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In this qualitative research, we present our concern with the formation of algebraic thinking and the concept of first degree equations from the perspective of teaching guiding activity (MOURA, 1992; 2000; 2001). The study was conducted with 27 students in the 7th grade of elementary school from a public school of the city of Uberlândia/MG (Brazil), aged between 12 and 15 years old. The guiding principles of these activities regard the concept of algebra links: fluency, variation field and variable (SOUSA, 2004), which can be grasped in the light of Historical-Cultural Theory (VIGOTSKI, 1989; 1991; LEONTIEV, 1978; 1983) and the principles of Davidov (1982, 1987) about the construction of theoretical knowledge. We conducted a historical study of the emergence of algebra (BAUMGART, 1992; EVES, 2002, among others) because we believe that the conceptual connections are present along the historical construction of the concept, a brief analysis of textbooks present in the school where the research took place and a survey of previous studies in order to verify if these links are highlighted. Given this, we established the following research question: What pedagogical implications for the process o f formation o f algebraic thinking and the concept o f first degree equation for elementary school students the teaching activity, developed in the perspective o f the Teaching Guiding Activity, can provide? Seeking to answer this question, we aimed at analyzing possible pedagogical implications for the formation of algebraic thinking and learning the concept of first degree equation for students in the 7th grade of elementary school through the teaching activity. For analytical purposes, we categorized the data in episodes and scenes (MOURA, 2004) discussing the movements made possible by triggering learning situations, as well as the actions and thoughts of students towards the proposed situations. Through the performed analyses, it seems that there was the formation of algebraic thinking by students and they have appropriated the concept of first degree equation, as we also noted evidence that the algebraic conceptual links are extremely relevant to learning algebra, in a movement in which the students comprehended the reasons for their actions upon the needs that motivated them, allowing students to allocate new quality to the process of apprehension of the algebraic concepts, in which knowing how to think prevailed instead of knowing how to do, enabling us to perceive evidence of a development of the theoretical knowledge, in an environment of respect to the ideas presented by the other and collective construction of algebraic meaning. We hope this work will contribute to the field of Mathematics Education, especially with the teaching of equation through triggering learning situations that encourage the formation of theoretical knowledge.

A álgebra na perspectiva histórico-cultural: uma proposta de ensino para o trabalho com equações de 1° grau