scholarly journals Konstruktywistyczna dydaktyka w edukacji matematycznej

2020 ◽  
Vol 51 (4) ◽  
pp. 114-125
Author(s):  
Alina Kalinowska-Iżykowska

Didactics as science is a sub-discipline of paradigmatically pluralistic pedagogy. Its key categories, concepts, and relations between them are subject to changes in meaning. Constructivist mathematical education has to offer tools for a different understanding of educational phenomena. The text shows examples of significant transformations of didactic knowledge. The necessity to reconstruct how mathematical knowledge functions concerning students and teachers also implies requirement for changes in methodological assumptions. It becomes necessary to undertake qualitative research approaches to deepen the understanding of what is happening in lessons.

Author(s):  
Iara Da Silva França ◽  
Antonio Flavio Claras

Os professores primários paranaenses denominados efetivos tinham formação diferente daquela ofertada pela Escola Normal e possuíam, em sua maioria, somente o Curso Primário. Nos estudos aqui apresentados interessou-nos saber que saberes matemáticos o curso primário proporcionava a esses futuros professores efetivos durante a Primeira República. Amparados na história cultural, buscamos respostas nos documentos oficiais pertinentes, em especial, nos Programas de Ensino. O estudo evidencia para os professores efetivos da Primeira República uma formação geral, com os saberes necessários a ensinar, carecendo em grande medida, dos saberes para ensinar matemática. As mudanças ocorridas nos Programas buscavam sustentar a finalidade do ensino primário, sem proporcionar a formação para ensinar, visto não ser essa a sua finalidade.Palavras-chave: História da Educação. Formação de Professores. Saberes Matemáticos.AbstractThe primary teachers of Paraná called effective had different formation from that offered by the Normal School and had, in their majority, only the Primary Course. In the studies presented here, we were interested to know what mathematical knowledge the primary course provided to these future effective teachers during the First Republic. Based on cultural history, we seek answers in the pertinent official documents, especially in the Teaching Programs. The study shows for the effective teachers of the First Republic a general formation, with the necessary knowledge to teach, lacking in great measure, the knowledge to teach mathematics. The changes that occurred in the Programs sought to support the purpose of primary education, without providing the training to teach, since this is not its purpose.Keyword: History of Education. Mathematical Education. Mathematical Knowledge.


Author(s):  
Petra Langhorst

Mathematical development processes begin long before school starts and the importance of previous mathematical knowledge for later school achievements is beyond dispute. For a suitable pre-school education, the focus of interest must be to find out which early learning processes prepare children best. In this article, the acquisition of the key concepts of numeracy is presented in a developmental model, which served as framework for a supportive programme for 4-8 year-old children. The research into this intervention shows how development-oriented support of key arithmetic concepts can be constructed and taught systematically. The immediate and sustainable effect of the programme Mina and the Mole on the mathematical competencies of children has already been demonstrated in an evaluation study of 248 children aged 5-7. Considering the strong language-orientation of the programme, the present study focused on aspects of phonological awareness and of phonological working memory. It was evident that these phonological language processing aspects correlated with mathematic skills. Furthermore, it was found that the dominant linguistic focus of the training did not constitute a disadvantage – even linguistically weak children significantly improved their mathematical skills. Moreover, children with poor or average phonological performance could profit from the supportive programme also regarding their phonological language processing.


Author(s):  
Neura Maria De Rossi Giusti ◽  
Claudia Lisete Oliveira Groenwald

ResumoO artigo apresenta um recorte de uma pesquisa desenvolvida no município de Vacaria, no estado do Rio Grande do Sul, onde investigou-se a integração e divulgação de conhecimentos matemáticos na comunidade, a partir de um contexto educativo para a socialização de conceitos da educação básica, tendo em vista a aprendizagem social e, especificamente neste trabalho, o desenvolvimento do pensamento algébrico. Para a pesquisa qualitativa de investigação-ação foram utilizadas entrevistas dirigidas a comunidade participante e registros fotográficos com as resoluções das tarefas. As análises se apoiam sobre a Base Nacional Comum Curricular e as demandas cognitivas. As diferentes formas de aprender a aprender matemática, a mobilização, o interesse, os compartilhamentos dos conhecimentos matemáticos foram considerados, assim como as diferentes formas de resoluções e de raciocínio matemático empregado perante as tarefas apresentadas. As evidências apontam que os conhecimentos relacionados ao desenvolvimento do pensamento algébrico ofereceram empecilhos na interpretação e na compreensão da simbologia algébrica, visto que operar com letras e outros símbolos requer conhecimentos da linguagem algébrica para que se possa estabelecer generalizações, análises e resoluções. Também destacamos a importância da escola sobre o desenvolvimento de competências básicas.Palavras-chave: Educação matemática, Aprendizagem social, Aprender a aprender, Pensamento algébrico.AbstractThe article presents a snippet of a research developed in Vacaria in the state of Rio Grande do Sul, where the integration and disclosure of mathematical knowledge in the community was investigated, from an educational context to the socialisation of basic education concepts, in view of the social learning and, specifically in this study, the development of algebraic thinking. With a qualitative approach of investigation-action we verified direct interviews to the participating community and photographic records with the resolutions of the tasks. The analyses are based on the Common National Curriculum Base and the cognitive demands. The different forms of learn to learn mathematics, the mobilisation, the interest, the mathematical knowledge sharing were considered, as the different forms of resolutions and mathematical reasoning employed in front of presented tasks. The evidences indicate that knowledge related to development of algebraic thinking offered obstacles in the interpretation and understanding of algebraic simbology, since operating with letters and others symbols requires knowledge of algebraic language to establish generalisations, analyses, and resolutions. We also emphasise the importance of school for basic skills development.Keywords: Mathematical education, Social learning, Learn to learn, Algebraic thinking.ResumenEl artículo presenta un extracto de una investigación desarrollada en la ciudad de Vacaria, en el estado de Rio Grande do Sul, donde se investigó la integración y divulgación del conocimiento matemático en la comunidad, desde un contexto educativo para la socialización de conceptos de la enseãnza básica, con miras al aprendizaje social y, específicamente en este trabajo, el desarrollo del pensamiento algebraico. Con un enfoque cualitativo de la investigación-acción, se verificaron entrevistas orientadas a la comunidad participante y registros fotográficos con las resoluciones de las tareas. Los análisis se basan en la Base Curricular Nacional Común y las demandas cognitivas. Se consideraron las diferentes maneras de aprender a aprender matemáticas, la movilización, el interés, el intercambio de conocimientos matemáticos, así como las diferentes maneras de resoluciones y razonamientos matemáticos empleados en las tareas presentadas. Las evidencias apuntan que los conocimientos relacionados con el desarrollo del pensamiento algebraico ofrecieron obstáculos en la interpretación y comprensión de la simbología algebraica, ya que operar con letras y otros símbolos requiere conocimientos del lenguaje algebraico para poder establecer generalizaciones, análisis y resoluciones. También destacamos la importancia de la escuela en el desarrollo de habilidades básicas.Palabras clave: Educación matemática, Aprendizaje social, Aprender a aprender, Pensamiento algebraico.


Author(s):  
Yohana Taise Hoffmann ◽  
David Antonio da Costa

Este texto tem como objetivo analisar o Programa de Ensino dos Grupos Escolares de 1920 de Santa Catarina, privilegiando conteúdos e métodos prescritos relativos aos saberes matemáticos. A partir dos estudos de Valente (2015, 2016) e Trouvé (2008), são tomadas as categorias elementar e rudimentar caracterizadas por Condorcet e Pestalozzi. Arrolando demais documentos normativos e dialogando com as pesquisas realizadas no âmbito da história da educação e da história da educação matemática traçou-se um cenário educacional catarinense. Evidenciamse as características do método intuitivo, com os exercícios práticos que desenvolvem o raciocínio dos alunos, a matéria “lições de coisas” com a utilização de objetos e o uso de instrumentos associados à vida diária dos alunos. Sendo a natureza do ensino dos saberes matemáticos, rudimentares.Palavras-chave: Saber matemático. Elementar. Rudimentar. Condorcet. Pestalozzi.AbstractThis text aims to analyze the Program of Teaching of School Groups of 1920 of Santa Catarina, privileging contents and prescribed methods related to mathematical knowledge. From the studies of Valente (2015, 2016) and Trouvé (2008), the elementary and rudimentary categories characterized by Condorcet and Pestalozzi are taken. Listing other normative documents and dialoguing with the researches carried in the context of the history of education and the history of mathematical education a Santa Catarina educational scenario was traced. They are evidenced the characteristics of the intuitive method, with the practical exercises that develop students’ reasoning, the subject “lessons of things” with the use of objects and the use of instruments associated with the daily life of students. Being the nature of the teaching of mathematical, rudimentaryKeywords: Know mathematical. Elementary. Rudimentary. Condorcet. Pestalozzi


Author(s):  
S.V. Saryglar ◽  

Statement of the problem. The article deals with the problem of visualization in teaching mathematics using animated drawings. The purpose of the article is to present the analysis of the experimental work on computer animation in the GeoGebra environment as a means of improving mathematical education at school. Research methodology. The methodological foundations of the research include activity-based, informational and visual approaches to teaching mathematics, a synthesis of the author’s work experience in testing computer animation at school. Research results. The results of the experimental work confirmed the expediency of using computer animation in the process of teaching algebra in the 7th grade (educational activity of students increased, as well as interest in research work and quality of mastering mathematical knowledge and skills). Conclusion. The use of computer animation in math lessons at school increases the level of understanding and assimilation of mathematical knowledge by providing clear illustrations of mathematical concepts and statements. The analysis of experimental work using the animation capabilities of computer environments shows an increase in the technological equipment of modern mathematics teachers, which help them achieve higher educational results.


Author(s):  
Olena KHODAKOVSKA ◽  
◽  
Svitlana USTYCHENKO ◽  

Introduction. In recent years, teachers of most technical and natural sciences faculties find the level of freshmen starting a course of higher mathematics insuf-ficient to comprehend the basics of logical constructions. It is difficult for students to clearly realize that, for example, they should learn to prove a statement as a theorem or give a counter-example; in mathematics there are such terms as necessary and sufficient conditions, cause and effect; the system of equations and their totality are dif-ferent things; the properties of mathematical objects are subject of study; solving inequalities or equations requires understanding but not mechanical memorization. All these semantic subtleties make up the concept of mathematical culture based on clear logic reasoning and conclusion. Logical thinking is required in most activities, from business to programming. The relevance of the research is caused by the neces-sity to create a new educational environment free from such negative facts that some students have a low level of mathematical knowledge, skills and abilities; they are enable to independently acquire new mathematical knowledge and skills; their experience in mathematical, communicative and cognitive activity, necessary for a successful future career, is insufficient. International and Ukrainian scientists in the field of pedagogy and psychology diversely studied the problems of intellectual development and mathematical culture of students. (Jean Piaget , Jerome Seymour BrunerLev Vygotsky, Yuriy Hilbukh, Leonid Zankov, Vasilii Davydov, Daniil Elkonin, G.S. Kostiuk, Z.I. Kalmykova, N.O. Menchynska, S. L.Rubinstein, V.F. Palamarchuk, N.F.Talysina etc).The purpose of the articleis to generalize the pedagog-ical essence of mathematical culture, determine the place and role of mathematical education in the formation of students' mathematical culture, study pedagogical pre-requisites and specific technologies of its formation while teaching mathematics and determine conditions for crea-tion of the culture of mathematical language. The methods of analysis, comparison, explication, ab-straction are used in the study. Results. The development of mathematical culture of students involves a number of stages: formation of the student as a subject of educational mathematical activity; awareness of the mathematical education value; creating a holistic view of mathematical activity of the student; understanding mathematical learning materials; reflection of the general structure of mathematical activity in the educational activity; mathematical language acquisition, ability to correctly express and explain operations, ability to use mathematical signs and symbols; gaining under-standing of mathematical modeling as a mathematical method of reality cognition; mastering the system of mathematical concepts, general methods of operations; intellectual and spiritual development of students, includ-ing the development of mathematical thinking, meeting the requirements of modern information society, the develop-ment of children's motivation, creativity, research skills. The culture of mathematical language can only devel-op if the student has a sufficiently strong scientific base that allows him not to concentrate on thinking about the scientific accuracy of a story but to focus on how to speak. Originality. The Internet provides lots of opportunities to develop mathematical culture and present information of different nature: 1) mathematical information for com-pulsory learning i.e. comprehensible knowledge, filled with personal meaning should become a student's acqui-sition; 2) mathematical information for expanding ideas about the subject i.e. elements of logic, combinatorics, probability theory; 3) background information plays an important role in acquiring information, realizing its value, and creating the interest and need to study mathematics.Conclusions. The level of mathematical culture of stu-dents significantly increases under condition of taking nto account the leading ideas of modern international and Ukrainian psychological and pedagogical science about intellectual development of the personality; theoreti-cal substantiation of the content of students' mathemati-cal culture; working out a science-based approach to the technology of development of mathematical qualities of the personality when studying mathematics. In order to improve the culture of mathematical lan-guage, it is necessary to increase the classroom time for the development of oral language skills; allocate 10-15 minutes for oral questioning at every lesson; organize home test papers with an oral performance report in the form of an interview; conduct credit tests orally. Such forms of work contribute to the development of students' mathematical language


Author(s):  
Milagros Elena Rodríguez

ResumenEn la indagación se interpelan las investigaciones modernistas-coloniales de la Educación Matemática, es importante decolonizar la matemática ante el Sur, sus indagaciones y educación ante la imposición occidental en una matemática excluyente. En la perspectiva decolonialidad convergen grupos de investigadores conscientes de la urgencia de salvaguardar los conocimientos matemáticos soterrados, y disminuir las creencias y actitudes negativas hacia dicha ciencia. El reconocimiento del conocimiento matemático del Sur no desmitifica al de Occidente, complejiza dichos saberes y los muestra en toda su complejidad. Así se cumple con el objetivo complejo de sustentar las investigaciones transparadigmáticas en la Educación Matemática Decolonial Transcompleja, desde la deconstrucción rizomático como transmétodo. La investigación se presenta en rizomas que se conectan en un complexus maravilloso introspectivo: motivación, interrogantes, justificación y transmetodología; crisis de las investigaciones metodológicas modernistas en la Educación Matemática; perspectivas de las investigaciones transparadigmáticas en la Educación Matemática Decolonial Transcompleja y las conclusiones en la continuación de la línea de investigación. En estas conclusiones se exponen como los transmétodos enriquecen compleja y transdisciplinarmente a la Educación Matemática, así en la decolonialidad como premisa indispensable emergen categorías como: ecosofía, diatopía, antropolítica y antropoética que dan esencias de la matemática como ciencia legado de la humanidad.Keywords: transparadigmáticas, transmétodos, Educación Matemática Decolonial Transcompleja, complejidad, transdisciplinariedad. ResumoNesta investigação questiona-se as investigações colonial-modernistas da Educação Matemática. Reforçamos a importância da descolonização da matemática antes do Sul, suas investigações e a educação antes da imposição ocidental em uma matemática exclusiva. Na perspectiva descolonial, convergem grupos de pesquisadores, conscientes da urgência em salvaguardar o conhecimento matemático subterrâneo e reduzir as crenças e atitudes negativas em relação a essa ciência. O reconhecimento do conhecimento matemático do Sul não desmistifica o do Ocidente, complica esse conhecimento e o mostra em toda a sua complexidade. Assim, o complexo objetivo de apoiar investigações transparadigmáticas na Educação Matemática Decolonial Transcomplex é cumprido, a partir da desconstrução rizomática como transmétodo. A pesquisa é apresentada em rizomas que estão conectados em um maravilhoso complexo introspectivo: motivação, questionamentos, justificativa e transmetodologia; crise das investigações metodológicas modernistas em Educação Matemática; perspectivas das investigações transparadigmáticas em Educação Matemática Decolonial Transcomplex e as conclusões na continuação da linha de pesquisa. Nessas conclusões, expõe-se como os transmétodos enriquecem a Educação Matemática complexa e transdisciplinar, pois na descolonialidade como premissa indispensável, surgem categorias como ecosofia, diatopia, antropolítica e antropoética que dão essências da matemática como legado científico da humanidade.Palabras Clave: transparadigmática, transmétodos, educação matemática descolonial transcomplexa, complexidade, transdisciplinaridade.AbstractIn the inquiry the modernist-colonial investigations of Mathematical Education are questioned, being important to decolonize mathematics before the South, its inquiries and education before the western imposition in an exclusive mathematics. In the decolonial perspective, groups of researchers converge aware of the urgency of safeguarding underground mathematical knowledge, and reducing negative beliefs and attitudes towards said science. The recognition of mathematical knowledge of the South does not demystify that of the West, it complexifies this knowledge and shows it in all its complexity. Thus, it is fulfilled the complex objective of supporting transparadigmatic investigations in Transcomplex Decolonial Mathematics Education, from rhizomatic deconstruction as transmethod. This research is presented in rhizomes that are connected in a wonderful introspective complexus: motivation, questions, justification and transmethodology; crisis of modernist methodological research in Mathematics Education; perspectives of transparadigmatic investigations in Transcomplex Decolonial Mathematical Education and the conclusions in the continuation of the research line. These conclusions show how transmethods enrich Mathematics Education in a complex and transdisciplinary way, and in decoloniality as an indispensable premise, categories emerge such as: ecosophy, diatopia, anthropolitics and anthropoetics that give essences of mathematics as a science legacy of humanity.Keywords: transparadigmatics, transmethods, Transcomplex Decolonial Mathematical Education, complexity, transdisciplinarity.


Author(s):  
Juliana Gabriele Kiefer ◽  
Rita De Cássia Pistóia Mariani

ResumoO objetivo deste artigo é mapear estudos realizados na perspectiva teórico-metodológica da meta-análise no campo da Educação Matemática, disponíveis na Biblioteca Digital Brasileira de Teses e Dissertações (BDTD), com ênfase em aspectos institucionais, procedimentais e temáticos, bem como analisar duas investigações do tipo metanálise que abordam conceitos de perímetro e área. Para tanto, esta pesquisa caracteriza-se como qualitativa do tipo mapeamento. Os resultados indicam aumento no número de produções desenvolvidas por pesquisadores de diversas instituições de ensino superior do país e ampliação de discussões sobre esse procedimento metodológico, tendo em vista a diversidade dos referenciais teórico-metodológicos utilizados. Identifica-se variação no tipo e na quantidade de trabalhos analisados, sendo que a temática mais frequente está relacionada aos processos de ensino e aprendizagem da Matemática considerando o estudo de conceitos da matemática escolar (12 de 26 pesquisas), como por exemplo, área e perímetro, identificados como objeto de investigação das duas pesquisas apreciadas.Palavras-chave: Pesquisa qualitativa, Estudos de revisão, Metanálise.AbstractThe aim of this essay is to map subsidized studies in the theoretical-methodological perspective of meta-analysis within the field of Mathematical Education, available at the Biblioteca Digital Brasileira de Teses e Dissertações (Brazilian Digital Library of Thesis and Dissertations, BDTD), with an emphasis on institutional, procedural and thematic aspects, as well as to analyze two meta-analysis investigations that address concepts perimeter and area. Therefore, this research is characterizes as qualitative of the mapping type. The results show an increase in the number of productions developed by researchers from several higher education institutions in the country and the increase of discussions about this methodological procedure, in view of the diversity of methodological and theoretical references used. Variation in the type and quantity of studies analyzed is verified, with the most frequent theme is related to the processes of teaching and learning Mathematics regarding the study of concepts of school math (12 out of 26 studies), for example, area and perimeter, identified as the object of investigation of the two researches assessed.Keywords: Qualitative research, Review studies, Meta-analysis. ResumenEl objetivo de este artículo es mapear estudios subvencionados en la perspectiva teórico-metodológica del metaanálisis en el campo de la Educación Matemática, disponibles en la Biblioteca Digital Brasileña de Tesis y Disertaciones (BDTD), con énfasis en aspectos institucionales procedimentales y temáticos, así como analizar dos investigaciones de metaanálisis que abordan conceptos de perímetro y área. Por tanto, esta investigación se caracteriza por ser cualitativa de tipo cartográfico. Los resultados indican un aumento en el número de producciones desarrolladas por investigadores de varias instituciones de educación superior del país y un aumento en las discusiones sobre este procedimiento metodológico, dada la diversidad de referencias teóricas y metodológicas utilizadas. Se identifica variación en el tipo y cantidad de trabajos analizados, siendo el tema más frecuente el relacionado con los procesos de enseñanza y aprendizaje de las Matemáticas considerando el estudio de conceptos matemáticos escolares (12 de 26 investigaciones), tales como, perímetro, identificado como objeto de investigación de las dos investigaciones evaluadas.Palabras clave: Investigación cualitativa, estudios de revisión, metaanálisis.


Author(s):  
Gabriela Castro Silva Cavalheiro ◽  
Renata Cristina Geromel Meneghetti

Este artigo apresenta uma pesquisa que buscou responder ao seguinte questionamento: Como licenciandos em Matemática avaliam a metodologia de ensino-aprendizagem-avaliação de Matemática através da Resolução de Problemas (RP) implementada por um docente formador-pesquisador em disciplina específica da área? Para desenvolvê-la, adotou-se uma abordagem qualitativa de investigação, coletando-se os dados por meio de um questionário, após implementação da metodologia em uma turma de 18 licenciandos em Matemática que cursavam a disciplina Aritmética. O objetivo desse instrumento foi identificar, na perspectiva desses sujeitos, as possíveis contribuições da metodologia para a aprendizagem dos conteúdos matemáticos e dos demais conhecimentos necessários à formação do licenciado em Matemática. Os principais achados foram organizados em função do tripé aprendizagem, ensino e avaliação de Matemática. Diante das conclusões obtidas, embora a maioria dos sujeitos tenha conseguido perceber a importância do uso dessa metodologia para sua Formação Matemática, Pedagógica ou em Educação Matemática, considera-se importante o desenvolvimento de mais estudos na mesma linha, ou seja, trabalhos que possibilitem ao licenciando em Matemática vivenciar efetivamente várias vezes as diversas metodologias de ensino, aprendizagem e avaliação, por meio de RP e de outras abordagens alternativas, seja na condição de aluno ou de futuro professor.   Palavras-chave: Licenciatura em Matemática. Futuro Professor. Docente Formador-Pesquisador. Aritmética. Metodologia Qualitativa.   Abstract This article presents a research that sought to answer the following question: How do students of a Mathematics Degree course evaluate the methodology of teaching-learning-assessment of Mathematics through Problem Solving (PR) implemented by a teacher trainer-researcher in a specific discipline in the area? To develop it, a qualitative research approach was adopted, collecting the data through a questionnaire, after implementing the methodology in a class of 18 graduating in Mathematics who studied the Arithmetic discipline. The aim of this instrument was to identify, from the perspective of these subjects, the possible contributions of the methodology to the learning of the mathematical contents and other knowledge necessary for the formation of the graduate in Mathematics. The main findings were organized according to tripod learning, teaching and assessment of mathematics. In view of the conclusions obtained, although the majority of the subjects were able to perceive the importance of using this methodology for their Mathematical Formation, Pedagogical Formation or Mathematical Education Formation, it is considered important to develop further studies in the same line, that is, works that allow the graduating in Mathematics to effectively experience several times the different methodologies of teaching, learning and evaluation, through PR and other alternative approaches, whether as a student or future teacher.   Keywords: Degree in Mathematics. Future Teacher. Teacher Trainer-Researcher. Arithmetic. Qualitative Methodology.


Author(s):  
Ma. Cristina Naya-Rivero ◽  
◽  
Tania F. Gómez-Sánchez ◽  
Ma. Begoña Rumbo-Arcas ◽  
Ma. Elena Segade-Pampín ◽  
...  

This article analyses the initial training in Mathematical Education of the Degree in Primary Education in the public universities in Spain. The aim is to study the type of mathematical knowledge defined in syllabus. For this purpose, it has been carried out a comparative study about preservice teachers' curriculum. Two comparison parameters included in the TEDS-M International report have been into account: knowledge of mathematical content and knowledge of pedagogical content. The results obtained show a high variability in the distribution of the number and nature of ECTS offered and a prevalence of the knowledge of the mathematical content in relation to the pedagogical content.


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