Humanizing mathematics education: quantitative and arithmetic argumentation of indigenous cultural practices

Dehumanized and globalized mathematics education in the last centuries has led to established learning processes disconnected from indigenous knowledge. The effect of cognitive imperialism, given the systematic negation of the language and the culture, has as a disastrous consequence of the gradual and systematic loss of knowledge and indigenous reasoning. Thus, recognizing, appreciating and updating it turns into a task and challenge for the teaching and learning of math in the intercultural classroom. Therefore, the purpose of this research is to focus on analyzing the mathematical reasoning of the indigenous student while encoding and decoding an historic numeric registry artifact called puron (knot in the Mapuche language). The study was conducted in three schools on Mapuche territory of Araucania Region in Chile, using the Participatory Action Research method. The results show that encoding/decoding quantities helps indigenous students to recognize structures and to establish a numeration system close to the historically reported cultural practices of the Mapuche people. Moreover, it extends the mathematical quantitative structure and reasoning to an arithmetic one seen in the present day cultural practices such as the measurement of fields for planting. Thus, the experience contributes to the students' linguistic awareness of Mapudungun (Mapuche language) in a numeration system framework.