A sound education in mathematics, both for the mass of ordinary pupils and for the mathematically more able, is important for any modern economy. This has been well-argued elsewhere (e.g. Dainton (1968) [5], Cockcroft (1982) [3]). Here we draw attention to the following points.
In an increasing number of areas of science, technology, management and commerce, mathematics is the only effective language for the analysis of problems and for the communication of results and ideas. If our ordinary school leavers do not achieve a level of fluency in this language comparable to that in other countries, Britain will be at a considerable disadvantage. In addition, if our more able students lag behind those in other countries, British graduates will be unable to keep up with developments in their fields. We will then become ever more dependent on other countries for inventions, specialists and products.
Mathematics is now important in many areas where it has not previously played much of a role (these include biology and the social sciences). Mathematically based techniques are increasingly used in the workplace, and have transformed the way decisions are made and the way business is done (for example, in stock control, in scheduling, to improve industrial design, to achieve reduced energy consumption, to increase efficiency, and to reduce manufacturing costs). Before implementing new regimes it is frequently necessary to construct mathematical models of processes or operations (prior to subsequent computer simulation and analysis). If specialists, despite their training, do not fully understand the principles underlying these models, or the conditions limiting their validity, their advice will leave decision makers vulnerable in unintended and unpredictable ways. Some people have mistakenly concluded that the increased availability of computers reduces the need for mathematics: in fact the very opposite is true. Computers make mathematical techniques readily available to many who might previously have never thought of using them. The user does not need to understand all the details of the associated software, but a basic understanding of elementary mathematics is crucial if the output is to be used wisely and critically.
The pace of change in technology is increasing. In order to be able to adapt to new technologies and techniques, people in a variety of fields need to undergo periods of retraining throughout their working lives. Such retraining often presumes a significant element of basic mathematics. Some things have to be learned when young, and basic mathematics would appear to be one example. If the proper mathematical foundation has not been laid during adolescence, it becomes increasingly difficult to address these weaknesses in later life. The attempt to confront these shortcomings during retraining in later life is wasteful, painful, and usually only partly successful.
The mathematics used today was developed in earlier times --- sometimes centuries ago, sometimes relatively recently. Much of the theory required was developed not by users for practical applications, but rather for its own sake by research mathematicians. Modern examples include the application of chaos theory to studies of turbulence, number theory to cryptography, and abstract algebra to error correcting codes. The notion that mathematics is of interest in its own right must be made clear within the curriculum. It follows that there should not be an insistence on all problems being presented `in context' --- simple arithmetic questions on fractions should not automatically be translated into problems about dividing pizzas.
The primary concern of scientists, engineers, and other potential users of mathematics is likely to be whether their students or employees can reliably perform certain basic routines. It has therefore not always been easy to convince them that one of the most important things that mathematics has to offer the mass of pupils is that of an intellectual training for the mind. One of the striking consequences of the current widespread concern has been the realisation by many engineers and scientists that this kind of preparation has been perhaps the most significant loss in recent years. This was part of what was meant when the working group was told by a leading figure from the Engineering Council: ``What is missing is the idea of mathematics as a precise analytic tool''.
The fundamental importance of mathematics is well summed up in the assertion by a Fellow of the Royal Academy of Engineering that ``The one thing that would most help recruitment to engineering is better mathematics teaching in schools''. Students appreciate the key role of mathematics in such subjects as physics and engineering and are often deterred from following them because of inadequate mathematical preparation.
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