Elementary-school children from a Shipibo-Konibo indigenous community in the Ucayali region, in the Amazonian rainforest of Perú, were evaluated regarding their abilities to solve addition and subtraction problems. These operations were assessed by two means: through Jean Piaget's clinical-critical method (using culturally contextualized problems and concrete materials such as pictures of Amazonian fish, pictures of arrows, or beads and thread to make necklaces), and by a traditional pencil-and-paper test. Both the clinical interview and the pencil-and-paper test evaluated the same type of operations, which were taken from the national curricular program for these school grades. The Shipibo-Konibo people are an Amazonian indigenous group that speaks a native language in the Panoan family; since most members of this group are fluent in Spanish, however, no translator was needed and the assessments were conducted in Spanish. The Shipibo-Konibo people are principally settled along the Ucayali River in the Amazon rainforest in Perú, although currently many of them have relocated to other areas of the country, including Lima the capital city, in search of better work or education opportunities. After the Asháninka and the Awajún, the Shipibo-Konibo is the third largest Amazonian indigenous group in Perú. Informed consent was obtained following the guidelines of Frisancho, Delgado, and Lam (2015), which are based on previous experience working with Amazonian indigenous communities in the Ucayali region of Peru. As research has shown that individuals from cultural diverse backgrounds may have different expectations for the research process, and may perceive it in a different way than people from industrialized nations (Lakes, Vaughan, Jones, Burke, Baker, & Swanson 2012), informed consent included both individual consent and a communitarian meeting. It also included the donation of gifts (tools, groceries, and other useful items) for the community, and a debriefing meeting with the community's school teachers. The assessment was conducted by two researchers in a school classroom. It took around 30 minutes with the older children and 45 with the younger ones. In all cases the clinical-critical interview was applied first (addition and then subtraction), and finally the pencil-and-paper test. Although a native speaker of shipibo was present during the evaluation, his services were not needed as children were fluent in Spanish. Results show that children have difficulties in the development of both addition and subtraction. They make counting mistakes and have trouble understanding the logic of subtraction (taking a number from another, larger one). Some do not conceptualize subtraction as the opposite of addition and, in consequence, cannot foresee that joining two numbers that were previously separated will result in the same original quantity. Children aged seven were unable to solve any of the operations in the pencil-and-paper test. However, better results were obtained through qualitative, Piagetian assessments, in contrast to the quantitative, pencil-and-paper assessments. During the interviews, children were able to show their cognitive processes and ways of thinking while solving the problems, and with scaffolding, the use of concrete materials such as pictures or beads, and strategic help from the evaluators (Parrat, 2016a, 2016b), many of them were also able to develop a better comprehension of the problem and self-correct their initial answers. Developmental levels for addition and subtraction consistent with Piagetian theory were identified. These levels show a progression from the impossibility of grasping logical addition or subtraction, to the capabilities of psychological reversibility and logical composition of inverse and direct operations. The results are discussed using Piaget's theory and the problem of particulars and universals in cognitive development, and analyzing critically how this kind of assessment can help elementary school teachers respond to the needs of intercultural bilingual education in Peru's Amazonian indigenous communities.
Se presentan los resultados de una evaluación de las operaciones matemáticas de adición y sustracción, en un grupo de niños de enseñanza primaria (5 niñas y 2 niños) de 7, 9 y 11 años, de una comunidad nativa Shipibo-Konibo de la región Ucayali, en la Amazonía del Perú. Se realizó con dos métodos distintos, la Entrevista Clínico-crítica de Piaget, que incluyó problemas culturalmente contextualizados y material representativo y manipulable como figuras de animales y bolitas para armar collares, y una prueba tradicional de lápiz y papel. Ambas pruebas evaluaron el mismo tipo de operaciones, extraídas de lo que propone el diseño curricular nacional para esos grados. Los resultados muestran que los niños tienen dificultades tanto en la adición como en la sustracción y no logran resolver con éxito todas las tareas. Sin embargo, se pueden observar mejores resultados con la evaluación cualitativa por medio de la entrevista clínico-crítica, en contraste con la evaluación tradicional de lápiz y papel que evidencia resultados mucho más pobres. La primera otorga además mayor información sobre el proceso operativo de los niños y muestra que los niveles de desarrollo de sus competencias matemáticas van de la mano con lo que plantea la teoría piagetiana. Los resultados se discuten señalando la universalidad del conocimiento lógico-matemático y su pertinencia para comprender los procesos de aprendizaje en contextos de diversidad cultural y analizando críticamente el modo en que la evaluación constructivista ofrece mayor información y recursos para los docentes de educación intercultural bilingüe de comunidades amazónicas del Perú.
