The Case of Francisca and the Sense Attributed to Decimals Numbers

Abstract

In a qualitative research carried out in a night elementary school in Mexico City, we performed the case study of a young woman of 19 years of age and fifth grade student at the school, who is a stationery's employee. She solved problems, which involved the use of decimal numbers and their basic operations. Francisca chose from a questionnaire in which she evidenced an adequate overall performance although not without errors. Two follow-up instruments were used in Francisca's case: questionnaire and interview; the latter and some of its dialogs were the fundamental support of this research. Our general research question was: how does the adult assign sense to decimal numbers in the resolution of problems with those numbers? Francisca signified such numbers through familiar situations of life and working experiences. In problem solving, she assigned decimal numbers establishing equivalence between those numbers and mainly natural numbers, while she linked secondly decimal numbers with fractions. When this young woman produced new problems, she favored the use of money and length measures represented by the decimal metric system. Some of Francisca's difficulties were referred to the interpretations of the decimal positions and decimal notations. Also, she made mistakes in reading, writing, or in operations linked to certain unstable positional notions.

Keywords: Decimals; Sense; Signification; Decimal Point (Decimal Comma); Problem Solving