Mathematics in Finance and Economics: Importance of Teaching Higher Order Mathematical Thinking Skills in Finance

Article excerpt

ABSTRACT

This paper addresses the importance of teaching mathematics in business and finance schools of tertiary institutions of Australia. The paper explores the nature of thinking and reasoning required for advancement financial or economic studies involves the use of higher order thinking and creativity skills (HOTS) for teaching in mathematics classes. The paper demonstrates how various skills required in finance are related to the mathematical way of thinking and reasoning. The 2007 global crisis has focused attention on financial thinking generally and mathematics teaching of finance in particular for the lack of skills by finance personnel. This could be addressed through student learning and teaching by reshaping business schools to include well designed financial mathematics courses that are compulsory, in degree programs. The mathematical reasoning patterns, thinking, explanations, simplifications required in transfer of knowledge to students is effectively taught if experts in the field are explicating or presenting proofs. The essence of the conceptual development of models and their assumptions and solutions requires training beyond those of the non-mathematics personnel, mainly due to their lack of years of time spent on such mathematically work. If the methodology described is adhered to our future business and finance students could be afforded a better educational experience in mathematical thinking and reasoning as well as higher order thinking and creative skills in their courses and degree programs.

Keywords: Financial mathematics; applied mathematics, higher order thinking (HOTS), mathematical reasoning, finance education

JEL Classification: A22, C02

PsycINFO Classification: 3530

FoR Code: 1302; 1502

(ProQuest: ... denotes formulae omitted.)

Introduction

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. …