Mathematics

The UK’s poor performance in developing young people’s mathematical skills has been concerning for some time. In this article Dr Dick Evans explores the current state of play.

Having written extensively about skills shortages over the past few years I would like to focus on a number of recent developments in one key area namely mathematics and numeracy. The importance of these subjects cannot be over emphasised not only as an intellectual pursuit in their own right but for their pivotal role in strategic subjects crucial for the economy such as science/engi-neering/technology/computing and indeed all elements of the workplace and for society and its citizens in general.

Increasing concern has been expressed over many decades about the growing crisis in mathematics at all stages of education, training and employment. A good example has been that universities have had to devise diagnostic tests for undergraduates entering degree programmes that require mathematics and then introduce compensatory programmes for students. Analysis of results from the tests over the past twenty years starkly show the continued decline in mathematical knowledge and skills of these students in spite of their possession of good GCE A level grades in mathematics and other subjects requiring mathematical skills. Successive reports have also highlighted the difficulty in recruiting mathematics teachers into schools and colleges arising from a significant decrease in numbers studying the subject as a main elective in BEd and PGCE programmes. In spite of various initiatives to increase recruitment and retention of teachers and the introduction of intensive retraining programmes for teachers the position has not improved. In addition annual statistics from government departments have shown consistent low take up of mathematical subjects post-16 and stubbornly low pass rates at GCSE level (50% of candidates fail to gain a grade C in the subject). International comparisons also showed fundamental weaknesses in levels of numeracy and mathematical competence through out the country.

Target Explanatory Notes
All young people to reach age 19 ready for skilled employment or higher education
10. By 2008, 60% of those aged 16 to achieve the equivalent of 5 GCSEs at grades A* – C; and in all schools at least 20% of pupils to achieve this standard by 2004, rising to 25% by 2006 and 30% by 2008
  • This target may be reviewed in the light of Tomlinson recommendations
  • Qualifications included under the revised performance tables listings can be included
  • This is a rolled forward target where there has been some slippage
11. Increase the proportion of 19 year olds who achieve at least Level 2 by 3 percentage points between 2004 and 2006, and a further 2 percentage points between 2006 and 2008 and increase the proportion of young people who achieve Level 3
  • The list of qualifications to be counted will be reviewed post Tomlison but currently include accredited qualifications on the QCA list1 and some non regulated vocational qualifications
  • This includes those gaining NVQs and Tech Certs through Apprenticeships
  • This is a rolled forward target on course
12. Reduce the proportion of young people not in education, employment or training by 2 percentage points by 2010
  • This is a new target
  • Data sources will include Annual Schools’ Census, LFS and LSC stats
  • The proportion in this group is due to drop by 10% by Nov under a key target for Connexions
Tackle the adult skills gap
13. Increase the number of adults with the skills required for employability and progression through:

  • Improving the basic skill levels of 2.25m adults between 2001 and 2010 with a milestone of 1,5m in 2007
  • Reducing by at least 40% the number of adults in the workforce who lack a Level 2 by 2010 with lm adults achieving Level 2 between 2003 and 2006
  • The target refers to individuals significantly improving their basic skills
  • This is a rolled forward target and is on course
  • Achieving a 40% reduction requires an additional 3.6m first Level 2 or higher qualifications gained by 2010
  • This is a rolled forward target that is on course
Raise and widen participation in higher education
14. By 2010, increase participation in HE towards 50% of those aged 18-30 and also make significant progress year on year towards fair access and bear down on rates of non -completion
  • Since April 2004, the HE Initial Participation Rate now measures this. The main difference is that HE is defined as courses of at least 6 months as opposed to 12 months under the previous Rate
  • This is a rolled forward target that is on course. The provisional 2002/3 figure is 44%
  • Progress on fair access will be measured by increases in representation from certain groups

More recent concerns have been expressed by the HMI. For example the 2000/01 report from the chief HMI stated “In Mathematics there are insufficient teachers to match the demands of the mathematics curriculum in one school in eight, a situation that has deteriorated from the previous year”. In the 2001/02 the report again stated, “Across secondary schools there remain significant difficulties in the recruitment of specialist teachers, particularly, but not exclusively, in mathematics. In many schools because of the limited amount of specialist teachers’ expertise is deployed largely on post-16 courses”.

In the light of these long term concerns the government commissioned a review into the supply of people with science, technology, engineering and mathematical skills. The review was carried out by Gareth Roberts and the resulting report was called “”SET for Success: The Supply of people with science, technology, engineering and mathematics skills”(l). The Roberts report examined the supply of science and engineering skills in the UK in the specific biological, computer, physical sciences, engineering and mathematics contexts. The main theme identified in the report was the mismatch of supply and demand in these specialisms and that this would adversely affect the Government’s productivity and innovation strategy. Another, if not surprising finding, was that employers had expressed growing concerns about the mismatch between skills acquired during formal education and those required in the workplace. One of the most important aspects identified by the Roberts report was the manifest problems that exist in mathematics and the centrality of the subject for a successful knowledge economy.

As a result of the Roberts report the government announced an inquiry into mathematics chaired by Professor Adrian Smith with the following terms of reference:

“To make recommendations on changes to the curriculum, qualifications and pedagogy for those aged 14 and over in schools, colleges and higher education institutions to enable those students to acquire the mathematical knowledge and skills necessary to meet the requirements of employers and further and higher education”.

The inquiry was established in November 2002 and was published in February 2004. The final report comprised 171 pages and generated 44 recommendations and was one of the most important reports published since the Cockcroft Report (2).

The post-14 inquiry identified major concerns in three key areas namely:

  • The acute shortage of specialist mathematics teachers, particularly in England and Wales.
  • The failure of the current curriculum, assessment and qualifications framework in England, Wales and Northern Ireland to meet the needs of many learners and to satisfy the requirements and expectations of employers and higher education institutions.
  • The lack of resources, infrastructure and a sustained continuing professional development culture to support and nurture all teachers of mathematics.

One disturbing but again not surprising finding was the lack of accurate statistics on the number of qualified teachers in schools and colleges. In particular strong concern was expressed about the data collection or lack of it in colleges. The absence of a standardised Management Information Systems (MIS) in post-16 institutions has existed for a long time and results from a failure by previous funding councils to develop one and to leave institutions to buy or develop their own.

The comprehensive set of recommendations identify a series of actions that must be accepted including the following:

  • The appointment of a “maths tsar” and that the DfES and LSC to create a coherent strategy for mathematics education. An enhanced role for the Advisory Committee on Mathematics Education (ACME), (recomms 1.1,1.3).
  • DfES to develop more effective data collections systems and to consider a series of financial incentives to increase significantly the recruitment, retention of mathematics teachers and to introduce a new mathematics teacher certification scheme, (recomms 2.1 to 2.8).
  • The introduction of a double award in mathematics and consideration for provision for more able learners both at GCSE and GCE levels. An urgent review of the more vocational elements of the subject including special reference to Application of Number, Adult Numeracy qualifications and the Free Standing mathematics Units.
  • Review the location of data handling and statistics within the National Curriculum i.e. their integration into other disciplines. (Recomms 4.1 to 4.11).
  • Programmes of Continuous Professional Development (CPD) to form part of the conditions of service for mathematics teachers in schools and colleges and that additional remuneration be linked to successful completion of recognised CPD activities. The development of a national infrastructure to support teachers including those on CPD programmes. (Recomms. 5.1 to 5.4).
  • Enhanced role for the National Numeracy Strategy and mathematics strand of Key Stage 3.
  • Introduce a programme to pay selected volunteer undergraduate and postgraduate students in mathematical subjects to teach in schools and colleges.
  • Assess the potential benefits of using ICT.
  • Improve careers advise via SETNET. Establish a National Centre of Excellence in the Teaching of Mathematics and a network of Regional Mathematics Centres. (Recomms 6.1 to 6.18).

Following the submission of the inquiry the government eventually responded in late June and announced a package of reforms. Clearly such a welcomed and radical agenda if accepted would require significant additional funding and would require a number of fundamental changes to the way teachers’ salaries and conditions of service are determined.

Unveiling the 47-page response the Secretary of State restated the government’s commitment to addressing the current crisis in the subject. The government proposed the following set of actions arising from the Smith Report the main ones being:

  • Appointment of a mathematics tsar with a salary of c£80 000 as soon as possible.
  • Creation of a National Centre for Excellence in Mathematics Teaching. Bids to operate centre from March 2005.
  • Establish a network of 1 500 to 2 000 primary maths centres to improve teaching for under- 12s.
  • Create centres to operate online further mathematics ‘A’-level courses across England.
  • Extra £2 000 for postgraduate trainees and minimum pay for maths Advanced Skills Teachers (ASTs) to rise from £30 501 to £40 000 and no limit on pay for mathematics ASTs. (Current maximum for ASTs is £50 000 schools could pay above this limit no date for implementation of this action) Teacher- training bursaries increased by £1 000 to £7 000 for mathematics graduates and an increase of £1 000 in “golden hello’s” for postgraduate mathematics trainees to £5 000 from September 2005.
  • Development of extension curriculum for more able learners. Pilot from January 2005 and possible rollout in 2006.
  • Double number of unpaid under- and postgraduates on student associate schemes to work in schools.
  • Develop an improved and comprehensive database to record number of mathematics teachers and to track vacancies.
  • Introduce a two-tier GCSE possibly from 2008 after piloting. This will replace the current three-tier system.
  • Review the place of data handling and statistics in the current mathematics GCSE syllabuses.

The responses were generally welcomed by the subject associations but reservations were expressed by the teachers unions about creating differential salaries, which would be divisive within the teaching profession. Other commentators felt that the extra pay for ASTs represented a classic example of tinkering around the edges of the problem and that the £1 000 premium would have little significance in attracting mathematics graduates into the profession. Previous attempts to introduce golden hellos, handshakes and even handcuffs have had limited success both in education and health professions.

Time will only tell if these actions will attract more people into the profession. The problems are so serious that I feel the solutions could easily take a generation to resolve and even this view is predicated on the assumption that the participation in the subject will increase at all levels at education and training. I agree with a number of commentators that there is a longstanding historical and cultural hostility to mathematics in this country. After all many people happily admit and will boast, “that they were never any good at maths”. If this perception is true then people will continue to avoid the subject and even if teacher numbers are increased then the problems associated with adult numeracy and mathematical competence will persist.

What I find interesting are the elements not accepted or only partly acknowledged by the government as further analysis of the future actions would seem to indicate caution on the long-term implications namely the cost and indeed if more teachers will be recruited. The number of graduates in mathematics and mathematical related subjects is now so low that major issues are raised about supply and demand. Graduates and postgraduates in mathematics and statistics have over the past few years entered careers that attract much higher salaries and are free from all the problems that teaching involves e.g. financial services. Therefore it could be that there is an implicit assumption that the measures proposed would not increase the number of qualified teachers. For example the response did not accept the Smith recommendation to introduce a double award possibly because this would require inevitably more curriculum time and hence more teachers. A similar view could also exist in the current discussions and developments associated with the Tomlinson review and the exact place of science and other key shortage areas like modern languages in the frameworks being proposed. After all if schools cannot recruit sufficient teachers in the physical sciences and modern languages then it makes political and financial sense to construct a curriculum framework that does not give these subjects a central part and as a result require a disproportionate part of the curriculum time.

Welcome as the Smith inquiry is and the subsequent response by the government its terms of reference limited the scope and opportunity for the review to consider in depth particular areas such as mathematics and numeracy in the work place. This aspect has been neglected for too long and has not been given the recognition that it deserves. Employers are finding it increasingly difficult to recruit people with the relevant skills in numeracy and mathematics. Although some reference was made in the inquiry to these critical elements little evidence exists that they will receive attention in the immediate future. There needs to be an urgent review and reform of numeracy/mathematics in the vocational curriculum especially as applied GCSEs, and Apprenticeship programmes are developed. Employers must be involved in such developments to make certain the content is relevant and fit for purpose for the specific occupations. Also there seems little reference in the inquiry to the special requirement of colleges and other training providers who are expected to deliver the majority of the occupationally specific programmes in the National Qualifications Framework and as a result little hope of improving the situation in vocational aspects of numeracy and mathematics.

In spite of a number of fundamental reservations about the inquiry and the response it has at least put mathematics on the agenda – but it’s going to take a long time before any real and lasting improvements are forth coming.

References:

  • (1)“SET for Success”. April 2002.
  • (2) “Mathematics Counts” 1982.
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