14-19 Level Three Engineering Diploma

The origin and purpose of the additional mathematics module

Engineering bridges the so-called academic-vocational divide because it applies scientific principles in order to create something which has never previously existed. But in order to apply these principles, it is essential in all but the most trivial of cases to quantify the scale of the components to be used, be it the depth of a foundation, the resistance of an electrical resistor, the thickness of the wall of a containment vessel…..and so on.  Such quantification requires us to be able to handle numbers confidently and, in this increasingly competitive world, to optimise the resulting design. This usually means forming equations which can then be manipulated in order to yield some desired optimum result…..the lightest, the longest, the fastest. Mathematics is therefore a key requirement in the creative process; it has been rightly called the language of engineering.

Leonard da Vinci’s designs, so beautifully drawn in his notebooks, are notorious for being difficult or even impossible to manufacture. Why? The mathematics of his day was simply inadequate to provide him with the tools he needed to turn his creative genius into practical reality. By the time Isambard Kingdom Brunel came along, however, the mathematical tools were available, enabling him to use his equally extraordinary genius to design real structures.  

There is thus a need for all potential engineers to be reasonably fluent with mathematics. However, mathematics can be a demanding subject if treated as an intellectual exercise without the incentive of practical applications; it is best taught in an applied context. When the first indicative curriculum for the new Engineering Diploma was published in the spring of 2007, many engineers in higher education were concerned that the mathematics contained within the mandatory core (i.e. the Principal Learning) was insufficient in order to prepare those taking the diploma for entry to engineering degrees irrespective of their other qualities. It was therefore decided to propose an additional module which could be taken as an optional element (in the Additional/Specialist Learning) to meet this need.

Many universities mount special foundation years to prepare students lacking the traditional entry requirements to meet the needs of the first year of their engineering degrees. Loughborough University provides such a course which has stood the test of time and enabled significant numbers of students to complete successfully subsequent degree courses, with outstanding results in a number of cases. The mathematics from this course was used as the basis for the proposed module. However, given the nature of the new diplomas, it was also decided to explore how to build in as many examples of actually applying the mathematics as possible. It has been agreed that each discrete mathematics topic in the new module will be accompanied by an exemplar giving one or more examples of exactly how that particular mathematical manipulation or transformation is used to help create a real product. Each of these exemplars will be illustrated by the activities of a relevant industrial company – JCB for a mechanics example based on the design of the arm on an earth moving excavator, Rolls Royce for a thermodynamics application within a jet engine…..etc.

Growing concern has been expressed over recent years that even those students passing Mathematics at A Level with a high grade do not necessarily possess the mathematical facility and particularly fluency of their predecessors, and struggle on engineering degree courses. Many in higher education believe that this arises from the rather abstract way that mathematics is taught in some schools…..not surprising given that few teachers have worked as engineers. Engineering Diploma graduates could therefore have an advantage over traditional A level students when entering university if their mathematics is well grounded in applications from day one. The suite of practical exemplars built into the new mathematics module could even serve to enliven A level teaching and thus help to arrest the perceived drop in mathematics ability of many first year engineering undergraduates.   

FJM  19.11.’07.