We are now into the second year of introducing a revised mathematics curriculum for undergraduate engineering programmes at UCL. This is part of a faculty-wide, multi-disciplinary curriculum redesign of our undergraduate engineering programmes. The primary purpose of this redesign is to enhance the student experience by introducing project-based activities across the degree programmes. These activities will run from the first year of the study programme, right up to the final year of study. Our aim in so doing is to ensure that from the first day that students enter our degree programmes, they will be able to study and use mathematics and engineering science in the context of engineering problem-solving.
Positioning Mathematics Teaching Within Engineering Education
Engineering is closely tied to economic and technical development. Prior to the 19th century engineering existed largely as a practice-based vocation passed down from generation to generation primarily through on the-job learning. However, starting from the latter half of the 19th century, university education increasingly became an important entry route into engineering as it became more professionalised. A key consequence of this move to professionalise engineering was that in addition to practice-based education, science and mathematics became central to engineering education.
However, determining an appropriate balance between practice and science in engineering education is problematic. Since the early twentieth century debates have raged over how much practice and how much theory to include in engineering education. Prior to the First World War, engineering education in the UK leaned more towards a higher practical content. However, over the years, the pendulum has swung towards a higher theoretical content. Lately, however, engineering employers and students have begun to demand for more practical content within engineering education. The pendulum is therefore swinging back towards more practical content in engineering education. Where does this leave engineering mathematics then?
At UCL we subscribe to the notion that mathematics is central to both engineering education and practice. We are of the viewpoint that engineers need to master mathematical concepts and to be able to apply these concepts to solving engineering problems. However, studies indicate that students often find it difficult to apply their knowledge of mathematics to real world problems. To alleviate this, we have integrated mathematical modelling and simulation in our teaching. To reinforce the link between mathematics and engineering practice, we now use the term “mathematical modelling and analysis” to refer to our mathematics modules.
Our Revised Approach to Teaching Mathematics to Engineers
We use a blended approach in our delivery of the mathematical modelling and analysis modules. In addition to face-to-face lectures and weekly workshops, we have provided an online suite of mathematical support resources. This includes pre- and post- lecture online quizzes, lecture notes, and MATLAB simulations and demonstrations. Lectures and workshops are delivered by engineering academics, and wherever possible, examples of current academic research and practice are used to illustrate key mathematical concepts. One outcome of this approach is that mathematics seizes to become a “dry” subject as students begin to see its utility in everyday research and practice. In addition, students get to know and interact with ongoing academic research within engineering.
Students enter into engineering with significant differences in prior mathematical knowledge and competence. In addition, students have different learning and mastery rates. We have introduced a pre-course mathematical quiz to assess individual competence levels in key elementary areas such as calculus and algebra. An additional weekly class has been created to provide additional student support. Throughout the course, students also have access to a walk-in, student-led support team. This helps to encourage peer-to-peer learning, and to establish connections between undergraduate and postgraduate students.
A Preliminary Assessment
Has this been a walk in the park? Certainly not. Combining theory and modelling in mathematics has been a challenge for both academics and students. For the academics, the main issue has been deciding what content to include and exclude given the constraints of time. In addition, breaking down research to a level where the students can understand and engage with it mathematically requires careful thought. For the students, the main challenge has been the demand for more independent work, both prior and after lectures. In addition, developing a working knowledge of MATLAB has been a challenge.
Despite these challenges, the emerging results are encouraging. Compared to previous cohorts at the same stage, students from this cohort appear to have a deeper awareness of their engineering disciplines, and a greater appreciation of the research taking place within the faculty. The module is more activity oriented than the previous module. Amongst the students this is helping to foster a higher level of self-direction and independence. In addition, students show a greater willingness to engage with teaching staff, and a markedly higher assertiveness when it comes to feedback and demands for quality learning. With regard to academics, this module is helping to foster collaboration in curriculum development and teaching between different engineering disciplines. Such interaction between departments can only be good for both the research and teaching within the faculty. Most importantly, the introduction of the module has encouraged academics to adopt a more critical approach to their own teaching. This is leading to greater academic interest in learning and teaching approaches and technologies.
So what are my interim conclusions? The journey has been demanding for both students and academics. But it has been fruitful, and it has generated an excitement and a buzz unlike previous years. Most importantly, the module appears to have increased the engagement of both students and academics. And so, to the next year, here we come.