Mathematics education in the United Kingdom

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Mathematics education in the United Kingdom is largely carried out at ages 5–16 at primary school and secondary school (though basic numeracy is taught at an earlier age). However voluntary Mathematics education in the UK takes place from 16 to 18, in sixth forms and other forms of further education. Whilst adults can study the subject at universities and higher education more widely. Mathematics education is not taught uniformly as exams and the syllabus vary across the countries of the United Kingdom, notably Scotland.

The School Certificate was established in 1918, for education up to 16, with the Higher School Certificate for education up to 18; these were both established by the Secondary Schools Examinations Council (SSEC), which had been established in 1917.

The Association of Teachers of Mathematics was founded in 1950.

The Joint Mathematical Council was formed in 1963 to improve the teaching of mathematics in UK schools. The Ministry of Education had been created in 1944, which became the Department of Education and Science in 1964. The Schools Council was formed in 1964, which regulated the syllabus of exams in the UK, and existed until 1984. The exam body Mathematics in Education and Industry in Trowbridge was formed in 1963, formed by the Mathematical Association; the first exam Additional Mathematics was first set in 1965. The Institute of Mathematics and its Applications was formed in 1964, and is the UK's chartered body for mathematicians, being based in Essex.

Before calculators, many calculations would be done by hand with slide rules and log tables.

The Nuffield Mathematics Teaching Project started in September 1964, lasting until 1971, to look at primary education, under Edith Biggs, from the Schools Inspectorate.^[1]

Decimal Day, on 15 February 1971, allowed less time on numerical calculations at school. The Metric system has curtailed lengthy calculations as well; the US, conversely, largely does not have the metric system.

At Ruskin College on Monday 18 October 1976 Labour Prime Minister Jim Callaghan made a radical speech decrying the lack of numeracy in school leavers, possibly prompted by the William Tyndale affair in 1975.^[2] The Prime Minister also questioned why so many girls gave up science before leaving secondary school.

But the Labour Party, instead, took curriculum change slowly, merely setting up the Committee of Inquiry into the Teaching of Mathematics in Schools, under Sir Wilfred Cockcroft, with Hilary Shuard and Elizabeth Williams. The subsequent report Mathematics Counts, was published in 1982; it offered few radical changes.

Electronic calculators began to be owned at school from the early 1980s, becoming widespread from the mid-1980s. Parents and teachers believed that calculators would diminish abilities of mental arithmetic. Scientific calculators came to the aid for those working out logarithms and trigonometric functions.

The Trends in International Mathematics and Science Study (TIMSS) showed that in some topics, the UK apparently had adequate Mathematics teaching, and from such reports Sir Keith Joseph merely implemented feasibility studies of national attainment standards, but the next education secretary, Kenneth Baker, Baron Baker of Dorking, wanted a lot more than mere feasibility studies. From hearing reports of national industrial failure being caused by insufficient mathematical abilities, he swiftly proposed a national curriculum in January 1987, to start in September 1988. Anita Straker and Hilary Shuard were part of the team that developed the primary national curriculum.

Since 1988, exams in Mathematics at age sixteen, except Scotland, have been provided by the GCSE.

From the 1990s, mainly the late 1990s, computers became integrated into mathematics education at primary and secondary levels in the UK.

On Wednesday 18 November 1992 exam league tables were published for 108 local authorities, in England, under the Education Secretary John Patten, Baron Patten. The tables showed GCSE and A-levels for all 4,400 state secondary schools in England. Independent schools results were shown from 1993, and would include truancy rates. Left-wing parent groups, teachers' unions had opposed the move. Labour said it showed the government's simplistic approach to education standards, adding that raw results cannot reflect the real achievement of schools. The Liberal Democrats were not opposed, but thought that any information being provided was limited. Ofsted would be brought in the next year by Education Minister Emily Blatch, Baroness Blatch.^[3]

The specialist schools programme was introduced in the mid-1990s in England. Fifteen new City Technology Colleges (CTCs) from the early 1990s often focussed on Maths.

In 1996 the United Kingdom Mathematics Trust was formed to run the British Mathematical Olympiad, run by the British Mathematical Olympiad Subtrust. The United Kingdom Mathematics Trust summer school is held at The Queen's Foundation in Birmingham each year.

Mathematics and Computing Colleges were introduced in 2002 as part of the widened specialist schools programme; by 2007 there were 222 of these in England.

The Excellence in Cities report was launched in March 1999, which led to the Advanced Extension Award in 2002, replacing the S-level for the top 10% of A-level candidates. Since 2008, the AEA is only available for Maths, provided by Edexcel; the scheme was introduced when the A* grade was introduced; the scheme was provided until 2018.

In a 2006 House of Lords report on science education, the Lib Dem chair Baroness Sharp, took an interest in the reduced participation in Maths in schools; she had worked with the Science Policy Research Unit at the University of Sussex. The 2001 report by the Lords Science and Technology Committee led to the National Science Learning Centre (Science Learning Centres) at National STEM Centre, with the University of York in 2006, with a Maths centre at University of Southampton.

The National Centre for Excellence in the Teaching of Mathematics was founded 2006, after the Smith Report, being now in Sheffield.

The National Higher Education Science, Technology, Engineering and Mathematics (HE STEM) Programme was founded in August 2009 by HEFCE and HEFCW; the scheme had six regions across England and Wales, working with the universities of Bath, Birmingham, Bradford, Manchester Metropolitan, Southampton and Swansea; it was funded by £21m, and developed by the University of Birmingham STEM Education Centre; the scheme finished in July 2012.^[4] Also involved was the MSOR centre of the HEA (now Advance HE) Subject Centre, and the Centre for Excellence in University Wide Mathematics and Statistics Support at Loughborough University.^[5]

The HEA subject centres closed in August 2011.

Mathematics free schools were opened in 2014 - the King's College London Mathematics School in Lambeth, and Exeter Mathematics School in Devon; both were selective sixth form colleges; others opened at Liverpool and Lancaster; more selective sixth form maths schools are to open in Cambridge, Surrey, and Durham.

A newer curriculum for Maths GCSE (and English) was introduced in September 2015, with a new grading scale of 1–9.

Mathematics education in England up to the age of 19 is provided in the National Curriculum by the Department for Education, which was established in 2010.

Early years education is called the Early Years Foundation Stage in England, which includes arithmetic. In England there are 24,300 schools, of which 3,400 are secondary.

The National Curriculum for mathematics aims to ensure that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
• can solve problems by applying their mathematics to various routine and non-routine problems with increasing sophistication, including breaking down problems into a series of more straightforward steps and persevering in seeking solutions.

Mathematics is a related subject in which pupils must be able to move fluently between representations of mathematical ideas. It is essential to everyday life, critical to science, technology and engineering, an appreciation of the beauty and power of mathematics, and a sense of and necessary for financial literacy and most forms of employment. A high-quality mathematics education, therefore, provides a foundation for understanding the world, the ability to reason mathematically, and curiosity about the subject. Pupils should build connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge in science, geography, computing and other subjects.^[6]

Wales takes the GCSE and A-level in Mathematics, but has its own Department for Education and Skills. Wales does not produce school league tables. Wales has 1550 schools, of which 180 are secondary.

Education Scotland, formed in 2011, regulates education at school in Scotland, with qualifications monitored by the Scottish Qualifications Authority (SQA) and the Mathematics syllabus follows the country's Curriculum for Excellence. Scotland does not produce school league tables. Scotland has 5,050 schools, of which 350 are secondary.

Northern Ireland is the only country in the UK to have exclusively selective schools - it has sixty nine grammar schools. Mathematics education is provided by the Department of Education (DENI), with further education provided by the Department for Employment and Learning. Northern Ireland has 1120 schools, of which 190 are secondary.

The Department of Education and Science set up an Assessment of Performance Unit in 1976 to monitor attainment of children at a national level, with standards of mathematics being monitored from 1978 by the National Foundation for Educational Research (NFER). Before this time, assessment of primary school standards had not been carried out at a national level.

Children at primary school are expected to know their times tables. Children are taught about long division, fractions, decimals, averages, ratios, negative numbers, and long multiplication.

Study of Mathematics is compulsory up to the school leaving age.

The Programme for International Student Assessment coordinated by the OECD currently ranks the knowledge and skills of British 15-year-olds in mathematics and science above OECD averages.^[7] In 2011, the Trends in International Mathematics and Science Study (TIMSS) rated 13–14-year-old pupils in England and Wales 10th in the world for maths and 9th for science.^[8]

Qualifications vary by region; the East Midlands and London have the most degree-qualified Maths teachers and North East England the least.^[9] For England about 40% mostly have a maths degree and around 20% have a BSc degree with QTS or a BEd degree. Around 20% have a PGCE, and around 10% have no higher qualification than A level Maths.

For schools without sixth forms, only around 30% of Maths teachers have a degree, but for schools with sixth forms and sixth form colleges around 50% have a Maths degree.

There are around 27,500 Maths teachers in England, of whom around 21,000 are Maths specialists; there are around 31,000 science teachers in England.

You will need at least grade 6 at GCSE to study Maths in the sixth form, and many sixth forms will only accept people with a grade 7 at GCSE.

At A-level, participation by gender is broadly mixed; about 60% of A-level entrants are male, and around 40% are female.^[10] Further Mathematics is an additional course available at A-level. A greater proportion of females take Further Maths (30%) than take Physics (15%), which at A-level is overwhelmingly a male subject.

From the UPMAP project (Understanding Participation rates in post-16 Mathematics and Physics) of the ESRC Targeted Initiative on Science and Mathematics Education (TISME), in conjunction with the Institute of Physics, it was found that uptake of Maths A-level was linked to the grade at GCSE. From 2012 figures, 79% with A*, 48% of A, 15% of B and 1% of grade C chose Maths in the 6th form. For English, History and Geography, 30% with grade B, and 10% with grade C chose the course in the 6th form.

The House of Lords July 2012 report Higher Education in STEM Subjects recommended that everyone study some type of Maths after 16. For less-able sixth formers, there was the AS level titled 'Use of Mathematics'.^[11]

Professor Robert Coe,^[12] Director of the Centre for Evaluation and Monitoring (CEM) at Durham University conducted research on grade inflation. By 2007, 25% of Maths A-level grades were an A; he found that an A grade A-level would have been a grade B in 1996 and a grade C in 1988. The Labour government wanted to expand higher education, so required 'proof' that academic standards at A-level appeared to be rising, or at least not falling, so requiring higher education to expand for this wider apparent academic achievement.

Admission to Mathematics at university in the UK will require three A-levels, often good A-levels. It is prevalently males who study Maths at university, and has been for decades.

There are around 42–43,000 Maths undergraduates at British universities, with around 27,000 being male and around 16–17,000 being female. Mathematics at university is also taught for other physical sciences and Engineering, but much fewer women than men are taught on these types of courses.

Educational series on television have included

• Mathematics and Life on BBC TV in 1961^[13]
• Mathematics in Action BBC1 from the early 1970s to the late 1980s, with Malcolm Bevan, Prof John Crank, Kenneth Wigley, and Prof John Crane^[14]
• Maths Today on BBC1 in the early 1970s with Brenda Briggs, the wife of Trevor Jack Cole, and Stewart Gartside^[15]
• Maths Workshop on BBC1 in the early 1970s with Jim Boucher and Michael Holt (author)^[16]
• Middle School Mathematics in the late 1960s with Alan Tammadge, the President of the Mathematical Association in 1978^[17]

Of all A-level entrants at Key Stage 5, 23% take Maths A-level, with 16% of all female entrants and 30% of all male entrants; 4% of all entrants take Further Maths, with 2% of female entrants and 6% of male entrants. By number of A-level entries, 11.0% were Maths A-levels with 7.7% female and 15.0% male.^[18]

In England in 2016 there were 81,533 entries for Maths A-level, with 65,474 from the state sector; there were 14,848 entries for Further Maths with 10,376 from the state sector

Entries for Further Maths in 2016 by region -

• South East 2987
• East of England 1270
• North West 1111
• South West 1070
• West Midlands 868
• East Midlands 774
• Yorkshire and the Humber 749
• North East 414

Results shown are for 2016. In the 1980s, some areas with low Maths participation at A-level lost all sixth forms at the area's comprehensive schools, being replaced with stand-alone sixth form colleges, such as in Manchester and Portsmouth; this course of action may have helped in attracting qualified Maths teachers to those areas.

The supply of qualified (QTS in England and Wales) Maths teachers in the UK is largely a postcode lottery.

The north of England (except Lancashire) has a worse record for Mathematics entries at A-level than other regions.

• Knowsley 6
• Portsmouth 51
• Salford 66 (Manchester entered 647 as a comparison)
• Halton 70
• Middlesbrough 79
• South Tyneside 85
• Barnsley 96

• Hampshire 2573
• Hertfordshire 2039
• Kent 1775
• Surrey 1668
• Essex 1499
• Lancashire 1492
• Birmingham 1403
• Buckinghamshire 1284
• Barnet 1189

Trafford entered 505, which is high for a small borough and almost the same number as Cumbria. Kirklees entered 661, which is more than Sheffield's 596; Kirklees is a much smaller borough by population than Sheffield.^[19]

• Knowsley 0 (Knowsley only entered 61 A-level exams in 2016)
• Sandwell 5
• Blackburn with Darwen 6
• Salford 7
• Portsmouth 8
• North East Lincolnshire 9
• Middlesbrough 11
• Stoke-on-Trent 15
• Barnsley 15
• Halton 16
• Southampton 16
• Torbay 16
• Bury 18
• Merton 18
• Rochdale 19

Hampshire and Hertfordshire are the top two for Maths and Further Maths

• Hampshire 381
• Hertfordshire 370
• Kent 297
• Surrey 276
• Essex 260
• Buckinghamshire 244
• Lancashire 206

• Association of Teachers of Mathematics
• Education in the United Kingdom
• National Centre for Excellence in the Teaching of Mathematics
• Uses of trigonometry

• Mathematics 5 to 11, 1979