Abstract:

Psychological factors influencing mathematics learning can be broadly grouped into two main categories:
(i) students’ drive and motivation, and
(ii) mathematical self-beliefs, dispositions, and engagement.

When instruction does not incorporate concrete, real-world problems, students often fail to recognize the relevance of mathematics, leading to reduced intrinsic motivation and persistence. Furthermore, when mathematical content is presented in isolation across different courses, students tend to perceive their knowledge as fragmented, which negatively affects their self-concept, increases uncertainty or anxiety, and discourages active engagement with mathematical tasks.

This work is conducted by a teaching team responsible for first-year undergraduate courses in Algebra, Calculus, and Statistics in industrial engineering degree programs, with one instructor holding specialized training in applied mathematical modeling in hydraulic engineering. The proposed methodology focuses on the design of learning situations based on real-world problems closely related to the students’ field of study, combined with problem-solving strategies that require the integration of mathematical concepts traditionally taught separately. These tasks are deliberately constructed to encourage the articulation of tools from algebra, geometry, calculus, and statistics within a unified problem-solving framework.

As an illustrative example, we propose a learning situation based on sedimentation processes in hydraulic reservoirs. Erosion in a watershed leads to sediment accumulation in reservoirs, causing a progressive loss of storage capacity. Students are asked to estimate the water volume of a reservoir by computing the surface area of the water at different height levels. This task relies on the application of Cavalieri’s principle, which involves the estimation of a definite integral, and is complemented with statistical techniques to obtain an unbiased estimate of the reservoir volume. Through this activity, students explicitly combine concepts from calculus and statistics to solve a realistic engineering problem.

The results of this approach indicate that integrated learning situations facilitate the simultaneous mobilization of multiple mathematical domains, helping students perceive meaningful connections between them and strengthening their mathematical self-concept and engagement. In addition, solving concrete, real-world problems enhances students’ motivation by reinforcing the perceived usefulness and applicability of mathematics in engineering contexts.

In conclusion, this project contributes to motivating undergraduate engineering students who often view mathematics as an abstract and compartmentalized body of knowledge. By framing mathematical learning around authentic applications and emphasizing conceptual integration across the curriculum, students develop a more coherent, relevant, and motivating understanding of mathematics. This approach is aligned with the principles of Universal Design for Learning (UDL), as it accommodates diverse learning preferences and backgrounds.

Acknowledgement:
This work was supported by the projects 57293 (2025), Universal Design for Learning (UDL) in Statistics and Mathematics, and 57912 (2025), Mathematical Bridge: Strengthening Key Competencies for Success in Science and Engineering Degrees, funded by the Unitat de Formació i Innovació Educativa of the Universitat Jaume I.

Keywords:

Mathematics Learning, Motivation and Self-efficacy, Problem-based Learning, Universal Design for Learning (UDL).