Structural sense of first-year university students

Abstract

This paper aimed to analyze, from a structural sense, the answers given by newly admitted university students to questions, in which either direct factorization or some type of factorization was required to continue with the exercise as part of the first test of an introductory college math course. This qualitative research had a descriptive and exploratory approach with a content analysis design. The study was conducted in 2019 and the sample included first-year university students from two groups from the General Mathematics courses at Universidad Nacional (UNA), Costa Rica. Results show that students can recognize a familiar structure in its simplest form in expressions that involve a common factor, but not when they have to choose appropriate manipulations to make the best use of a structure in expressions involving two or more different methods of factoring. It is concluded that their lack of structural sense is what generates errors in the factorization procedures. This suggests that student training is insufficient, which generates an alert since it is prior knowledge that is fundamental to successfully advance in later contents such as operations with algebraic fractions.