The section on the reasons for (or causes of) the problems in mathematics education identified teachers as a cause; firstly in terms of the supply of teachers of mathematics, and secondly in terms of the subject knowledge of these teachers. The recommendations relating to these causes are outlined below.

### Supply of teachers

A set of recommendations suggest that the number of (specialist) teachers of mathematics should be maximized (Royal Society, 2011; Science Learning Centre, 2013; Select Committee on Science and Technology, 2012).

In terms of recruitment of teachers, it is recommended that sustained funding is put into bursary schemes in order to attract STEM graduates into teaching, and that STEM undergraduates be provided with opportunities to work in schools (to encourage them to go into teaching) (Science Learning Centre, 2013). The Select Committee also recommends that the Government should ‘boost specialist STEM teacher recruitment’ (p 79), adding, however, that:

The Government should assess which existing initiatives have yielded positive results and which have not worked, so that resources can be concentrated on those schemes that produce the best outcomes. (2012, p. 79).

Whereas these recommendations relate to the mathematics teachers generally, further recommendations concern the supply of teachers at post-16 level, particularly in the light of the proposal to make some form of mathematics compulsory for this age group. ACME, for example, recommends that the Department for Education should consider the numbers of staff needed and how to ensure that there are enough teachers. As it explains:

Achieving the substantial increase needed in post-16 participation in mathematics across the full range of provision including GCSE Mathematics and A-level, will mean having a larger workforce ready, willing and able to deliver new and existing qualifications. (ACME, 2012a, p. 4)

In terms of retention of teachers, further recommendations are provided, mainly related to the provision of professional development (see below).

### Subject knowledge

Some reports make recommendations in terms of the level of subject knowledge required by teachers. For example, Burghes, in his report on mathematics teacher training (2011) suggests that teachers should have a secure knowledge of mathematics at a higher level than that at which they are teaching. He explains that teachers should be aware of the mathematics their students will encounter later. He recommends suitable levels of qualification:

Three-year undergraduate degree in mathematical sciences for secondary mathematics teachers and one-year teacher training course (or equivalent) PLUS part time modular study during first school post (but with significant release time) at Master’s level with the intention of completing the masters degree within three to four years and with enhanced pay for each module completed successfully (2011, p. 48).

Other recommendations suggest that the subject knowledge of teachers should be up to date (Science Learning Centre, 2013), but see also the section on CPD below.

In terms of specific areas of subject knowledge, Porkess (2012) recommends that mathematics departments should make sure that there are teachers with expertise in statistics.

A number of reports make recommendations specifically aimed at teachers in primary schools. Overall these amount to a recommendation that mathematics subject knowledge of primary teachers should be improved (All Party Parliamentary Group on Financial Education, 2011; Burghes, 2011; Vorderman, Porkess, Budd, Dunne, & Rahman-hart, 2011). More specifically, Burghes recommends that all prospective primary school teachers should continue to study mathematics until they enter initial teacher education courses and the All Party Parliamentary Group recommends that these teachers should have achieved at least a Grade B at GCSE level.

### Teaching approaches

The section on the causes of the problems identified approaches to teaching as a reason for the problems. This section provides recommendations related to addressing this cause. General recommendations are that ‘innovative teaching’ is needed for children who struggle in primary school (Vorderman et al., 2011) and that efforts need to be made to better understand teaching approaches which would provide students with continuity in their mathematical experiences (ACME, 2011a).

A number of recommendations refer to the sorts of activities in which students should engage, such as collaboration and discussion, and making decisions about the mathematics they should use, with a recommendation that teachers encourage students to use more mathematical language (Hodgen & Marks, 2013; Southwood & Dixon, 2012). Some recommend that teachers relate classroom mathematics more to the real world, to the lives of the learners, to careers in STEM and to other subject areas (British Academy, 2012; NFER, 2013; Ofsted, 2011a; Southwood & Dixon, 2012).

Reports recommend that within teaching activity, students should be given the opportunity to use computers, practical resources and visual images (Hodgen & Marks, 2013; NFER, 2013; Ofsted, 2012). They further recommend an emphasis on developing students’ mathematical understanding of concepts (Ofsted, 2011a, 2011b, 2012).

### Professional development

Many reports recommend more and better subject-specific professional development for in-service teachers, both to ensure a good supply of competent teachers and to ensure better teaching (ACME, 2011a, 2011b, 2012a, 2012b, 2012c; All Party Parliamentary Group on Financial Education, 2011; Burghes, 2011; Clark-Wilson, Oldknow, & Sutherland, 2011; Finegold, 2011; Ofsted, 2011b, 2011a; Royal Society, 2011; Science Learning Centre, 2013; Select Committee on Science and Technology, 2012; Walker, Straw, Sainsbury, & Clarke, 2013). Other recommendations address teacher learning in initial teacher education (ACME, 2012b; Burghes, 2011; Ofsted, 2012; Vorderman et al., 2011). One recommendation relates to CPD for curriculum leaders in the design of learning pathways, relevant curricula and engaging pedagogy (Noyes, Drake, Wake, & Murphy, 2011) and one to tutors in initial teacher education (ACME, 2012b).

Some reports recommend a specific mathematical focus for CPD, such as the use of problem-solving and doing mathematics in non-routine situations; connections between mathematical concepts and the development of mathematics over time (ACME, 2011a, 2011b, 2012b; Ofsted, 2012).

Some reports recommend a specific mathematical and pedagogical focus for CPD, such as the use of problem-solving and doing mathematics in non-routine situations; connections between mathematical concepts and the development of mathematics over time (ACME, 2011a, 2011b, 2012b; Ofsted, 2012).

Others recommend a professional development emphasis on the use of digital technologies (ACME, 2011b; Clark-Wilson et al., 2011; Ofsted, 2012), careers guidance and the mathematics needed in the workplace (ACME, 2011b; Finegold, 2011; Hodgen & Marks, 2013; Select Committee on Science and Technology, 2012). Ofsted (2012) recommends that professional development should also back up policies and guidance.

In terms of funding, it is recommended that funding should be provided to support professional development (ACME, 2011a, 2012b; Royal Society, 2011; Science Learning Centre, 2013) and in particular that the National Centre for Excellence in the Teaching of Mathematics should be continued (Royal Society, 2011). ACME recommends that funding ‘should be found’ to provide professional development for non-specialist teachers to take courses in mathematics (ACME, 2011a).

For schools, the recommendations include adopting whole-school approaches in primary schools (Ofsted, 2011b) and the use of coaching and peer support including lesson study (ACME, 2012c, 2013; Burghes, 2011; Ofsted, 2011a). Some reports further recommend that school leaders should be committed to the professional development of the mathematics teachers in their schools (Clark-Wilson et al., 2011; Ofsted, 2011b; Science Learning Centre, 2013; Walker et al., 2013).

For Government, it is recommended that the MaST programme, which provides professional development to develop mathematics subject specialists in primary schools, should be endorsed and promoted. (Walker et al., 2013)

## References

ACME. (2011a). *Mathematical Needs of Learners*. London.

ACME. (2011b). *Mathematical Needs Mathematics in the workplace and in Higher Education*. London.

ACME. (2012a). *Increasing provision and participation in post-16 mathematics*. London. ACME. (2012b). *Raising the bar: developing able young mathematicians* (pp. 1–4). London.

ACME. (2012c). *ACME’s response to the draft Primary National Curriculum for Mathematics published on 11 June 2012* (pp. 1–15). London.

ACME. (2013). *ACME’s response to the consultation on the draft programmes of study for the National Curriculum*. London.

All Party Parliamentary Group on Financial Education. (2011). *Financial Education & the Curriculum*. London.

British Academy. (2012). *Society Counts: Quantitative Skills in the Social Sciences (A Position Paper)*. London.

Burghes, D. (2011). *International comparative study in mathematics teacher training*. London.

Clark-Wilson, A., Oldknow, A., & Sutherland, R. (2011). *Digital technologies and mathematics education: A report from a working group of the Joint Mathematical Council of the United Kingdom*. London.

Finegold, P. (2011). *Good Timing*. London.

Hodgen, J., & Marks, R. (2013). *The Employment Equation: Why our young people need more maths for today’s jobs*. London.

NFER. (2013). *NFER Thinks: Improving young people’s engagement with science, technology, engineering and mathematics (STEM)*. Slough.

Noyes, A., Drake, P., Wake, G., & Murphy, R. (2011). *Evaluating Mathematics Pathways Final Report*. London.

Ofsted. (2011a). *Tackling the challenge of low numeracy skills in young people and adults*. Manchester.

Ofsted. (2011b). *Good practice in primary mathematics*. Manchester: Ofsted.

Ofsted. (2012). *Mathematics** **: made to measure*. Manchester.

Porkess, R. (2012). *The Future of Statistics*. London.

Royal Society. (2011). *Preparing for the transfer from school and college science and mathematics education to UK STEM higher education*. London.

Science Learning Centre. (2013). *The future of STEM education*. York.

Select Committee on Science and Technology. (2012). *Higher Education in Science, Technology, Engineering and Mathematics ( STEM ) subjects*. London.

Southwood, S., & Dixon, L. (2012). *The Vital Ingredients: Adults learning maths*. Leicester.

Vorderman, C., Porkess, R., Budd, C., Dunne, R., & Rahman-hart, P. (2011). *A world-class mathematics education for all our young people*. London.

Walker, M., Straw, S., Sainsbury, M., & Clarke, C. (2013). *Evaluation of the Mathematics Specialist Teacher (MaST) programme Research report*. London.

EXCELLENT WORK.HOW CAN THESE BE IMPLEMENTED IN A COUNTRY WHERE EDUCATION IS NOT PRIORITISED?QUITE SAD TO SEE SUCH YOUR EFFORT NOT GLOBALLY SUPPORTED-

Hi thanks for your comment. I think we all agree that it would be great if the recommendations were carefully considered and weighed up against one another (of course, everything has a cost) and then decisions were made. Some of these recommendations have already been acted on – I still have to write that section – but one example is the move in England to make mathematics of some sort compulsory post-16.

THERE IS STILL A MAJOR PROBLEM IN NIGERIA ALTHOUGH MATHEMATICS IS VERY COMPULSORY UP TO SENIOR SECONDARY SCHOOL LEVEL-OUR PROBLEM IS ON IMPLEMENTATION