Enhancing the quality of mathematics education in Scotland: Quality of learning and teaching in mathematics

Practitioners and teachers’ mathematical knowledge and professional learning

Most staff are participating in professional learning to improve their practice in teaching mathematics. What is required next is an improved approach so that all staff in all local authorities can access high-quality professional learning. In addition, practitioners and primary and special school staff should continue to deepen their mathematical subject knowledge.

What is currently working well

In settings and primary and special schools where leadership is strong, practitioners and teachers show increased confidence and improved quality in their teaching. Senior leaders focus on improving mathematics teaching and deepening staff’s conceptual understanding of mathematics. This in turn is ensuring that children and young people are having higher quality experiences.

In secondary schools, mathematics teachers have a strong understanding of the subject content.

Across all sectors, engagement of practitioners and teachers in professional learning in mathematics, including professional enquiry, is increasing. More staff are participating in local and national training, both formally and informally. In the most positive examples, this is tailored to the specific context of the setting or school and includes research-based learning.

In many schools, pupil support assistants provide helpful and meaningful support to children and young people who require additional support. In the best examples, pupil support assistants are engaging in the same professional learning in mathematics as teachers. This is building the capacity of pupil support assistants and helping them better assist children and young people.

What needs to improve

In settings and primary and special schools, staff need to ensure that they have sufficient subject knowledge to provide accurate mathematical explanations, as well as the appropriate use of terminology and vocabulary. A solid grasp of mathematical concepts is essential for fostering children and young people’s understanding and confidence.

Many secondary school mathematics teachers could benefit from further professional learning to deepen their understanding of the most effective ways to teach mathematics. Engaging in additional professional learning opportunities will equip them with the tools to better engage young people and improve learning outcomes.

There is a clear need for more professional learning to help teachers and practitioners support children and young people who face difficulties in numeracy and mathematics. This includes addressing specific challenges, including dyscalculia, and developing strategies to support these learners in overcoming their barriers to mathematical success.

Mathematical language and vocabulary

In many primary schools, teachers have well-developed approaches to helping children explain their mathematical thinking. However, many teachers need to think more carefully about how they develop language and vocabulary in their lessons. It is important that they dedicate time to this important aspect of children and young people’s mathematic development.

What is currently working well

In many settings and primary schools, there has been an increased focus on enabling children and young people to explain their thinking and engage in meaningful mathematical discussions. There are a few positive examples of practitioners and teachers thinking carefully about their use of mathematical vocabulary and supporting children to discuss different strategies for solving mathematical problems.

Gaelic Medium staff work very well to build children’s subject-specific understanding of vocabulary. Older children and young people demonstrate confidence when discussing mathematics in Gaelic.

What needs to improve

In primary schools, teachers should avoid using informal language when describing mathematical procedures. Across sectors, teachers need be more consistent in modelling, and encouraging the use of, accurate mathematical language and vocabulary.

In secondary schools, some teachers need to raise their expectations of young people’s written and oral work. They should improve how young people demonstrate a deeper understanding of mathematical concepts in both formats.

Secondary mathematics teachers should also encourage increased dialogue from young people during lessons reducing the dominance of the teacher’s voice. Too often, the over-reliance of teacher talk constrains young people’s communication and language skills in mathematics.

Planning for learning in mathematics

Practitioners and teachers regularly adapt their planning in mathematics to support children’s progress. While overall, practitioners and teachers plan coverage of curricular content well, more effective planning for individual children and young people is needed.

What is currently working well

Across settings and schools, staff are improving approaches to planning in numeracy and mathematics. In settings and primary and special schools, this is often supported well by progressive planners along with local authority or national guidance. In the best examples, teachers include planning for vocabulary, questioning, word problems and problem-solving approaches that children need in order to learn effectively. In many settings and special schools, staff have a clear focus on ensuring that they take into account children and young people’s interests when planning to sustain and capture their interest.

In secondary schools, teachers have well-developed approaches to planning courses in the senior phase. These are linked closely to the requirements of National Qualifications in mathematics and the application of mathematics.

Many practitioners and teachers successfully build on and reinforce prior mathematics concepts. They use starter activities well in primary and secondary schools to help children and young people recall and practise key knowledge. Some use their knowledge of children and young people’s learning beyond numeracy and mathematics to address barriers. For example, they take into account children and young people’s reading and literacy skills when planning tasks and activities.

Practitioners and teachers have a good understanding of the diverse needs of children and young people. It is clear that children’s needs are increasing, both in terms of supporting children and young people who require additional support and those whose needs are related to socio-economic challenges. In the best examples, staff have developed clear strategies for supporting and engaging families to improve mathematic experiences, confidence and learning.

What needs to improve

Across settings and schools, most staff need to improve planning for children and young people, including those who are more able in mathematics and those who require additional support to meet individual learning needs. In too many primary schools, self-selected challenge activities do not provide the appropriate level of difficulty children need in order for them to progress. In many secondary schools, teachers’ planning in S1 to S3 is too focused on content coverage.

In primary schools, teachers should link knowledge, concepts and skills across the mathematics curriculum more effectively. This will help children to understand and apply links between distinct aspects of the mathematics curriculum.

Senior leaders and teachers should more clearly demonstrate how their planned interventions, including those funded through Pupil Equity Funding, are effectively closing the attainment gap in mathematics. Ensuring a clearer link between interventions and measurable outcomes will support better evaluation of the impact on children and young people’s mathematical achievement.

Teaching of mathematics

The quality of mathematics teaching varies widely across Scotland. While most teachers provide well-structured lessons with clear explanations, there is a need to raise the overall quality of mathematics teaching to ensure that all children and young people benefit from high-quality learning experiences. By focusing on improving teaching practices, we can help ensure that every child and young person makes the best possible progress.

What is currently working well

Across settings and schools, practitioners and teachers are clear about the purpose of the learning they are planning for children and young people. In settings, practitioners often intentionally use specific numeracy and mathematics areas as well as indoor or outdoor spaces when supporting children’s learning.

In primary and secondary schools, teachers have established clear classroom routines and lesson structures. In primary schools, most lessons include a range of effective features, such as mental agility practice, working through examples collaboratively and discussing mathematical strategies.

Practitioners and teachers generally provide clear explanations of mathematical content. In settings and special schools, mathematics is taught both in specific lessons and through activities such as baking, outdoor learning and community experiences. In primary and secondary schools, teachers often model mathematics concepts, asking guiding questions and providing children and young people opportunities to practice new learning.

What needs to improve

Teachers need to ensure a better balance between various aspects of mathematical learning – developing conceptual understanding, factual knowledge and procedural fluency and skills. Currently, in both primary and secondary schools, many teachers do not focus enough on skills development in mathematics.

In the early years of primary school, there needs to be a better balance of direct teaching and play-based learning to support progress in mathematics. The current approaches to play are not always challenging enough to support children's mathematical progress. Additionally, in both primary and early secondary education, teachers should provide more opportunities for children and young people to use physical objects and pictorial representations. This would help children and young people deepen their understanding of mathematical concepts.

In secondary schools, teachers should focus on enhancing their interactions with young people. This can be done by improving approaches to modelling, asking thoughtful questions and encouraging deeper classroom dialogue. These strategies would help young people engage more fully and enhance their learning.

In special schools, teachers should provide more opportunities for independent learning in mathematics. By doing so, children and young people will be able to take greater ownership of their learning process, which can lead to improved outcomes.

Assessment and feedback

Assessment and feedback in mathematics show areas of strength alongside opportunities for improvement. Approaches to formative assessment are increasingly being used effectively, although there is scope to provide more specific guidance on next steps for learners. Moderation practices are developing, with positive examples of collaboration in some schools. Feedback is generally supportive, but further focus on providing clear, actionable steps for improvement would help deepen learning and progress.

What is currently working well

In settings and primary and special schools, practitioners and teachers use a range of effective formative assessment approaches, including verbal feedback, to support children and young people’s learning and progress.

In primary schools, formative assessment is usually well developed. For example, teachers check children’s understanding routinely during lessons. They use this to make timely interventions that support progress. Some teachers also support children very well to peer- and self-assess their work. This is helping children to know themselves as learners.

In settings, most practitioners skilfully observe and capture evidence of children’s mathematical language and knowledge in numeracy. Increasingly, they evaluate children’s learning well and outline the next steps needed for progress.

In secondary schools, many teachers engage well with individual young people to check on their progress during lessons. They are also confident in using summative assessments to measure young people’s knowledge and progress in mathematics. These are well-developed and closely linked to the needs of National Qualifications in the senior phase.

What needs to improve

In settings, practitioners should take more opportunities to assess a child’s mathematical understanding through listening to and carefully observing their language and play with other children across the day.

Teachers should develop assessment approaches which require children and young people to apply their knowledge and skills in new and unfamiliar contexts. Currently, assessments in primary and secondary schools focus too much on assessing children and young people’s knowledge and understanding of procedures. Moreover, in primary and secondary school teachers should improve the quality of the written and oral feedback they provide so that it more actively moves children and young people’s mathematics learning forward.

Teachers should work together more closely to improve how children transition from primary to secondary mathematics learning. They should engage in further collaboration to establish a common understanding of standards and expectations in mathematics.

In secondary schools, teachers should enhance formative assessment approaches to check young people’s understanding. This includes ‘in the moment’ assessment to support progress in learning.