Abstract

BUSTAMANTE-SANTOS, Alfonso J.  and  FLORES-MACIAS, Rosa del Carmen. Andrea's Reflections: A Microgenetic Analysis of the Understanding of Division in the Context of a Problem. Educ. mat. [online]. 2017, vol.29, n.1, pp.91-116.  Epub Feb 14, 2022. ISSN 2448-8089.  https://doi.org/10.24844/em2901.04.

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.