A matemática em ação no ensino superior: possibilidades por meio do problem-based learning
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2021-12-20
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Universidade Estadual Paulista (Unesp)
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Este estudo tem como proposta encaminhar discussões relativas ao campo da Educação Matemática nas universidades. Seu objetivo é compreender de que formas os aspectos da matemática em ação podem emergir no Ensino Superior, sob perspectivas do Problem-Based Learning, o PBL. Tal propósito foi delineado a partir da seguinte questão diretriz: Como os aspectos da matemática em ação podem emergir no Ensino Superior, sob perspectivas do Problem-Based Learning? O referencial teórico desta pesquisa se pautou no conceito da matemática em ação, inspirado por Ole Skovsmose, que se refere aos interesses da Educação Matemática Crítica, e também foi conduzido por princípios de aprendizagem associados ao Problem-Based Learning. O contexto deste estudo se desenvolveu por meio de uma abordagem qualitativa, fundamentando-se em um estudo de caso e na observação participante. A produção de dados foi realizada em duas instituições de Ensino Superior públicas de São Paulo. Na primeira instituição, chamada de instituição A, a produção de dados teve a participação de quatro estudantes do primeiro ano do curso de Engenharia Civil. Isso aconteceu no contraturno das aulas regulares, por meio de quatro encontros e da realização de entrevistas semiestruturadas. Já no segundo caso, na instituição B, o contexto envolveu as aulas de Cálculo Diferencial e Integral II de uma turma do segundo ano de Ecologia e também foram realizados quatro encontros, incluindo algumas apresentações finais. As discussões foram mobilizadas a partir da apresentação de um problema relacionado aos impactos ambientais causados por poluentes químicos. Na instituição A, as discussões foram conduzidas pela própria pesquisadora. No caso da instituição B, além da pesquisadora, esse processo também foi conduzido por outros dois professores, responsáveis pelas aulas de Cálculo. Em ambos os casos, esses três participantes assumiram o papel de facilitadores da aprendizagem. Logo, o registro dos dados produzidos ocorreu por meio de gravações em áudio e anotações no diário de campo. A análise dos dados se constituiu a partir da elaboração de quatro temas centrais, inspirados nos cinco aspectos da matemática em ação e nas potencialidades de se explorar os princípios do PBL em aulas de matemática do Ensino Superior. Esses processos foram realizados de acordo com a questão de pesquisa definida, considerando-se o objetivo proposto. Muitos elementos vieram à tona. Dentre eles, podem-se mencionar: o uso e a aplicação de fórmulas e conceitos matemáticos em diferentes situações; discussões acerca de legitimações e justificações por meio da matemática; reflexões sobre responsabilidade, ética e valoração; a construção de saberes por meio da prática e da pesquisa. A partir dos resultados obtidos foi possível perceber um novo aspecto da matemática em ação, o qual foi nomeado como Classificação. A caracterização deste aspecto corresponde à possibilidade de se estabelecerem fatos, semelhanças ou diferenças, além de organizar ou ordenar elementos e conhecimentos, a respeito de enfoques ligados à matemática ou às suas aplicações na realidade. Sua elaboração amplia considerações relativas ao campo da Educação Matemática Crítica e da própria Educação Matemática, no que tange às reflexões acerca das diferentes aplicações da matemática em diversas situações, seja no contexto universitário ou na sociedade de forma geral.
This study proposes to raise discussions concerning the field of mathematics education in universities. Its objective is to understand how aspects of mathematics in action can emerge from the perspectives of Problem-Based Learning (PBL) in Higher Education. The objective was outlined from the following guiding question: How can aspects of mathematics in action emerge in Higher Education, from the perspectives of Problem-Based Learning? The theoretical framework of this research was based on the concept of mathematics in action, inspired by Ole Skovsmose and conceptions about learning principles associated with Problem-Based Learning. The research was developed through a qualitative approach, based on a case study and through participant-observation. The data production was carried out in two universities located in São Paulo State. All process were done from of presentation of a real problem related to environmental impacts caused by chemical pollutants. In the institution A, the process involved a study group and semi structured interviews with four Civil Engineering undergraduate students. In the institution B, the participation involved thirty Ecology students in the second year; the discussions occurred in some classes of Calculus II. In the last class, the groups presented some research that they had developed. In the institution A, the discussions were conducted by the researcher herself. In institution B, in addition to the researcher, other two teachers that was responsible for the Calculus classes, contributed to the development of this stage. In both cases, the three participants took on the role of learning facilitators. The data were recorded, and some notes were done in the field diary. The data analysis consisted of elaboration of four central themes inspired by five aspects of mathematics in action and the potential to explore the principles of PBL in higher education mathematics classes. These processes were carried out according to the defined research question, considering the proposed objective. Many elements emerged, among them: the application of formulas and mathematical concepts in different situations; discussions about legitimizations and justifications through mathematics; reflections on responsibility, ethics, and valuation; the construction of knowledge through practice and research. From the results obtained, it was possible to perceive a new aspect of mathematics in action, which was named by the researcher as classification. The characterization of this aspect corresponds to the possibility of establishing facts, similarities, or differences, in addition organizing or ordering elements and knowledge, regarding approaches linked to mathematics or its applications in real life. Its elaboration broadens considerations related to the field of critical mathematics education and mathematics education itself, regarding to reflections on the different applications of mathematics in different situations, whether in the university context or in society in general.
This study proposes to raise discussions concerning the field of mathematics education in universities. Its objective is to understand how aspects of mathematics in action can emerge from the perspectives of Problem-Based Learning (PBL) in Higher Education. The objective was outlined from the following guiding question: How can aspects of mathematics in action emerge in Higher Education, from the perspectives of Problem-Based Learning? The theoretical framework of this research was based on the concept of mathematics in action, inspired by Ole Skovsmose and conceptions about learning principles associated with Problem-Based Learning. The research was developed through a qualitative approach, based on a case study and through participant-observation. The data production was carried out in two universities located in São Paulo State. All process were done from of presentation of a real problem related to environmental impacts caused by chemical pollutants. In the institution A, the process involved a study group and semi structured interviews with four Civil Engineering undergraduate students. In the institution B, the participation involved thirty Ecology students in the second year; the discussions occurred in some classes of Calculus II. In the last class, the groups presented some research that they had developed. In the institution A, the discussions were conducted by the researcher herself. In institution B, in addition to the researcher, other two teachers that was responsible for the Calculus classes, contributed to the development of this stage. In both cases, the three participants took on the role of learning facilitators. The data were recorded, and some notes were done in the field diary. The data analysis consisted of elaboration of four central themes inspired by five aspects of mathematics in action and the potential to explore the principles of PBL in higher education mathematics classes. These processes were carried out according to the defined research question, considering the proposed objective. Many elements emerged, among them: the application of formulas and mathematical concepts in different situations; discussions about legitimizations and justifications through mathematics; reflections on responsibility, ethics, and valuation; the construction of knowledge through practice and research. From the results obtained, it was possible to perceive a new aspect of mathematics in action, which was named by the researcher as classification. The characterization of this aspect corresponds to the possibility of establishing facts, similarities, or differences, in addition organizing or ordering elements and knowledge, regarding approaches linked to mathematics or its applications in real life. Its elaboration broadens considerations related to the field of critical mathematics education and mathematics education itself, regarding to reflections on the different applications of mathematics in different situations, whether in the university context or in society in general.
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Cálculo diferencial e integral, Engenharia civil, Ecologia, Educação Matemática, Educação Matemática Crítica, Calculus, Civil Engineering, Ecology, Mathematics Education, Critical Mathematics Education