Abstract

VASCONCELOS, Isabel Cristina Peregrina; MAMEDE, Ema Paula Botelho da Costa  and  DORNELES, Beatriz Vargas. The comprehension of numerical relationships in the learning of fractions: a comparative study with Brazilian and Portuguese children. R. Bras. Est. Pedag. [online]. 2017, vol.98, n.249, pp.251-269. ISSN 2176-6681.  https://doi.org/10.24109/2176-6681.rbep.98i249.3043.

The understanding of rational numbers is one of the major conceptual challenges faced by students in mathematics learning in basic education. Regarding fractions, to establish the inverse relationship between the numerator and the denominator becomes a key issue in concept formation. The main goals of this study were: to understand if the inverse relationship between smaller quantities than the unit in quotient and part-whole situations influences the learning of fractions; and to compare Brazilian and Portuguese students’ comprehension of the inverse relationship between quantities in fraction problems, using quotient and part-whole situations. The results indicate that students have a better grasp of the inverse relationship between the quantities in the quotient situation and also showed that Portuguese students performed significantly better than Brazilian students in the both types of situations. The discrepancy in student performance can be explained by differences in the curricula of mathematics in grade four in these countries. Implications for the teaching of mathematics in these two countries were also discussed.

Keywords : rational numbers; fractions; inverse relation.

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