Student motivation is a crucial factor in educational success, especially in subjects that are often perceived as abstract, such as mathematics. In engineering courses, the disconnect between theory and practice in mathematics teaching sometimes leads to demotivation and low student performance. According to Resnick, learning is more effective when students can relate new knowledge to real-world contexts, as it promotes a deeper and lasting understanding of concepts. According to Lesh & Doerr, real problems arouse students' interest, making learning more relevant and interesting. Jonassen states that despite the benefits, the implementation of real problems presents challenges, such as the need for additional resources and, in addition, some students may initially feel unmotivated by the complexity of the problems.

This work presents an experience that was carried out in a curricular unit (UC) of Linear Algebra and Analytical Geometry (ALGEA), in the 1st year, 2nd semester, of a degree in Engineering and Industrial Management at an Engineering school, in the academic year 2023/2024. To increase student motivation and engagement, several exercises were introduced throughout the semester to apply real problems to the content taught at the UC.

The application exercises were used in all topics studied at the UC, whether in theoretical classes or practical classes, whether in individual work or group work. As an example of operations with matrices (matrix multiplication, calculation of the inverse of a matrix) the students carried out group work on cryptography (coding and decoding messages). Students also carried out individual exercises on Leontief's open economy, image processing, geometric transformations, calculation of areas of parallelograms and triangles in the plane and space, calculation of the volume of tetrahedra, traffic management, and graphs, among others. To try to understand the impact of this methodology on student motivation and learning, at the end of the semester, an anonymous questionnaire was made available on Moodle to students who were enrolled in this UC to gauge their opinion regarding the inclusion of application exercises in the UC.

The questionnaire consisted of 8 closed questions, the first two of which intended to characterize the student in terms of gender and number of enrollments in the curricular unit. There were 4 questions to assess students' opinions regarding the use of application exercises in theoretical and practical classes. The last two closed questions were about the material made available and the involvement of students in the UC. Finally, the questionnaire ended with an open question in which the student was asked to indicate what, in their opinion, were the main negative and positive points of this experience.

As an example of the answers to the open question, a student stated that “I really liked the methods that the teacher used to teach the subject as they were dynamic, different, and captivating”. In general, students reported that real problems made classes more dynamic and interesting. They also mentioned that this approach helped them visualize the practical application of the concepts learned, increasing their motivation to learn. The integration of real problems into teaching in ALGEA appears to have been an effective strategy for increasing student motivation and engagement. Despite implementation challenges, the learning benefits appear to have been substantial.

Keywords: Education, application problems, mathematics.