This paper presents the research results of what the process of mathematics tеaching should be under the competency-based approach allowing the development of a university student's mathematical competency. It indicates that integrative structure of mathematical competency containing cognitive, practical, motivational and valuebased, reflexive and assessment-based components, updates the polyparadigm approach in teaching mathematics as an open cluster of approaches; their integrated utilization under the leading role of competency-based approach contributes to developing all mathematical competency components. It justifies that competency-based, context-based, interdisciplinary, discipline-based and information technology approaches and fundamentalization play a critical part in the polyparadigm approach; the integrated utilization of all approaches results in a synergetic effect. Within this framework the basic principles of competency-based mathematics teaching as well as a coherent system to select the content of mathematics teaching for engineering educational institution students are developed.Keywords: Mathematical competency. Polyparadigm approach. Didactic basis. Cluster of approaches. System to select the content of mathematics teaching.
ResumoEste artigo apresenta resultados de pesquisa sobre como deve ser o processo de ensino da Matemática dentro da abordagem baseada na competência de modo a possibilitar o desenvolvimento das capacidades matemáticas do estudante universitário. Os resultados indicam que a estrutura integrante da competência matemática, contemplando os aspectos cognitivo, prático, motivacional, valor intrínseco, reflexivo e avaliativo, confirma a abordagem poliparadigmática do ensino da Matemática como sendo um cluster aberto de abordagens; a utilização inte- ISSN 1980-4415 DOI: http://dx.doi.org/10.1590/1980-4415v30n56a14 Bolema, Rio Claro (SP), v. 30, n. 56, p. 1113 -1126, dez. 2016 1114 grada dessas abordagens sob a óptica da competência contribui para o desenvolvimento de todos os componentes do domínio da matemática. A pesquisa justifica que as abordagens baseadas em competência, contexto, interdisciplinaridade, organização e tecnologia da informação desempenham um papel fundamental na abordagem poliparadigmática. A utilização integrada de todas as abordagens resulta em um efeito sinergético. Dentro desta estrutura, são desenvolvidos os princípios básicos do ensino da Matemática baseado na competência, assim como um sistema coerente para selecionar conteúdos de ensino para escolas de engenharia.Palavras-chave: Competência matemática. Abordagem poliparadigmática. Base didática. Cluster de abordagens. Sistema para selecionar conteúdos de ensino.
The problem of individualisation in education in terms of e-learning remains relevant despite a lot of research done in the area. The present article is intended to review existing education practice individualisation in e-learning and to determine the prospects of development of adaptive e-learning courses that provide the student with an individual educational environment content which focuses on the individual characteristics of students. The authors arrive at the conclusion that building an individual educational trajectory in the adaptive e-learning course has a significant advantage in organising education in the electronic environment for both the student and the teacher. The main feature of these courses becomes the selection of educational content that best matches the individual abilities, needs and needs of the student in an electronic environment. The results of the research are universally applicable and can serve as a basis for organising adaptive web-based teaching not only for mathematics, but also for other disciplines in institutions of secondary, higher and further education
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