Enhancing the quality of mathematics education in Scotland: Sector-specific findings
Children’s engagement in mathematics
Practitioners in early learning and childcare settings are successfully promoting a positive attitude towards numeracy and mathematics among children. In strong settings, senior leaders and practitioners have a clear and shared focus on ensuring that they provide high-quality numeracy and mathematics experiences throughout the setting. Most children are keen to show and talk about their knowledge in mathematics and overall are very confident about their abilities. They see themselves as capable mathematicians and happily try applying their skills to new learning and situations.
Practitioners create engaging learning spaces that support children’s numeracy and mathematics development effectively. They design learning spaces with a variety of materials across different contexts that capture children’s interest in mathematics well. In playrooms, children eagerly explore mathematical concepts through activities like block play, using weighing scales and filling and pouring objects, as well as equipment such as rulers, timers and calculators. In outdoor environments, many children are keen to choose and play with natural objects, large loose materials or mud kitchens. They often use mathematical language, such as ‘fast’, ‘slow’, ‘big’ or ‘long’ during activities like riding and scooting. In a number of settings, practitioners are improving the range and quality of numeracy and mathematics learning on offer to children in the outdoor environment. This is helping children to practise their mathematical skills in new and authentic ways.
Practitioners engage and build on children’s interests in mathematics, encouraging curiosity and deepening learning effectively through a wide range of activities. They respond to children’s new and growing interests very well. They are responsive and regularly set up provocations that encourage children’s curiosity and develop numeracy and mathematics understanding. Increasingly, practitioners are offering activities or experiences that link learning across science, technologies, engineering and mathematics (STEM). This is helping children to begin to make meaningful connections across their learning. In most settings, staff effectively use stories, songs and rhymes to introduce numbers and mathematical vocabulary, supporting children to practise using mathematical language. Many children show particular enjoyment and enthusiasm during these experiences.
Children show a strong interest in play and activities related to numbers, measurement, patterns and shapes, especially when these are connected to real-life experiences. We saw children engaging in learning for sustained periods of time during such experiences. Examples included comparing sizes and shapes of plants in the garden, weighing ingredients when baking, and counting out items when setting the table for snack.
We saw examples of practitioners creatively extending and enhancing children’s numeracy and mathematics learning very well through digital technologies. For example, children used digital tools, such as timers, scales and laser devices to measure, or applied their learning about directions and position to programme digital toys. When available, some children enjoy using interactive boards, laptops or tablets to watch or play number games or animations of songs and stories. Practitioners should consider the value of digital technologies in providing opportunities for children to develop and demonstrate their understanding of mathematics.
Overall, practitioners are successfully engaging with families to encourage their involvement in their child’s mathematics learning. Many settings offer a well-considered range of events, materials and targeted resources that are helping parents to talk to their children about mathematics. This includes sharing advice on no- or low-cost activities to do at home and providing stay and play sessions. These approaches are equipping parents to support children’s numeracy and mathematics outside the setting. Family learning approaches are most successful when staff in settings have carefully considered their community context and tailored their support accordingly. In one example, children’s mathematical language was an area of focus. The setting provided parents with themed story sacks to use at home, which helped to build children’s vocabulary. However, a number of settings still need to do more work to help engage families in their children’s learning in numeracy and mathematics.
Learning and teaching in mathematics
Overall, practitioners are effective role models, integrating mathematics into daily routines. However, some miss opportunities to extend learning during interactions. Many intentionally, and often skilfully, thread mathematics learning and language throughout the children’s day, for example through routines and social times. However, practitioners should be mindful of spontaneous opportunities to extend numeracy and mathematics learning during interactions with children, particularly in one-on-one moments.
Across Scotland, there are many examples of practitioners supporting children to practise and apply their mathematics learning beyond their setting, such as trips to local shops, with people in the community or when visiting large natural places. This is helping children to understand the relevance of mathematics in their lives.
Practitioners offer helpful explanations and ask thoughtful questions when interacting with children, although at times the mathematical terminology is sometimes inaccurate or imprecise. Most staff provide useful commentary and support children to use the language of mathematics in their play. They are careful to ensure that they do this in relevant and meaningful ways through a range of positive environments and engaging provocations. Overall, practitioners are improving their use of questioning to support and extend children’s learning in mathematics. We saw examples of skilled interactions during play where open-ended questions encouraged children’s curiosity and independent thinking. Some practitioners need to further develop their understanding of accurate, developmentally appropriate mathematical terminology and vocabulary. Ambiguous or inaccurate terms and explanations can lead to children developing misconceptions. Further training and support should help staff to feel more confident introducing and extending children’s mathematical language.
Senior staff and practitioners are continuing to develop and refine approaches to planning in numeracy and mathematics, incorporating both responsive and intentional strategies. This is often supported well by progressive planning pathways, trackers and local authority and national guidance. We found strong examples of practitioners planning for mathematical vocabulary, interactions and questioning. Overall, practitioners use children’s interests effectively when planning. They are also flexible, ensuring that there is time and space for new directions in children’s learning. This adaptability supports children’s engagement well.
Practitioners provide children with learning experiences across varied aspects of the numeracy and mathematics curriculum. Most staff plan real-life experiences to support and practise learning. They also link learning in other areas of the curriculum to numeracy and mathematics well, such as science. However, in a number of settings, practitioners are not regularly planning experiences for children across the mathematics curriculum organisers. Planning for knowledge and skills within aspects such as time, money or information handling can lack sufficient depth. Practitioners should ensure that children have regular experiences and learning opportunities across the full breadth of the early level mathematics curriculum.
There are examples of highly skilled practitioners providing challenge for more able children through well-planned mathematical provocations and open-ended problem-solving tasks. Where offered, these are popular with children, and they engage meaningfully in these activities. A number of settings have seen an increase in children attending for a third year due to parents choosing to defer entry to school. In response, staff are beginning to further adapt experiences and spaces to offer greater challenge or new learning opportunities. In a few settings, practitioners need to plan and provide activities and experiences that are more difficult, to better meet the needs of more able children.
Most practitioners take well-considered steps to address gaps they identify in children’s understanding of and skills in numeracy and mathematics. This is often through one-to-one or small group sessions focused on specific aspects of numeracy and mathematics. This enables practitioners to provide support which is tailored to meet individual needs. In a few examples, staff are taking action across the setting to address and support gaps in mathematical vocabulary. In settings with high-quality provision, practitioners clearly evidence the impact of interventions and can demonstrate children’s progress towards numeracy and mathematics milestones. However, some settings need to improve how they record and evaluate the impact of change on children’s outcomes. This will help ensure that children receive the best possible support.
There are examples of high-quality written mathematics observations in learning journals where skilled practitioners clearly outline the new experiences or knowledge children need to extend their learning. Practitioners regularly record children’s comments to document their growing mathematical language and confidence. Most often, these comments come from the numeracy and mathematics area of the setting. Practitioners should observe children’s use of mathematical language and skills more regularly across all aspects of the curriculum and all areas of the setting, including when children are talking and playing with each other. This will help staff recognise where and how children are developing and applying their mathematical skills and knowledge. The quality of written observations also depends on individual practitioner’s knowledge of how children’s mathematical skills develop. Some practitioners require further support to better understand how early mathematical concepts link and build over time. This will help them to make more informed evaluations of children’s learning in mathematics and identify appropriate next steps.
Senior staff recognise the importance of developing approaches to moderation that suit their own settings. They arrange regular planning and tracking conversations where staff discuss and record children’s progress in numeracy and mathematics. Staff in a few settings need to make better use of ongoing assessment evidence to support children’s progress. Increasingly, practitioners are moderating their assessment judgements through a team discussion. There are also positive examples of wider moderation opportunities occurring across a group of settings or with primary school colleagues. This is helping staff ensure that their judgements about children’s progress are robust and accurate.
Overall, practitioners are increasingly engaging in professional learning that is improving their understanding and practice in numeracy and mathematics, through local authority, national and commercial courses. Many practitioners highlighted recent professional learning opportunities that have a positive impact on the quality of mathematics experiences and interactions for children. These included aspects of practice such as schemas, large block play and outdoor learning, as well as work focusing on national practice guidance. Settings with high-quality practice have clearly defined leadership roles for numeracy and mathematics in place. Staff in these roles take ownership and are given time to develop provision and practice across their setting. They provide valuable guidance and support that is helping to upskill practitioners and build their confidence.
Children’s engagement in mathematics
In primary schools, teachers are successfully creating positive learning environments that engage children in mathematics. Relationships between staff and children are nurturing. This creates classroom environments during mathematics lessons that are almost always calm and positive. Overall, children feel comfortable to ‘have a go’ in mathematics and know that understanding mistakes helps them to learn. During lessons, they regularly help each other and offer encouragement. They know a range of helpful strategies to use if they become ‘stuck’.
Mathematics has a highly positive profile across school and classroom environments, which helps to stimulate children’s curiosity and enthusiasm. Many schools participate in competitions, events and campaigns that capture children and families’ interest and engagement. Teachers regularly celebrate children’s progress and effort in mathematics through certificates or awards. Children say these rewards are motivating.
All children understand that learning mathematics is important. They say that their families share this belief. Across early and first Curriculum for Excellence (CfE) levels, most children are highly enthusiastic about mathematics and often say that it is their favourite subject. However, older children are less likely to consider mathematics as their favourite.
Teachers use a range of well-considered approaches to engage children in mathematics effectively. They create relevant displays, including examples of class work, that help children recall key prior learning. Where practice is highly effective, teachers refer to these displays during explanations and when responding to children’s questions. Most teachers give children time to discuss answers in pairs or groups. This supports children to remain engaged in learning. Children find physical objects and visual resources that teachers provide helpful. These resources sustain children’s interest and encourage more independence. Across the primary stages, teachers should carefully consider the sequence and balance of using physical objects, pictorial representations and abstract examples when helping children engage with mathematical ideas. This will support children’s development of a deep understanding of mathematical concepts.
Integrating real-life experiences into mathematics lessons enhances children’s engagement and understanding. Many teachers use outdoor environments effectively to provide opportunities for children to apply their knowledge in meaningful ways. Children particularly enjoy experiences with an authentic purpose, for example budgeting for an event or measuring out and building items for a school garden. This approach could be used more regularly in more schools. This would help children recognise connections between mathematics in the classroom and its practical role in daily life.
Support staff play a critical role in helping individual children experience success during mathematics lessons. They are encouraging and responsive to each child’s needs. They support children by helping to break tasks into smaller steps, reading questions aloud and answering questions. This targeted support helps build children’s confidence in mathematics.
It is essential that teachers provide the right levels of difficulty in lessons to help children to remain engaged in their learning. When activities or lessons are too easy, children often lose concentration. This typically occurs when too much time is spent on knowledge children have already mastered.
Addressing children’s mathematics-related anxiety is essential for encouraging positive attitudes. When children are less confident with mathematics, they can feel anxious during activities that require quick responses such as timed practice and ‘mental maths’ testing. Similarly, they can feel worried during class games which require them to give individual answers in front of peers. Teachers should provide children who are less confident with enough thinking time and consider different ways in which they can demonstrate their understanding. It is crucial children experience success to help build their confidence and develop positive attitudes towards mathematics.
During lessons, most teachers use digital technologies and software effectively to engage children and sustain their interest. For younger children, staff carefully consider digital usage, such as managing screen time. Many children enjoy playing digital games to help build their mental agility. A few teachers are providing creative ways for children to link and apply mathematical skills using digital technologies. For example, older children use software to collate information from their own surveys. They create digital graphs and pie charts to display results and explain their reasoning for presentation choices.
Learning and teaching in mathematics
In primary schools that deliver high-quality mathematics, staff have a deep professional understanding of the specific needs of children in their school. They use this knowledge to inform, plan and implement targeted approaches to improve learning and teaching in mathematics, such as when assessment evidence shows that children are not yet fluent in their recall of facts. Staff focus on providing more targeted teaching and increase opportunities for meaningful practice, including using motivating contexts. By offering children further engaging opportunities to practice, they help sustain children’s interest and motivation while reinforcing key skills.
Across Scotland, teachers are increasingly exploring and using mathematics teaching approaches based on research to inform their planning, for example teaching children a range of mathematical strategies. Most schools are using their own or a local authority progression pathway to ensure that they cover CfE mathematics experiences and outcomes throughout the academic year. In smaller rural schools, teachers carefully plan curriculum coverage for multi-stage composite classes. However, a few schools need to revisit certain aspects of mathematics, such as information handling, more frequently.
Currently, teachers’ planning for mathematics focuses heavily on children’s knowledge and understanding of concepts, with less consideration given to developing mathematical skills. Teachers make regular use of CfE experiences and outcomes and of the national benchmarks when planning learning and assessment. However, most staff are not yet considering how to support children to demonstrate, link and apply the key ‘numeracy and mathematical skills’ embedded in the experiences and outcomes and outlined explicitly at the start of the national benchmarks. To better support children to develop these important skills, teachers need to plan how these skills will be practised through learning experiences, questioning and assessments.
In schools with strong practice, teachers are aware of and understand common misconceptions within mathematical concepts at each CfE level. They plan for and use these misconceptions well during teaching to aid children’s understanding. It is important for all teachers to use assessment data to identify and address misconceptions and errors. Doing so will help children develop a deeper understanding of mathematics.
Some teachers use inaccurate mathematical vocabulary and terminology during lessons and on wall displays, which can hinder children’s understanding. It is crucial for teachers and support staff to discuss and develop their own understanding to model mathematics accurately when supporting children. There are highly effective examples of staff developing and planning for a school-wide progressive approach to subject-specific vocabulary. However, this is not yet common practice.
In most schools, teachers discuss effective features of mathematics teaching and agree a consistent lesson structure. Almost all teachers make the purpose of the lesson clear and help children understand how to be successful in their learning. They provide opportunities for collaborative learning, using a range of strategies to check for understanding. However, many lessons do not provide enough challenge. Children’s tasks and activities are frequently too simple, such as repetitive written exercises which do not extend thinking. Too often, children are allowed to self-select their level of challenge. This leads to superficial differentiation which does not meet their needs. This highlights the importance of using assessment information effectively when planning lessons and activities, ensuring that content is tailored appropriately to children’s stages of understanding and development and provides enough challenge for them to progress.
At early primary stages, teachers frequently use play experiences as part of mathematics lessons. This approach can vary in effectiveness. In the best examples, teachers provide high-quality play spaces and experiences. They observe learning skilfully and interact with children effectively during play, asking thoughtful questions to extend or deepen learning and understanding. To maximise the benefits of this approach, teachers need to further develop their understanding of high-quality play. Activities and experiences should progressively support and extend children’s mathematical knowledge and skills. They should also make sure that they are balancing planned direct teacher instruction and child-initiated play to provide the right level of challenge.
Most children are increasing their knowledge of a range of strategies to use in mental mathematics, and they are becoming more confident in discussing their methods and thinking. However, a few teachers still use informal nicknames for strategies or types of calculations which can hinder children’s ability to clearly explain their reasoning using mathematical language. This can have a detrimental impact on their understanding as concepts and processes become more complex. Towards the end of CfE second level, many children are not yet readily able to identify the most efficient strategy for a given calculation. Teachers should provide more support to help children develop and practise this critical skill.
Currently, many schools do not plan sufficiently for, or provide, progressive problem-solving and open-ended challenges in mathematics. Children report that they find word-problems or multi-step calculations challenging and are often unsure where to begin. Teachers need to involve children regularly in interpreting what is being asked of them and identifying the steps needed to tackle the problem. Modelling the process of working through examples is important in building children’s confidence.
Teachers use questioning well to check for understanding and prompt children to recall and practise prior learning. Often, children discuss their answer with a partner or group before sharing with the class, which they find supportive. Teachers should more regularly plan and ask questions where children need to apply their knowledge or make links across different aspects of mathematics. This will help children to engage more deeply with their learning.
Children value the verbal feedback and encouragement they receive from their teachers in mathematics. They find opportunities to peer- and self-assess their work helpful. Younger children told us they enjoy the stickers and stampers teachers add to their work. It helps them to understand where they have worked well. However, most written feedback in mathematics is focused on effort rather than illustrating progress. Comments do not often guide children on what they need to do next. In the schools visited, only a few children could clearly talk about their individual targets and progress in mathematics.
There are strong examples of teachers’ planning effectively for individual children who require additional support. However, structured interventions need to be more carefully managed. In schools with highly effective practice, teachers set measurable targets in children’s individual plans that clearly address the specific barriers to their progress in mathematics. In several schools visited, children who require support are withdrawn from class for interventions. Whilst these interventions do help many children make progress in numeracy, this approach should be considered and managed carefully. Withdrawal from class can mean that children miss important content. It can also limit the range of their experiences in mathematics and reduce the opportunity to learn from others.
In a few schools visited, there are clear plans to challenge older children who perform above nationally expected CfE mathematics levels. These are often through partnerships with universities and secondary schools. However, many children who are more able in mathematics are not challenged enough during lessons. Teachers should explore ways to extend both their mathematical thinking and skills. For example, teachers could use open-ended problems that require children to link and apply their learning across various mathematics concepts.
Senior leaders and staff are most effective in reducing poverty-related challenges in mathematics where there is an agreed school-wide strategy and a consistent, embedded approach. These strategies are informed by a deep understanding of the context of the school and effective self-evaluation. In some schools, teachers are successfully raising attainment for identified children as part of classroom lessons. However, more often, small groups or individuals are withdrawn from lessons for ‘catch-up’ interventions, many provided by support staff. Schools are able to demonstrate that these interventions support most children to improve their recall of key number facts. However, it is not always clear if the approach is reducing the overall poverty-related attainment gap. Staff should more rigorously measure the impact of interventions and approaches to understand which interventions have the most positive effect on narrowing this gap.
Overall, teachers assess children’s knowledge of discrete concepts and their ability to complete number operations well. They should now consider ways to assess how well children apply their skills, including through non-routine questions and in less familiar contexts.
Some senior leaders and teachers are using Scottish national standardised assessments (SNSA) diagnostic information very well to identify and plan for gaps in both individual children’s learning and cohorts. Expanding the use of SNSA data to analyse whole-school information for mathematics could further inform decision-making and improvement work.
Some teachers are regularly involved in moderation processes for mathematics within their own school and with other schools. In a few effective examples, staff across sectors work together to discuss children’s progression and achievement. This is not yet common practice across Scotland but where it does happen, teachers are able to plan learning taking better account of children’s prior achievement and next steps. Regularly sharing standards and expectations and discussing learning, teaching, and assessment in mathematics would benefit teachers and improve consistency.
In schools visited, many teachers are participating in professional learning relating to mathematics, including local authority training or practitioner enquiry projects. However, some teachers could strengthen their subject knowledge in mathematics. In a few lessons visited, gaps or inaccuracies in teachers’ understanding were evident when explaining particular concepts. Staff report that they find observing colleagues’ mathematics lessons and engaging in team-teaching particularly helpful.
Young people’s engagement in mathematics
In secondary school mathematics departments, teachers have a crucial role in creating positive and supportive learning environments. However, challenges such as young people not enjoying their mathematics learning and staffing inconsistencies such as long term and short-term vacancies are adversely affecting their efforts to improve young people’s engagement. There are many positive examples of teachers working well to create conditions where young people can learn in a supportive and calm environment. These are often underpinned by whole-school values and professional learning on building strong relationships.
In several schools, young people, particularly in S1 to S3, were observed becoming disengaged with learning. This disengagement can lead to low-level disruption, such as talking to their peers, shouting out or using mobile phones inappropriately. Teachers generally manage these situations well, and at times skilfully, often relying on their strong relationships with young people to maintain a focused environment.
While young people understand the importance of learning mathematics, this does not always translate into a genuine enthusiasm or love for the subject. They do, however, highly value the genuine support and care their teachers show them. They appreciate the enthusiasm teachers show for mathematics and their willingness to provide help beyond the classroom through digital tools, lunchtime clubs and after-school support.
The majority of secondary schools visited report ongoing difficulties securing and retaining specialist mathematics teachers. In these schools, it is often more challenging to establish and maintain positive relationships between teachers and young people. In some schools, young people in the S1 and S2 are not always taught by a specialised mathematics teacher, limiting their access to the depth of knowledge required for effective learning.
Improvements are required to ensure that learning environments fully support young people to engage with mathematics. Young people are noticeably more engaged when classrooms foster interactive learning. For example, engagement is enhanced when young people have opportunities to engage in high-quality discussions or collaborate through shared spaces. This includes approaches such as large write-on boards, group tasks or whole-class strategies such as using mini white boards. It is important, however, for teachers to ensure that collaborative tasks are not just engaging experiences but provide meaningful, high-quality learning opportunities.
Many young people are often unaware of how physical objects (manipulatives) can be used to support their understanding of mathematical concepts. Although many teachers have had professional learning about using these resources, they are not widely used in practice well. Incorporating manipulatives, along with pictorial representations would greatly benefit some young people, especially supporting their conceptual understanding of mathematics ideas. It will be helpful for teachers to incorporate better use of manipulatives into their lessons and make these materials more readily available to young people.
Young people report a clear contrast in their mathematics education experiences, with the early years of secondary education lacking sufficient challenge and later years becoming increasingly demanding. Young people report that they often find mathematics in S1 to S3 too easy compared with other subjects. It can be repetitive, overly focused on textbooks or worksheets and does not build enough on their prior learning. By contrast, in S4 to S6, young people find senior phase courses in mathematics harder than their other subjects. They find the volume of material to cover in courses challenging. They feel they must work too much on their own and would welcome more collaborative approaches with more focus on problem-solving skills. To address these challenges, teachers should continue to review the S1 to S3 curriculum to ensure that it provides progression into the senior phase more effectively. Additionally, they should ensure that young people’s experiences both in the lead up to and during the senior phase prepare them fully for the demands of their courses in S5 and S6.
Young people express a significant concern in their mathematics learning: its lack of relevance to their daily lives. Teachers, particularly in S1 to S3, often miss opportunities to connect mathematical concepts to real-life contexts. They tend to use abstract examples when other more practical applications could be used. By contrast, in S4 to S6, where teachers have developed pathways to include applications of mathematics courses, young people report increased relevance and at times enjoyment. It is important for teachers to help young people understand how mathematics impacts their day-to-day lives by striking a balance between using practical, real-life examples and conveying the relevance and importance of abstract mathematical content.
Teachers are continuing to develop their use of digital platforms to improve engagement and learning experiences. For example, in a few schools, teachers use creative digital approaches to involve young people in feedback and sharing planning with young people to support access to learning materials. Young people are positive about the use of online platforms for notes, games, worksheets, homework and revision materials. These are particularly valuable for young people during periods of absence or when preparing for exams, providing easy and flexible access to the resources they need.
Teachers have a clear understanding of the socio-economic challenges their young people and families face, although they are not fully clear how they can contribute to closing poverty-related attainment gaps or accelerate young people’s progress in mathematics. Across mathematics departments, teachers have implemented a number of universal supports, such as providing access to materials and calculators for all young people. Principal teachers and senior leaders have a better understanding of how targeted supports are improving numeracy outcomes. They should continue working with teachers to ensure that all staff understand these approaches and can review the progress they are making in addressing equity gaps.
Teachers report that they are seeing an increase in the needs of young people, including those who require additional support. They are concerned about a decline in young people’s knowledge of mathematics compared with previous years, including when transitioning from primary school. However, many teachers are not yet sufficiently adapting their planning to address the full range of learners in their classes, including the most able. Teachers should continue to develop their approaches to better meet the diverse needs of all young people.
Pupil support assistants are providing helpful, consistent support to young people in most schools. Several schools have pupil support assistants dedicated to supporting young people in mathematics. In the best examples, pupil support assistants engage in professional learning activities alongside mathematics teachers, enabling them to provide improved quality, subject-specific support to young people.
Learning and teaching in mathematics
Across schools in Scotland and within mathematics departments, the quality of mathematics teaching is too inconsistent. Young people’s experiences of mathematics are therefore too varied and too dependent on the teacher. While there are examples of very effective teaching providing high-quality mathematics instruction, many young people do not consistently receive this experience.
While mathematics teachers have a strong grasp of the subject matter, some do not always have a clear understanding of the most effective ways to teach mathematics. To improve practice, teachers should consider how they balance factual knowledge, procedural fluency, conceptual understanding and skills development in their teaching.
Most teachers would benefit from further, targeted professional learning to deepen their understanding of high-quality mathematics instruction and should apply this learning to their teaching. Positively, all teachers engage in professional learning in mathematics, whether through personal study, training that is supported or provided by their local authority, or professional dialogue with colleagues in their departments. It is not always clear the impact this professional learning is having on young people’s experiences. Where practice is strongest, teachers work together to ensure a consistent approach to new strategies across their department. They closely monitor that the impact on improving young people’s experiences and progress.
Planning approaches vary across schools and within mathematics departments. In the most successful examples, teachers are working very well together to plan over different time scales, ensuring consistency in young people’s experiences. For example, agreed common methodologies, aligned with national standards, are used to help young people be successful. A few schools are particularly successful in planning learning activities connected to meaningful contexts, such as word problems, problem-solving tasks or project-based learning opportunities.
In most schools, mathematics departments have a clear lesson structure and well-established classroom routines. Teachers generally provide clear explanations of mathematical content to young people. They are confident in teaching procedures, knowledge and facts. However, there is inconsistency in setting expectations for young people to use the correct mathematical language or vocabulary during discussions. In schools with the best practices, teachers are skilled at highlighting common errors and misconceptions as part of their explanations. They ask young people to explain their thinking and elicit more detailed answers and meaningful mathematical discussions. These teachers often plan questions in advance and reinforce vocabulary through wall displays and highlighting key words in written problems. However, in many lessons, the teacher’s voice can dominate, limiting opportunities for young people to engage in rich discussions. Teachers should consider young people’s reading skills and mathematical vocabulary knowledge when planning to create more opportunities for verbal reasoning.
There is a significant need to improve how teachers check whether young people have understood their learning. Teachers share the purpose of learning and how to be successful with young people. Yet these learning intentions and success criteria are often not of a sufficient quality to be a useful tool in checking young people’s progress or understanding. In addition, teachers need to consider how to make the end of lessons more meaningful to young people. Linking the end of the lesson back to planned learning and checking young people have understood, mastered and been successful should be an integral part of each lesson.
Assessment practices across mathematics departments vary, with some schools showing clear strengths while others require improvement. In the senior phase, summative assessments are well developed and closely aligned with National Qualification requirements. These assessments help young people identify gaps in their learning through targeted feedback. However, in the broad general education, assessment practices are less consistent. Too often, assessments do not match the range of learners’ abilities, resulting in some young people facing tasks that are either too difficult or too easy.
The most successful assessments are carefully designed to test a variety of skills and knowledge, with differentiation to ensure that all young people can demonstrate their learning. In these examples, assessments provide an appropriate level of challenge, engaging young people at different skill levels.
Teachers often provide both verbal and written feedback. However, many young people are unclear about how to use this feedback to improve their work, particularly in S1 to S3. To make feedback more meaningful, teachers should focus on providing clear, actionable steps that young people can apply to their learning.
Many teachers interact well with young people while they practice mathematics in class, providing one-to-one support to address individual learning issues. In some cases, this support is provided very skilfully. However, formative assessment strategies are not used consistently across departments. To enhance learning outcomes, teachers should focus on more effectively checking young people’s understanding throughout learning activities. By clearly sharing the purpose of learning and incorporating appropriately designed strategies to review young people’s progress and understanding, teachers can ensure that their approaches are both meaningful and impactful. Additionally, creating purposeful moments during a lesson to revisit key learning points helps confirm that young people have grasped and mastered the material. This ongoing process of checking for understanding, aligned with a clear sense of the learning purpose, will support young people to be engaged and make progress in their learning.
Children and young people’s engagement in mathematics
In special schools, teachers have a sound understanding of the needs of children and young people. They work very well to create positive relationships with children and young people that support numeracy and mathematics learning. They demonstrate skill in communicating with children and young people with additional support needs.
Staff in special schools support children and young people in learning numeracy and mathematics through a range of real-life and meaningful contexts. They use indoor and outdoor spaces well to promote engagement and the application of skills. This includes the positive use of their local communities to promote independence, such as using bus timetables to plan journeys and money to plan visits to cafés.
Staff use the classroom environment effectively to engage children and young people. They use a range of practical materials, games and songs to help children and young people learn important numeracy and mathematical skills. They also weave mathematical learning, such as time, into everyday routines. However, while this high level of support is valuable, in some schools, staff provide too much support. It is important for staff to provide a balance between providing support and allowing children and young people time to explore learning independently and develop problem-solving skills.
Children and young people are very positive about their experiences in numeracy and mathematics. They find their learning to be of the right level of difficulty. Children and young people particularly enjoy and value the real-life contexts used in their learning, such as weighing ingredients for cooking or measuring and planning how to use garden spaces.
Staff use digital technology well as an important communication tool for children and young people learning mathematics. Children and young people’s engagement is increased with the use of assistive technologies, such as augmentative and alternative communication packages. This helps them to participate and communicate more readily through videos, songs and games. Teachers monitor the use of digital technologies carefully to keep children and young people’s screen time at appropriate levels and reduce an over-reliance on technology. At times, it is unclear how certain online videos, songs and games contribute to learning or progression in numeracy and mathematics. While digital tools are used effectively to enhance engagement, there are opportunities to further refine their application, ensuring that every tool used contributes meaningfully to learning and progression in numeracy and mathematics.
Learning and teaching in mathematics
Teachers focus on planning personalised and progressive learning experiences in numeracy and mathematics to improve children and young people’s knowledge and skills. Their planning is adaptive and supports children and young people to make progress. In the best examples, this includes a focus on vocabulary, real-life contexts and problem-solving, including the use of open-ended activities.
Teachers provide lessons to meet the needs, interests and skills of children and young people. Their explanations are clear and are often enhanced by visual prompts and the repetition of concepts. Teachers are skilled in differentiating learning, adapting environments and resources to support individual needs. Staff have implemented several strategies which are having a positive impact on children and young people’s learning in mathematics. These strategies focus on ensuring that the needs of each child and young person are met, embedding numeracy throughout the school day and using of real-life contexts, such as community work or social enterprise projects. Many teachers incorporate numeracy and mathematics into play-based activities. They respond well to spontaneous opportunities to enhance learning.
Teachers need to better support the diverse ways in which children and young people who require significant additional support learn. They would benefit from further professional learning and moderation activities focused on milestones and early mathematics. This will help develop a shared understanding and consistency in reporting children and young people’s progress.
Some staff report that they have limited access to sector-specific professional learning in numeracy and mathematics. This is limiting how they improve approaches to learning and teaching in their schools. Expanding these opportunities would empower staff to further enhance their approaches and better meet the diverse needs of their learners.
Staff use observations of learning effectively to support children and young people’s progress in numeracy and mathematics. Some teachers are successfully using profiles, including photographs, to capture children and young people’s learning. This helps provide a clearer understanding of children and young people’s progress and supports moderation activities. To enhance this further, teachers need to deepen their understanding of national standards in numeracy and mathematics. They tell us that they would welcome greater opportunities to collaborate and moderate with colleagues in special schools who work with children and young people with similar additional support needs. This could help create consistency in expectations and teaching approaches to better support children and young people, especially those with complex additional support needs.
Staff report an increase in class sizes as well as an increase in children and young people with more complex additional support needs. Ongoing staffing challenges within the additional support needs sector are further impacting their ability to fully meet these needs.
Children and young people’s engagement in mathematics
In sgoil-àraich (nursery), bun-sgoil (primary) and àrd-sgoil (secondary), children and young people eagerly engage in learning mathematics through the medium of Gaelic. Practitioners and teachers are skilled at creating and providing an encouraging learning environment. They foster strong, supportive relationships with children and young people and guide them to do the same with their peers during pair and group activities. When available, support staff who speak Gaelic work well alongside practitioners and teachers. They model accurate language using commentary and support children to engage with their learning. As a result, children and young people feel confident in developing both their mathematical skills and language through Gaelic. In bun-sgoil, many children wanted lessons to be more challenging to sustain their interest and enthusiasm for mathematics.
All staff ensure that Gaelic mathematical language has a high profile in sgoil-àraich playrooms and bun-sgoil classrooms. They use helpful visuals, signage and accessible physical objects (manipulatives) to stimulate children’s interest and support their learning. Practitioners and teachers provide engaging ways for children to hear, learn and use Gaelic in mathematics. Stories, songs and routines reinforce accurate Gaelic mathematical terminology. In àrd-sgoil, young people strive to meet teachers’ high expectations, often participating in national UK challenges for mathematics through the medium of English. In mathematics classrooms in àrd-sgoil, a few teachers add specialist vocabulary in Gaelic to learning walls. This increases young people’s engagement. However, there are more mathematics posters in English. Increasing the presence of Gaelic mathematical terminology will help young people more to consolidate their understanding and use of specialist terms.
Almost all practitioners and teachers demonstrate a deep professional understanding of the principles of immersion. They understand the importance of their role in building children’s Gaelic language skills to enable them to explore and explain their thinking in mathematics. In bun-sgoil, teachers effectively model and scaffold class discussions using accurate Gaelic mathematical terminology. They provide regular opportunities for children to share their strategies and reasoning. Children find classroom wall displays, class activities and homework very helpful. Teachers could further support children by introducing more strategies that help build and record their mathematics vocabulary.
The quality of learning and teaching in mathematics
In highly effective immersion, practitioners and teachers create authentic and relevant experiences in Gaelic that enable children to practise, extend and apply their numeracy and mathematical skills. Most schools work very well with Gaelic-specific businesses, organisations and partners. This provides regular, meaningful opportunities for children to practise their skills. For example, children practise mental agility when running their own café event or develop knowledge about finance when working with local community shops. Teachers in àrd-sgoil should integrate Gaelic contexts, such as island economy, to help young people see connections between class learning and their lives.
Problem-solving and open-ended challenges in Gaelic should feature more regularly across the mathematics curriculum for all children and young people. In àrd-sgoil, many young people articulate their mathematical thinking clearly in Gaelic, offering thorough explanations and detailed reasoning. They would like more opportunities to work in groups and pairs to discuss mathematics. Teachers should build on this by providing more collaborative problem-solving activities and non-routine mathematical tasks in Gaelic.
In sgoil-àraich, practitioners develop children’s numeracy and mathematics knowledge and skills through well-considered provocations and planned experiences in Gaelic, particularly within the indoor environment. In a few settings, outdoor learning opportunities could be improved to provide a wider range of engaging opportunities that support young children’s mathematics learning through Gaelic.
In the early stages of total immersion, many teachers incorporate child-initiated play and discovery experiences into mathematics lessons. During these experiences, it is important for adults to interact regularly with children, providing commentary and asking questions to model and extend accurate Gaelic mathematical language. In a few settings, however, adults were not consistently observing children well enough to intervene effectively with questions, prompts and narrative in Gaelic. This lack of interaction diluted the immersion experience, resulting in missed opportunities to develop children’s mathematical knowledge.
In sgoil-àraich, the use of digital technologies is limited due to a lack of suitable Gaelic resources that support early mathematics skills. In contrast, in bun-sgoil, teachers use digital technologies effectively to capture children’s interest, sustain engagement and reinforce prior learning. High-quality examples include children sharing their work digitally and explaining the strategies they used for calculations using accurate Gaelic mathematical terminology. Staff also make very effective use of digital technologies and content in Gaelic to support high levels of parental engagement with children’s mathematics learning. This has a positive impact on children’s confidence and progress.
In àrd-sgoil, young people use digital apps and programmes to access mathematics course content and homework independently. They find this supports their revision and consolidates their learning. However, because these resources are in English, they diminish young people’s experiences of learning mathematics through Gaelic. Similarly, in some bun-sgoil classes, children spend considerable time on English online numeracy games to practise mental agility. These often do not provide appropriate levels of challenge and do not support the development of fluent Gaelic mathematical language. Teachers highlight the limited availability of digital resources and assistive technologies in Gaelic to help learners who require additional support.
Across the Gaelic sector, most staff plan mathematics lessons effectively using school, local and national guidance, along with national benchmarks. Almost all schools have reflected on ‘Advice on Gaelic Education’[1] to inform their mathematics frameworks, approaches and lesson structures. However, a few schools need to improve their planning and provision for children and young people facing difficulties in learning mathematics. Staff should consider how to provide targeted interventions, particularly during the total immersion phase, to better support children’s understanding and skills in mathematics through Gaelic.
Many practitioners and teachers in Gaelic Medium Education are planning for and using effective questioning into their lessons, particularly towards the end of the first CfE level. Teachers ask questions skilfully when checking for understanding and provide individual support. Well-attuned staff develop children and young people’s higher-order thinking skills, such as analysing and evaluating, whilst also scaffolding their fluency in using specialist mathematical language in Gaelic.
Teachers regularly have conversations in Gaelic with children and young people about their learning and progress in mathematics. During lessons, staff provide encouraging verbal feedback and, in bun-sgoil, children’s work often includes written feedback from teachers. In the strongest examples, written feedback highlight children’s strengths and offer clear next steps for improvement. Teachers should now further support children to talk about their individual targets and progress in mathematics. In àrd-sgoil, young people are clear on the level they are working at and their next steps in learning. In S1 to S3, young people would appreciate more feedback to help them improve their work.
Practitioners, support staff and teachers are increasingly participating in professional learning focused on mathematics. Teachers recognise the importance of accessing high-quality development in mathematics. However, they expressed that training content delivered in English with staff discussions in Gaelic is not sufficient to address and improve Gaelic sector-specific mathematics practice. Positively, many support staff have received professional learning in Gaelic language, which is helping them to support children in mathematics.
Teachers engage well in school moderation activities to share national standards and expectations in mathematics. This helps them to make confident professional judgements about children and young people’s achievement of a CfE level. To strengthen this work further, more teachers should have regular opportunities to engage in moderation processes with colleagues from other schools providing Gaelic Medium Education.
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[1] Advice on Gaelic Education | Resources | Education Scotland
