Significados e representações dos números racionais abordados no Exame Nacional do Ensino Médio - ENEM

Abstract

This research proposes to investigate what are the meanings and the representations of the rational numbers that are contemplated in the National High School Exam – ENEM. Therefore, then we take as reference the studies of Romanatto (1997) and Gomes (2010) and we adopted the following meanings for the rational numbers: measure (part-whole), quotient, reason, multiplicative operator, probability, a number in straight numerical and percentages. To we analyze the records of representations of the rational numbers that are contemplated in ENEM, We use the Theory of the Representations semiotics Raymond Duval who considers that mathematical objects are not directly perceptible and that access to them is possible only through a system of representation. The methodological route that we have adopted consisted of the two stages. In step I we analyze the tests general knowledge of the ENEMs 1998 to 2008 and math tests and their technologies of the ENEMs from 2009 to 2011, in the sense of identify items that mobilized the concept of rational numbers in their different meanings. In step II, we analyze the items identified in step I, regarding the math tests and their technologies of ENEM 2009 to 2011, as to records of representations contained in the structure of the item and in particular of the records of the rational numbers, and also, regarding as to records of representations, treatments and conversions that could be mobilized during the resolution of the item. We concluded that, in the evidence of general knowledge of the ENEMs 1998 to 2008, approximately 5.6% of the items (3.9 items per tests) involved the concept of rational numbers. While in math tests and their technologies of the ENEMs 2009 to 2011 (new ENEM), approximately 21% of the items (9.6 items per tests) mobilized this concept. The meanings identified in the items relative at the ENEM 1998 to 2008 were virtually the same identified in the period of the ENEM new, part-whole, reason, percentages and probability. Being the meaning, percentage, as the more addressed. Some items involved more than one meaning. The items related to math tests and their technologies of the ENEMs 2009 to 2011 had a predominance in its structure (enunciated, bracket, command, and alternatives of the answer), among the records of semiotic representations of rational numbers, the numeric registration, percentages. The semiotic register of rational numbers who else could be mobilized during for the resolutions of the items was the record fractional numerical. Conversions between the records of rational numbers only occurred in only one direction, with the exception of one item of the ENEM 2010.