Stuff: What I do now - an essay on 'functional' maths

First off - don't panic, I haven't done this for fun (it's part of a course), but feel like sharing it as it's what I attempt (sometimes forlornly) to do now...

Before discussing the role of mathematics in today’s world, let us briefly look at its historical and cultural development. The needs of mankind over time are directly correlated to the development of mathematics. From helping develop concepts of time, dates and distance, to early trade and commerce, mathematics has been a fundamental necessity. The first known example of mathematical symbols was found in Africa on a bone which dates from around 35,000 years ago, and therefore pre-dates the written language by thousands of years (Learner.org, 2011). It has a series of tally marks which may represent simple counting. Another bone, now known as the ‘Ishango bone’, dated to 25,000 years ago, has groups of markings, some of which represent prime numbers. The precise use for this bone is still being debated but it was possibly used as a lunar calendar, and proves that mathematical concepts, and possibly prime numbers, were being used as early as 23,000 BC. The early twentieth century saw the astonishing underwater discovery of the remains of a small bronze analogue computer, built by the Greeks and dated to the year 87 BC, and known as the Antikythera Mechanism. It is thought to have been used to calculate the movements of stars and planets in astronomy, and to make astronomical calculations and predictions. Technological artefacts of similar complexity and workmanship did not reappear until the 14th century.

Trade and commerce in ancient times necessitated the need for arithmetic in order to count goods – to record what was sold, bought or bartered. The first recorded teaching of addition, subtraction, multiplication and division was by the merchants of Venice so that they could expand their commercial influence (Swetz, 1987). The surveying of land would naturally have led to mathematical concepts of geometry and trigonometry, being practised thousands of years ago, whilst circles and their properties would have been studied during the construction of arenas and water tanks. This led to the discovery of the properties of shapes and solids, formulae for area and volume and to the classification of curves and shapes. Early algebraic problems could have been practical ones such as calculating logistical needs, allocating resources and also working out areas and volumes.

In the past, it was not seen as important to have a numerate society as a whole. Maths was the domain of mathematicians, and the subject, for most, gladly left behind at school (or never learned at all). Mathematics as a common demand and need, however, can be seen as a product of industrialisation, and particularly, post-war globalisation. The fast development of technology, the proliferation of computers and the development of the internet over the last twenty years have led to a huge abundance of data: information that needs to be read, understood and interpreted by a large proportion of the population.

In today’s world, good levels of basic numeracy (and literacy) are particularly important for any nation that expects to compete in the global economy. In the last thirty years this has led to a drive to improve the levels of everyday numeracy so that the largest possible number of people can function in society and be able to do things such as plan journeys and read and write timetables, and read and understand the meanings of graphs, statistics, data, percentages, finance, tax and insurance. In Britain, practical numeracy skills were described by the Cockcroft Report (‘Mathematics Counts’,1986) as those mathematical skills that ‘enable an individual to cope with the practical demands of everyday life.’ It was becoming increasingly apparent that the levels of basic mathematics at home (and in many other developed nations) were simply not good enough if Britain was to compete in an ever-changing, high-tech, ‘global village’ world. This report was commissioned because of ‘the apparent lack of basic computation skills in many children, the increasing mathematical demands made on adults, the lack of qualified maths teachers, the multiplicity of syllabuses for old, new and mixed maths, the lack of communication between further and higher education, employers and schools about each group's needs and viewpoints…' (Cockcroft Report, 1986).

The outcome of this report and other similar commissions such as the Moser Report (1998) led to National Strategy for Adult Basic Skills and the development of the National Core Curriculum and such qualifications as Key and Functional Skills – these included mathematics courses that addressed the real, everyday world.

The Moser report also acknowledged that their recommendations, designed to improve basic levels of numeracy, were easier said than done (Lifelong Learning, 2000): ‘There are inevitably problems of motivation among prospective learners. This is partly because people with difficulties are often understandably reluctant to acknowledge, or are unaware, that they have a problem; or that it matters or indeed that there are ways of tackling it. Moreover, few employers take a constructive approach to advancing basic skills in their workforce.’

Even though much work has been done and thousands of people have improved their numeracy skills over the past two decades because of a national strategy, mathematics is still a taboo area for many people. Low levels of numeracy can be exacerbated by poor public perceptions of mathematics. Both employers and employees can be very insecure – an insecurity often brought about by poor experiences of maths lessons at school. There are plenty of well-educated and well-paid people out there who may be virtually innumerate, or who avoid careers or tasks that may involve mathematics, however basic. So the push to improve levels of numeracy has also had to improve people’s confidence in it, so that they can make effective use of whatever mathematics they have already learned, and so that they can then appropriately use numeracy to whatever level that suits their circumstances. A related finding is the perception that numeracy is not as relevant as literacy – and this view is sometimes held not only by learners but also by some vocational teaching staff. Even some managers and employers are reportedly not as concerned about numeracy as they are about literacy and communication skills (QIA Skills for Life Improvement Programme – Numeracy Overview, 2008). Therefore all the barriers experienced by would-be learners of numeracy may be the same for teachers – fear, anxiety, low priority, perceived irrelevance, lack of time and commitment and negative school experience.

It is again worth pointing out here that learner motivation can be aided by addressing the issue of poor public perception and by linking mathematics to life and work in general. If the maths involved is useful in a practical way and can be seen to help job-seeking opportunities, then it is far more likely to be seen to be beneficial and be tackled in a positive way.

It is also quite clear from research that innumeracy can be closely linked to other social issues. To illustrate this point The Moser Report used this example: ‘Some 60% of people in prison suffer from functional illiteracy and/or innumeracy.’ (Lifelong Learning, 2000). The Programme for International Student Assessment Report of 2006 (PISA Report) stated that: ‘With the growing role of science, mathematics and technology in modern life, the objectives of personal fulfilment, employment and full participation in society increasingly require that all adults… should be mathematically, scientifically and technologically literate.’

The point is clear. Being confident with basic mathematical concepts may not only improve chances of employability, but also aid personal development. A better educated, numerate person may also be a more confident, rounded, contented person. Boris Johnson, the Mayor of London, recently claimed that a ‘systemic fight against educational underachievement can tackle the social exclusion that lay behind last summer's riots’ (The Guardian, 23^rd March 2012). The implication is that if people feel socially excluded, then they will feel that they have no future in society. Achieving at maths (and English), at any level and at any age, can help a person believe that they do have a future, that this may help them gain employment and find a place in that society.

Johnson went on to directly link poor basic skills to social unrest, and therefore by proxy to low self-esteem, by arguing that tackling illiteracy and innumeracy was the best antidote to the ‘nihilism’ and ‘exclusion’ revealed by the riots. The challenge is therefore to encourage learners to realise that learning and becoming adept at practical numeracy can help their personal development for a number of reasons, and not just economic ones. This is why The PISA Report (2006) states that ‘deficiencies among lower-performing students in mathematics can have negative consequences for individuals’ labour-market and earnings prospects and for their capacity to participate fully in society.’

Furthermore, learning Functional Skills mathematics requires a problem solving approach, and the skills required for problem solving are in turn more than a vehicle for teaching and reinforcing mathematical knowledge and helping to meet everyday challenges. They are ‘skills which can enhance logical reasoning. Individuals can no longer function optimally in society by just knowing the rules to follow to obtain a correct answer. They also need to be able to decide through a process of logical deduction what algorithm, if any, a situation requires, and sometimes need to be able to develop their own rules in a situation where an algorithm cannot be directly applied. For these reasons problem solving can be developed as a valuable skill in itself, a way of thinking rather than just as the means to an end of finding the correct answer (NCTM website).

This gives teachers of mathematics a social responsibility and the task of encouraging their learners to realise the wider implications and to help them to realise their own potential. This may involve serving a wide range of student abilities and include those who are motivated and who may perform well, to those who are apathetic and indifferent to mathematics and who may be most in need. With the help of governmental public policies (as already mentioned above), appropriate institutional support and good professional practice teachers can contribute to providing equal opportunities, equitable learning and personal development outcomes for all students.

Bibliography

Bartlett, S. & Burton, D. (2003) Educational Studies: Essential Issues, London: Sage Publications Ltd

Curzon, L.B. (1997) Teaching in Further Education, an Outline of Principles and Practice, 5th Edition, London: Continuum Education

Frank J. Swetz, Capitalism and Arithmetic. Peru, Illinois: Open Court, 1987.

Official Publications

PISA Report, 2006: Science Competencies For Tomorrow’s World. Volume 1: Analysis. OECD Publishing. Available at:

www.oecd.org/pages/0,3417,en_32252351_32236191_1_1_1_1_1,00.html

(accessed 27-3-12)

QIA Skills for Life Improvement Programme, 2008 – Numeracy overview. Available at: sflip.excellencegateway.org.uk/docs/DA_numeracy_briefing_for_Rob_Pheasant_NC_70908.doc · DOC file

(accessed 27-3-12)

Wilfred H. Cockcroft, Mathematics Counts. London: Her Majesty's Stationery Office, 1986

Electronic References

Antikythera website. Available at:

http://www.antikythera-mechanism.com/

(accessed 11-5-12

Education England website. Available at:

http://www.educationengland.org.uk/documents/cockcroft/

(accessed 22-3-12)

Learner.org website. Available at:

http://www.learner.org/courses/mathilluminated/units/1/textbook/01.php

(accessed 27-3-12)