Abstract

VALENCIA, Evelyn  and  AVILA, Alicia. Previous ideas about multiplication and division with decimals: its evolution from an experience with the Laberinto de decimales. Educ. mat. [online]. 2015, vol.27, n.3, pp.81-110.  Epub Apr 08, 2022. ISSN 2448-8089.

For several decades, students' learning processes of decimal numbers have been investigated. Difficulties and obstacles have been identified, some of which can be attributed to the instructional approaches that are used. One of those obstacles is related to the intuitive models of the meaning of multiplication and division, which students develop as they engage with these operations in the context of natural numbers. In this paper, results are analyzed of the implementation of a didactical situation, named "The maze of decimals", aimed at overcoming those models. The analysis centers on the evolution of students' reasoning while engaging in the situation. It is noticeable how students struggle to abandon the conceptions of "multiplication makes bigger, division shrinks." This process is mediated by diverse ideas that lead to the construction of new rules about the meaning of multiplication and division.

Keywords : multiplication and division with decimals; intuitive models; learning decimals; didactic situations; knowledge building.

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