Questions continue to be raised about the teaching and learning of mathematics in schools and colleges and the relative levels of participation in the subject post-16. Questions continue to arise about its purpose and centrality in the schools national curriculum and the introduction of functional mathematics in vocational awards. In addition, concerns are being raised about the quality and quantity of students entering further and higher education to study courses that require mathematics.
We live in a technologogical society based on mathematics and science, so it is perplexing that schools, colleges and universities continue to turn out students in large numbers who not only lack adequate mathematical and numeracy skills but also the students constantly state that the subjects are boring and irrelevant. There surely needs to be a vigorous national debate, on ways to tackle this complex and multidimensional problem.
Hopefully these debates will once and for all establish a consensus about these problems with the subjects and how to resolve them. Equally importantly is the urgent need to recognise and identify the problems associated with these subjects in the workplace. Work-based mathematics and numeracy are too often overlooked and neglected when reviews are carried out. Meaningful research on mathematics and numeracy in the work place has been minimal and as a result there is a dearth of evidence and even then scant attention paid to what the real issues are.
Towards a new lexicology
This situation is partly explained by the fact that clear understandings of the factors and determinants involved in work based mathematics and numeracy have not been established. It is also essential to develop more precise definitions of the various elements involved. In any research there is a requirement that a precise lexicology is developed and adhered to. These requirements are important given the different mathematical and numerical skills and competences that exist in different work place situations e.g. health professions, process plant operations, retailing/distribution, construction crafts etc. Key questions need to be answered including:
· What mathematical and numerical skills are important in each identified work situation and how best are these identified?
· What attitudes towards numeracy and mathematics need to be developed and encouraged by employers, employees, parents and teachers?
· How best can these subjects be taught and learnt in traditional classroom situations and how important is the context in which teaching and learning takes place?
· How does the context of numeracy and mathematics in the workplace become formalised in order to bring about an identification and understanding of the kind of skills that are needed in a given setting?
In the limited research on numeracy in the workplace, the lack amongst many emplees of ‘a feeling for number’ has been highlighted as a problem. It would seem that the school curriculum particularly at primary level has paid little attention to this extremely important element and it remains to be seen if the numeracy strategy will bring about a sustained and lasting improvement. The inability to manipulate and understand the fundamental operations associated with number creates later problems irrespective of the ultimate aspiration of the learners. For example, the inability to estimate and transpose numbers and equations makes for fundamental difficulties later.
Too often in the past, reforms to the mathematics curriculum diluted these essential building blocks for numeracy skills. An illustration is given in the classic book by Jan Gullberg (1) in the following quote:
‘In the 1950s educators and reformers introduced the language of sets as a basis for mathematical studies in schools. Many pupils started studying sets before they could count the number of elements in the sets. The language of sets and the surrounding ‘New Maths’ created chaos in schools in the 1950s, 60s and 70s. It was a frustrating time in education. Strange symbols were introduced for seemingly simple things: teachers had to be retrained and most parents had no idea what their children were doing in mathematics.
The concepts of set theory are simple, but they require a precision and maturity of language that is beyond the power of many learners. An idea that was meant to simplify in fact complicated matters. A dull but useful drill was replaced by a dull and useless drill. In England and many countries the New Maths created a generation with sometimes very limited arithmetic skills’
This long but helpful and insightful quotation highlights an important issue in the wider debates on work based mathematics and numeracy namely the essential need to lay the foundations of these important subjects. The relevance and fitness of purpose of the school/college mathematics content needs to match the future needs and aspirations of the learners.
This is important, as the young adults leaving these institutions will enter a wide variety of work situations and occupations that will in turn require varying degrees of numerical and mathematical skills and competences. Careful thought and analysis is needed to identify and then introduce the appropriate content at the right time into the curriculum.
The role of employers.
Clearly there are fundamental elements that all learners require to learn but with the necessary differentiations that reflect their ability and career intentions. It must be accepted that very few will study mathematics to any depth whilst the vast majority will require a basic foundation and grounding in numerical skills and mathematical techniques in order to cope with the needs of chosen occupations. The curriculum needs to be configured to recognise these demands and at the same time excite and stimulate the learners whatever their needs.
One real challenge for the curriculum reformers is the fact that the whole curriculum is by definition restrictive, arising from the necessity of including other key curriculum subjects whether in the core offer of in course options. The expectation that numerical skills and mathematical techniques taught in schools and colleges should be capable of satisfying the total needs of the learners whatever their career intention is absurd. Thecontent must be seen as relevant and be significantly informed by employers. Employers must be involved in assisting the identification of what is required in their particular work place. Sadly to date this essential element has been lacking. The primary challenge is to provide the necessary grounding to the learners both those starting work and equally important for those already in work.
The recent farce surrounding the introduction of functional mathematics again highlights that there is still a long way to go before the problems with the teaching and learning of work based mathematics and numeracy are resolved.
Let us hope there will be along and meaningful debate of this strategically important topic.
(1) Gullberg J. ‘Mathematics from the Birth of Numbers.’ Norton and Company. 1997.