Formalizando las operaciones aritméticas como sistemas matemáticos mediante la Yupana y la Chakana.

Abstract

The purpose of the study » Formalizing arithmetic operations as mathematical systems by means of the Yupana and the Chakana» is to axiomatically design addition, subtraction, multiplication and division of natural numbers as mathematical systems using the Yupana, the Chakana and their applications to the teaching-learning process in regular basic education. Both instruments are emblematic symbols of the Inca Civilization; the Tawa Pukllay Method is the starting theoretical reference for the Yupana; on the other way, the direct experience in workshops with teachers and students allows to derive the scientific fundamentals with the Chakana, confirming in theory and practice successful, valid, reliable results that configure the theoretical proposal and its original and innovative didactic strategies related to complex mental games to learn mathematics. Undefined terms, axioms, theorems, definitions, specific language, applications for each object were developed; also, valuable didactic conclusions were deduced to maximize the learning of mathematics in the first grades of schooling. Keywords: Yupana, chakana, formalization, mathematical system