Mathematical modelling and Problem Solving in Engineering Education

Licentiate thesis, 2021

Background
Innovation and technology have made the 21st century engineering workplace problems more diverse and challenging. Mathematical modelling is being increasingly used as the primary form of engineering design and is fundamental in everyday engineering problem solving. The demand on engineering education is to prepare graduates to meet the challenges and needs of this rapid changing society. One of the keys to do so is to develop skills to be able to integrate knowledge from multiple domains and adapt to solving novel, complex problems in workplace. This means engineering education needs to create learning environments that are effective and mindful of the authentic practices of engineers.

Purpose
The goal of this thesis is to contribute to research efforts of improving engineering education, focusing on developing students’ ability to solve mathematical modelling problems. In pursuit of this goal, this thesis examines an alternative learning design in a mathematical modelling and problem-solving course for engineers and understand how the learning design contributes to students’ learning.

Scope/Method
The two empirical studies presented in this thesis employed a qualitative case study methodology. The case under investigation is a course in mathematical modelling and problem solving offered to undergraduate engineering students at Chalmers University of Technology. The first study aimed to understand how engineering students approach mathematical modelling problems early in the course and how the course impacts their learning. The second study aimed to contribute to the knowledge base of authentic learning by examining students’ perceptions of different elements of authentic learning in the course.

Findings
The results show that students had little experience of mathematical modelling and solving realistic problems that lead to experiencing challenges early in the course. Many were unaware of the importance of understanding the problem and exploring alternatives which related to their lack of self-regulation or metacognitive skills and was impeded by different types of beliefs, attitude and expectations shaped by their prior experiences. The most important impact of the course was on students’ metacognitive development. In the analysis of students’ perception of this alternative learning environment, the results showed that students experienced elements of authentic learning in the course. Even though the tasks were not entirely ‘real’, the student experience them authentic and ‘bought in’. Students engaged in deep reflective thinking in the course and presented several mechanisms of learning that linked elements of authentic learning and the course.

Conclusion
The findings in this thesis demonstrates the importance of self-regulation and beliefs in developing students’ mathematical problem-solving abilities and exemplifies how the learning environment in the course contributed to developing students’ mathematical modelling and realistic problem-solving skills as well as metacognitive skills. Furthermore, the thesis presents interesting outlook on students’ perception of authenticity in the course’s learning environment contributing to the knowledge base of authentic learning in engineering education. Finally, we recommend expanding this course’s concept to other engineering programs and offer pointers to design courses that intend to provide authentic learning experience.