in the group.
arXiv: Group Theory, 2017
In this paper the number of isomorphism classes of the right transversals of the symmetric group ... more In this paper the number of isomorphism classes of the right transversals of the symmetric group Sigman−1\Sigma_{n-1}Sigman−1 in the symmetric group Sigman\Sigma_nSigman is calculated. This result together with the techniques employed along the paper may be used to go forward in the study and classification of the subgroups with a certain number of isomorphism classes of transversals in the group.
Applied Mathematics and Computation
Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple s... more 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 different results in the aggregation of the same set of data. In this paper, some possible classifications of OWA operators are suggested when they are defined 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.
Sustainability
Sustainable decisions in education are those which pursue long-term achievements for students. In... more Sustainable decisions in education are those which pursue long-term achievements for students. In many cases, the principals of the schools are those who must make these decisions. In this paper we explore some of the factors that influence the students’ long-term development by means of an analysis of the correlation between certain organizational aspects of the schools which directly depend on the principals and the scores that their students have obtained in the International Assessment PISA 2018 in mathematics, reading and science. The results point to a better long-term student achievement when the organizational decisions are designed to enhance interpersonal relationships (teacher-teacher, teacher-student and student-student), responding to the specific needs of each person and based on trust. Conversely, it seems that when the organizational decisions are merely made to control academic life, they either bear upon academic achievement in a negative way or do not significantl...
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion.... more Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion. If the data are real numbers, then OWA operators can be characterized either as a special kind of discrete Choquet integral or simply as an arithmetic mean of the given values previously ordered. This paper analyzes the possible generalizations of these characterizations when OWA operators are defined on a complete lattice. In addition, the set of all n-ary OWA operators is studied as a sublattice of the lattice of all the n-ary aggregation functions defined on a distributive lattice.
IEEE Transactions on Fuzzy Systems
International Journal of Approximate Reasoning
Axioms
Aggregation functions are mathematical operators that merge given data in order to obtain a globa... more 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.
Communications in Computer and Information Science, 2016
Acta Mathematica Sinica English Series, Feb 15, 2010
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 2015
In this work we deal with the problem of using OWA operators in color image reduction algorithms.... more In this work we deal with the problem of using OWA operators in color image reduction algorithms. For this reason, we study OWA operators defined on an arbitrary finite lattice endowed with a t-norm and a t-conorm. In the case of RGB color images, we apply OWA operators defined on a finite product lattice. Depending on the OWA operator considered, we see that the reduced images become brighter or darker. Then, we make a preliminary study of a qualitative orness measure for classifying each lattice OWA operator according to its proximity to the maximum of the given data.
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 2015
Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transfo... more Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0, 1].
Advances in Intelligent and Soft Computing, 2011
Aggregation Functions in Theory and in Practise, 2013
Journal of Pure and Applied Algebra, 1998
There are many analogies between permutation representations and linear representations. Neverthe... more There are many analogies between permutation representations and linear representations. Nevertheless, no version of projective representations is known in the context of the Burnside ring. In this paper, a decomposition theorem of irreducible G-sets similar to Clifford's one which expresses an irreducible linear representation as a product of two projective representations is obtained. As a consequence, the definition of the
Journal of Pure and Applied Algebra, 2001
It is known that the natural concept of projective representation of a group G has also signiÿcan... more It is known that the natural concept of projective representation of a group G has also signiÿcance for permutation representations (G-sets). In this paper the implications of the corresponding idea for G-groups are explored. As a consequence, di erent relations with some well-known concepts as crowns, wreath products, primitive groups, common complements and diagonal subgroups are obtained.
Journal of Algebra, 2000
In this paper a Clifford theory for semisimple G-groups is developed, as a particular case of an ... more In this paper a Clifford theory for semisimple G-groups is developed, as a particular case of an abstract Clifford theory for G-functors. ᮊ
Education Sciences
The question of transfer is a special challenge in mathematics teaching because the wide range an... more 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, lo...
In this paper, we present a new format for mathematical workshops for pre-service teachers (PSTs)... more In this paper, we present a new format for mathematical workshops for pre-service teachers (PSTs) that seek to bring their university mathematical training closer to the school classroom reality while addressing issues such as confidence and their previous experiences of maths at school. The aim is to provide the participants with a group lived experience in order to change both their beliefs about the nature of mathematics and their attitude towards teaching it. The results of the implementation of an initial version of the workshops in a pilot phase of the project are presented here.
Estudios sobre Educación
Antes de hablar de innovación educativa, necesitamos determinar qué entendemos por perfeccionar t... more 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.
In this paper the number of isomorphism classes of the right transversals of the symmetric group ... more In this paper the number of isomorphism classes of the right transversals of the symmetric group Σ_n-1 in the symmetric group Σ_n is calculated. This result together with the techniques employed along the paper may be used to go forward in the study and classification of the subgroups with a certain number of isomorphism classes of transversals in the group.
arXiv: Group Theory, 2017
In this paper the number of isomorphism classes of the right transversals of the symmetric group ... more In this paper the number of isomorphism classes of the right transversals of the symmetric group Sigman−1\Sigma_{n-1}Sigman−1 in the symmetric group Sigman\Sigma_nSigman is calculated. This result together with the techniques employed along the paper may be used to go forward in the study and classification of the subgroups with a certain number of isomorphism classes of transversals in the group.
Applied Mathematics and Computation
Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple s... more 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 different results in the aggregation of the same set of data. In this paper, some possible classifications of OWA operators are suggested when they are defined 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.
Sustainability
Sustainable decisions in education are those which pursue long-term achievements for students. In... more Sustainable decisions in education are those which pursue long-term achievements for students. In many cases, the principals of the schools are those who must make these decisions. In this paper we explore some of the factors that influence the students’ long-term development by means of an analysis of the correlation between certain organizational aspects of the schools which directly depend on the principals and the scores that their students have obtained in the International Assessment PISA 2018 in mathematics, reading and science. The results point to a better long-term student achievement when the organizational decisions are designed to enhance interpersonal relationships (teacher-teacher, teacher-student and student-student), responding to the specific needs of each person and based on trust. Conversely, it seems that when the organizational decisions are merely made to control academic life, they either bear upon academic achievement in a negative way or do not significantl...
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion.... more Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion. If the data are real numbers, then OWA operators can be characterized either as a special kind of discrete Choquet integral or simply as an arithmetic mean of the given values previously ordered. This paper analyzes the possible generalizations of these characterizations when OWA operators are defined on a complete lattice. In addition, the set of all n-ary OWA operators is studied as a sublattice of the lattice of all the n-ary aggregation functions defined on a distributive lattice.
IEEE Transactions on Fuzzy Systems
International Journal of Approximate Reasoning
Axioms
Aggregation functions are mathematical operators that merge given data in order to obtain a globa... more 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.
Communications in Computer and Information Science, 2016
Acta Mathematica Sinica English Series, Feb 15, 2010
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 2015
In this work we deal with the problem of using OWA operators in color image reduction algorithms.... more In this work we deal with the problem of using OWA operators in color image reduction algorithms. For this reason, we study OWA operators defined on an arbitrary finite lattice endowed with a t-norm and a t-conorm. In the case of RGB color images, we apply OWA operators defined on a finite product lattice. Depending on the OWA operator considered, we see that the reduced images become brighter or darker. Then, we make a preliminary study of a qualitative orness measure for classifying each lattice OWA operator according to its proximity to the maximum of the given data.
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 2015
Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transfo... more Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0, 1].
Advances in Intelligent and Soft Computing, 2011
Aggregation Functions in Theory and in Practise, 2013
Journal of Pure and Applied Algebra, 1998
There are many analogies between permutation representations and linear representations. Neverthe... more There are many analogies between permutation representations and linear representations. Nevertheless, no version of projective representations is known in the context of the Burnside ring. In this paper, a decomposition theorem of irreducible G-sets similar to Clifford's one which expresses an irreducible linear representation as a product of two projective representations is obtained. As a consequence, the definition of the
Journal of Pure and Applied Algebra, 2001
It is known that the natural concept of projective representation of a group G has also signiÿcan... more It is known that the natural concept of projective representation of a group G has also signiÿcance for permutation representations (G-sets). In this paper the implications of the corresponding idea for G-groups are explored. As a consequence, di erent relations with some well-known concepts as crowns, wreath products, primitive groups, common complements and diagonal subgroups are obtained.
Journal of Algebra, 2000
In this paper a Clifford theory for semisimple G-groups is developed, as a particular case of an ... more In this paper a Clifford theory for semisimple G-groups is developed, as a particular case of an abstract Clifford theory for G-functors. ᮊ