2025 ASEE Annual Conference & Exposition

In traditional post-secondary mathematics education for engineering students, a significant challenge is the disconnect between theoretical instruction and practical application. This gap often arises from teaching complex mathematical concepts in isolation, without contextualizing them within real-world engineering applications. To address this issue, we are developing and implementing a holistic, collaborative pedagogical approach that emphasizes contextualized, application-based teaching and learning, specifically tailored to mathematics-related classrooms in both engineering and mathematics disciplines. This paper shares our early insights and seeks feedback on our experimentation with teaching strategies such as problem-based learning in a second-year numerical methods course designed for engineering students.

With our primary goal of contextualized and application-based learning, we aim to create an enriched environment that equips students with the skills to effectively apply various numerical methods as engineering tools for solving complex real-world problems. Emphasizing practical applications, we have reviewed existing best practices, restructured the entire course, developed new materials and collaborative projects, and diversified assessments to better meet learner needs prior to implementation. In Fall 2024, we implemented our instructional approach, still in its development stage, in its first classroom setting. At the beginning of the term, we gathered pre-course reflections from students that guided our adaptations to teaching methods. Post-course feedback was used to evaluate the success of our implementation. Initial observations from this first iteration reveal both successes and challenges in promoting contextualized learning as educators. In addition to enhancing problem-solving skills and applying numerical methods to various real-world scenarios, we also emphasize the application of computer programming abilities, which are essential in engineering contexts.

As this is our first iteration, we welcome constructive feedback from the audience to further refine our approach. Through shared insights, we hope to enhance the effectiveness of our approach and ultimately improve outcomes in mathematics courses for engineering students. In future iterations of our research, we aim to explore, and measure how context-based education support the overall well-being of learners throughout their educational journeys.