The Maths Problem

Dick Evans continues his analysis of training needs and skill shortages with a look at the world of numeracy.

The Government has three distinct strands for its educational agenda, namely standards, skills and widening participation.

A large number of reforms and initiatives continue to be introduced to realise these important elements of the wider agenda to develop a culture of lifelong learning and to raise the competitiveness of the workforce in this country. A number of these reforms and initiatives include:

  • Reforms to the national curriculum, including more rigorous testing of pupils throughout their school lives.
  • The introduction of programmes of numeracy and literacy into primary schools.
  • The basic skills quality initiative.
  • The Learning and Skills Council Bill, which will bring about fundamental changes to the planning, management, inspecting and funding of post-sixteen education and training.
  • Reforms to the 16-19 curriculum, namely Curriculum 2000.
  • The creation of Ufl/Learndirect © Review of National Training Organisations (NTOs).
  • Reform of Apprenticeships Programme e.g. foundation, advanced and the development of the Graduate Apprenticeship.

These developments are important if this country wishes to achieve equivalence in education/ training attainment with other developed and developing countries.

Related to these imperatives is the need to tackle the issues around low productivity levels in many areas of employment, but particularly in manufacturing and engineering sectors, as well as a number of service based industries. Hopefully, increased productivity will allow this country to re-establish and then maintain its competitive edge over other countries although continuing concerns about international exchange rate could make it even more difficult to achieve competitive productivity levels. The ever accelerating impact of the global economy adds an even greater urgency to the need to realise the Government’s agenda.

The emerging so-called ‘knowledge based economy’ will require increased competence, capability and skill in a number of key disciplines including mathematics and Information Technology (IT). These factors have been highlighted in a number of reports that have emanated from the National Skills Task Force. International comparisons, across a wide range of performance measures, starkly show that this country has a ‘steep mountain to climb’ and time is not on our side. Skills shortages are already clearly evident and it is essential that we face the issues around skills needs, including their identification and the capability to track them and address them quickly and effectively. Skill gaps and shortages already exist across a wide spectrum of employment, especially in some professional, technical and craft areas; hopefully the new structures set in place by the Learning and Skills Council will quickly tackle the fundamental issues – supply and demand and adequacy and sufficiency.

One subject area that is central to these issues of educational attainment and competitiveness is that associated with mathematical capability, numeracy and application of number. This is both a complex and multidimensional issue that in many ways mirrors some of the problems that confront all sectors of education and training in this country. Innumerable reports over many years have highlighted the continuing difficulties associated with mathematics and numeracy and have mapped out the possible causes and made innumerable recommendations to improve the situation. Sadly, in spite of all these laudable endeavours, very little has happened and concerns continue about the inadequacy of mathematical and numerical abilities of college/university applicants, employees and people in society in general. It is but one of the eternal concerns about this country’s educational tradition, mirroring and possibly linked with the cultural hostility to vocational education and certain strategically important disciplines, namely science, engineering, technology and the built environment.

One of the difficulties about this topic is that the majority of the reports approach the problem from one direction only, with all its inevitable self-interest and parochial associations. A large number of the reports have, quite rightly, emanated from universities with admissions tutors articulating the difficulties they experience in recruiting students to subjects that require mathematical capability to courses such as science and engineering. Even though the interest from universities is understandable, the problems are far wider and embrace all learners and individuals who have to live in an increasingly scientific and technological society now being influenced by information communication learning technologies.

What is surely needed now is a far ranging and well informed national debate, indeed a committee of enquiry into this whole area of mathematics and numeracy. Any such group must be truly representative, with membership drawn from all the key areas including educationalists from all sectors, employers and members from other groups who are tackling basic numeracy problems. This wide but balanced representation will overcome the dangers of more parochial views or narrow perspectives that have in the past caused a very fragmented view of this key problem. It has many dimensions that need to be explored in a holistic and searching way.

To assist the presentation and to indicate how some improvements are being introduced into the educational system, a number of aspects will now be explored. This country is almost unique in the fact it offers little incentive or opportunity for either young learners or adults to develop their mathematical skills beyond basic levels. Only a few continue with specialised maths studies post-sixteen and others receive little or no further dedicated mathematics teaching. Comparisons with other countries, particularly in Europe and North America, starkly highlights the difficulty. In all European educational systems there is a requirement for students to continue maths full-time right up to the end of their secondary school education i.e. all therefore go well beyond the GCSE levels. In France, 60% study maths at AS equivalent level and in America 90% of school children are required to study ‘mathematics’ full-time up until the point they leave school. Therefore the first challenge is to develop curriculum frameworks and the associated qualifications that will increase the take-up of maths education post-GCSE level. A number of recent developments give hope that this will now happen. Under the reforms of Curriculum 2000, initially aimed at 16 – 19 year olds, the new reconfigured AS offers hope and early indications are that this has increased participation in maths post-GCSE level. However there are still difficulties for providers in delivering the AS in one year and it does present some unique problems in attempting to make it equivalent to half a full A Level. Also, there is still a problem that maths at AS is still too theoretical and not really relevant to most learners’ needs for their future employment or higher education studies.

One really exciting development has been the creation of the Free Standing Maths Units (FSMUs) developed by Geoff Wake and colleagues at Manchester University in conjunction with the Qualifications Curriculum Authority(QCA). The Free Standing Maths Units require sixty hours tuition. They are assessed 50% by tests and 50% by portfolio presentation and can be linked to the key skill of Application of Number. Free Standing Maths Units are offered in a number of specific topics, closely aligned to the requirements of different occupations and HE programmes of study. At the advanced level they can carry UCAS points and hence offer admissions tutors in universities and higher educational institutions a greater confidence that the students have covered relevant mathematics in their intended higher studies. This should go part way to helping relieve the concerns that universities and HEIs have about the mathematical background of their students, particularly in such areas as science, engineering, built environment technologies and economics as well as a host of other subjects which are increasingly dependent on quantitative methods e.g. life science, business studies, information technology programmes of study.

Figure 1 attempts to show the current Free Standing Maths Units that are being offered at a number of levels.

Foundation level = NVQ 1
Managing money
Working in 2 & 3 dimension
Making sense of data
Intermediate level = NVQ 2
Calculating finances,
Solving problems in shape and spaceHandling and interpreting data
Making connections in mathematicsUsing algebra functions and graphs
Foundation level = NVQ 3
Understanding mathematical thinkingUsing and applying statistics
Working with algebraic and graphical techniquesModelling with calculus

You can see from Table 1 (above) that the Free Standing Maths Units are very much about relevance, preparing students for their intended careers or higher education studies, but also attempting to cover gaps and deficiencies that are most certainly present in the national curriculum in maths. One of the main criticisms by higher education institutions is the increasing neglect of trigonometry and algebra in the national curriculum at GCSE. Pupils can pass with top grades and still have large gaps and deficiencies in their mathematical knowledge and understanding of key topics that are most certainly required in their further studies.

Figure 2 shows how Free Standing Maths Units can be integrated into the programmes of study being developed within Curriculum 2000.

Business/Finance/EconomicsArt Design/TechnologyEducation
Foundation Level Managing money
Foundation Level Working in 2 & 3 dimension
Intermediate Level Making connections in mathematics
Intermediate Level calculating financesIntermediate Level Solving problems in shape and spaceIntermediate Level understanding mathematical thinking
Science/Technology/Engineering/ Built Environment Technologies
Statistics - supporting life sciences, the social sciences
Foundation level Making sense of dataFoundation level Making sense of data
Intermediate Level Using algebra, function and graphicsIntermediate Level Handling and interpreting data
Advanced Level Working with algebraic and graphical techniques, modelling with calculusAdvanced Level Using and applying statistics

The programme subjects could be based around A Levels, GNVQs or occupationally specific NVQs or RVQs. The additionality of Free Standing Maths Units adds both breadth and balance to those programmes of study and addresses some of the key weaknesses that are most certainly manifest in many learners leaving the compulsory school phase of education. One really exciting development is that pilots are now under way developing a new AS which is made up of a number of combinations of the existing Free Standing Maths Units. A new AS will be developed using three of the units at the Advanced level. This new AS would overcome some of the difficulties already being experienced with the reconfigured AS, which is very much on traditional lines. The new AS will be both relevant and more appropriate for many of the learners studying at school or college. One other possible driver is to extend the concessions already given to IT training to that of maths post-sixteen, possibly incorporating this discount into the emerging individual learning accounts that are now being introduced to encourage increased and widening participation post-sixteen.

The introduction of the Application of Number Key Skills will also’assist in providing learning opportunities to post-sixteen learners which will improve the level of understanding of number and its application and most certainly related to their core programme of study. Again, successful completion of the Key Skill will give greater confidence to employers and HEI admissions tutors.

However, as mentioned earlier, there are more deep-seated difficulties with the level of numeracy and numerical understanding in society. The Moser report highlighted the real problems in the maths skills within adults in this country. The scale of the problem was very clearly stated by the report namely “one adult in five in this country is not functionally literate and far more have problems with numeracy”. The number having problems with numeracy is estimated to be over 40%. Many argue that it is nearer 50%, and those with very severe problems and/or very low numeracy ability number over 20%. The Moser report was possibly the most comprehensive report that addressed the issue of basic literacy and numeracy amongst adults in this country. It joins a number of other reports over the past decades, including the Cockroft Enquiry (1978-82), the FEFC’s Sector Report (1998) and the Basic Skills Agency Report (1996). All these have shown a whole series of causes for the current situation, which include:

  • Home circumstances.
  • Previous experience / schooling.
  • Maths anxiety/fear of failure.
  • Employers’ attitudes.
  • Learner motivation and need.

Numeracy does present some unique difficulties. The perceptions and attitudes of people to maths are summarised in a few statements as follows:

  • “It’s a difficult subject.”
  • “People can either do it or they can’t.”
  • “When I see a maths problem, my mind goes blank – I just don’t know which bits to use.”
  • “I never know if my answers are right or wrong.”

Other factors and reasons cited relate to their teachers’ attitudes to formal methods of teaching. Many see the lack of relevance in the maths that they did at school. Others fear appearing stupid -or too clever. Many are disturbed by rules, rules and more rules associated with maths. One can summarise these perceptions and attitudes by saying that there seems to be a lack of confidence in many people about their ability to deal with number activity; many see what they have been taught as not being relevant, not sufficiently practised and they have difficulty in retaining that knowledge and understanding. This possibly begs a very big question about the way maths is taught in schools. The Cockroft Report argued very strongly that maths should be contextualised so that it was seen to be relevant to everyday activity. This clearly makes sense but since Cockroft and the various reforms that were put in place since its publication, concerns have been voiced, particularly by academics, who feel that the contextualisation elements have gone too far. Perhaps it is a matter of getting a more sensible balance.

One point that comes out of the various reports is that many people feel that maths is not related to everyday life or everyday situations. After all, very few will go on to do maths in any depth and again, it is important to deal with this increasingly diverse learner population. Britain and America are both experiencing similar difficulties with maths and basic numeracy within their populations and they have similar approaches to maths, too often taught in a very theoretical, pure and abstract way. Most other countries (Japan and many countries in Europe) approach the teaching the other way by getting the balance right in that the maths is seen to be relevant, applied to real and understandable situations and appropriate and as a result levels of participation and achievement are far greater. Hopefully, with the introduction of the reforms with Curriculum 2000, key skills and the new AS and the Free Standing Maths Units we possibly can begin to resolve some of the problems in post-sixteen aspects of mathematical knowledge and understanding for those who wish to enter areas of employment which require a good basis of mathematical knowledge or to progress on to HE, where their studies will most certainly require that depth and balance. However, equally important is that we offer all learners, whether young or old, learning opportunities that will help to give them confidence in dealing with number activities in their lives and work.

The Government’s acceptance of the recommendations of the Moser Report and the funding that is now being made available to tackle the basic skills of literacy and numeracy in the country is a beginning. But, there still needs to be a holistic approach to the issues around numeracy and mathematics.

However, and this is a big however, in spite of all these positive developments, one essential problem continues to exist, namely teacher shortages. Schools and colleges are finding it increasingly difficult to recruit properly qualified teachers in sufficient numbers at all levels to teach mathematics and numeracy. The number of students electing to study mathematics at degree level and on teacher training courses, e.g. BEd and PGCE continues to decline. Also, many teachers entering the profession possess relatively weak mathematical backgrounds. Indeed, in many schools, many teachers of mathematics have little knowledge beyond O Level/GCSE. Indeed, because of the low enrolments at BEd and PGCE with maths as the primary or subsidiary election, the quality of maths teachers entering the profession is relatively low and small in number. The problem is further exacerbated because many experienced and capable teachers are leaving the profession and most certainly are not being replaced in sufficient numbers. Poor teaching produces poor student understanding and motivation in maths and this creates a downward spiral with fewer and more poorly qualified maths teachers entering the profession. Therefore there are real difficulties in the stock and flow of mathematics and numeracy teachers. An increasing difficulty has been experienced by colleges attempting to respond to the basic skills quality initiative. They are finding it very difficult to recruit properly experienced and qualified staff. This teacher shortage is becoming critical and if not addressed quickly enough will undermine some of the worthy developments given above.

In summary:

*A committee of enquiry should be established to look at the whole area of maths and numeracy across all sectors of education and to include the work of the basic skills agency.

*That encouragement should be given to increasing participation in post-GCSE maths by introducing concessions in costing maths training, similar to that that is afforded to IT training.

*The critical position with teacher shortages must be recognised, addressed and positive action taken by the Government and its appropriate departments.

Perhaps if these recommendations are accepted, then we can accelerate the Government’s agenda on standards, skills and widening participation we will have to wait and see!

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