Conhecimento matemático para ensinar Álgebra nos Anos Iniciais do Ensino Fundamental

Abstract

ResumoVárias são as pesquisas, sobretudo realizadas no exterior, que evidenciam a importância do trabalho com o Pensamento Algébrico nos Anos Iniciais do Ensino Fundamental, porém elas vêm focando essencialmente o aluno e o que ele aprende, deixando o professor à margem dessa discussão. Em razão da importância, para a aprendizagem dos alunos, do conhecimento matemático para ensinar e também da potencialidade do trabalho com o Pensamento Algébrico nos Anos Iniciais, este artigo tem por objetivo debater o conhecimento matemático revelado por um grupo de professores dos Anos Iniciais, ao discutir tarefas com potencial algébrico. Os dados foram coletados no contexto de um curso de extensão de 32 horas, e os resultados evidenciam a ainda pouca familiaridade dos participantes com as questões centrais que envolvem a caracterização e o trabalho com o Pensamento Algébrico. Palavras-chave:Álgebra nos Anos Iniciais, Pensamento Algébrico, Conhecimento matemático dos professores. AbstractSeveral researches bring to front the important of Algebraic Thinking at early years (mainly at international level). But such researches focus mainly on students and their learning, leaving aside the teachers and their knowledge. Considering, in an intertwined manner, the importance and role of teachers' knowledge in students learning and the potentialities of Algebraic Thinking at early grades, this paper aims at identify and discuss the mathematical knowledge for teaching revealed by a group of teachers when discussing tasks aimed at enhancing the Algebraic Thinking. Data has been gathered in a professional development course and the results reveal some problematic issues concerning the core aspects related with Algebraic Thinking.

Teachers’ Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective

“…Ferreira, Ribeiro, and Ribeiro [65] deal with generalized arithmetic through numerical relationships, the properties of numbers and operations, and the meaning of the equal sign as an equivalence relationship.…”

“…Ferreira, Ribeiro, and Ribeiro [65] consider how teachers understand and identify a mathematical situation that contains an error, especially the source and the reasons that lead to the occurrence of this error [72]. Finally, Zapatera and Callejo [66] focus on identifying significant mathematical elements that are evident in the performance of an algebraic task.…”

“…By contrast, studies that delve into the subdomain of knowledge of content and students (KCS), such as the study by Wilkie [59], focus on how teachers understand the possible errors that students can make when performing an algebraic task. The studies carried out by Wilkie [63], Ferreira, Riberiro, and Ribeiro [65], Souza, Ribeiro, and Pazuch [70], and Souza, Pazuch, and Ribeiro [72] analyze situations that allows teachers to anticipate what the students think and the difficulties they may experience in an algebraic task.…”

“…Other studies reveal the limitations in the knowledge of the content, such as the recognition of the different mathematical meanings of the equal sign (e.g., [60]); solving algebraic tasks mainly by trial and error, not paying attention to the structure of the problem and the knowledge involved in developing algebraic thinking (e.g., [64]); difficulties solving problems involving the generalization of patterns related to the discrimination of strategies in the use of proportionality, explanation of a growth pattern and obtaining a general rule (e.g., [66,68]); ignorance of the central issues that the characterization of and working with algebraic thinking imply, such as solving mathematical problems that require the representation of unknown quantities (e.g., [56]) and the case of the generalization of arithmetic with the properties of numbers, the operations and the meaning of the equal sign as equivalence (e.g., [65]); and a lack of strategies for generalizing functional relationships, and problems understanding and connecting the different representations of functions (e.g., [71]).…”

Entendendo e discutindo as possibilidades do ensino de álgebra nos anos iniciais do Ensino Fundamental

“…Vale destacar que a álgebra, por muito tempo, foi vista como uma área da matemática destinada a estudar as operações entre os números e a resolução de equações BRANCO;MATOS, 2009;MILIES, 2013), associada exclusivamente à manipulação de regras e articulações de uma determinada linguagem. Esse modo de ver a álgebra fez com que, em sala de aula, ela fosse tratada com base em conteúdos específicos e do desenvolvimento de determinadas habilidades e, em decorrência de um currículo hierarquizado, a possibilidade de seu trabalho nos anos iniciais foi afastada (PRESTES et al, 2014;MOREIRA, 2016, FERREIRA;RIBEIRO;RIBEIRO, 2017).…”