Andrea’s Reflections: A Microgenetic Analysis of the Understanding of Division in the Context of a Problem

Alfonso J. Bustamante-Santos
Rosa del Carmen Flores-Macías

Abstract: This study describes changes in the meanings of the written representation
of the division algorithm within a partition word problem in Andrea, a
student from sixth grade in a public school. Through a clinical interview, she
solves various word problems. Based on the theory of conceptual fields, we
discuss the changes in different theorems-in-act and concepts-in-act that she
uses. She reflects on the relationships between the components of the division,
and reformulates her ideas on how these relationships must be expressed. The
most significant change observed in Andrea during the interview is related to
her understanding of the division algorithm; she initially writes it based on ideas
like “the bigger number must be inside” but, at the end of the interview, she
showed understanding of the relationship between the word problem and the
written algorithm. Likewise, are observed changes in the way she conceives
the measured-magnitude relationship. Discussion analyzes the relevance of
taken into consideration student’s concepts and theorems-in-act to strengthen
the mathematic learning.

Keywords: problem solving, simple proportionality, division, conceptualization,
graphic representation.


DOI: 10.24844/EM2901.04



Marcar como favorito enlace permanente.

Comentarios cerrados.