Abstract
Various approaches to the teaching and learning of algebra within Mathematics Education come from classical studies in the History of Mathematics. For this reason, a review of contemporary sources in this second discipline was carried out to determine new elements that could contribute to the strengthening of these approaches. We report in this paper at least six considerations that can be problematized from the perspective of Mathematics Education, which generate new routes of investigation and that with them could contribute significantly to a more robust and profound understanding of algebraic activity in general, and positively impact on mathematical education.