Do Engineers Need Math - Essay Example

Introduction Modern business and industry, the esteemed engineering profession and the dignified field of mathematics are all functionally integrated given the fact that they use and serve each other to excel and perform their respective functions. Business establishments hire engineers or technocrats for maximizing profits and engineers employ the skills, tools and logics of mathematics ensuring satisfactory delivery of goods & services necessary for profits. Along the years, all aspects of business as well as the domains of engineering and mathematics have undergone series of changes [1], refinements and up-gradations in terms of value, utility, efficiency, applications and approaches. This situation saw rise in demands for engineers and at the same time highlighted the urgency for supplying more engineers for meeting the demands [1] and most importantly called for enhancing the knowledge base and skill-sets of the modern engineering students so that they are well prepared to fit into their envisaged future role as dynamic professionals capable of performing in diverse and multi-functional platforms under changing business environments [2]. The business sectors and the engineering education system shifted emphasis towards quality management practices and practical learning curriculums [3] respectively, adapting to the emerging market conditions and undergoing value additions in the process. Mathematics too, saw some innovations and got embedded and transformed into user-friendlier computer programmes and tools [4] but notably, this advancement was restricted and available only to the upper stages of the education cycle and unfortunately failed to spread throughout the entire system [5]. The subject of mathematics, precisely classical or conventional mathematics, happens to be regarded as a difficult and complex subject meant only for few extra caliber peoples [6] and this deep-rooted perception gave rise to a fear (called the 'mathematics problem' or 'mathematics phobia') discouraging learners of all levels (primary, secondary, higher and advanced levels) from taking up and putting their hearts into the study of mathematics [7). This phobia is a reality, which propagates limiting the mathematical knowledge base and skills of numerous pupils throughout the world ultimately stagnating the overall progress of the institution of conventional mathematics. This erosion in knowledge of a subject whose proficiency has proved to capacitate or facilitate understanding of almost all other subjects [6, 7], is definitely a 'social handicap'. Moreover, many research studies have confirmed that this 'mathematics problem' also has cross-subject effects. Generally, engineering is considered to be a complex and mathematically-rich domain [8] and as such faces the menace of the mathematics phobia. Reductions in enrollments and first-year abstractions in engineering education has become a common phenomenon in various countries including UK and the USA [6]. Following the growing status and demands, many aspiring students join engineering courses only to pull out at a later stage fearing the mathematics involved in such courses. There are various societal, financial and attitudinal reasons for abstractions and non-completion of engineering education [6] however, the distaste for mathematics is found to be a dominant reason in recent years. Under all these circumstances, loosing budding engineers to the mathematics phobia has become a concern big enough, questioning the utility or necessity of the mathematics embedded in engineering education. A number of research studies have been carried out during the last decade for assessing the impacts of the mathematics problem and providing appropriate solutions for controlling abstraction in engineering education and boosting supply of skilled engineers. This paper presents a broad and complete picture of the dynamics, advancements and functional inter-links of engineering and mathematical studies. Objectives This study aims to re-search and review the emerging trends and transformations in the field of engineering and mathematical studies and finally assess the compatibility and relevance of mathematics, if any in the diverse and enhanced functions of modern engineering. The dynamics of the 'mathematics problem', shifts in engineering degree enrollments and other emerging market implications have been critically explored here for arriving at an unbiased opinion on the all important issue, - 'whether modern engineering needs mathematics any more'. Engineering & Mathematics - Emerging Trends & Transformations As sectors of education, both engineering and mathematics occupy dignified positions on their own rights. Any branch of knowledge like engineering and maths, essentially exist in two broad levels or forms- educational or academic levels and professional or practice levels. Engineering is a very dynamic stream having a complex academic level and very broad and undefined professional level. This implies that engineering students with their academic knowledge land into more broader and challenging job environments or practice levels where they may require added skills and expertise. On the other hand, mathematics has methodological and numerically intensive drills in the academic levels and it's on the job or practice level is perceived to be a tough and less enterprising one. Interestingly, at a higher academic level mathematics transforms into more user-friendly and powerful computer embedded softwares and programmes, a land mark transition which is also known as advanced interactive computing. However, this advancement was restricted and available only to the upper stages of the education cycle and unfortunately failed to spread throughout the entire system [5]. Figure-1: Growth in Engineering Jobs [1996 vs. 2006 (projected)] (Source: Science & Engineering Indicators) Thus, along the years the domains of engineering and mathematics have undergone series of changes [1], refinements and up-gradations in terms of value, utility, efficiency, applications and approaches. This situation saw rise in demands for engineers (figure-1) and at the same time highlighted the urgency for supplying more engineers for meeting the demands [1] and most importantly called for enhancing the knowledge base and skill-sets of the modern engineering students so that they are well prepared to fit into their envisaged future role as dynamic professionals capable of performing in diverse, broader and undefined platforms where they are expected to land up in the professional stage. The business sectors and the engineering education system slowly shifted emphasis towards quality management practices and practical learning curriculums [3] respectively, adapting to the emerging market conditions. Figure-2: Students specifying hardships for Maths & Science [2004] (Source: Science & Engineering Indicators) On the other hand, classical or conventional mathematics, happens to be regarded as a difficult and complex subject (Figures-2, 3) meant only for few extra caliber peoples [6] and this deep-rooted perception gave rise to a fear (called the 'mathematics problem' or 'mathematics phobia') discouraging learners of all levels (primary, secondary, higher and advanced levels) from taking up and putting their hearts into the study of mathematics [7). This phobia is a reality, which propagates limiting the mathematical knowledge base and skills of numerous pupils throughout the world ultimately stagnating the overall progress of the institution of conventional mathematics. Modern students exhibit comparatively poor average performance in simple numerical mathematics, Cartesians, vectors, matrix, etc. as shown in Figure-3. Figure-3: Average Problem Performance of Students (Source: Mathematics in Engineering, Gergana Bounova, MIT) The above are results from mathematical diagnostic quiz taken by 65 juniors. Questions were each worth two points, and are as follows. 1a: plotting complex numbers; 1b: conversion from Cartesian to polar coordinates; 1c: multiplication and addition of complex numbers; 2a: integration of a function; 2b: integration by parts; 3a: matrix-vector multiplication; 3b: calculate eigenvalues and eigenvectors of a second-order system. The 'Mathematics Problem' - Evidences & Engineering Links Already mentioned earlier, the phobia or fear for mathematics is very deep-rooted spreading from the lower primary levels of education to the higher doctorate & research levels. There are enough evidences of this menace in the undergraduate and engineering degree paths of education and it gets manifested as increasing abstractions in engineering enrollments, first-year non-completion of degrees and lowering average survival or continuation rate throughout the entire path of mathematical education. As evidences to these problems, real-life survey data gathered from various research studies have been presented below (Figures-4, 5,6 Figure-4: Average International Survival Rates in Engineering (Source: OECD Education at a glance, 2002) Figure-5: UK Dropouts in First-Year Engineering (Source: G. Cutler, Investigating UK Engineering, Hull Univ.) Figure-6: Interruptions in Studies in US & UK (Source: G. Cutler, Investigating UK Engineering, Hull Univ.) Conclusions & Recommendations Before taking part in the debate of utility of mathematics in engineering, it is very much necessary to consider the professional practice of the engineer against the academic progression of the engineer. In practice, a lot of mathematics is 'embedded' in the engineering but most of the time even the engineers do not mind to call the high-end software programmes they use are intrinsically modern or applied mathematics. Thus the transformed conventional mathematics, that is in the form of computer applications and programmes are basically the real tools of engineers. Therefore, we need some new models for mathematics, including the collaboration of engineers and mathematicians in new ways mathematical software (like Maple, Mathcad, Matlab, etc.). And, given this set-up, engineering courses may easily and increasingly welcome the wonders of embedded mathematics (computer applications) and progress fast in this route and if this is successfully done, there should not be any problems if the classical mathematics components of engineering curriculums are taken out replacing with the modern, efficient and user-friendly ones. Moreover, the approach of mathematics teaching in the pre-engineering academic levels require rejuvenations and appropriate refinements with the aim to make mathematics an interesting involvement thereby reducing abstractions and motivating students to put in their hearts in this subject at the same time. Finally, be whatever the situations and circumstances, we just cannot afford to get rid of the calibers of mathematics and let it perish because mathematics serves us with unparallel knowledge and wisdom. References [1] Otung. I, "Putting Engineering First and Mathematics Second in engineering Education", University of Glamorgan, August 2002. [2] Redfern Sam & caoimhin o' nuallain, "Increasing student retention and improving problem solving skills by engaging students with the use of new technology and pedagogy", Department of information technology, National university of Ireland, Galway,Ireland, 2005. [3] Claes Niklasson, " How Can Mathematics Support a Deeper Learning Approach in applied Engineering Subjects" Chalmers University of Technology, S-41296 Gteborg, Sweden, Said Irandoust. [4] [www.ltsneng.ac.uk],Presentation given at the LTSN Engineering conference on "Learning and Teaching Support and Resources for Engineers", Phillip Kent and Richard Noss, Loughborough University, 5 September 2002. [5] Presentation by Celia Hoyles, Chief Adviser for Mathematics "Increasing the Supply of Mathematics Graduates -What education is doing and what might it do". [6] John C. Hall, " Retention and Wastage in FE and HE", 2001. [7] Gavin L. Cutler & Susan H. Pulko, "Investigating UK Engineering Attrition and Countermeasures", The University of Hull, Department of Engineering. [8] University of Waterloo-"Performance Indicators 2005". ------ Read More