Trayectorias hipotéticas de aprendizaje del número y la amplitud articuladas con las prácticas de agrimensura y las prácticas ancestrales de los indígenas Wayúu

Abstract

This research search to promote the learning of mathematics in rural educational institutions of the Guajira, and aims to characterize articulations between the practices of surveying and ancient practices of the indigenous Wayúu, from the design and evolution of the Hypothetical Learning Trajectories (HLT) of the number and amplitude. The hypotheses are based on the following categories: place-based education, place-based mathematics education, the Hypothetical Learning Trajectories of Clements and Sarama (2015), the natural number, the angular amplitude magnitude, surveying and the ancient practice of building sheepfolds. This research is based on an approach to teaching experiments, since the HLT of the number and angular amplitude magnitude was designed, articulating surveying practices with ancient practices; focusing on the construction of sheepfolds. Which were validated with sixth grade students, from the indigenous educational institution # 5, Pipamana headquarters, to be able to identify the real learning trajectories of each one. Likewise, this research was developed taking into account five phases, where the activities were established, the techniques and instruments for the formulation of relationships between the practices of Surveying and the ancient Wayúu practices. In the initial phase, empirical sources are highlighted, such as: that of cultural knowers, authorities, elders and members of some communities. The design of the HLT articulates 10 processes: 1) Subitization, 2) counting, 3) comparison, order and estimation, 4) addition and subtraction operations, (5) multiplication and division operations, (6) perception and identification of angular amplitude magnitude, 7) decision-making process, 8) construction of sheepfolds, 9) measurement of land and 10) drawing of plans. In relation to the results of this research, we emphasize the hypotheses for the Hypothetical Learning Trajectory, that links not only the aforementioned processes, but also sub-processes and indicators. The analysis was carried out previously and in retrospect of the activities of each level, in total there are 10 levels and the synthesis of the real trajectories of each of the students.