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This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval’s Cognitive Model. The sample of the study was comprised of 51 newly-enrolled 9thgrade students between the ages of 14 and 15, who had not received any prior geometry instruc...
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... This coordination encompasses the integration of various cognitive processes, including perceptual apprehension, characterized by the straightforward identification of a configuration, which is the first to appear in cognitive development and the most intuitive. The effective coordination of these apprehensions in problem-solving situations is crucial for geometric reasoning, particularly in the context of justification processes in geometric proof problems (Karpuz & Güven, 2022;Llinares & Clemente, 2014). ...
Geometric reasoning is an indispensable skill within the domain of civil engineering, where professionals are required to comprehend and manipulate geometric figures for the creation of stable and functional structures. This paper evaluates the geometric reasoning abilities of four groups of civil engineering students who engaged with a complex geometric problem: constructing a parallelogram using three distinct triangular shapes. To decode the students’ reasoning processes, we employed theoretical frameworks from the didactics of mathematics, focusing particularly on geometric reasoning, discursive organization, and the integrated processes of discursive apprehension and operational engagement in solving and rationalizing problems tied to the geometry of triangles. The findings of this study reveal that introducing challenging problems in educational settings facilitates the enhancement of geometric reasoning. Furthermore, it fosters the assimilation and application of concepts and properties across diverse contexts, thereby encouraging advanced levels of mathematical thought. Additionally, the strategic use of guiding questions significantly improves argumentative skills and the accurate employment of mathematical terminology.
Esta pesquisa teve como objetivo investigar possibilidades de apreensões figurais mobilizadas durante a resolução de problemas geométricos por alunos do 8.º ano do Ensino Fundamental. Utilizaram-se os estudos de Duval (1994, 1995, 2006, 2012, 2018) sobre apreensões para conduzir esta investigação – de caráter qualitativo e com características intervencionistas –, envolvendo 23 estudantes de uma escola particular em São Paulo. A coleta de dados incluiu protocolos de tarefas respondidas pelos participantes, observações e registros escritos e gravados em vídeo e áudio. Os resultados destacaram que a manipulação direta com figuras potencializa o desenvolvimento das apreensões figurais, em especial para compreender conceitos geométricos; incentiva a exploração de estratégias; estimula a visualização espacial e o raciocínio dedutivo; proporcionando aos alunos uma aprendizagem mais significativa A sistematização dessas estratégias e o uso de materiais manipulativos desempenharam um papel relevante no desenvolvimento das habilidades matemáticas dos alunos, preparando-os para enfrentar situações-problema com confiança e criatividade. Salienta-se, assim, a relevância das apreensões e manipulações figurativas como elementos potencialmente ricos no ensino de Geometria. Palavras-chave: Ensino e aprendizagem de Matemática. Ensino Fundamental. Apreensão Figural. Resolução de Problemas. Materiais Manipuláveis.
p style="text-align: justify;">Misconceptions are one of the biggest obstacles in learning mathematics. This study aimed to investigate students’ common errors and misunderstandings they cause when defining the angle and the triangle. In addition, we investigated the metacognition/ drawing/ writing/ intervention (MDWI) strategy to change students’ understanding of the wrong concepts to the correct ones. A research design was used to achieve this goal. It identified and solved the errors in the definition of angle and triangle among first-year students in the Department of Mathematics Education at an excellent private college in Mataram, Indonesia. The steps were as follows: A test instrument with open-ended questions and in-depth interviews were used to identify the errors, causes, and reasons for the students’ misconceptions. Then, the MDWI approach was used to identify a way to correct these errors. It was found that students generally failed in interpreting the concept images, reasoning, and knowledge connection needed to define angles and triangles. The MDWI approach eliminated the misconceptions in generalization, errors in concept images, and incompetence in linking geometry features.</p
