I am currently responsible for first and second year engineering mathematics at UCL. Instead of the term “engineering mathematics”, at UCL we prefer the term “mathematical modelling and analysis”. This is because we believe that engineers don’t usually learn mathematics for the sake of mathematics. Instead, we believe that engineers study mathematics in order to gain proficiency in applying mathematical techniques to analyse and model engineering problems, and as a tool to design robust solutions to these engineering problems.
For the engineer, therefore, learning mathematics is not only about mastering mathematical theories and being able to solve contrived mathematical problems thrown at them. It is also about using mathematics to resolve engineering problems. Given a problem, an engineer recasts the problem into a mathematical problem, solves and analyses it, and then recasts the solution back into an appropriate real-life engineering solution. To make the analysis and modelling stages more tractable, the engineer typically uses spreadsheets, like Excel, or mathematical analysis and modelling software like Matlab. Hence, the engineer has to gain competence in Excel and in mathematical modelling software at the same time as he or she is gaining proficiency in mathematical theory. Consequently, at UCL we require our engineering students to simultaneously engage with mathematics, spreadsheets and Matlab.
At UCL we have approximately 600 students in the first year, and 500 students in the second year. Students are provided with online resources via Moodle, and have access to both Excel and Matlab. In addition, our students also have access to online study materials from Mathworks, the providers of Matlab. Students are expected to be proactive in their studies, and it is a requirement that students should adequately prepare before coming to lectures or to workshops. Lectures are meant to be headline events that rapidly cover mathematical theory, and also expose the students to research applications of the topics that they are studying. Hence individual lectures are delivered by active researchers, and demonstrations of research applications are a staple in the standard UCL engineering mathematics lecture. Workshops are meant to offer students opportunities to participate in active, collaborative, problem-based learning. Hence, the students has to be adequately prepared, and the material availed to them should be pitched at just the right level, and delivered at just the right time.
To achieve effective learning delivery, a lot of organisational effort is required. Lecturers need to coordinate closely with workshop leads, and with postgraduate teaching assistants who provide in-class and out-of-class assistance to the students. On average, 40 lecturers and postgraduate teaching assistants work on each module, and below is a simplified staffing organogram for each of the two engineering mathematics modules.
This organogram depicts a hierarchical structure, but in practice, communication and control is network-oriented. The module coordinator (IEP Coordinator) reports directly to the IEP programme director. However, he also communicates directly with each of the undergraduate engineering programme directors in each of the engineering departments, and liaises directly with the module lecturers, workshop leads, and departmental course administrators. This is in addition to communicating along the faculty-based Integrated Engineering Programme (IEP) chain of command.
For effective teaching, lecturers have to communicate closely with each other to ensure smooth handover from lecture topic to lecture topic. At the same time they have to communicate directly with the workshop leads who will be guiding the students in the problem-based workshop exercises taking place within the departments, and with the postgraduate teaching assistants who maintain close in-class and out-of-class contact with the students. Despite differences in personal and departmental perceptions of “good mathematics teaching”, the teaching team has to work effectively as a well-oiled machine. Effective team rapport is paramount, communication has to be timely and absolutely clear, and role and task-assignment has to be non-ambiguous. This requires effective planning, coordination, task-scheduling, and sensitivity to the teaching and learning environment. As shown in the diagram below, team-working skills are central to our ability to deliver each of the two mathematics modules in a manner that enhances the overall quality of the student experience.
There is currently very little coverage of large-class team-teaching in the engineering education literature. One could be forgiven for believing that all that is needed to be an effective engineering educator is mastery of the engineering subject content and the ability to deliver spell-binding lectures. Indeed this is what the typical student witnesses when attending classes, but in a large-class team-taught module, this is only the outcome of a coordinated array of activities spanning multiple departments.
And our message to the engineering education community is this: Effective team-teaching skills are essential to good teaching practice, don’t underrate them.
And for faculty and departmental heads in the engineering schools, our message is this: Don’t just randomly assign people to undergraduate programme management roles, including coordination of early stage engineering modules. Seek for people with the right people skills, in addition to their subject competence. And invest in them through appropriate team leadership training, and be available to support them throughout the academic year.
And for the engineering academic, our message is this: Teaching is no longer just a lecture-and-examine process. In today’s world, higher education teaching has become a highly complex role that demands subject-matter competence, teaching delivery skills, team-working and team-building skills. Therefore, if you want to excel as an engineering academic, then you should invest time and effort in acquiring and sharpening these skills.