Resumo

FERNANDEZ, Ceneida; IVARS, Pedro; ROJAS, Francisco  e  CASTILLO, Salvador. From additive to proportional strategies: Features identified with middle and high school students in Ecuador. Educ. mat. [online]. 2024, vol.36, n.2, pp.68-91.  Epub 21-Jan-2025. ISSN 2448-8089.  https://doi.org/10.24844/em3602.03.

Previous studies have shown that students move, when solving proportional and additive situations, from using additive relations indiscriminately to using multiplicative relations indiscriminately. In addition, the type of ratio and the nature of the quantities seem to influence the use of these relations. This study explores the strategies used by Ecuadorian middle and high school students when solving additive and proportional missing-value problems with integer/non-integer ratios and discrete/ continuous quantities. The results show a different pattern: when students stop using the additive strategy indiscriminately, they do not use proportionality indiscriminately, they use incorrect procedures to solve proportional problems. Moreover, both variables were significantly influenced: (I) additive strategies were used more with non-integer ratios/relations and proportional strategies were used more with integer ratios/relations; and (II) proportional strategies were used more in proportional problems with discrete quantities and additive strategies were used more in additive problems with continuous quantities.

Palavras-chave : Proportional reasoning; transition from additive to multiplicative thinking; type of ratio; nature of quantities; middle and high school education.

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