IMPROVING CONFIDENCE AND FLUENCY IN MATHS FOR CHILDREN, YOUNG PEOPLE, PARENTS AND ALL THOSE WHO DELIVER MATHS EDUCATION
Improving confidence and fluency in the learning and teaching of maths is essential for creating greater enthusiasm and raising attainment. We considered how best to do this across a range of areas from tackling maths anxiety and improving progression pathways to enhancing teacher education and better supporting parental and family learning. This section presents our findings and recommendations in these areas.
"There should be no such thing as boring Mathematics."
Professor Edsger Dijkstra, computer scientist
Tackling Maths Anxiety
Our interim report highlighted findings from the 2012 PISA (Programme for International Student Assessment) survey contained in the OECD report Improving Schools in Scotland: An OECD Perspective  that some 30% of Scottish learners reported that they feel very tense and nervous when doing maths work and more than 50% worry that maths will be difficult.
The anxiety levels reported by Scottish 15 year olds are similar to the OECD average and similar to those of Canadian, Irish and New Zealand students, but higher than the levels reported in the Netherlands and Norway. The OECD recommended that the issue of maths anxiety in Scotland warrants close attention. The OECD's report also highlights that girls are more prone to low self-confidence in ability to learn maths than boys, even when they perform at similar levels. This is an issue across OECD countries. Scotland is no different in this regard than elsewhere.
In addition, the 2015 SSLN  survey indicates the need to improve learning and teaching to raise attainment in maths.
We believe that promoting a growth mind-set approach, and other methods of improving learner confidence such as positive learning dispositions, are essential to addressing maths anxiety and raising attainment. Promoting a growth mind-set means encouraging learners to understand that their abilities are not fixed and they can improve their skills through effort and dedication. This involves setting challenging but achievable goals and understanding where to obtain support when necessary. It also means learning from mistakes and using this experience to embrace new challenges.
These methods need to be a strong and explicit part of maths learning and teaching throughout early years and school education. This leads to our fourth recommendation:
All schools and nurseries should use a wide range of effective learning and teaching approaches to promote positive attitudes and develop high expectations, confidence and resilience in maths.
Lasswade Primary School in Midlothian has developed eight "Learning Superheroes" based upon learning dispositions and skills which have been demonstrated by research to play a role in the development of a growth mindset. So, for example, Tough Tina represents resilience and never giving up, while Curious Kevin instils in pupils the importance of asking questions and being inquisitive. The research was initially carried out with P1 pupils in 2014/15 and the approach has now been embedded across the school. Future plans include considering using the approach in the associated nursery.
Although the Learning Superheroes underpin learning throughout the school, they have particularly helped pupils develop mathematical resilience. For example, Mike the Mistake Maker models a growth mindset and encourages children to use mistakes as opportunities for learning. Learning Lola promotes an enthusiasm for learning in maths and encourages children to use a variety of strategies when faced with a challenge. One P3 pupil commented, "I love maths now because the Superheroes help me!
Improving Progression Pathways in Maths
Research evidence  and feedback from our focus groups emphasised the importance of ensuring good progression pathways in maths. Maths is a sequential subject and the learning achieved at each stage provides the foundation for the next stage.
To help achieve this, progression pathways should develop good understanding of, and confidence in:
- calculating mentally
- using appropriate mathematical language and notation
- applying key mathematical properties
- developing understanding about relationships between numbers and mathematical concepts.
Good learning and teaching should emphasise the connections between:
- different aspects of maths (for example, connections between topics such as shape, number and algebra)
- different representations of mathematics (for example, moving between symbols, words, diagrams, objects and graphs)
- learners' methods (for example, encouraging learners to explain their thinking and promoting collaborative learning).
Ensuring effective transitions between primary and secondary education is particularly important. This should include providing continuity and progression in learning through professional dialogue between staff and effective reporting of pupils' achievements including through P7 profiles. Consideration should also be given to developing joint Career Long Professional Learning ( CLPL) activities particularly in relation to progression, assessment and moderation.
Currently, there is great interest in maths mastery approaches from South Asia. Professor Ruth Merttens  suggests that some of the general principles of these methods can be beneficial particularly for Scottish primary school education. However, Professor Merttens warns against adopting these methods wholesale as a "one-size-fits-all" approach. The general principles that Professor Merttens recommends are:
- a coherent approach to skills development and progression
- consistency in models, images and pedagogic vocabulary
- an emphasis on memorised facts to help learners develop a secure bank of memorised number facts to support them in making mental calculations and other aspects of maths
- "over-learning" - drawing repeatedly on fundamental concepts and key skills
- practising skills, strategies and methods to embed learning
- constant small interventions and differentiating learning with an emphasis on supporting pupils to achieve their best and ensuring that there are no gaps in learning.
We support these principles as key to improving learning and teaching and raising attainment.
Education Scotland is continuing to produce advice and support to help schools gain a deeper understanding of how learners can progress in maths in line with the experiences and outcomes for Curriculum for Excellence and help prepare learners for National Qualifications in Mathematics. This includes benchmarks for numeracy and mathematics and the National Numeracy and Mathematics Progression Framework  available on the National Improvement Hub  .
However, further work is needed to improve the quality of learning and attainment. This leads to our fifth recommendation:
Education Scotland should evaluate the quality of children's and young people's learning experiences and attainment in maths and share examples of good practice.
Interdisciplinary learning  helps learners to make connections across different subject areas to deepen their understanding and apply their learning in different contexts. Feedback from our focus groups and other discussions indicates that there is significant scope to improve interdisciplinary learning with a maths context and at an appropriate level of challenge. This could cover STEM (Science, Technology, Engineering and Mathematics) topics or using maths and historical studies to investigate famous Scottish mathematicians and the impact of their work. It could also involve promoting cross-subject approaches to the use of particular aspects of maths such as statistics and graphs.
The Making Maths Count blogs can be used as a starting point for interdisciplinary learning as they cover issues ranging from the use of maths in sport and psychology to creating computer games to cookery. Interdisciplinary learning provides good opportunities to develop employability skills. The blogs contain examples of how maths is used in jobs ranging from engineering to marketing to beauty therapy.
Financial education topics also provide a strong basis for interdisciplinary learning. Education Scotland has produced resources  for financial education that can be used within interdisciplinary learning.
Interdisciplinary learning needs to have clear purposes and learning outcomes and help learners develop their skills, knowledge and understanding of maths. STEMEC has produced advice  on developing interdisciplinary learning within STEM subjects.
The Group's interim report discussed entry figures and pass rates for National Qualifications in Mathematics. Initial results data for 2016 are now available  . These show a decline in entry figures for Higher Mathematics from 21,074 in 2015 to 18,868 in 2016. This contrasts with a rise in the entry figures for Higher English from 35,354 in 2015 to 36,356 in 2016. Our interim report highlighted the growing gap in entry patterns between Higher Maths and Higher English and it is disappointing to see this trend continue and increase with the latest figures. The total number of passes for Higher Mathematics also decreased in 2016 (13,863) compared with 2015 (15,169).
More positively, both numbers of entries and number of passes increased for National 5 Mathematics. The number of entries increased from 36,475 in 2015 to 41,780 in 2016 and the number of passes increased from 22,536 in 2015 to 26,412 in 2016.
Our focus groups provided views from pupils and teachers on National Qualifications courses in Mathematics. Feedback from the focus groups indicates concerns over the amount of assessment within these courses. Pupils in S4 to S6 perceived Mathematics as different from other subjects in terms of the time pressures particularly at Higher level: "You are constantly moving from one thing to the next and it makes it difficult if you are struggling with a particular aspect; it's also hard to remember what you have done and catch up if you fall behind." They did however enjoy the process of working out a problem and getting the right answer. The pupils thought that this was a more satisfying experience in Mathematics than other subjects that they were studying.
The pupils in our focus groups who decided not to pursue National Qualifications in Mathematics beyond S4 reported that they had lost confidence due to concerns over the potential volume of content and lack of time to absorb this material. Their perceptions of Mathematics contrasted with those of other subjects such as English which they believed to have a slower pace of learning. The perception of a faster pace of learning in maths meant that some pupils were concerned that there might not be enough time for them to receive the support they might need if they choose to pursue National Qualifications in Mathematics.
Teachers said that the pace of learning, coupled with maths anxiety, is creating difficulties for some pupils. They noted that the volume of assessment is curtailing the opportunities to consolidate learning. Some also expressed concern that the broad general education may not be preparing pupils for National Qualifications in Mathematics as effectively as possible.
Teachers surveyed in research  by the Scottish Qualifications Authority ( SQA) raised similar concerns: "The high volume of content is an issue in some subjects". This was indicated in a number of centres - especially in subjects such as Maths, Sciences and History. Teachers also felt that there was a huge jump in the "step up" from National 4 to National 5, but less so from National 5 to Higher.
The Assessment and National Qualifications Group has been taking action to address these concerns. The Group brings together national and local government, teacher professional associations, SQA, Education Scotland and other partners. The Group's remit is to make recommendations on:
- the policy framework within which National Qualifications are developed and operate
- assessment policy and practice from ages 3-18, and the best means of supporting improvements.
The Group's first report provided a series of actions to reduce the assessment demands for National Qualifications. As part of this, SQA published individual subject reviews. In relation to National Qualifications for Mathematics  , the actions include introducing cut-off scores for unit assessments. Similar action has already been taken for Lifeskills Mathematics  .
The Scottish Government's Delivery Plan for Education  includes commitments to explore further means of reducing workload demands associated with National Qualifications. We would encourage SQA to take account of the concerns of learners and teachers over the volume of content within National Qualifications for Mathematics.
The Mathematics Development Group is a practitioner-led group tasked with providing greater support for National Qualifications in Mathematics at National 5, Higher and Advanced Higher levels. This includes advice and support on:
- closing the gap for learners between National 4 and National 5 Mathematics
- aspects of National 5 Mathematics covering vectors, quadratics, straight line and Indices and surds
- aspects of Higher Mathematics including problem solving, indices and inverse functions.
The Group has also provided support for Lifeskills Mathematics at National 5 level in relation to the geometry measures unit.
The materials are available on the National Qualifications site on Glow - the digital environment for Scottish schools and educational establishments. Education Scotland's National Numeracy and Mathematics Hub is also promoting and supporting use of the resources.
Initial Teacher Education
Our focus groups included discussions with students in Initial Teacher Education covering primary school teaching and secondary school teaching in maths and other subjects.
The students in our focus groups were generally positive about their tuition. Those on ITE courses for primary school teaching would like to have more of their course time dedicated to maths. The students on ITE courses for secondary school maths teachers had degrees either in maths or with significant maths content and therefore felt well prepared in teaching the content of maths courses. The students would find it helpful for ITE courses to include more of a focus on how teachers can better understand and support children's thinking processes in maths. The students on ITE courses for secondary school teaching in other subjects believed that they had sufficient maths skills to cover maths-related content in their subjects which ranged from Geography to Business Studies to Science.
The views expressed in our focus groups are reflected in the findings of a much wider survey of the views of current probationers and early careers teachers undertaken as part of an evaluation report on the impact of the implementation of Teaching Scotland's Future  . The majority of current probationers and early careers teachers surveyed felt that numeracy (and literacy) were adequately covered during ITE - more so in primary than in secondary. However, as with all aspects of ITE, respondents felt that more practical strategies would be beneficial. Respondents were asked their views on how useful they found different aspects of their ITE courses in helping to prepare them for their first teaching post. With specific reference to the numeracy aspects of ITE courses, 56% of the 903 respondents said that this had been useful or very useful; 20% said that it had been neither useful nor not useful and 21% reported that it was not useful or not at all useful.
Currently, the minimum entry requirements to ITE courses in Scotland are for applicants to have attained a National Qualification in Mathematics at SCQF (Scottish Credit and Qualifications Framework) level 5 (e.g. National 5 or Standard Grade Credit or Intermediate 2 level). The current requirement in relation to English is for applicants to have attained a National Qualification Course award at SCQF level 6 (e.g. Higher level).
The General Teaching Council for Scotland ( GTCS) plan to begin a review of minimum entry requirements in January 2018 with revised requirements due to be published in June 2018 to have effect for the ITE intake in August 2019. We would wish this review to consider the case for raising the minimum entry qualifications for Mathematics to the same level as that for English.
The students in our focus groups did however express some concern if the minimum entry requirements for maths were raised to SCQF level 6 as this would preclude some of them from entering teaching. They suggested that online testing of applicants' maths and numeracy skills and/or greater use of subject specific entry requirements would be better than raising minimum entry requirements in general. These options should be considered as part of the review.
The content of ITE courses is not prescribed centrally but decided by individual institutions themselves subject to accreditation by the GTCS. We need our primary teachers in particular to be more confident and skilled in the teaching of maths.
These issues lead to our sixth recommendation:
The GTCS, in partnership with Initial Teacher Education Institutions, Education Scotland and local authorities, should undertake research on how well ITE students are being prepared to teach maths as newly qualified teachers. The research should include a review of:
- Minimum entry requirements to ITE for Maths.
- Other means of ensuring applicants have good quality maths skills, e.g. online testing of applicants' numeracy skills.
- The extent to which there is sufficient coverage of maths in primary ITE programmes to allow meaningful, quality maths learning in primary schools.
- The means by which ITE institutions continuously update and improve their programmes and provide a practical focus on teaching and learning styles that instils teacher confidence in delivering maths.
- The extent to which the probationary year promotes good quality teaching and learning styles and improving confidence in maths.
Career Long Professional Learning
International evidence supports the view that teachers benefit from enhanced Career Long Professional Learning ( CLPL) opportunities to increase their confidence and professional practices in teaching maths. For example, the European Commission's Eurydice network report Mathematics Education in Europe: Common Challenges and National Policies  states that participation in CLPL opportunities can have a substantial impact on teachers' "work, their achievement, skills and attitudes as well as on their performance and job satisfaction." Furthermore, "an overwhelming amount of research evidence shows that teachers' professional development has a positive effect on student achievement."
In relation to the content of CLPL activities, the report highlighted research findings that the most effective approaches "went beyond generic pedagogy by providing teachers with a range of mathematics-based content and teaching methods that were specific and exclusive to mathematics."
Successful activities "shared an emphasis on developing students' conceptual understanding of mathematics and encouraged multiple approaches to mathematical problem-solving." They also "developed not only teachers' understanding of their students' mathematical thinking but also their ability to evaluate it."
In Scotland, there is a range of support that local authorities and schools can draw upon to provide CLPL specific to maths. This includes resources on the National Numeracy and Mathematics Hub - a virtual learning environment, administered by Education Scotland and accessed through Glow. There are also opportunities through partnerships with universities including formally accredited learning at SCQF level 11 (often referred to as "masters" level learning). The Professional Update process provides a chance for teachers to consider their CLPL needs and opportunities.
Local authorities are developing their approaches to providing effective CLPL for teachers in maths as exemplified by the following case study:
Fife Council's Pedagogy Team helps to develop primary school teachers' skills in improving pupils' conceptual understanding and confidence in maths. There is a particular focus on improving outcomes for the most vulnerable learners. The team uses baseline and diagnostic assessments to identify pupil needs and progress. Teachers are encouraged to provide greater opportunities and support to pupils to talk about maths. This helps to boost pupils' mathematical understanding, memory, reasoning and language development. Pupils are circulated round different groups to facilitate greater interest and promote peer learning. The Team also supports teachers working across clusters with associated schools and nurseries to promote professional dialogue in maths teaching and learning.
We believe that there is a clear case for further enhancing CLPL provision for maths. This should be aimed at assisting staff to promote more engaging teaching styles; developing and consolidating key concepts in maths; logical thinking (e.g. problem solving); promoting growth mind set approaches in relation to maths and highlighting the relevance of maths to everyday life and work. This leads to our seventh recommendation:
All sectors of education should promote access to high-quality career-long professional learning ( CLPL) to increase staff confidence and enhance professional practices in teaching maths to children, young people and adult learners. Each local authority should design, implement and evaluate the impact of a CLPL strategy for teachers and community learning staff to develop their professional practices in teaching maths.
Our online questionnaire asked respondents if they would like to improve their maths skills. Fifty-eight per cent (1446) of adult respondents said that they did. The most common reason that they gave for wishing to improve their skills was to better help their children with their learning.
Parents participating in our focus groups, and meetings with parental organisations, showed a similar desire to better support their children's learning in maths. They also highlighted the barriers they faced. Some lacked confidence in their own skills and found it difficult to access the help they needed. Others were unsure about how maths is currently taught in schools and worried about confusing their children by showing them the "wrong" methods: "Parents can be nervous about trying to help in case they are teaching them something in a way which conflicts with how they're doing it at school." Some reflected upon their own experiences at school and how this created problems for them in helping their own children: "The maths department at my school was scary. I didn't like maths. Still don't like maths."
The parents recognised that their children are attuned to the feelings of family members about maths. Some sought to hide their lack of confidence by encouraging their children to seek support from other family members. Others told their children how important maths is for everyday life and work. Some of these parents wished that they had received similar advice when they were at school: "Maths is in everything. I wish I had known this sooner, if I had I might have stuck with maths at school."
Some parents stressed the need for schools to make maths more relevant and enjoyable for their children. They would welcome greater outreach activities and engagement work including homework clubs that parents or other family members such as grandparents could attend with their children. This would help them to better understand how schools are currently teaching maths.
The following case study provides an example of the work taking place to support family learning in maths:
Glasgow City Council has introduced Play-a-long Maths in more than 30 early years and primary establishments across the city. Staff have had considerable success in engaging parents in a closer partnership, through providing the children and parents with games and activities to play at home. Play-a-long Maths is a language-based programme which uses a variety of games and activities to encourage parents and children to play together 10-15 minutes a day, 5 to 6 days a week for 6 to 8 weeks. The children choose a different game each week and the parents have weekly sessions with school staff to discuss their experience of the game. The aims for the child include the building of a mathematical vocabulary and mathematical concepts by providing experiences of the mathematical language of sorting, grouping and relationships.
Support for adults who wish to improve their maths skills is available through community learning providers, colleges and a range of websites. We will consider in the section on "Maths as an Essential Skill for Employment" how government, national agencies and employers can work together to further improve adult maths skills and therefore benefit parents.
The opinions that parents expressed in our focus groups and meetings are reflected in international research. The Eurydice report Mathematics Education in Europe: Common Challenges and National Policies  states that "Parents should be encouraged to help their children to learn and enjoy mathematics. Moreover, the involvement of parents is vital for the success of intervention programmes. At the same time, in view of the data on the level of adult numeracy skills, it should be recognised that some parents might not be able to provide adequate support for their children's learning."
As discussed earlier, our third recommendation is that each local authority should develop a strategy to ensure that all schools and nurseries engage with parents, employers and others in their local communities to help children and young people develop greater awareness of the importance of maths to everyday life and future jobs. Education Scotland and local authorities should collaborate to share and disseminate good practice.
Scottish Attainment Challenge
The Scottish Attainment Challenge has been set up to improve educational outcomes in communities with a high concentration of children living in poverty. There is a specific focus on improving literacy, numeracy and health and wellbeing. Initial support has been directed at primary schools in seven local authority areas (Glasgow, Dundee, Inverclyde, West Dunbartonshire, North Ayrshire, Clackmannanshire and North Lanarkshire). The programme was extended in June 2016 to include secondary schools and two further local authorities (East Ayrshire and Renfrewshire). Funding for the Scottish Attainment Challenge has also been increased to £750 million over the next five years.
The Group welcomes this additional support which will help many more children and young people develop their maths skills. Early indications are that in the first year many of the primary schools involved have taken a focus on improving literacy. However, it is essential that schools take account of all three priorities during the lifetime of the programme, and this leads to our eighth recommendation:
Schools supported by the Attainment Scotland Fund as part of the Scottish Attainment Challenge should increase their focus on raising attainment in numeracy and include parental engagement as part of their plans.
Email: Frank Creamer, Frank.Creamer@gov.scot