The answer to this long standing question is a resounding no! This is especially certainly true for the mathematics that will be required by most post-16 learners who will progress into employment. The subject is most certainly, fundamental and essential as a body of knowledge but it is the way it is taught and learnt that precipitates the problems. This is particularly important in its application in the workplace and the ability of people to use basic mathematical concepts in everyday life. The level of understanding and ability of the majority of people to apply mathematical and numerical concepts is woefully inadequate in England to cope with the future challenges whether in employment or life in the increasingly scientific and technological world. This sad state is not new one only has to review the innumerable reports, commissions, working parties, focus groups and supposed think traps over the decades. Many of these have presented excellent surveys of the situation but with little effect or impact either in the short and long term. Think tanks indeed! What is needed is DO tanks in the long term! This country is world class in creating bodies to address important issues but these are seldom capable of developing effective and sustained strategies and tactics that bring about solutions to this incredibly important problem.
The evidence from these reports is a matter of record accumulated over many decades and have consistently highlighted the inevitable crisis’s that will confront this strategically important subject at all levels where it is required. Problems exist at all sectors of education, training, in the workplace and with functional numeracy.
Many causes and effects have contributed to this sad state of affairs and include:
- Cultural factors
- The existing qualifications frameworks for mathematics and numeracy are flawed and require root and branch reform NOT fudge and mudge/tinkering approaches
- The way mathematics and numeracy programmes are taught and learnt and this coupled with poor teaching produced a damaging cocktail
- The environment in which teaching and learning takes place – this is particularly relevant for technical and vocational education and training – the context is absolutely critical for successful and sustained learning
- The obsession with assessment and testing regimes e.g. teaching to the test syndrome – this results in distortion of content and learning and leads to a lack of understanding of the subjects
- Issues associated with whether or not learning mathematics is perceived as either a pleasurable or painful experience by many learners. (the Cockcroft Report (1982) highlighted this factor)
- The general perception of mathematics, particularly by peers, parents and society in general towards the subject
- The lack of perceived obviousness or immediacy so that people do not turn to mathematics as a first resort to solve everyday problems or to understand the world.
- People often claim to survive and earn a living without having to resort to mathematics
- The increased use of computers, calculators and ICT multimedia with little thought of how these techniques and technologies are managed to develop critical capability. Badly managed teaching and learning methods using these techniques creates a passivity or acceptance in the way people want to or indeed expect to learn. A number of commentators have suggested that the obsession of retrieving information from the internet without the critical second stage of reflection, analysis and verification will eventually bring about an outsourcing of the memory to the internet. A thought – could these technologies actually erode the crucial element of curiosity so essential in the learning and understanding of these subjects?
- Many textbooks are still narrow or mechanical in format and content. Teachers and learners must have access to a wide range of learning materials which are fit for purpose for the learner’s ability and future needs whether for further, higher education and ultimate employment. It is essential that the learning resources are managed effectively by the teachers and this requires appropriate initial and CPD programmes
Perhaps it is too simplistic just to view the negative perception towards the subject in terms of a series of causes and effects. If the problem is about the formation of negative attitudes towards the subject then this must be recognised as a complex process that invariably involves the interaction of a number of factors that ultimately cannot be simply or completely identified and explained. Too often commentators are inclined to regard a consequence as a result of a direct relationship between cause and effect. However, this may be an over simplification. As a consequence it might be more productive to think in terms of what factors the problem is related to instead of what causes the problem. In other words it is about the subtle and complex interactions that occur between the contributing facts cited above rather than a simple causation. Any further reviews must attempt to adopt this approach.
Time and space does not allow these elements to be more fully explored in this brief paper as many have been rehearsed over years but I would like to focus on the critical area of the mathematics and numerical elements required in technical and commercial education and training. Of all the areas of the mathematics problem this is the one that has been the most neglected and ignored. The majority of the reviews have been associated with the so called academic routes i.e. GCSEs, ‘A’ levels and honours degrees with little or no real analysis of the qualifications frameworks for the vast majority of people who require mathematical and numerical skills for the workplace or life in general. I include in this functional numeracy, financial literacy and the needs of people employed in the main occupational sectors of technical and commercial enterprises. This fact mirrors the neglect of technical education and training in this country over centuries .Part of the problem is the hostility and negative view of technical and vocational subjects which are all too often seen as second class. One of the contributing factors to this negative perception and the hostility to technical subjects is that they often include mathematics and if people have an inadequate background or negative experiences of mathematics when entering post-16 studies they will avoid these subjects.
The current qualifications system is skewed towards the supposed needs of academic study with the misplaced assumption that the content is relevant for all those who will progress onto enter most employment. Any effective curriculum framework must possess the essential characteristics of balance, breadth and balance that are fit for purpose for the learner’s employment intentions and needs. The mathematics for employment in addition to possessing the correct balance of these critical characteristics must be seen as relevant both to the learner and also be appropriate to the area of employment that they will enter. Employers must be involved in the development of the programmes not in a tokenistic way but as equal partners in the process. Too often academics state that employers do not know what they require – a classic example of academic elitistism and arrogance! A successful work based education and training system must be predicated and based on an equal working partnership with employers! The evolving apprentice programmes must work closely with employers and their professional bodies in order to create relevant and up-to-date programmes. Awarding bodies particularly those associated with technical, commercial and vocational qualifications must also keep their programmes under constant review and also involve all interested parties through advisory committees especially employers to achieve an effective monitoring function. A number of Further Education colleges have developed innovative and effective ways of teaching the technical and practical but too often resource constraints have curtailed many of these approaches. Some colleges have developed realistic working environments (RWEs) and as a result are more able to provide more relevant context for the learners. Rigid and inflexible curriculum frameworks taught in inappropriate environments too often stifle creative teaching and learning methods.
The way forward.
- A root and branch review is urgently required of mathematics and numeracy that is truly fundamental and recognises the differences that are required in content, emphasis, relevance and ultimate use of the subject by the whole spectrum of learners.
- Many of the problems start at primary school and the reviews must once and for all identify meaningful actions that build a strong foundation for the subject for progression on to the secondary stage of education. A good start has been made with the Rose and Williams report but much, more needs to be done.
- GCSEs and ‘A’ levels are a mess and urgently need a significant over haul -they are most certainly not fit for purpose for the majority of learners.
- Pre-16 learners who intend to undertake apprenticeships or enter college to study technical and commercial programmes must have opportunities and access to more relevant and appropriate work related experiences. Previous attempts such as application of number, functional mathematics have had a limited impact and a radical rethink is urgently required. Attractive and appropriate learning environments must be created in order to facilitate more and or more effective partnerships with local colleges and employers established.
- Post- 16 education and training also requires an urgent review particularly if the school leaving age is raised – the situation will become even more fractured with leaner’s if they have to do more of the same! A comprehensive new set of qualifications are urgently required that are fit for purpose for all the learners.
- Existing technical and vocational programmes must be made more flexible and teachers given more freedom to innovate work based education and training methods. Colleges must be resourced more adequately. The creation of more realistic working environments (RWEs) is essential to establish the correct context for teaching and learning. In addition enhancing links with employers by increasing work placements/sandwich programmes for learners with the relevant employers in order to show how mathematics and numerical concepts are used in the work place.
- The major technical and vocational awarding bodies should as a matter of urgency carry out a fundamental review and audit of their mathematical content of all its programmes to see if they match the requirements of the occupational sectors that the programmes are aimed at.
- The major technical and vocational awarding bodies should establish stronger working links with mathematics organisations and bodies and establish more effective lobbying strategies to government, politicians and civil servants.
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