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Authors
Abstract(s)
Esta tese tem como objetivo caraterizar a aprendizagem do Cálculo I à luz das
teorias APOS e da Reificação de Ed Dubinsky e Anna Sfard, respetivamente. Para
contextualizar o quadro teórico, faz-se uma abordagem de teorias de Investigação em
Educação Matemática e de teorias da aprendizagem antes de se abordar mais concretamente
as duas teorias à luz das quais este estudo é feito. A teoria APOS e a da Reificação são duas
teorias cognitivistas consequentes do Construtivismo Cognitivista de Jean Piaget. Ambas
permitiram-nos perceber melhor como os alunos constroem o seu conhecimento, bem como
fenómenos e situações que interferem na sua construção. Com base num paradigma
interpretativo, numa metodologia qualitativa, na modalidade de estudo de caso, foram
aplicados aos alunos questionários seguidos de entrevistas. Quanto aos alunos, para além
dos questionários, foram recolhidos dados das provas parcelares realizadas. Os dados
recolhidos foram analisados à luz de teorias e estudos antecedentes. O estudo, realizado
numa instituição de ensino superior de Angola, incidiu inicialmente sobre 10 alunos e,
posteriormente, em função de conveniência do próprio estudo, restringiu-se a três alunos.
De uma maneira geral os alunos têm maior compreensão operacional do que concetual,
manifestada predominantemente no desempenho algébrico. A associação entre processos
anteriores e a compreensão dos alunos nem sempre é de sucesso-sucesso ou de insucessoinsucesso.
A aprendizagem dos alunos é heterogénea resultando de fatores como o seu nível
de preparação, seu empenho e tipo de abordagem do Cálculo. Intrínsicas ao contexto, a
investigação teve como limitações a predominante representação algébrica — em
detrimento de maior equilíbrio com as representações gráfica, numérica e descritiva — dos
conceitos do Cálculo I na sala de aula, bem como a necessidade de maior abrangência do
trabalho colaborativo para tornar a construção do conhecimento mais social. Intrínsica à
própria investigação, temos como limitação a necessidade de se prolongar o estudo no
tempo.
This thesis aims to characterize the learning of Calculus I in light of the APOS and Reification theories by Ed Dubinsky and Anna Sfard, respectively. In order to contextualize the theoretical framework, an approach is made to theories of Research in Mathematical Education and learning theories before more concretely addressing the two theories in the light of which this study is made. The APOS theory and that of Reification are two cognitive theories consequent upon Jean Piaget's Cognitive Constructivism. Both allowed us to perceive better how the students construct their knowledge, as well as phenomena and situations that interfere in its construction. Based on an interpretative paradigm, in a qualitative methodology, in the case study modality, questionnaires followed by interviews were applied to the students. As for the students, in addition to the questionnaires, data were collected from the partial tests carried out. The collected data were analyzed in light of previous theories and studies. The study, carried out in a higher education institution in Angola, focused initially on 10 students and, later on, according to the convenience of the study itself, was restricted to three students. In general students have greater operational understanding than conceptual, manifested predominantly in algebraic performance. The association between prior processes and student understanding is not always success-success or failure-failure. Students' learning is heterogeneous resulting from factors such as their level of preparation, their commitment and type of approach to Calculus. Intrinsic to the context, the research had as limitations the predominant algebraic representation - to the detriment of a better balance with the graphical, numerical and descriptive representations - of the concepts of Calculus I in the classroom, as well as the need for greater comprehension of the collaborative work to make more social the construction of knowledge. Intrinsic to the investigation itself, we have as limitation the need to prolong the study in time.
This thesis aims to characterize the learning of Calculus I in light of the APOS and Reification theories by Ed Dubinsky and Anna Sfard, respectively. In order to contextualize the theoretical framework, an approach is made to theories of Research in Mathematical Education and learning theories before more concretely addressing the two theories in the light of which this study is made. The APOS theory and that of Reification are two cognitive theories consequent upon Jean Piaget's Cognitive Constructivism. Both allowed us to perceive better how the students construct their knowledge, as well as phenomena and situations that interfere in its construction. Based on an interpretative paradigm, in a qualitative methodology, in the case study modality, questionnaires followed by interviews were applied to the students. As for the students, in addition to the questionnaires, data were collected from the partial tests carried out. The collected data were analyzed in light of previous theories and studies. The study, carried out in a higher education institution in Angola, focused initially on 10 students and, later on, according to the convenience of the study itself, was restricted to three students. In general students have greater operational understanding than conceptual, manifested predominantly in algebraic performance. The association between prior processes and student understanding is not always success-success or failure-failure. Students' learning is heterogeneous resulting from factors such as their level of preparation, their commitment and type of approach to Calculus. Intrinsic to the context, the research had as limitations the predominant algebraic representation - to the detriment of a better balance with the graphical, numerical and descriptive representations - of the concepts of Calculus I in the classroom, as well as the need for greater comprehension of the collaborative work to make more social the construction of knowledge. Intrinsic to the investigation itself, we have as limitation the need to prolong the study in time.
Description
Keywords
Ensino da Matemática - Estudantes - Ensino Superior Ensino da Matemática - Cálculo - Estratégias de Ensino-aprendizagem Ensino da Matemática - Análise da Matemática - Estratégias de Ensino-aprendizagem