The aspects of reversible thinking in solving algebraic problems by an elementary student winning National Olympiad medals in science

Abstract

This study aimed to identify the aspects of reversible thinking of an elementary student who had won national Olympiad medals in science in solving particular algebraic problems. In this qualitative research, data were collected by a reversible thinking task contained a simple equation and an interview. The results showed that when making an equation, the only aspect of reversible thinking identified was reciprocity. This could be seen from the strategy the subject used in making the equation. It was done by dividing both sides of the equation by the same element, taking the square root of those two sides, and adding them with the same element. When reversing the new equation to its starting point, the aspects of reversible thinking identified were negation and reciprocity. It could be seen from the strategy the subject used in reversing the equation to its starting point. Negation was identified when the subject moved the parts of a known element, and in this case, the subject used a subtraction operation, which was the inversion of addition operation within the initial equation. Reciprocity was identified when the subject squared the both sides of the equation.