Resumo

POWELL, Arthur B.. Reaching back to advance: Towards a 21st-century approach to fraction knowledge with the 4A-Instructional Model. Perspectiva [online]. 2018, vol.36, n.2, pp.399-420.  Epub 24-Jul-2019. ISSN 2175-795X.  https://doi.org/10.5007/2175-795x.2018v36n2p399.

In daily life, rational numbers are ever-present and extraordinarily useful. Unfortunately, for teachers and students alike, fractions have proven to be conceptually difficult. We argue that conceptual difficulties of fraction knowledge have two causes: ontological and epistemological. The ontological problem rests on dominant ahistorical theorizations of fractions that are the basis of current curricular proposals. The epistemological challenge of fraction knowledge originates in instructional inattention to fostering learners’ fractional number sense. From a cultural-historical perspective, inspired by theoretical and empirical work of Davydov and Gattegno, we propose ontological and epistemological perspectives as alternatives for the construction of fraction knowledge. Finally, we present a pedagogical instrument—the 4A-Instructional Model—designed to engender learners’ view of themselves as empowered agents of mathematical knowledge.

Palavras-chave : 4A-Instructional Model; Cultural-Historical Perspective; Davydov; Gattegno; Rational Numbers.

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