This section should be read in conjunction with learning pack 1, Introduction to teachers’ professional enquiry which introduces reflective practice. It encourages you to draw on key reading from Topic 2 of this module, ‘Understanding numeracy’. It also makes direct links to Topic 3 and ‘Learning and teaching numeracy’.
In the ‘Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools’, Williams (2008, p.7) stated:
Teachers and practitioners in primary schools or early years settings are not, of course, usually ‘Mathematics Specialists’, nor do they necessarily aspire to be. Indeed, it would be a mistake to equate specialist knowledge of mathematics alone with excellent teaching at this or any level.
He continues by drawing attention to a small-scale study (Askew et al., Effective Teachers of Numeracy (Final Report), London: King’s College, 1997) undertaken at the time by the Teacher Training Agency which found that having an A level in mathematics was not strongly correlated with effective teaching of numeracy. Instead, Williams argues that ‘a combination of deep subject knowledge and pedagogical skill is required to promote effective learning’ (p.-7). Furthermore, the Welsh Government acknowledges that the skills and abilities required to make an excellent teacher are not ‘restricted’ to education attainment ‘in isolation’ (Welsh Government, 2012, p.-5).
Research (for example, Shulman (1986), Ball (1989), Hill et al (2005), Pollard (2010) and Smith (2004)) underlines the importance of teachers acquiring ‘deep subject knowledge’. Shulman (1986) identified three forms of subject knowledge.
- Subject matter content knowledge.
- Pedagogical content knowledge.
- Curricular knowledge.
Consider what each of these forms of ‘knowledge’ might be in relation to ‘numeracy’.
What implications might this have for your development and training?
Smith’s report on 14–19 mathematics (2004) found that not only was it critical for teachers of mathematics to have sufficient subject knowledge, but they should also appreciate how learners learn mathematics (p.112) and the barriers or obstacles to learning that might be faced. As Shulman (1986, pp.9–10) stated:
Pedagogical content knowledge also includes an understanding of what makes the learning of specific topics easy or difficult: the conceptions and preconceptions that students of different ages and backgrounds bring with them to the learning . . . If those preconceptions are misconceptions, which they so often are, teachers need knowledge of the strategies most likely to be fruitful in reorganizing the understanding of learners, because those learners are unlikely to appear before them as blank slates.
Barriers to learning are further explored in both Topic 2, ‘Understanding numeracy’ and Topic 5, ‘Numeracy and inclusive practice.’
Within the National Numeracy Programme (NNP) it is clear that all teachers are now expected to be teachers of ‘numeracy’. They may not be mathematics specialists, but all teachers can become excellent teachers of numeracy and embed this within their subject. Clearly, practitioner development and training is a critical aspect of this goal.
Initial teacher training (ITT)
Within the current Qualified Teacher Status Standards (external link) WALES 2009, trainees must demonstrate that:
They can teach the required or expected skills, knowledge, and understanding relevant to the curriculum for learners in the age range for which they are trained, and as relevant to the age range they are trained to teach make appropriate use of the Curriculum Cymreig for learners aged 7–14 and Wales, Europe and the World for learners aged 14–19.
In 2007 the influential McKinsey and Company report identified that the selection mechanism for entrants to (ITT) as a key feature of the world’s top-performing school systems. This includes, ‘a high overall level of literacy and numeracy’ in its trainees (p.17).
Within the Requirements for the Provision of Initial Teacher Training Courses in Wales (Welsh Government, 2009), there are statutory provisions relating to the assessment of personal numeracy skills of entrants to ITT programmes. In addition, a number of providers use tests or assessments as part of entry selection criteria and undertake assessments of trainees’ numeracy skills during their training. However, for programmes commencing the academic year 2013/14, there is a specific additional requirement for all ITT providers to ensure that entrants to programmes are functionally numerate. Providers must also make sure that throughout their training, trainees are ‘regularly and accurately assessed’ to ensure that they continue to meet the required standards’ (Welsh Government, 2012, p.12).
From 2014/15 academic year, all entrants to initial teacher training programmes in Wales must have a minimum grade B GCSE or equivalent academic qualification in mathematics. This raising of the statutory entry requirement from the previous ‘C’ grade is part of the NNP's priority of advancing teachers’ own skills in numeracy and mathematics in order to improve the quality of numeracy teaching (Welsh Government, 2012).
The Universities’ Council for the Education of Teachers in Wales (UCET Cymru) has funded and developed numeracy test materials that all applicants to teacher training courses in Wales will be required to pass as a condition of entry.
1. Reflect upon the knowledge, skills and understanding of ‘numeracy’ (and mathematics) you had acquired by the end of your ITT programme. Consider the following questions.
How confident did you feel in teaching numeracy (or mathematics) across the age range that you were qualified to teach?
Did this confidence (or lack of it) stem from:
- your university-based studies on your ITT programme?
- your school-based experience on your ITT programme?
- a first degree/previous qualifications?
- your own experiences as a ‘learner’ of numeracy/mathematics?
2. Do you think that raising the entry requirements to ITT programmes (i.e. a GCSE ‘B’ grade (or equivalent) in mathematics) will support the raising of numeracy standards in primary and secondary schools? Will this increase the ‘quality’ of entrants to the teaching profession? How can we raise the quality of entrants to the teaching profession’?
3. What do you think is meant by the phrase ‘functional numeracy skills applicable to a professional teaching context’ (Welsh Government, 2012, p.12)? Reflect upon the concepts of numeracy presented in Topic 2, ‘What is numeracy?’
4. How might ITT providers further develop trainees’ abilities to teach numeracy? Is it possible for ITT programmes to develop the ‘deep subject knowledge’ in all its trainees that the Williams Report (2008) suggests is necessary to raise standards of mathematics and numeracy teaching?
5. Undertake this example numeracy test (external link) developed by the Universities Council for the Education of Teachers, Wales (UCET Cymru) to develop your knowledge of the requirements for new entrants to ITT programmes in Wales.
6. With reference to Topic 2, ‘Practitioner attitudes, beliefs and emotions’, reflect upon your emotions whilst undertaking this test in your professional journal. What numeracy skills and knowledge are being tested?
Induction and continuing professional development (CPD)
Induction is a statutory requirement for all newly-qualified teachers (NQTs) in Wales who gain qualified teacher status (QTS) after 1 April 2003. The statutory induction period provides all NQTs with a bridge from initial teacher education and training to effective professional practice as qualified teachers along a ‘continuum’ of personal and professional development.
All NQTs undertaking the induction period are entitled to a programme of professional development, monitoring and support based around the core priorities in the areas that we know are key to improving standards of teaching and for improving learner outcomes. This includes ‘numeracy’.
All NQTs in Wales are assessed against the prescribed national standards – i.e. the Practising Teacher Standards and are expected to meet these at the end of their induction period. This forms part of the practice review and development process which provides the context for their long-term professional development (Welsh Government, 2012).
Within the PTS (which all practising teachers must continue to meet through their career) (Welsh Government, 2011), ‘numeracy’ and the importance of subject matter content knowledge, pedagogical content knowledge and curricular knowledge (Shulman, 1986) is clearly identified (p.6):
Professional knowledge and understanding
16. Maintain an up-to-date understanding of their subjects/curriculum areas and related pedagogy in order to inform practice.
17. Understand their role in improving literacy and numeracy skills across the curriculum.
Masters in Educational Practice (MEP)
Within his address entitled, ‘Teaching makes a difference’ (2 February 2011), the former Minister for Children, Education and Lifelong Learning, Leighton Andrews AM, outlined his intention to seek a Master’s level profession for teaching.
As part of their induction period, NQTs working in Wales, may be eligible to apply for a place on the MEP programme (external link), a world-leading practice-based higher level qualification designed to challenge NQTs and develop high-quality teaching which will improve outcomes for learners in Wales.
Within year 2 of the MEP programme students on the programme will study a ‘numeracy’ module, one of nine core modules on the programme which reflect the three national priorities of: literacy, numeracy and reducing the impact of poverty on attainment. In addition, the three core areas that have also been identified as priorities for induction and the early professional development of NQTs are included: additional learning needs (ALN), behaviour management and reflective practice.
Visit the MEP Wales website (external link) to find out further information about the MEP programme.
View the video of ‘MEP Students Thoughts: Feedback about the Masters in Educational Practice programme so far’. Do any common themes emerge from this?
Outstanding teachers of numeracy (OTN)
Within its Improving schools document (2012, p.15), the Welsh Government sets out its three key priorities for improving the quality of learning and teaching in schools.
- Improving the quality of teaching in literacy and numeracy.
- Supporting teacher and support staff professional development.
- Strengthening our approaches to inclusion and safeguarding.
Within priority 1, it asks regional consortia to lead the identification and deployment of outstanding teachers of literacy (OTLs) and outstanding teachers of numeracy (OLNs). These practitioners will be used to coach and mentor their peers to raise the skills of the workforce across each region in Wales through both the National Support Programme (NSP) (supporting implementation of the National Literacy and Numeracy Framework (LNF)) and professional learning communities (PLCs).
An OTN is defined as:
- a very good classroom teacher who already demonstrates effective classroom practice, planning and assessment processes
- a member of staff with the desire and skills to influence, support and coach teachers and learning assistants (not necessarily teach their classes).
An OTN will also need to:
- complement the work of the mathematics coordinator
- demonstrate good practice with regard to the learning and teaching of mathematics
- be keen to improve their own teaching of mathematics and willing to share the lessons learnt from this with other staff
- seek to reduce variation throughout the school and embed consistent and effect practice in all classes
- be motivated, interested and willing to share their expertise with other teachers and schools (e.g. planning and delivering staff meetings, supporting PLCs within their own school and with other schools).
Professional learning communities (PLCs)
A professional learning community (PLC) is a group of practitioners working together using a structured process of enquiry to focus on a specific area of their teaching to improve learner outcomes and so raise school standards.
(Welsh Government, 2011)
Following extensive research and a pilot programme led by Professor Alma Harris, the Welsh Government has provided a national model and guidance for PLCs which encompasses seven phases to take practitioners through the process of setting up and running an effective PLC.
The Welsh Government’s rationale for PLCs is to ‘encourage collaboration and meaningful professional dialogue between practitioners at all levels with the ultimate aim of improving learner outcomes’ (Welsh Government 2011). This is based on extensive research evidence which shows that teachers who are part of a PLC tend to be more effective in the classroom and achieve better student outcomes (Lewis and Andrews, 2004). PLCs can also improve teachers’ professional learning and secure improved school performance, irrespective of the school context and its socio-economic profile (Elmore, 2002; Goldenberg, 2004).
Read the introduction to Professional Learning Communities (external link) by Alma Harris and Michelle Jones.
1. Look at your school or department’s improvement plan and consider the following the questions.
- Does ‘numeracy’ feature in this plan?
- Is there reference to developing the numeracy skills and expertise of teachers? If so, do you think this will help to meet your own professional development needs? How?
- Are there any priorities in the plan in relation to numeracy, for which you feel you may need professional development, but which you had not previously considered?
- Have you self-identified any professional development needs in relation to numeracy which are not addressed in this school or department plan?
2. Think about the range of professional development opportunities currently available to you (e.g. the MEP, the LNF NSP, participation in PLCs). Using the following list as a starting point, reflect upon which methods of professional learning you most enjoy. For example:
- school-based training
- off-site training (e.g. a day’s course)
- action research or enquiry (e.g. individual or collaborative enquiry such as a PLC)
- self-directed study
- directed learning (e.g. through distance or online learning materials)
- coaching, mentoring or tutoring
- peer networking
- working parties or collaborative projects (e.g. as a ‘cluster’ of schools)
- placement in another school/setting
- an online discussion forum
- demonstration and observation activities (e.g. a lesson modelled by an OTN)
- professional journaling.
3. Now identify three aspects of professional learning that you have been involved in during the past year (e.g. understanding the LNF) and note down the professional learning methods that you experienced.
|Focus for the professional learning||Professional learning method(s) experienced|
|e.g. Understanding the LNF||Self-directed study, Off-site training|
Now consider how worthwhile these activities were in terms of your personal and professional development. How satisfied were you with the professional learning experience?
In evaluating effectiveness, Craft (2000, p.86) identifies the following areas for consideration in terms of ‘impact’.
- Teachers’ knowledge, attitudes and skills.
- Teachers’ practice or personal growth.
- Teachers’ careers or roles.
- School or team culture.
- Learners’ learning.
- School or team management and organisation.
- Which of these do you think is the most important? Provide reasons to support your response.
- Did the professional learning methods you engaged with lead to a change in your practice? If yes, how? What was the outcome of this? If no, what do you think the reasons for this are?
- Did your professional learning experience lead to a change in the practice of others? (e.g. colleagues in your school/another school)
4. Return to the professional development needs that you identified in part 1 of this activity. Which methods of professional learning might you engage in, in order to meet your needs? How will you evaluate the effectiveness of your learning? Which criteria will you use?
Represent your learning and action throughout this activity in your professional journal. Remember that the focus is upon how you will improve your own numeracy skills and knowledge to ensure you can teach your learners effectively.
Continuing professional development for practitioners working with 16 to 19 learners
Essential Skills for Work and Life (Level 1–3) qualifications recognise that learner skills do not always sit comfortably within a level so they have the opportunity to mix the levels of units within the qualification. Learners based in the workplace can design the qualification content to suit the specific needs of the industry within which they are based. Staff can also use the qualifications as part of their own CPD.
Essential Skills Practitioner Qualifications are:
- Level 3 Certificates for Essential Skills Practitioners-Numeracy, (Literacy and English Speakers of Other Languages (ESOL)) gives practitioners the knowledge required to work with young people and adults with essential skills needs and the skills required to assess, plan and deliver their learning
- Level 2 Award in Supporting Adults and Young People in Essential Skills enables practitioners to develop the skills to engage and support adults and young people with communication, numeracy, or ESOL needs.
Level 5 Certificate in Teaching Adult (post-16) Numeracy (Literacy or ESOL) is a nationally recognised qualification designed for current teachers who wish to study to gain a nationally recognised specialist qualification. The specialist certificate provides an opportunity to review and extend numeracy subject knowledge and pedagogy, and to develop professionally.
Agored Cymru has also developed units which support CPD in key areas of essential skills delivery. These Embedding Numeracy in Mixed Ability Vocational Groups, Teaching to Mixed Ability Groups, Diagnostic Assessment and also some which use action research to explore teaching strategies. A number of organisations have produced useful teacher education resources which can be used to support the delivery of these units (see useful links below).
Andrews, L. (2011) Teaching makes a difference. Reardon Smith Theatre, National Museum of Wales, Cardiff. Transcript. (accessed 30 September 2013)
Craft, A. (2000) Continuing Professional Development: A practical guide for teachers and schools (2nd Edition). London: RoutlegeFalmer.
Hill, H. C., Rowan, B. and Ball, D. (2005) Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement. American Education Research Journal, 42 (2), pp. 371–406.
Pollard, A. (2012) Reflective teaching: evidence-informed professional practice. 3rd Edition. London: Continuum.
Shulman, L. (1986) Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15 (2). pp.4–14
Welsh Government (2011) Revised professional standards for education practitioners in Wales. Cardiff: Welsh Government.
Welsh Government (2012) Improving schools. Cardiff: Welsh Government.
Welsh Government (2012) Induction for newly-qualified teachers in Wales (revised September 2012). Cardiff: Welsh Government.
Welsh Government (2013) Professional learning communities. Cardiff: Welsh Government.
Williams, P. (2008) Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools.
The Department for Education (England) website (external link) provides practice materials for the numeracy professional skills test for trainee teachers which entrants to ITT courses in England must successfully pass. Current ITT trainees need to pass the tests before they can be recommended for the award of QTS. Applicants starting ITT training courses from September 2013 need to pass the tests before starting their course.
Visit YoutTube for the numeracy tests (external link).
The McKinsey report (2007) (external link) provides information on how high-performing countries recruit high-quality entrants to the teaching profession.
Professional learning communities and system improvement (external link) – An ‘improving schools’ article by Alma Harris and Michelle Jones.
Teachers who may have difficulty with numeracy (external link) This offers an opportunity ‘to check your understanding of the mathematics you are teaching and to explore ideas on how to develop your practice’.
A set of teaching resources on the Excellence Gateway (external link) ranging from Entry level 1 to Level 2 for ESOL, literacy and numeracy.
Thinking Through Mathematics (external link) resource for numeracy CPD and collaborative teaching resources.
Improving Learning in Mathematics (external link) provides resources for learners at Level 1 and Level 2.
National Research and Development Centre for Adult Literacy and Numeracy (NRDC) (external link) conducts research and development projects to improve literacy, numeracy, language and related skills and knowledge. They provide a range of resources to support staff CPD.
Skills for life (external link) resources all mapped to the literacy, numeracy and ESOL core curriculum.
Diagnostic tools (external link) for use in assessing the specific numeracy skills needs of post-16 learners once initial assessment has given an approximate level from Excellence Gateway.
Essential Skills Wales (external link)
The Embedded Learning Portal (external link) hosts a range of teaching resources for embedding essential skills into contexts ranging from hairdressing to horticulture.
Hwb Wales (external link) provides an excellent source of interactive resources at all levels.
The Welsh Financial Education Unit (WFEU) (external link) provides support to practitioners who are delivering financial education to 7 to 19-year-olds.
‘Talent’ (external link) is a support site for teachers of ESOL, numeracy and literacy, providing resources and links to other useful sites.
Citizen Advice (external link) provides resources which use everyday consumer situations, such as choosing a mobile phone, as contexts for learning numeracy and literacy.
For teachers may have difficulty with numeracy, the National Centre for Teaching Excellence (external link)offers and opportunity ‘to check your understanding of the mathematics you are teaching and to explore ideas on how to develop your practice’.