The motivation of the students in Physical Education classes with an eminently practical nature is opposed to the rejection in other areas with more theoretical classes and with more abstract ...content. This article aims to assess the motivation, difficulties and learning involved in the interdisciplinary work of Mathematics and Physical Education. For this, an intervention is carried out in the Physical Education classes, where different contents of the area of mathematics are taught through the sport of volleyball. Seventy-two sixth-grade primary school students were part of this study, divided into two groups, the experimental group (n = 36) and the control group (n = 36). A mixed methodology is used quantitative descriptive and qualitative, through the performance of a pedagogical test (pre-test and post-test) and the analysis of the students' diaries. After the analysis of the results, it is found that the students showed great motivation towards work and an assimilation of the proposed learning, not encountering any notable difficulties during the intervention. The contents of geometry, perimeter, probability and statistics, have been those that increased the percentage of success in greater measure after the intervention. It is concluded that Physical Education constitutes a valid and motivating tool to work on mathematical content.
La motivación de los alumnos en las clases de Educación Física con carácter eminentemente práctico se contrapone al rechazo en otras áreas con clases más teóricas y con contenidos más abstractos. El presente artículo pretende valorar la motivación, las dificultades y el aprendizaje que supone el trabajo interdisciplinar de Matemáticas y Educación Física. Para ello se realiza una intervención en las clases de Educación Física, donde a través del deporte del voleibol se imparten diferentes contenidos propios del área de matemáticas. Setenta y dos alumnos/as de sexto curso de Primaria formaron parte de este estudio distribuidos en dos grupos, grupo experimental (n=36) y grupo control (n=36). Se utiliza una metodología mixta, cuantitativa descriptiva y cualitativa, a través de la realización de un test pedagógico (pre-test y post test) y el análisis de los diarios del alumnado. Tras el análisis de los resultados, se constata que los estudiantes mostraron gran motivación hacia el trabajo y una asimilación de los aprendizajes planteados, no encontrándose dificultades destacadas durante la intervención. Los contenidos de geometría, perímetro, probabilidad y estadística han sido los que aumentaron el porcentaje de acierto en mayor medida tras la intervención. Se concluye que la Educación Física constituye una herramienta válida y motivadora para trabajar contenidos matemáticos.
Troubles with mathematical contents Facchin, Marco
Philosophical psychology,
09/2022, Letnik:
ahead-of-print, Številka:
ahead-of-print
Journal Article
Recenzirano
Odprti dostop
To account for the explanatory role representations play in cognitive science, Egan's deflationary account introduces a distinction between cognitive and mathematical contents. According to that ...account, only the latter are genuine explanatory posits of cognitive-scientific theories, as they represent the arguments and values cognitive devices need to represent to compute. Here, I argue that the deflationary account suffers from two important problems, whose roots trace back to the introduction of mathematical contents. First, I will argue that mathematical contents do not satisfy important and widely accepted desiderata all theories of content are called to satisfy, such as content determinacy and naturalism. Secondly, I will claim that there are cases in which mathematical contents cannot play the explanatory role the deflationary account claims they play, proposing an empirical counterexample. Lastly, I will conclude the paper highlighting two important implications of my arguments, concerning recent theoretical proposals to naturalize representations via physical computation, and the popular predictive processing theory of cognition.
Paweł Gładziejewski has recently argued that the framework of predictive processing (PP) postulates genuine representations. His focus is on establishing that certain structures posited by PP ...actually play a representational role. The goal of this paper is to promote this discussion by exploring the contents of representations posited by PP. Gładziejewski already points out that structural theories of representational content can successfully be applied to PP. Here, I propose to make the treatment slightly more rigorous by invoking Francis Egan’s distinction between mathematical and cognitive contents. Applying this distinction to representational contents in PP, I first show that cognitive contents in PP are (partly) determined by mathematical contents, at least in the sense that computational descriptions in PP put constraints on ascriptions of cognitive contents. After that, I explore to what extent these constraints are specific (i.e., whether PP puts unique constraints on ascriptions of cognitive contents). I argue that the general mathematical contents posited by PP do not constrain ascriptions of cognitive content in a specific way (because they are not relevantly different from mathematical contents entailed by, for instance, emulators in Rick Grush’s emulation theory). However, there are at least three aspects of PP that constrain ascriptions of cognitive contents in more specific ways: (i) formal PP models posit specific mathematical contents that define more specific constraints; (ii) PP entails claims about how computational mechanisms underpin cognitive phenomena (e.g. attention); (iii) the processing hierarchy posited by PP goes along with more specific constraints.
This article seeks to show that learning environments centered on an everyday or professional topics, usually in the interest of students and supported by technology, contribute favorably to minimize ...the feeling of irrelevance of mathematical contents, common among students. The problems proposed were based on work carried out in Linear Programming discipline from an Information Systems Course in which many of the students involved also execute professional activities, making it difficult to dedicate to the studies. Through the experience, it was possible to observe that the use of everyday or professional subjects contribute to minimize the sense of irrelevance of the discipline and, in addition, the students became more critical and involved with the information received.
O objetivo deste artigo é discorrer sobre duas açöes de formaçâo continuada e como elas se constituíram em ambientes colaborativos de aprendizagem. Tais açöes focalizaram a realizaçâo de atividades ...experimentais com o software GeoGebra, nas quais participaram pesquisadores e professores de Matemática da Educaçâo Básica. Ademais, alguns dados empíricos sâo apresentados e discutidos aqui, com a finalidade de elucidarnos as discussöes acerca de duas dessas atividades. Tais açöes de formaçâo continuada compöem o cenário de investigaçâo de uma pesquisa de doutorado de cunho qualitativo, que está em desenvolvimento, vinculada a um projeto temático de grande envergadura que vem sendo realizado dentro do Grupo de Pesquisa em Informática, outras Mídias e Educaçâo Matemática (GPIMEM). Uma das açöes aconteceu na cidade de Bauru/SP e a outra na cidade de Coimbra, em Portugal. As atividades abordadas nessas açöes, assim como nas demais desenvolvidas em outros projetos de pesquisa do grupo, de modo geral, tem um enfoque teórico-metodológico de natureza experimental. Conclui-se que os professores, ao mesmo tempo em que realizaram tais atividades e opinaram acerca de outros conteúdos matemáticos que poderiam ter sido contemplados nelas, estudaram as funcionalidades do software, tecendo críticas as abordagens propostas, culminando em sugestöes de adaptaçöes, tornando-as viáveis para serem aplicadas em suas respectivas salas de aula. Por fim, evidencia-se que a participaçâo em tais açöes lhes possibilitou vislumbrar maneiras para se constituir ambientes colaborativos de aprendizagem também em seus respectivos contextos de trabalho.
Sequencing contents is of great importance for instructional design within the teaching planning processes. We believe that it is key for a meaningful learning. Therefore, we propose to formally ...establish a partial order relation among the contents. We have chosen the binary relation "to be a prerequisite" for that purpose. We have applied this approach to the mathematical contents of the compulsory Secondary Education of the Spanish educational system and the information obtained has been modeled as a graph. The amount of contents considered (814) and the number of ordered pairs in the order relation considered (17,782) has produced a big graph. In order to work effectively with that amount of data, we have used software specialized in network analysis. More precisely, we have used the software packages Pajek and Gephi. This software, together with the use of techniques borrowed from graph theory, has allowed providing a tool for debugging curriculum developments (similar to rule based expert systems verification).
In the first part, the article presents a series of theoretical aspects about interdisciplinarity, a concept which under the present conditions of the new curriculum for preschool education, requires ...a new approach of mathematical contents and particularly another modality of using didactic strategies. The second part of the article focuses on the presentation of two models of interdisciplinary activities, which are meant to emphasize those methodical aspects, which should be taken into account by the teacher, in approaching mathematical contents and in correlating them by means of the other experiential fields. In the end, the stress is laid on some conclusions regarding the use of interdisciplinarity in approaching mathematical contents at the level of preschool education.
La Investigación Iberoamericana sobre eficacia escolar proporciona una teoría y metodología para determinar cuáles son los factores educativos asociados a una educación de calidad. En Cuba para ...obtener carreras universitarias los alumnos deben aprobar pruebas de ingreso de Matemática, Español e Historia. Profesores de la Facultad de Ciencias de la Universidad de Ciencias Pedagógicas Félix Varela iniciaron el presente estudio con el objetivo de determinar algunos factores educativos que influyen en los problemas de aprendizaje de los contenidos matemáticos de los alumnos que solicitan carreras pedagógicas. Se identifican los contenidos matemáticos donde los alumnos presentan las mayores dificultades y se verifica que los factores educativos del nivel alumno: la orientación profesional pedagógica inicial, del nivel aula: los años de experiencia de los docentes y del nivel institución escolar: el tipo de preuniversitario, y el tamaño de dichas instituciones influyen en los logros en el aprendizaje de contenidos matemáticos.
The Iberoamerican Research on school efficacy offers a theory and a methodology to determine the educative factors associated with a quality education. In Cuba to be granted the university, the students should pass admission tests on Mathematics, Spanish Language and History of Cuba. Teachers from the Sciences Faculty at Felix Varela Morales Pedagogical University have developed a research on this topic to determine the educative factors that influence on the students difficulties in the learning of mathematical contents.
There were identified the mathematical contents in which the students have the greatest difficulties. It was verified, that the variables related to the student (initial pedagogical professional orientation), to the class (teachers experience) and to the school institution (kind and size) are factors that influence on the success of the mathematical contents learning.
En este artículo se presenta una visión de la enseñanza de las matemáticas en las primeras edades que prioriza que los niños y niñas aprendan a usar las matemáticas en su vida cotidiana. Se argumenta ...que para aprender a usar las matemáticas es necesario partir de un currículo de matemáticas que contemple dos tipos de conocimientos: los contenidos matemáticos (razonamiento lógico-matemático; numeración y calculo; geometría; medida; y estadística y probabilidad) y, sobre todo, los procesos matemáticos (la resolución de problemas; el razonamiento y la demostración; la comunicación; las conexiones; y la representación), ya que estos procesos ponen de relieve las formas de adquisición y uso de los contenidos matemáticos. Se ofrecen orientaciones didácticas para planificar y gestionar actividades que contemplen las conexiones entre los contenidos y los procesos matemáticos mediante la presentación de dos experiencias implementadas en diferentes centros escolares de la geografía española.
Razvoj misaonih struktura djeteta utječe na uspješnost u savladavanju matematičkih pojmova. Pojava konkretnog logičkog mišljenja i njegovi indikatori (pojmovi konzervacije) značajni su za pozitivno ...školsko postignuće učenika u okviru matematičkih sadržaja. Oblikovanjem formalnih operacija, kao posljednjom najsavršenijom fazom razvoja mišljenja, omogućuju se najsloženiji vidovi konzervacije. Kombinatorika predstavlja generalizaciju operacija stečenih u stadiju konkretnih operacija i obilježje posljednje faze razvoja mišljenja.
Cilj ovog rada usmjeren je na procjenu razvoja misaonih struktura konkretnih logičkih operacija (ostvarivanjem konzervacije broja, duljine, mase i volumena) i formalnih operacija (ostvarivanjem kombinatorike), kao i njihovu povezanost s matematičkim postignućem učenika s blažim intelektualnim teškoćama starije školske dobi.
U istraživanju je sudjelovalo 120 učenika oba spola (43,3% djevojčica i 56,7% dječaka), kronološke dobi od 12 do 15 godina. Sudionici su učenici od V do VIII razreda beogradskih osnovnih škola za djecu s blažim intelektualnim teškoćama.
Za procjenu operativnosti mišljenja korišteni su standardni Piagetovi zadaci za procjenu konzervacije (broja, duljine, mase i volumena) i kombinatorike, a za procjenu usvajanja matematičkih sadržaja korišten je kriterijski test znanja, posebno konstruiran za potrebe ovog istraživanja.
Rezultatima istraživanja je utvrđena povezanost između stupnja misaone razvijenosti na svim primijenjenim zadacima i razine savladavanja gradiva matematike.
Imajući u vidu loša postignuća ispitanika našeg istraživanja u svim segmentima rada, naglašavamo značaj prezentiranja Piagetovih i matematičkih zadataka kroz igru, kao što i Piagetova teorija zastupa stav o primjeni igara kojima se potiču reverzibilnost, identitet i konzervacija te kojima se matematičko mišljenje čini gipkijim, aktivnijim, širim, dubljim i originalnijim.
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