Do Fiscal and Political Decentralization Raise Students’ Performance? A Cross-Country Analysis

The low quality of education is a persistent problem in many developed countries. Parallel to in the last decades exists a tendency towards decentralization in many developed and developing countries. Using micro data from the Programme for International Student Assessment (PISA) referred to 22 countries, we test whether there exists an impact of fiscal and political decentralization on student performance in the areas of mathematics, reading skills and science. We observe that fiscal decentralization exerts an unequivocal positive effect on students’ outcomes in all areas, while the effect of political decentralization is more ambiguous. On the one hand, the capacity of the subnational governments to rule on its region has a positive effect on students’ performance in mathematics. On the other hand, the capacity to influence the country as a whole has a negative impact on mathematics achievement. As a general result, we observe that students’ performance in Mathematics is more sensible to these exogenous variations than in Sciences and reading skills. Keywords: School outcomes, PISA, fiscal decentralization, political decentralization JEL codes: H11, H77, I21

Resolució de problemes i mètode de raonament en l'educació matemàtica

Des del principi dels temps històrics, la Matemàtica s'ha generat en totes les civilitzacions sobre la base de la resolució de problemes pràctics.Tanmateix, a partir del període grec la Història ens mostra la necessitat de fer un pas més endavant: l'evolució històrica de la Matemàtica situa els mètodes de raonament com a eix central de la recerca en Matemàtica. A partir d'una ullada als objectius i mètodes de treball d'alguns autors cabdals en la Història dels conceptes matemàtics postulem l'aprenentatge de les formes de raonament matemàtic com l'objectiu central de l'educació matemàtica, i la resolució de problemes com el mitjà més eficient per a coronar aquest objectiu.English version.From the beginning of the historical times, mathematics has been generated in all the civilizations on the base of the resolution of practical problems. Nevertheless, from the greek period History shows us the necessity to take one more step: the historical evolution of mathematics locates the methods of reasoning as the central axis of the research in mathematics. Glancing over the objectives and methods of work used bysome fundamental authors in the History of the mathematical concepts we postulated the learning of the forms of mathematical reasoning like the central objective of the mathematical education, and the resolution of problems as the most efficient way to carry out this objective.

Rising to Greatness An Imperative for Improving Iowa’s Schools, 2011

In the early 1990s, the Cold War ended, Back to the Future III was in theaters, and Iowa led the nation in reading and mathematics. Times have changed. A decade into the 21st century, Iowa has conceded its place at the top. During the past 20 years, achievement trends illustrate Iowa’s slide from a national leader in PK-12 education to a national average―sometimes below average―performer as other states (and nations) have accelerated past the state. Iowa students’ futures are at risk. Collectively, Iowa students are not hitting the mark in mathematics and reading competency. Sure, Iowa has its share of super-achievers. But the mass of Iowa students—not just underprivileged or minority students, but many of the majority white, relatively affluent students as well—are falling short of what is needed to attain quality jobs, growing incomes, and secure livelihoods in today’s globally competitive world. The world has moved beyond the industrial age and information age and is now in the innovation age. Students must be armed not only with knowledge, but also with skills and insights needed to critically analyze and innovate. The pressing problems and grand opportunities the world faces require that many more people contribute as innovators and problem solvers, not order takers and implementers. Innovators will prosper. Order takers will stagnate. The days of an abundance of low-skill jobs have come to an end.

Diversitat cultural i matemàtiques

En aquesta recerca es presenten els resultats i les conclusions d’unes entrevistes realitzades a pares i mares d’alumnes de quart de primària de diferents orígens culturals, amb l’objectiu de descobrir el valor que cada família dóna a les matemàtiques, d’observar amb quines dificultats es troben els pares i mares quan han d’ajudar als seus fills i filles a fer els deures de matemàtiques, a més d’esbrinar quins recursos i/o estratègies tenen per ajudar-los. Per altra banda, també es vol saber si les experiències que tenen els adults en relació amb les matemàtiques afecta a l’ensenyament-aprenentatge dels seus fills i filles.

Matematiikan opetuksen virtuaaliympäristöjen pedagoginen käyttö

Tämän kandityön tarkoituksena on selvittää ja kehittää Lappeenrannan teknillisen yliopiston sovelletun matematiikan laitoksella luotua virtuaalimateriaalin käyttöä eri kohderyhmille sopivaksi sekä käyttäjäystävällisemmäksi. Matematiikan virtuaalimateriaali on luotu tukemaan lähiopetusta matematiikan perusopetuksessa. Matematiikan virtuaalimateriaalin hallintaympäristöä on kehitetty vuodesta 2001. Järjestelmää sekä sen opiskelumateriaalia on kehitetty opettajien ja opiskelijoiden avulla. Järjestelmä kattaa teknillisen yliopiston eri osastojen matematiikan peruskurssien materiaalit. Sen käytöllä opettajat voivat hankkia itselleen lisää aikaa opetuksen suunnitteluun materiaalin luomisen nopeutuessa, koska opetusmateriaali voidaan nopeasti kasata valmiista tehtävistä ja teoriaosioista. Opiskelijoiden kannalta hyvätasoinen oppimateriaali on jatkuvasti saatavilla ja sen avulla on myös helppo opiskella hyvien hakutoimintojen ansiosta.

Relaciones entre conocimiento del catalán y del castellano y el rendimiento matemático. Un estudio empírico

Este trabajo se desarrolla en el contexto sociocultural y lingüístico de la provincia de Lleida. En él se analiza la relación entre el dominio de las dos lenguas en contacto (catalán y castellano) con el rendimiento en matemáticas. Los resultados revelan que existe una correlación significativa entre el dominio de la lengua vehicular y el rendimiento matemático y, a su vez, que el mayor conocimiento de la lengua vehicular tiene efectos superiores en el rendimiento de los tres tipos de conocimiento que contempla la prueba de matemáticas. Por otra parte, se constata una elevada correlación entre el dominio del castellano y el resultado de la prueba de matemáticas, lo que revela que el conocimiento matemático obtenido a través de una de las lenguas se transfiere a la otra.

LUDOLITERACY Informe sobre la alfabetización mediática en el juego digital. Experiencias en Europa

El informe que a continuación presentamos recoge 18 experiencias, proyectos, actividades,investigaciones o políticas más significativas que se realizan en Europa relacionadas con la alfabetización mediática en el contexto de los videojuegos (ludoliteracy). La ludoliteracy tiene como finalidad potenciar las capacidades y competencias analíticas, reflexivas y creativas alrededor del juego digital. Se trata, en conjunto, de propuestas que permiten al ciudadano (joven o adulto, profesional o usuario) y a la sociedad en general ser más conscientes de nuestros propios placeres, tener capacidad crítica y competencia creativa en el campo específico de los juegos digitales.El objetivo final del informe es ofrecer recomendaciones en un campo socialmente controvertido y económicamente situado a la cabeza de las industrias culturales pero institucionalmente emplazado en los márgenes de las políticas educativas estatales y europeas.

Nuorten koherenssin tunne: mittaaminen, ennustavat tekijät, seuraukset

Sense of coherence in adolescence: measuring, predictive factors, consequences The aim of this study was to explore the stability of sense of coherence (SOC) in adolescence and the associations between childhood psychological symptoms and SOC in adolescence. Furthermore, the aim of this study was to explore whether the 13-item SOC scale for adults is applicable to adolescents 12 years of age and to determine which factors are associated with perceived health and SOC. Data relating to SOC and factors associated with perceived health and SOC were collected in class in a cross-sectional setting by self-administered questionnaires in all publicly funded elementary schools (N=35) of Turku. A total of 1 231 (83%) of 1 481 12-year-old schoolchildren participated in the study. The data was, with appropriated authority consent, anonymously completed with marks in mathematics, native and first foreign language at the end of sixth class. The examination of stability of SOC in adolescence and the associations between childhood psychological symptoms and SOC was based on data of a prospective population-based mail survey. The source population originated in 11 health authority areas of the Province of Turku and Pori. The study was carried out by using questionnaires at child’s ages of 3, 12, 15, and 18 years. Acceptably completed questionnaires were returned by 1 086 (84%) parents at the child’s age of 3, at the age of 12 by 70% adolescents and parents, at the age of 15, by 66% adolescents and 58% parents, and at the age of 18, by 61.5% adolescents and 61% parents. The results of the study showed that childhood behavioural problems from the age of 3 years predicted poor SOC at the age of 18 years. A poor SOC was associated with psychological symptoms and behavioural problems in adolescence. Contrary to assumptions in Antonovsky’s theory, there was no significant change in SOC between the ages of 15 to 18 years, and the stability of SOC did not depend on initial SOC. Slight fluctuation in SOC scores was seen at the individual level. When studied cross-sectionally, in 12-year-old schoolchildren, insufficient physical exercise, less than excellent marks in mathematics, weak SOC, insufficient social support from teachers, and perceived various problems in class climate associated with perception of poor health. Identification of behavioural problems in early childhood helps to identify the children at risk of ill-being and poor SOC in adolescence since problems seem to persist unchanged until adolescence. The 13-item SOC scale aimed at adults is applicable to adolescents of 12 years of age or older and the SOC scale is a useful tool in identifying adolescents in need of supportive interventions.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Proceso de transformación de las concepciones del profesorado sobre la resolución de problemas matemáticos

The aim of this study is to analyze the transformation of Primary School teachers’ conceptions about mathematical problem solving. We performed a study with 18 teachers from three public schools: in each class (from 1º to 6º) there were two interventions, and we were interviewed teachers before and after them. The results have show identified changes in: 1) teacher’s expectations about students’ abilities; classroom management; perception of diversity; mathematical strategies used by students; communication in the classroom; causes of the problems encountered; and relevance process of problem solving in mathematics teaching. The transformation of teachers’ conceptions is due to the following factors: a) awareness of the practice; b) systematic reflection; c) the contrast between different ways to work solving problems in math class

Hållpunkter för lärande : småbarns möten

Developed from human activities, mathematical knowledge is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans’ everyday life, an environment where people reach agreement regarding certain “laws” and principles in mathematics. Through interaction with worldly phenomena and people, children will always gain experience that they can then in turn use to understand future situations. Consequently, the environment in which a child grows up plays an important role in what that child experiences and what possibilities for learning that child has. Variation theory, a branch of phenomenographical research, defines human learning as changes in understanding and acting towards a specific phenomenon. Variation theory implies a focus on that which it is possible to learn in a specific learning situation, since only a limited number of critical aspects of a phenomenon can be simultaneously discerned and focused on. The aim of this study is to discern how toddlers experience and learn mathematics in a daycare environment. The study focuses on what toddlers experience, how their learning experience is formed, and how toddlers use their understanding to master their environment. Twenty-three children were observed videographically during everyday activities. The videographic methodology aims to describe and interpret human actions in natural settings. The children are aged from 1 year, 1 month to 3 years, 9 months. Descriptions of the toddlers’ actions and communication with other children and adults are analyzed phenomenographically in order to discover how the children come to understand the different aspects of mathematics they encounter. The study’s analysis reveals that toddlers encounter various mathematical concepts, similarities and differences, and the relationship between parts and whole. Children form their understanding of such aspects in interaction with other children and adults in their everyday life. The results also show that for a certain type of learning to occur, some critical conditions must exist. Variation, simultaneity, reasonableness and fixed points are critical conditions of learning that appear to be important for toddlers’ learning. These four critical conditions are integral parts of the learning process. How children understand mathematics influences how they use mathematics as a tool to master their surrounding world. The results of the study’s analysis of how children use their understanding of mathematics shows that children use mathematics to uphold societal rules, to describe their surrounding world, and as a tool for problem solving. Accordingly, mathematics can be considered a very important phenomenon that children should come into contact with in different ways and which needs to be recognized as a necessary part of children’s everyday life. Adults working with young children play an important role in setting perimeters for children’s experiences and possibilities to explore mathematical concepts and phenomena. Therefore, this study is significant as regards understanding how children learn mathematics through everyday activities.

Images of imagination : an aesthetic approach to education

Visual art practice has generally been described as a lonely affair, thinking about what an artist has experienced in the outside world. This study is an inquiry into a visual art practice of another kind: the relational one. The research purpose is twofold. The first purpose is to shed light on a visual artist’s conceptions of art, education and scholarship. The second purpose is to by reasoning on imagination and a rhizomatic formation interpret the relations created between art, multimodality and literacy learning as an aesthetic approach to education. By inquiry into a specific collaborated long-term art practice, the study conveys how the meaning making elements of an arts based learning practice gradually transform an artist’s and a teacher’s concepts of art education to an aesthetic approach to education. In the art practice examined the typical Finnish rye bread and a poem have represented a cultural theme that has been elaborated through art conventions. The poem and the rye bread have in the art practice been articulated as cultural representations of as well as symbolic projections on the Swedishspeaking minority culture in Finland. The study connects art informed inquiry to a hermeneutic research rationale where the research reasoning is generated through a rhizomatic alliance between empiric data and theories. The reasoning is constructed as an interpretation pattern that expands throughout the study. The study arguments that the rhizome as an aesthetic formation can be appropriate to refer to when articulating arts based meaning making and when creating arts based educational strategies, dialogues, aesthetic learning and multimodal literacy in education. The study investigates an aesthetic approach to research in education, which means that the art practice surveyed is interpreted through articulation appropriate to poetic aspects of art, education and research.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.