Dick Evans is concerned that functional maths will go the way of so many other initiatives in mathematics
A new term has appeared on the educational landscape namely functional mathematics. But has it been used before? Will it require a set of unique and radical solutions? I ask these important questions having witnessed a series of worthy reforms in the past which have inevitably regressed into narrow incremental tinkering with existing approaches and subjected to political dogma and interference. One immediate problem is how functional mathematics is defined. For example, is it the mathematics that all people need to participate more effectively in the workplace and in everyday life?
The concept of functionality in mathematics is essential if this country is to begin to address a series of fundamental weaknesses in this key strategic discipline in all its forms – whether it is numeracy, financial literacy, pure and applied mathematics.
Keepin’ it Real
The teaching of, and the subsequent learning of, mathematics in specific contexts that are rooted in real work and life situations is seen to be more motivating, more interesting, more realistic and most importantly, renders the content more relevant to learners. These characteristics if demonstrated by knowledgeable teachers supported by good learning materials do make a lasting and positive contribution to mathematical capability. Teachers who have taught vocational programmes post-16, for instance – such as hairdressing, construction and horticulture-have long realised the real challenges presented to them and the learners in making the mathematical content ‘come alive’. These learners from previous experiences have sadly developed deep-seated negative images of mathematics and are very often reluctant and resistant to see the relevance of any aspects of it in their intended careers. However, if the teacher can make them see the relevance of the subject in a work context their approach does improve. You only have to talk to employers about the current view of mathematical understanding in the work place to realise the critical state we are in. One important plus for functional mathematics is that it appears to satisfy employers’ needs. These concerns about mathematical ability at work are across the whole spectrum from basic mathematical/ arithmetical skills in society to the work place in all its aspects and levels including university entrants. The idea of functional mathematics must include not only learning and applying skills but must also be about life skills that will become increasingly important for all adults in the future both in their work and as citizens.
Too many Cooks?
Following the announcement to introduce functional mathematics as part of the 14 to 19 curriculum numerous conferences, seminars have been staged and a number of working groups e.g. Qualifications and Curriculum Authority (QCA), Advisory Committee on Mathematics Education (ACME) and awarding bodies have been established to inform its purpose, structure and scope. Inevitably a wide range of issues have been identified and significant differences of opinion and views have already emerged. The majority view is that they think they know what functional mathematics is but currently cannot define it. This I feel is the result of previous practice and existing understanding. In order to realise its basic intentions functional mathematics requires new models particularly on assessment regimes, delivery and content that is about application of mathematics in different work and life contexts. Otherwise this important initiative will join others mirroring current models and lead inevitably to its failure to impact on capability.
Parity of esteem
Some of the critical issues are associated with the levels to be addressed. The initial view from the government was it should be at levels 2 and 3 and a subset of mathematics and a GCSE:’The theme of functional mathematics must not be put in a box – ‘like a subject’ – but fully integrated across the various topics identified within it but equally important across the other subjects the learners are studying.’ If alternatively the narrow view prevails and it is ‘boxed’ it would create a second-class qualification and reflect and reinforce the negative view of vocational subjects. Curriculum reform is littered with worthy attempts to establish parity of esteem between the so-called academic and vocational subjects/programmes e.g. TVEI, GNVQ. Sadly in spite of all the positive expectations about functional mathematics, it could so easily result in failure. Functional mathematics is a necessity across all levels – it is as appropriate for university learners as it is for level 2 learners. The techniques, application and processes associated with the subject such as problem solving, number, data handling, statistical methods, estimation etc are universal and transferable with increasing degrees of sophistication throughout employment and life. These and other essential techniques will assist people to manage and understand the implications of many of their decisions in life and the work place.
One of the greatest challenges and critical dimensions of introducing the subject is the way the different contexts are defined as it is very much about preparing learners for work. To this end employers must be involved at all stages in its development. Functional mathematics could also form part of CPD programmes for employees and be an excellent example of learning at work. Equally important the learners must be consulted widely at this critical developmental stage. Unfortunately employers have inevitably been involved very much as a form of tokenism in past curriculum reforms and sadly little meaningful research has been conducted into work-based mathematics and this has led to a general level of disenchantment and misunderstandings between employers and educationalists. Learners, ordinary adults who are the target of numeracy initiatives, are rarely involved in such developments.
ICT will most certainly figure significantly in functional mathematics and be an essential feature in its design and delivery as the technologies figure more in every day activities. ICT will motivate and will also allow the learners to explore more independently the applications of mathematics in different contexts.
In order for functional mathematics to succeed and realise the intentions of its proponents it must:
- Not become a subset of mathematics, a GCSE or a subject in its own right
- Not be just at level 2 and 3 but span all stages and be a continuous and a long-term thread of the curriculum.
- Receive adequate funding underpinned with effective teaching and learning resources including ICT
- Ensure that staff involved receive appropriate ongoing training
- Ensure that employers and other key stakeholders including the learners are involved at all stages of its development- it must not be high-jacked by the educational and political communities
- Be integrated across the other topics within the theme of functional mathematics as well as across other subjects that the learner is undertaking
- Also be part of employers’ CPD programmes as an example of learning mathematics at work.
ACME is currently planning a major conference in October 2005, which will focus on functional mathematics. Let us hope it begins this debate.