This research study focuses on the mathematical work associated with two non-routine problems on binary operations with the objective of identifying mathematical thinking abilities that students apply when solving problems. An instrumental case study is designed where university students solve arithmetic and algebraic problems. Implicative statistics are applied to conduct quantitative and qualitative analyses of student answers. The results show that students use algebraic and arithmetic techniques without mentioning properties of an algebraic structure. In solving non-routine problems, school mathematics techniques are favored and little use is made of properties and concepts associated with a binary operation, typical of university-level mathematics. In conclusion, there should be an implementation of regular instances to promote solving non-routine problems by considering other mathematical domains such as algebra, geometry, and arithmetic.