In a thought-provoking interview, Professor David Perkins of the Harvard Graduate School of Education asks of University education: “What’s worth learning?”. In Perkins’ view, we need to teach students more “nimble” ways of thinking and interacting with our world. The rate of technological advance means that a great deal of what students learn in university will be obsolete in ten, twenty, or thirty years. The vast majority of university learning is made up of specific skills or “nuggets of knowledge” that students will never encounter again once they walk out the campus gates. Perkins argues persuasively that we need to reassess what we consider to be successful learning outcomes away from detail-oriented knowledge transfer and towards “understandings of wide scope”. To put it another way, we need to transform the university teaching experience from one of “surface learning” to “deep understanding”.
In this context, STEM subjects, and mathematics in particular, constitute both a prime example and a special case. In very large service courses like the Engineering Mathematics lectures I teach, there is a body of knowledge or tools that students are required by their programs to master and regurgitate in an exam. The lectures are almost entirely made up of worked examples rather than the underlying theory, and students practice problem in class, tutorials, and on their own. The hope is that the students will be able to recognise problem types, remember what tools or formulae are needed, and apply what they have learned in class. In short, this is a classic “surface” model of learning.
However, mathematics, like other “hard” sciences like physics, chemistry, and biology, requires students to master of a highly technical language. There are no short cuts to deep understanding in these subjects. Years of practice and application are required to reach the “unknown”. To use an analogy I often make in class: if the students want to be “Karate Kid”, then they have to wax-on and wax-off for many hours.
Of course, little of this is relevant for the vast majority of the students in my Engineering Mathematics course. These students just want to learn enough to do well in the exam, which is exactly the kind of behaviour that the curriculum demands. As Professor Perkins points out, curricula are the most difficult elements of education to transform. The challenge for me as an educator, then, is to find ways to encourage students to dive below the surface from time to time, to see what lies beneath.