Análises de aulas de cálculo diferencial e integral na perspectiva dos jogos de linguagem
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Data
2022-03-04
Autores
Silva, José Roberto Damasceno da
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Universidade Estadual Paulista (Unesp)
Resumo
Considera-se que posicionamentos dogmáticos derivados das divergências epistemológicas clássicas acerca dos fundamentos da Matemática e do conhecimento matemático mostram-se insuficientes para a superação dos obstáculos reiteradamente constatados nos processos de ensino e de aprendizagem de conceitos matemáticos. Expressiva parcela da literatura sustenta consenso em advogar a consistência com a qual a perspectiva normativa da linguagem matemática, a saber, a constituição de sentido a partir da especificação de uma gramática de regras de uso, assume relevância na imprescindível tarefa de esclarecimento dos conceitos matemáticos, com implicações para as práticas pedagógicas. Assim, a expressão jogo de linguagem de Ludwig Wittgenstein, enquanto práticas linguísticas submetidas a uma gramática de usos que, por sua vez, é contextualizada em formas de vida, constitui-se reconhecidamente como recurso relevante para a interpretação de interações dialógicas em processos de ensino e de aprendizagem. Contudo, caberia indagar: A literatura que, convincentemente, atesta as convergências e os consensos acerca da relevância dos jogos de linguagem é igualmente provedora de recursos instrucionais para viabilizar as necessárias demonstrações de tal relevância? Deste modo, o presente estudo sustenta o objetivo de investigar e de demonstrar em que extensão a resolução de exercícios, a saber, modos de agir de universitários, sustentariam correspondências com as aprendizagens preconizadas relacionadas com conteúdos curriculares de cálculo diferencial e integral a partir da exposição dos alunos a uma sequência de aulas nas modalidades remota e presencial caracterizadas por variações nas descrições de regras de uso que definem um jogo de linguagem (procedimentos) de professores em atividades de ensino. Participaram 36 graduandos regularmente matriculados no curso de Engenharia Elétrica de uma universidade pública federal. Todos os alunos foram expostos consecutivamente a seis videoaulas nas quais foram apresentadas as definições e regras fundamentais para o cálculo de limites e de derivadas, sendo as videoaulas selecionadas utilizadas nos cursos de engenharia de uma universidade pública estadual com funcionamento exclusivo na modalidade EAD. Após cada videoaula, foram aplicados exercícios sobre o conteúdo apresentado na respectiva videoaula. O objetivo foi o de coletar informações sobre o entendimento dos conceitos trabalhados a partir do jogo de linguagem utilizado pelo professor durante a explanação de cada conceito nas videoaulas. Imediatamente após cada videoaula e a resolução dos exercícios referentes aos conceitos estudados, os discentes foram expostos a uma aula presencial (aula de intervenção) sobre os mesmos conceitos matemáticos visto na respectiva videoaula seguindo o plano de ensino da disciplina Cálculo I do curso. Desta feita, utilizando novos elementos do jogo de linguagem do professor/pesquisador. A exemplo do procedimento adotado com as videoaulas, após cada aula presencial, a turma foi exposta aos mesmos exercícios previamente aplicados na respectiva videoaula. Nos exercícios analisados, consistentemente os discentes atestaram, em magnitudes variadas, maiores índices de acerto nos exercícios efetuados após as aulas de intervenção. Admite-se demonstrado que a inserção de novos elementos descritivos de regras normativas de uso, no âmbito do jogo de linguagem demarcado nas duas modalidades de aulas, constituiu-se em condição crítica para a emissão, pelos alunos, de ações consistentes com as aprendizagens curriculares preconizadas.
It is considered that dogmatic positions derived from classic epistemological divergences about the foundations of Mathematics and mathematical knowledge are insufficient to overcome the obstacles repeatedly found in the teaching and learning processes of mathematical concepts. An expressive part of the literature supports a consensus in advocating the consistency with which the normative perspective of mathematical language, namely, the constitution of meaning from the specification of a grammar of rules of use, assumes relevance in the essential task of clarifying mathematical concepts, with implications for pedagogical practices. Thus, the expression “language game” by Ludwig Wittgenstein, as linguistic practices submitted to a grammar of uses that, in turn, is contextualized in forms of life, is recognized as a relevant resource for the interpretation of dialogic interactions in processes. of teaching and learning. However, it should be asked: Does the literature that convincingly attest to the convergences and consensus on the relevance of language games also provide instructional resources to enable the necessary demonstrations of such relevance? In this way, the present study supports the objective of investigating and demonstrating to what extent the resolution of exercises, namely, university students' ways of acting, would support correspondences with the recommended learning related to curricular contents of differential and integral calculus from the exposure students to a sequence of classes in remote and face-to-face modalities characterized by variations in the descriptions of rules of use that define a language game (procedures) of teachers in teaching activities. Thirty-six undergraduates regularly enrolled in the Electrical Engineering course at a federal public university participated. All students were consecutively exposed to six video classes in which the definitions and fundamental rules for the calculation of limits and derivatives were presented, with the selected video classes used in engineering courses at a state public university operating exclusively in the EAD modality. After each video class, exercises were applied on the content presented in the respective video class. The objective was to collect information about the understanding of the concepts worked from the language game used by the teacher during the explanation of each concept in the video classes. Immediately after each video class and the resolution of the exercises referring to the concepts studied, the students were exposed to a face-to-face class (intervention class) on the same mathematical concepts seen in the respective video class, following the teaching plan of the course's Calculus I discipline. This time, using new elements of the teacher/researcher language game. As with the procedure adopted with the video classes, after each face-to-face class, the class was exposed to the same exercises previously applied in the respective video class. In the analyzed exercises, the students consistently attested, in varying magnitudes, higher hit rates in the exercises performed after the intervention classes. It is admitted that the insertion of new descriptive elements of normative rules of use, in the scope of the language game demarcated in the two modalities of classes, constituted a critical condition for the issuance, by the students, of actions consistent with the curricular learning advocated.
It is considered that dogmatic positions derived from classic epistemological divergences about the foundations of Mathematics and mathematical knowledge are insufficient to overcome the obstacles repeatedly found in the teaching and learning processes of mathematical concepts. An expressive part of the literature supports a consensus in advocating the consistency with which the normative perspective of mathematical language, namely, the constitution of meaning from the specification of a grammar of rules of use, assumes relevance in the essential task of clarifying mathematical concepts, with implications for pedagogical practices. Thus, the expression “language game” by Ludwig Wittgenstein, as linguistic practices submitted to a grammar of uses that, in turn, is contextualized in forms of life, is recognized as a relevant resource for the interpretation of dialogic interactions in processes. of teaching and learning. However, it should be asked: Does the literature that convincingly attest to the convergences and consensus on the relevance of language games also provide instructional resources to enable the necessary demonstrations of such relevance? In this way, the present study supports the objective of investigating and demonstrating to what extent the resolution of exercises, namely, university students' ways of acting, would support correspondences with the recommended learning related to curricular contents of differential and integral calculus from the exposure students to a sequence of classes in remote and face-to-face modalities characterized by variations in the descriptions of rules of use that define a language game (procedures) of teachers in teaching activities. Thirty-six undergraduates regularly enrolled in the Electrical Engineering course at a federal public university participated. All students were consecutively exposed to six video classes in which the definitions and fundamental rules for the calculation of limits and derivatives were presented, with the selected video classes used in engineering courses at a state public university operating exclusively in the EAD modality. After each video class, exercises were applied on the content presented in the respective video class. The objective was to collect information about the understanding of the concepts worked from the language game used by the teacher during the explanation of each concept in the video classes. Immediately after each video class and the resolution of the exercises referring to the concepts studied, the students were exposed to a face-to-face class (intervention class) on the same mathematical concepts seen in the respective video class, following the teaching plan of the course's Calculus I discipline. This time, using new elements of the teacher/researcher language game. As with the procedure adopted with the video classes, after each face-to-face class, the class was exposed to the same exercises previously applied in the respective video class. In the analyzed exercises, the students consistently attested, in varying magnitudes, higher hit rates in the exercises performed after the intervention classes. It is admitted that the insertion of new descriptive elements of normative rules of use, in the scope of the language game demarcated in the two modalities of classes, constituted a critical condition for the issuance, by the students, of actions consistent with the curricular learning advocated.
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Palavras-chave
Jogos de linguagem, Linguística, Ensino superior, Ensino à distância, Ensino presencial, Matemática, Cálculo diferencial, Cálculo integral, Language games, Higher education, Distance learning, Classroom teaching, Differential and integral calculus