Níveis de pensamento algébrico de licenciandos em Matemática na resolução de problemas de partilha

Abstract

The objective of this work was to identify the level of development of algebraic thinking in mathematics undergraduate students when solving quantity-sharing problems. For that, the model developed by Almeida (2016) was used as a basis, which proposes four levels of development of algebraic thinking in relation to sharing problems, level 0, absence of algebraic thinking; level 1, incipient algebraic thinking; level 2, intermediate algebraic thinking; and level 3, consolidated algebraic thinking. The research subjects were 64 students from the 1st period of the Mathematics Licentiate Course at a public university in the State of Pernambuco. Data collection took place through a test consisting of six sharing problems, which are characterized by having a known quantity that is split into unknown and unequal quantities. We found that most of the participants, 73%, found themselves with consolidated algebraic thinking when faced with a problem of sharing. However, some students arrive at the degree course in mathematics with this way of thinking without being fully developed, since 5% of the subjects are at level 1, that is, it mobilizes three characteristics of algebraic thinking, 8% of those surveyed find it if at level 2, that is, it mobilizes 4 features of algebraic thinking. It was also possible to notice that 14% of the research subjects are at level 0, that is, they cannot establish the necessary relationships to respond to a sharing problem, a problem that is related to a polynomial equation of the 1st degree, a mathematical object studied in elementary school.