Real-life maths solutions
Mathematics is used in thousands of ways in the "real world", and teachers are always trying to incorporate these examples into their teaching in order to show pupils the usefulness of the subject.
Unfortunately, once you leave the basic level activities, such as checking the milk bill or measuring for a new carpet, you meet situations in which the mathematics is the least understandable part of the problem. It is then all too easy to oversimplify so much that solving the problem becomes pointless, or the pupils feel patronised.
The real-life situations have to be interesting in their own right, or pupils will rightly argue that since, for example, they are extremely unlikely to be actuaries, there is little point in calculating mortality tables.
This pack from BT manages to avoid some of these hazards, but is not entirely successful in relating mathematical techniques to solving real problems. It is intended for pupils at key stage 4 or bands 1 to 3 in standard grade mathematics. There are nine assignments which have been tested with students in the target age range and each is estimated to take around 20 minutes.
The basic situation is that a new telecommunications link is to be built between the UK and Holland. Four different companies, each using a different technology, are bidding for the contract. Students have to consider the design problems and the costs of each technological solution.
Very few teachers will know much about co-axial cables, terrestrial microwaves, satellite microwaves or optical fibres, but there is a good glossary and the technology is only given in such detail as is necessary to understand the problem. There is also an interesting short history of telecommunications which provides further information.
The mathematics used includes graphical techniques, estimation, use of formulae, and standard form. The layout and presentation are good, but inevitably students have to wade through a good deal of written information setting the problems in context and explaining some of the terms before they can get down to doing some mathematics. For example, in the section on submarine optical fibres, I found my attention wandering when faced with a page full of statements such as "attenuation for monomode fibres at a transmission wavelength of 1.55 microns is 0.22 decibels per kilometre . . ."
Given that the author works for the Satellite Project in Dyfed, it is perhaps not surprising that the section on satellite microwaves is the clearest to follow.
Teachers will find some of these assignments useful as the basis for coursework or as supplementary material in their work schemes, but careful selection and adaptation will be needed.