JEL Classification: A22, C02
PsycINFO Classification: 3530
FoR Code: 1302; 1502
Years of lecturing mathematics and statistics and researching student learning allow lecturers at university to gain some knowledge about the many difficulties students freshly coming into universities and adult learners coming in later years, experience while learning mathematics. The non-routine task of lecturing first year students to supervising to their doctorate completions especially from widely different disciplines allows lecturers to comprehend more deeply student learning and understanding of procedures and concepts in their respective fields. In this way, university lecturers are researchers on the job and thus gain a deeper understanding of student prior knowledge as well as their ongoing university learning experiences. It seems that mathematics lecturers see greater numbers of students from a wide variety of course programs in universities for mathematics is a compulsory course for many programs, although this point may be debatable. In the author's experience this large pool of students allow math lecturers opportunities to observe more critically different student learning behaviours as many clearly find mathematics difficult and in many cases students believe mathematics to be a useless field of study and not applicable to their immediate life or their careers more generally. The "difficulty feature of mathematics" provides lecturers opportunities to learn about student prior math experiences, their understanding of concepts, their self-beliefs; the author claims perhaps more so than other disciplines since students complain more about their mathematics learning than many other courses (Tularam, 2013). The many types and expression of concerns with mathematics often exposes students' inadequacies. The author believes that from such a rich data base of experiences, mathematics lecturers may be able to provide significant insights in the progress of tertiary students in different disciplines especially those that require mathematical insights in their applications (Roca and Tularam, 2010; Tularam, 1997, 1998, 2002, 2011, 2013; Tularam et al, 2010).
Although a mathematician, the author's case is special in that he has had added opportunities to teach mathematics to finance students for a number of years; teaching courses such as risk management, time series, forecasting and financial modelling and stochastics and Ito calculus. In addition, the supervising of higher degree postgraduate students in finance, including those graduating with doctorates in mathematical finance have allowed the author significant opportunities to observe student learning throughout their university life till achievement of their highest education. The rich experiences gained over time has allowed the author access to deeper understating of students of finance in terms of their mathematical needs; that is, in terms of their capabilities and as well as their gaps or misconceptions in learning and understanding. This research paper is a reflective analysis from a rich data base of research experiences that may provide possible ways in which gaps in student learning may be filled in finance disciplines so that students may with understanding apply various mathematically based financial tools. Although such an analysis can be undertaken for other disciplines, this paper is focused on finance, and the analysis and research are qualitative, and based on a reflective analysis of student interviews and documented comments, A critical analysis is also presented regarding higher order mathematical thinking and its importance in financial studies.
The first part of this paper presents incoming student reflections from those thinking of taking up finance as a degree course followed by analysis of student experiences regarding their learning at the undergraduate and higher degree levels. A brief historical perspective is then presented on the influence of mathematics both in procedural and the more-deeper critical finance issues that itself has initiated a live and productive research area for mathematicians and in some cases propagated real advancements in higher mathematics itself. …