Functional Subjects Particularly Mathematics

 ‘Experience plus reflection equals learning.’ John Dewey
This is a powerful and apposite quotation by John Dewey which resonates with many of the issues that arise when one is considering how to make the technical and vocational curriculum in schools and colleges more relevant and meaningful. Recently the term functionality has been introduced into educational and training jargon. In curriculum development functionality is equally as important as context to which it is closely linked especially in the teaching and learning of practical, vocational and technical subjects. The curriculum developers have adopted the term ‘functional subjects’ to ‘represent a set of learning experiences that provide people with skills and abilities in order for them to be more effective in everyday life, the workplace and educational settings’ QCA – all a bit general.  As the skills agenda becomes more important across the world many countries are now focusing on the need to review and reform school and post-school curricula in order to make them more relevant and meaningful for people entering the world of work.  Employers in particular want to see a more vocationally and technically focused curriculum in schools and colleges that more effectively prepares people for employment. In this country functional skills and the associated qualifications are aimed at providing learners with practical skills in English, Information Technology (ICT) and Mathematics.
The government argues that the functional skills qualifications will be useful for: ‘ learners: will develop solving skills which will make sure that they’re well prepared for employment, further study and life in general, employers: help employees apply vital functional skills in work situations which will improve effectiveness and productivity, HE: competency in the key subjects of English, ICT and mathematics will help learners progress to further achievement and allow them to study independently.’ (All very worthy but as always the devil will be in the detail and the implementation!). The government, as also its predecessor, has created a strategy to address employability needs for the country in order to begin to address the woeful state of people’s skills. The OECD survey (2009) paints a bleak picture of this country’s performance when compared with 30 advanced industrial nations e.g. 17th for basic skills (Functional literacy, ICT and mathematics) 20th for intermediate skills (Technical and craft skills, for example, in advanced apprenticeships) and 11th in higher (Degree and post graduate programmes). The latest study from OECD in 2010, (known as the PISA survey (Programme for International Student Assessment), showed Britain slipping further down the international education league tables The country was ranked 25th for reading, 28th for mathematics and 16th for science. The study involved 470,000 15 year olds and the corresponding numbers for 2006 were 17th, 24th and 14th respectively. These figures sadly reflect and reinforce the decline in the effectiveness of the English educational and training system and align with the situation given in the history of technical education on this website. The country is now in absolute decline after years of relative decline in international league tables!
 I will focus on functional mathematics for this article as the subject is central to technical and commercial education and training as it is aimed at improving the understanding and appreciation of the application of mathematics and numerical concepts in the workplace. Any curriculum experience must surely begin to build the foundations that are able to tackle the continuing  problems associated with technical and technician education and training that will once and for produce a more qualified and skilled  workforce for the future.
As always such initiatives become politicised and embroiled in the old arguments about the academic vocational divide and pure versus applied subjects and the issue of achieving parity of esteem. The genesis of the term is itself interesting: some commentators say a key advisor in the previous government thought of it and qualified it by saying ‘no other country has used the term.’ – that really is a good rationale for any development – such is the paucity of intellect in the political classes?! The term has in fact been around for some time and its development and use well documented particularly in Europe. Since the appearance of the term functional mathematics in 2006/07 a flurry of activity has been focused on trying to define it, where to locate it in the curriculum, and whether it should be for all learners or just a particular group of learners. It’s a classic case example of the English education system – a multitude of individuals, professional organisations and working groups beavering away without any real understanding of what is really required. Couple this with frequent government interference, with their advisors putting forward their own narrow and ill-informed opinions, and you have a recipe for disaster. As a result of all this activity on a critical and important development, a bandwagon has been created with a great deal of momentum but little idea where it is going and, equally important, what it will do if it arrives somewhere! I fear the change of government will not improve the situation if one looks at what is already happening about to the development of the so-called vocational diplomas and their relative value to the so-called academic subjects e.g. GCE ‘A’ levels.
The major challenge with the introduction of functional mathematics is that the context and content must be realistic and derived from the realities of life and the work place and equally important applied to those realities. As a result an important element in functional mathematics concerns how it can be learnt. Effective and sustained learning will not be achieved through simulation or a pre-occupation with testing and assessment. It is essential that the appropriate contexts for the learning are carefully defined and managed (see article on context on this website). Functional mathematics must have universal application and available to all learners including undergraduate and post-graduate students. Learners must gain an understanding of ‘functionality’ both in terms of the ‘how’ and of the ‘why’. Functional mathematics must involve such elements as reflection, critical thought, reasoning, and problem solving. Process and thinking skills must be at the heart of this development. It must not be driven by heavily prescribed assessment regimes and must be relevant and delivered in realistic contexts and most certainly not be hi- jacked by the academics and pure mathematicians who have little understanding of technical and commercial environments.
The final challenge facing the introduction of an effective programme of functional mathematics will be those associated with the teacher’s ability to deliver the subject and the availability of the right resources and support for them. In order to introduce new curricula teachers have to fundamentally review and reflect on their teaching styles and practices. Such analysis must include the reasons for what is taught, what you can use it for, why it is taught and how you can apply it. Any curriculum experience is not just about the syllabus and how it is interpreted but is also about the learning and teaching styles adopted in the appropriate contexts, whilst maximising the available resources to facilitate effective learning. The most important resources are the teachers and they will need a great deal of support in order to introduce the subject. Sadly the shortage of sufficiently qualified mathematics teachers in schools and colleges coupled with the fact that many do not possess any real experience of teaching to the specifications that will define and figure in functional mathematics will create a massive set of challenges. Capability in handling mathematical concepts and their application in realistic contexts cannot be over emphasised as someone who has taught technical subjects I realise the centrality of the subject in this sector of education and training.
Final quote for curriculum developers: 
Any judgement on the value of any curriculum experience is its functionality – namely the outcomes achieved.’
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