Prior to this miniproject, the School of Mathematical Sciences at Queen Mary, University of London (QMUL) had been developing approaches to the learning of mathematics that involved the use of short writing tasks. The rationale for this was two-fold: first, students should develop effective communication skills enabling them to express mathematical ideas clearly and accurately in specialised and non-specialised language; second, the written articulation of such ideas contributes to students developing a ‘conceptual deep’ approach to disciplinary study i.e. the capacity to relate problem solving tasks to underlying concepts and theory and so properly understand the subject.
The miniproject team aimed to develop and run a course (three days) for beginning postgraduate students in mathematics that will equip them to work as Postgraduate Teaching Assistants (PGTAs) on the Mathematical Writing (MW) undergraduate course, whilst improving their own mathematical writing skills at an early stage in their PhD; and, evaluate the success of the undergraduate module and also the postgraduate course in preparing teaching assistants to support the module.
A complex picture of approaches to learning has emerged from this small-scale study. There is evidence that students on the MW course display features of a deep approach to learning and most students appear to be trying to understand and articulate fundamental mathematical concepts. They report being able to transfer knowledge learned on the MW course to other courses.
Students reported that it was their intention to develop their understanding of mathematical concepts and methods, to translate symbols into words and to write with precision. However, when faced with difficult tasks, many students, even those who were most successful on the course, adopted a strategic approach (by using strategies to maximise marks) and even a surface approach (by ignoring parts of the text which they found difficult). They aimed to maximise marks and meet the task requirements without fully understanding the reading text. They ignored difficult parts of the text and summarised the parts they understood. In some cases this worked well and students achieved a good mark.
This complexity is difficult to fit into the deep/surface dichotomy, and this has led to the project holders questioning its usefulness in describing students’ approaches to learning on this course.
The results of this study suggest that students need time to develop the skills needed for a deep approach to academic study. Academics take many years to develop their skills and it would be expected that the case would be the same for students. The MW course, with its emphasis on understanding mathematical theory, may help students to begin to develop their skills and during this development, it would be expected that students vary their approaches to learning. It was concluded that the elitist value placed on a deep approach to learning, and the disparagement of a surface approach, is not helpful in furthering understanding of how learners acquire the skills needed for a deep approach to learning in an academic context.