1. Introduction

This chapter is the result of conversations between the various authors about how to raise awareness among undergraduates about what research entails, and what support could be put in place to facilitate the development of those skills needed by researchers in mathematics and maths-related fields. We carry out a brief review of non-subject-specific research about transitioning to postgraduate education. We then suggest some strategies for engaging undergraduates, postgraduates and academics in a partnership intended to develop their subject-based research and enquiry skills, grounding their understanding about what research is and what researchers do from early on in their studies.

2. The current postgraduate transition landscape

Research suggests that the transition to postgraduate study deserves the same attention as that of the transition to undergraduate. In their project involving focus groups with 30 members of staff and 41 postgraduate students, and five in-depth individual interviews with postgraduate students (one PGCE, one MA, one MBA and two PhDs) at Greenwich University, Alsford and Smith (2013) found that postgraduate students want recognition that their study level is different and that their transitional needs are as valid as those of undergraduates. Indeed, there is a growing body of research into Masters and doctoral students’ that acknowledges that these students have particular transitional needs. Preparedness for postgraduate life and study, communication and socialisation skills, staff and student training – these various issues are now being acknowledged by research, with some institutions starting to improve their policy and practice around postgraduate transition (Alsford and Smith 2013).

Researchers have suggested that a lack of focus on the transitional needs of postgraduate students reflected an assumption that students were (a) somehow already prepared for postgraduate study since postgraduate-level study is simply ‘more of the same . . . taken to the next level’ (O’Donnell et al. 2009, 27) or (b) already experts in the realm of higher education and learning, and so would not even acknowledge moving on to the next level of study as being a transition issue (Tobbell et al. 2010). Indeed, it was only when working on his Masters project that Adam, one of the PhD students contributing to this chapter, formed a clearer idea about what his PhD research was going to be like. Many students who decide not to complete a Masters degree would graduate with no insight or experience about the research process, and therefore unprepared for a workplace that requires them to confidently tackle and solve problems.

3. Making the transition: the student experience

Both Sebastian and Pedro, PhD students in Engineering, reflect on their undergraduate experience and how it contributed to and supported their development as engineers. Pedro works with optimisation under uncertainty, which has applications in many fields, for example modelling and design of processes. He believes that the knowledge and skills he developed through studying pure mathematics for the first two years of his engineering degree developed his enquiring mind, paying attention to details and asking lots of ‘what if’ questions. These skills and knowledge empowered him not only to understand the ‘theory behind the models out there’ but also ‘to go inside’ those models and adapt them for the problem at hand. In his view, current engineering undergraduates would benefit from being made aware that understanding the principles behind how models work can enable them to modify, adapt and customise the models ‘to work for them’.

Sebastian thinks that undergraduates’ learning could be made more exciting. In his opinion, undergraduate engineers find it difficult to engage with mathematics. They find it ‘dry’ and as a result are not really motivated to know more than the final equation that is needed for the application of a model. For this reason, Sebastian suggests that undergraduates could be shown what research entails: engaging creatively with the ‘dry maths’ to create and improve the models.

4. The importance of doing research

In this chapter we propose that engaging students in research and inquiry could and should be supported from early on in their undergraduate studies. In their report for the Higher Education Academy, Healey and Jenkins (2009) argue that all undergraduates students in all higher education institutions should come as close as possible to the experience of academic staff in carrying out disciplinary research. Indeed, the UCL Connected Curriculum aims to ensure that all students are able to learn through participating in research and enquiry at all levels of their programme of study. Moreover, Hathaway et al. (2002) found that those undergraduates involved in research were more likely to pursue graduate education and postgraduate research activity than students who did not participate in undergraduate research.

Through exposure to disciplinary research, all students will benefit from asking the right questions in the right way, conducting experiments, and collating and evaluating information. In the UK, most undergraduate students experience research as part of their final-year dissertation. For their dissertation, students choose a topic of interest to them, and such interest is mainly shared with the supervisor and the second marker, with no further dissemination of the outcomes of their work. Adam recounted his near struggle at the beginning of his postgraduate degree with reading maths papers. These papers tend to be quite technical and difficult to understand. But once understanding was achieved, Adam found that he needed to develop a habit of sitting back and trying to see the bigger picture, rising above the maths propositions, lemmas, theorems, etc., and understanding where the ideas fit in the maths landscape. Adam’s view is that this skill should and could be learned early on, at undergraduate level, through collaboration with peers and researchers.

Although academic mathematicians are well aware of the role of intuition in mathematics (Burton 2004), they may not address it explicitly in their teaching beyond linking it with problem-solving. Just as Burton (1999) pleaded with anyone who has responsibility for the learning of mathematics to model their own intuitive processes, to create the conditions in which learners are encouraged to value and explore their own and colleagues’ intuitions, Adam too thinks that ‘intuition needs to be explicitly taught’. He tries to develop intuition in the tutorials he teaches to undergraduates, as intuition could then be used and developed further in acquiring new knowledge.