From the expression of the ratio with two natural numbers, to its expression with a fraction. Two didactic experiences at primary school and high school

Abstract

- The results of a didactic study about the transition from the expression of a ratio with two natural numbers, to its expression with a fraction and with a percentage, are presented. In this transition, the fractions acquire the meaning of ratios, that is, of relationships between quantities. The study consists of two short experiences of didactic engineering, with students between 11 and 13 years old, one in the sixth grade of primary school and the other in the first grade of high school (seventh grade). The results are encouraging in terms of the potential of the situations used to favor the consideration of ratios and to give rise to their expression with fractions. Likewise, they reveal weak points, and suggest ways to continue exploring.