Exploration of historical multiplication algorithms: a dialogue between Paulo Freire and decolonial ideas

Abstract

We report here an experience in which 5th grade students, from a municipal public school in Vitória-ES, became involved in learning multiplication, exploring alternative algorithms that were later developed with their parents, in a workshop held at the school. As students already had mastery of multiplication by the usual algorithm, we broadened their understanding by challenging them to discover “other ways” of doing it, learning the Arabic (or gelosia), Russian and Chinese algorithms. In line of thought with Freire (1996; 1987), we seek a teaching of mathematics in which the teacher leaves his position as the holder of knowledge and establishes a circle of knowledge with the student in which everyone teaches and learns – teachers, parents and students. Corroborating this thought, decolonial ideas merge with those presented by Freire (1987), when students rediscovered historical procedures of different cultures, reinvented solutions for multiplication with zero in the order of tens and better understood the groupings in base ten. The multiplication learning was made possible with playfulness, while the student constructed the conception of mathematics as a human creation, in different spaces and times, and not as a ready and finished knowledge that they would have to appropriate (Freire, 1987). The experience showed that the whole class came to the domain of operation, sharing new learning with their families, in a dialogical relationship that motivated research about historical algorithms and their origins in the classroom. With motivation and joy, students perceived mathematics as a learning and enjoyable discipline, knowledge that frees and does not oppress.