Good Practice in Primary Mathematics 1. Background 2. The seminars 3. Introduction to the seminars

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1 Good Practice in Primary Mathematics This is a report of two seminars held on 5 March 2012 at the Royal Society, London, cohosted by the Advisory Committee on Mathematics Education (ACME) and the Department for Education (DfE). The report summarises the main issues raised and describes views presented at the meeting. This report captures the views of participants and does not represent ACME or DfE policies. 1. Background These seminars followed the recent publication of the Ofsted report Good practice in primary arithmetic: evidence from 20 successful schools, 1 which identifies characteristics of effective practice in building pupils' secure knowledge, skills and understanding of number so that they demonstrate fluency in calculating, solving problems and reasoning about number. The aim of the seminars was to bring together practitioners and members of the mathematics community to discuss the Ofsted report and contribute to a wider discussion on improving the teaching of primary mathematics. 2. The seminars The seminars were chaired by Lynne McClure, a member of ACME and Director of NRICH. Around 80 teachers from primary and secondary schools, members of ACME, representatives from the DfE, researchers in mathematics education and publishers participated in the two seminars. To set the scene for each seminar and stimulate discussion Jane Jones HMI, National Adviser for Mathematics at Ofsted, presented background to the Ofsted report, the design of the study and the findings presented in the report. As National Adviser for Mathematics, Jones is responsible for Ofsted s work in mathematics 3-19, managing the annual mathematics survey programme and disseminating findings. The seminars each split into five small groups to discuss the issues raised by the report and the presentation. Group facilitators used the following themes as prompts for discussion: resources; organisational structure; education and training of teachers; National Curriculum Review. Each seminar concluded with a brief plenary from a representative from the DfE: Katie Farrington, Head of Standards and Testing Agency (STA), an executive agency of the DfE which is responsible for the development and delivery of all statutory assessments from Early Years to the end of Key Stage 3; and Stephen Rogers, Team Leader Raising Standards in Mathematics and Science at the DfE. 3. Introduction to the seminars Lynne McClure highlighted that the National Curriculum Review has ignited interest in arithmetic teaching. In response to concerns in the mathematics education community about emerging policy regarding primary arithmetic, ACME published its 2011 primary mathematics position paper, 2 which identifies the skills, knowledge and capabilities required by the end of 1 Ofsted, Good practice in primary arthimetic: evidence from 20 schools, 2011, 2 ACME primary mathematics position paper, 2011,

2 primary school. In its paper ACME concludes the development of memorisation, accuracy and fluency is recognised as important but this must take place in parallel with development of understanding and reasoning. This paper builds on the recommendations put forward in an ACME position paper on primary mathematics published in McClure welcomed the Ofsted report and the opportunity the DfE had provided through these seminars for stakeholders to discuss the report with a view to informing the National Curriculum Review. 4. The Ofsted report: Good practice in primary arithmetic: evidence from 20 successful schools Jane Jones explained that the report is the product of a ministerial request made to Ofsted to provide evidence of best practice in the teaching of mathematics in primary schools in England. The 10 maintained schools featured in the study were selected from 600 schools with above average curriculum-based assessment (CBA) scores for the past four years leading up to Jones explained that it was her decision to include 10 independent schools in the study, thus providing Ofsted with a valuable opportunity to collect data on mathematics teaching practice in this sector of primary education. During one-day visits to each school evidence was gathered through: discussions with teachers, leaders and pupils who had successfully overcome their initial difficulties with calculation; lesson observations and scrutiny of pupils' work; and analysis of documentation, including curriculum policies, and information on intervention strategies and professional development. The schools featured in the report established the best start in Early Years Foundation Stage and Key Stage 1 through practical, hands-on experiences of using, comparing and calculating with numbers and quantities, and the development of mental methods, coupled with opportunities to increase children's understanding and use of mathematical language. The schools encouraged children to think flexibly by placing a strong emphasis on problem solving. The schools offered a varied mix of problems, which were relevant to and engaging for pupils, to support learning. Activities ranged from short problems, such as counting daily attendances and working out the value-for-money of supermarket products, to measuring the school playground and preparing an estimate for the cost of new tarmac for its surface. Emphasis was placed on understanding of place value, fluency in mental methods, and good recall of number facts as essential precursors for learning algorithms, which older primary pupils tended to favour for written calculations. There was variety among schools in the methods taught and in the years in which they were taught.. Teachers felt it was important that pupils fully mastered each stage before the next steps were introduced. Crucially all the schools made sure pupils difficulties were quickly identified and timely well-focused help offered to overcome these. The schools recognised the importance of good subject knowledge and subject-specific teaching skills and sought to enhance these in their staff. Clear calculation policies and guidance made sure that all staff (teachers and teaching assistants) worked together on mathematics to develop their subject expertise. Some schools benefited from leaders who had high levels of expertise. Jones emphasised that the adoption of a clear calculation policy coupled with the whole-school approach to developing the subject expertise of teachers and teaching assistants offered the greatest potential to raise standards in the teaching of mathematics in primary schools. 3 ACME Position Paper: key issues for the future of primary mathematics learning and teaching, 2006,

3 4.1. Feedback on the Ofsted report Delegates broadly welcomed the Ofsted report, commenting that it emphasises the need to teach understanding of mathematical concepts while at the same time nurturing maths skills, such as good number fact recall, for pupils to become effective mathematicians. It was felt the Ofsted report also identifies good teaching practice from which schools could learn from and build on, e.g. making connection between mathematical concepts, using a variety of resources, and promoting a problem-solving approach to learning. It was suggested that staff in schools, and teacher trainers working with their trainees, should be encouraged to discuss the report to ensure its messages are disseminated and discussed effectively, rather than just sending copies of the report to schools and initial teacher education institutions. Delegates provided Ofsted with some useful comments about areas not covered in the report and areas open to interpretation. These included: the report provides limited discussion on the pitch of calculation methods teachers should aim for, i.e. when pupils should be expected to move on from one calculation method to become more efficient; other important aspects of successful calculation are not mentioned in the report, such as children's use of approximation and checking strategies other than the inverse function; elements of the report might be perceived to promote a focus on formal algorithmic approach to calculation. 5. Disseminating innovations in teaching practice There was general agreement that the culture of sharing ideas, approaches and developments in the teaching of mathematics, as exemplified by the successful schools in the Ofsted report, needs to be nurtured among the mathematics teaching community in the primary and secondary sectors. Senior management teams in primary and secondary schools, and the National Curriculum, were identified as the potential drivers for this change. Although isolated clusters of schools have started to form, it was felt that the removal of Local Area Agreements (LAAs) in 2011 had limited opportunities for teachers to share ideas and innovations in approaches to teaching. 6. Calculation policy It was recognised that the teaching of explicit calculation methodologies in primary schools in isolation can lead to significant problems for learners during transition to secondary schools, where alternative approaches to calculation may be favoured. Linked or local primary and secondary schools would benefit by collaborating on the development of an agreed calculation policy. As exemplified by the schools in the Ofsted report, all teachers teaching maths at primary and secondary level should be made aware of this policy and involved in its review and further development. 7. Education and training of teachers 7.1. CPD to implement the new National Curriculum Participants felt that teachers and teaching assistants should be provided with tailored CPD to support them in adopting and managing changes to the teaching of mathematics as a result of the National Curriculum Review. 3

4 7.2. Specialist teachers Throughout the seminars there was strong support for training and recruiting more specialist maths teachers in primary schools. The discussions highlighted that there are several different types of specialist mathematics teachers working in primary schools MaST teachers, trainees from training schools networks, and advanced skills teachers (ASTs). Each of these was seen to have different levels of specialism. Comments suggested that schools should be free to decide how their specialist teachers are deployed MaST programme There was strong support for the MaST programme, which has been successful in making nonspecialist primary teachers more confident about teaching maths. Teachers who complete the MaST programme benefit greatly from improved subject and pedagogical knowledge. Delegates placed a high value on the programme because its MaST-qualified teachers encourage the whole-school approach to staff training and development shown to be so effective in successful schools in the Ofsted report. There was strong support for further investment to expand the roll out and uptake of the programme across the country Training and Development Agency for Schools (TDA) consultation Discussion of the current TDA consultation highlighted concern among delegates regarding a proposal to increase the time trainees spend on school placement during the primary PGCE course. Delegates were not in favour of the proposed extra practical experience coming at the cost of time devoted to subject knowledge and subject-specific pedagogical knowledge, based on research and reflection.. Among the suggestions to avoid limiting time for research and reflection were: extend the PGCE course to two years; a requirement for teachers to undertake long-term, reflective CPD in their NQT year and beyond Teaching assistants Some delegates in the seminars were concerned that a common role of teaching assistants in maintained schools is to support the learning of low-achieving students, despite the varying degrees of teaching assistants' subject and pedagogical training. It was felt that teaching assistants should have access to and support for CPD to enhance their subject-specific and pedagogical knowledge and skills. 8. National Curriculum Review The National Curriculum Review represents an opportunity to effect a change in teaching practice and methods. During the seminars delegates mentioned that they would like to see the National Curriculum: capture the themes of coherence and progression in the teaching and learning of mathematics across the entire curriculum, rather than set tight boundaries for attainment at Year 6; avoid a discrete focus on calculation at the cost of developing deeper understanding of maths. Instead the National Curriculum should maintain the link between developing pupils' understanding of calculation alongside their fluency; promote children to talk about mathematics in the classroom to help develop their vocabulary of mathematics, thinking skills and mathematical processes; include a clear statement on the range of children's calculation abilities; promote a culture of sharing good practice among teachers, teaching assistants, headteachers and schools, in particular to support trainee teachers and newly qualified teachers. A discussion on the inclusion of conceptual understanding requirements for mathematics in the National Curriculum document led to the suggestion that professional bodies may have a role to play in supporting the DfE National Curriculum Review team in communicating these requirements in a clear and concise manner. 4

5 It was suggested that a programme of study for primary mathematics will need to emphasise the links with and connections between mathematical methods and topics covered. There was general agreement that Key Stage 3 and the transition from primary to secondary mathematics teaching are the big issues that need to be addressed. Delegates identified the lack of coherence between calculation policies across the primary and secondary interface and the deployment of non-specialist maths teachers at Key Stage 3 as factors affecting the quality of the learning experience during this phase. 9. Resources 9.1. Development of new resources Delegates representing publishers indicated that the outcomes of the National Curriculum Review are a key driver for the development of new teaching resources. The time-scale of the review and its implementation offers limited time for publishers to develop, test and review new resources Gaps in provision Discussions on resources identified several gaps in provision. These included resources that: encourage the use of traditional practical resources and promote a problem-solving approach; offer ideas for teaching approaches that are relevant and engaging for pupils; teachers and pupils can refer back to (textbooks) to maintain a coherence throughout young people's maths learning experience; support the role parents play in their children's maths learning; offer interactive assessment for learning; 9.3. Support for teachers evaluating resources Although there is a plethora of free online resources available to primary maths teachers, comments suggested that these are expensive with respect to time spent by teachers finding, evaluating and incorporating the resources in lesson plans. More CPD support to develop primary teachers' skills to evaluate resources is required, for example, several institutions already include an evaluating resources component in initial teacher education courses. 10. DfE plenary In their concluding plenary Katie Farrington and Stephen Rogers explained the goals set by the department s ministers with respect to mathematics:: for all pupils to leave primary education equipped to learn maths-related subjects in secondary education; ensuring that high-attaining students in secondary education are given the opportunities to perform at the highest level; and equipping students with the mathematical skills, knowledge and understanding to study subjects supported by maths post-16 and in HE, and to be effective employees on leaving education. Both Farrington and Rogers commented that the seminars had shown that there is strong support among the maths community for the MaST programme, which through collaboration with HEIs will continue as a self-funding programme. They added that the value and impact of the MaST programme in participating schools will be quantified in the independent evaluation report produced by NFER to be published in September Among the messages from the day's discussions the DfE representatives noted were: the importance of coherence throughout young people's maths learning experience; the need to support non-specialist teachers who might lack confidence in their teaching of maths; recognising the value of number facts and recall and that pupils need to develop efficient 5

6 calculation procedures alongside building a deeper understanding of numbers and calculation. the time-scale of the National Curriculum Review and the issues this causes for publishers. ACME and the DfE will come together to revisit issues in mathematics education and assess progress made at the ACME national conference in July Conclusions The seminar discussions show that the Ofsted report offers much food for thought for all primary schools in England as they strive to raise standards in mathematics through good teaching practice. Delegates concluded that the report, accompanied by supporting explanatory notes, should be discussed among headteachers, subject leaders and all teachers teaching mathematics in primary and secondary schools, as well as teacher trainers and their trainees. Through the seminars the delegates identified at least five factors that are essential to promote good practice in primary mathematics teaching: a coherent calculation policy which has the buy-in of the whole school; a culture of sharing ideas and innovations in teaching methods among the teaching community; a National Curriculum which ensures coherence throughout young people's maths learning experience; the recruitment of more specialist maths teachers; more support and opportunities for teachers and teaching assistants to undertake CPD that develops their subject-specific and pedagogical knowledge and skills. 6