Abstract

VILLALBA GARCES, J.; FRISANCHO HIDALGO, Susana  and  LAM PIMENTEL, Luis. The development of the notion of “half” in children from two Ucayali’s Shipibo-Konibo communities. Interdisciplinaria [online]. 2022, vol.39, n.2, pp.265-280.  Epub Feb 23, 2022. ISSN 1668-7027.  http://dx.doi.org/10.16888/interd.2022.39.2.17.

This research aims to identify and describe developmental levels of the notion of “half” in a group of children from two Shipibo-Konibo native communities of the Ucayali region, in the Peruvian Amazon rainforest. Fourteen students aged between 7 and 16 participated, six from Bethel community and eight from Bena Jema community. The community of Bethel is located approximately 6 hours by river from the city of Pucallpa, while Bena Jema is located within Pucallpa’s boundaries, in the Yarinacocha district. All participants were assessed using Jean Piaget’s clinical-critical method, with two tasks. In the first task, focusing on discrete quantities: different sets of cards with the picture of a fish were presented sequentially, some with an even number of units and some with an odd number. Participants were asked to choose and present back half of each set. In the second task, focusing on continuous quantities: participants were asked to choose and present half of a single raw spaghetti, which they needed to break with their hands. If the resulting pieces were unequal, they were asked to break them again and redistribute the results. Students from Bena Jema community were assessed with both tasks, while students from Bethel community were assessed only with the discrete quantities task. The results showed four developmental levels in the discrete quantities task. In the first level, participants took any one of two parts of the set to be “half”, without checking if they were equal or whether putting them back together reconstituted the original whole. In the second level, participants took any one of two equal parts to be "half", but were inconsistent and accepted the possibility of the parts being unequal. In the third level, participants only took any one of two equal parts to be “half” but had difficulties splitting odd-numbered sets, including sets with fewer elements than the even-numbered ones they had previously split correctly. In the fourth level, the task was solved successfully with both even-numbered and odd-numbered sets. For the continuous quantities task, three levels were found. In the first level, any one of two raw spaghetti pieces was taken to be “half”, without checking their evenness. In the second level, participants took any two equal pieces of the raw spaghetti to be “half”, but without checking whether putting them back together reconstituted the original whole, with no extra parts remaining. In the third level, participants took any one of two equal pieces to be “half”, checking whether putting them back together reconstituted the original whole. These results are consistent with reports from previous research assessing the notion of “half” in Western contexts. Results support universality in the development of the notion of “half”, but show a delay in the participants’ level of acquisition, taking Peru’s national curriculum as reference. This study is a contribution to the understanding of the development of the notion of “half” in indigenous children living in Amazonian native communities, and shows the relevance of the Piagetian clinical-critical interview in these sociocultural contexts. The implications of these findings are discussed in relation to the universality of logical-mathematical knowledge, as well as the need to rethink the timing and manner in which the notion of “half” appears in the curriculum.

Keywords : half; constructivism; clinical-critical method; mathematics; Shipibo-Konibo.

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