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Diferenciação pedagógica na resolução de problemas
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O presente Relatório Final resulta da Prática de Ensino Supervisionada II e integra um estudo centrado na influência das estratégias de diferenciação pedagógica no desempenho de alunos do 3.º ano na resolução de problemas matemáticos, com especial enfoque nas representações mobilizadas. A fundamentação teórica articula os princípios da escola inclusiva com os contributos de autores como Bruner (1999), Lesh, Post & Behr (1987) e Goldin (2003), destacando que a diferenciação pedagógica constitui um meio fundamental para responder à diversidade dos alunos e promover a equidade. São discutidos os diferentes tipos de representações matemáticas (ativas, icónicas e simbólicas), bem como o estabelecimento de conexões entre representações concretas e abstratas. O estudo assume uma metodologia qualitativa, de natureza descritiva e interpretativa, enquadrada no paradigma interpretativo, procurando perceber de que modo as estratégias de diferenciação pedagógica influenciam o desempenho dos alunos do 3.º ano na resolução de problemas matemáticos, com atenção particular às representações utilizadas. Participaram 17 alunos de uma turma do 3.º ano, tendo sido implementadas três tarefas de resolução de problemas com diferentes estruturas e graus de complexidade. A recolha de dados incluiu produções escritas, registos de observação, notas reflexivas e perceções dos alunos, analisados através de um processo de categorização segundo a tipologia de representações de Bruner. Os resultados evidenciam que, no primeiro problema, os alunos recorreram maioritariamente a representações simbólicas, revelando uma tendência inicial para a utilização mecânica do algoritmo. Nos problemas subsequentes, verificou-se uma progressiva diversificação das representações, com maior recurso a esquemas, diagramas e manipulação de materiais concretos, especialmente quando foram disponibilizadas pistas visuais, questionamento orientado e materiais manipuláveis. A diferenciação pedagógica mostrou-se determinante para apoiar os alunos com maiores dificuldades, permitindo-lhes realizar transições estruturadas entre representações ativas, icónicas e simbólicas. As perceções dos alunos reforçam o impacto positivo destas estratégias, uma vez que referiram sentir maior clareza e segurança quando podiam visualizar ou manipular elementos dos problemas.
This Final Report presents a study developed within the context of the Supervised Teaching Practice II, focusing on the influence of differentiated instructional strategies on the performance of 3rd grade students in mathematical problem solving, with particular attention to the representations they mobilise. The theoretical framework brings together the principles of inclusive education and the contributions of authors such as Bruner (1999), Lesh, Post and Behr (1987), and Goldin (2003), highlighting differentiated instruction as an essential means of responding to learner diversity and promoting equity. Different types of mathematical representations (enactive, iconic, and symbolic) are discussed, as well as the establishment of connections between concrete and abstract representations. The research followed a qualitative, descriptive and interpretative design, aligned with an interpretivist paradigm, aiming to understand how students construct and express mathematical reasoning in differentiated contexts. Seventeen 3rd-grade students participated in the study, during which three problem-solving tasks of varying structure and complexity were implemented. Data were collected through written productions, observation records, reflective notes and students’ perceptions, and analysed through an iterative categorisation process based on Bruner’s representational typology. Findings show that in the first task students predominantly used symbolic representations, often relying on the mechanical use of algorithms. As subsequent tasks were introduced, a gradual diversification of representations emerged, with increased use of diagrams, drawings and concrete materials, particularly when visual cues, guided questioning and manipulatives were provided. Differentiated instruction proved essential in supporting students with greater difficulties, enabling structured transitions between enactive, iconic and symbolic representations. Students’ perceptions further highlighted the positive impact of these strategies, noting greater clarity and confidence when able to visualise or manipulate elements of the problem.
This Final Report presents a study developed within the context of the Supervised Teaching Practice II, focusing on the influence of differentiated instructional strategies on the performance of 3rd grade students in mathematical problem solving, with particular attention to the representations they mobilise. The theoretical framework brings together the principles of inclusive education and the contributions of authors such as Bruner (1999), Lesh, Post and Behr (1987), and Goldin (2003), highlighting differentiated instruction as an essential means of responding to learner diversity and promoting equity. Different types of mathematical representations (enactive, iconic, and symbolic) are discussed, as well as the establishment of connections between concrete and abstract representations. The research followed a qualitative, descriptive and interpretative design, aligned with an interpretivist paradigm, aiming to understand how students construct and express mathematical reasoning in differentiated contexts. Seventeen 3rd-grade students participated in the study, during which three problem-solving tasks of varying structure and complexity were implemented. Data were collected through written productions, observation records, reflective notes and students’ perceptions, and analysed through an iterative categorisation process based on Bruner’s representational typology. Findings show that in the first task students predominantly used symbolic representations, often relying on the mechanical use of algorithms. As subsequent tasks were introduced, a gradual diversification of representations emerged, with increased use of diagrams, drawings and concrete materials, particularly when visual cues, guided questioning and manipulatives were provided. Differentiated instruction proved essential in supporting students with greater difficulties, enabling structured transitions between enactive, iconic and symbolic representations. Students’ perceptions further highlighted the positive impact of these strategies, noting greater clarity and confidence when able to visualise or manipulate elements of the problem.
Descrição
Relatório de Prática de Ensino Supervisionada apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º Ciclo do Ensino Básico e de Matemática e Ciências Naturais no 2.º Ciclo do Ensino Básico
Palavras-chave
Diferenciação pedagógica Resolução de problemas Representações matemáticas Differentiated instruction Problem solving Mathematical representations
Contexto Educativo
Citação
Reis, A. B. S. (2025). Diferenciação pedagógica na resolução de problemas [Dissertação de mestrado, Escola Superior de Educação de Lisboa, Instituto Politécnico de Lisboa]. Repositório Institucional do Politécnico de Lisboa http://hdl.handle.net/10400.21/22913