Aligning curriculum and assessment reform with teaching for mastery in secondary maths

Mathematics is essential, both for everyday problem solving in life and work, and to help shape the world around us, from industry and commerce to technological and scientific breakthroughs. Ensuring young people receive an effective and high-quality maths education requires a curriculum that is both rigorous and coherent, equipping students with the knowledge and confidence to succeed.

In this two-part series, Carol Knights, NCETM’s Director for Secondary Mathematics, and I suggest ways in which the curriculum and assessment of secondary mathematics might be improved. This first post considers curriculum content. The second addresses assessment, which exerts a powerful influence on the teaching and learning of secondary maths.

Part 1: Curriculum

Improving the Key Stage 2 to 3 transition in mathematics

In a previous NCETM Director’s blog post, Debbie Morgan, NCETM’s Director for Primary Mathematics, and I discussed the Key Stage 1 and 2 mathematics curriculum. We made the case that:

 ‘… an overloaded curriculum remains a barrier to realising the full potential of the mathematics Teaching for Mastery Programme. School leaders and teachers experience a tension between mastery and coverage, often unable to give all pupils sufficient time to fully master key concepts. Reducing curriculum content would allow expert teachers sufficient time to enable all pupils to establish deep and lasting foundations of essential content. This would result in better Key Stage 2 results – well beyond the current ‘pass mark’ of 50%, and cohorts of pupils ready to study mathematics, and mathematically-related subjects, at secondary school and beyond.’

This primary maths curriculum overload causes problems at Key Stage 3 in two ways:

1. Many students enter Key Stage 3 without a secure understanding of essential primary content. This means Year 7 teachers often have to re-teach foundational concepts instead of simply reviewing them, to ensure students can engage with the secondary curriculum.
2. Year 7 students often feel that they’ve ‘done this before’ - whether or not they have truly mastered a concept at a deeper level the first time. This can lead to demotivated, disengaged students who feel frustration at repeating what they believe they have already been taught.

A vital aspect of the NCETM’s Essence of Mathematics Teaching for Mastery is that: 

‘Significant time is spent developing deep understanding of the key ideas that are needed to underpin future learning.’

The Key Stage 3 mathematics guidance, created by the NCETM and published by the DfE in 2021, recognises the curriculum is overloaded  at Key Stage 2 and contains detailed advice on how to alleviate the problems it causes. This guidance helps secondary maths teachers to address the issue of pupils’ insufficient grasp of key primary maths content, but it can do nothing to address the negative impact on pupils’ motivation arising from the need to repeat ‘primary school’ work.

We know that pupil performance in maths often stalls at Key Stage 3, particularly for disadvantaged pupils ⁱ. Getting the curriculum right, so that students’ knowledge of the primary maths curriculum is secure and secondary teachers don’t need to re-teach key concepts, would help pupils to have a more positive experience in their transition to Key Stage 3 maths, supporting better engagement in Key Stage 3 and stronger outcomes by the end of Key Stage 4. 

One aspect of the KS2 curriculum that belongs in KS3 is formal calculation with fractions, for two main reasons:

• To allow sufficient time for KS2 pupils to gain a solid grasp of fractions before moving on.
• To teach formal calculation at a stage when pupils are ready, in line with high-performing jurisdictions internationally ⁱⁱ.

In Key Stage 2, the focus would shift to developing a deep understanding of fractions through comparison in various contexts. A strong emphasis on reasoning, including equivalence, would lay the groundwork for future use of common denominators and mental strategies to compare and order fractions, as well as to calculate with fractions.

Teacher experience indicates that students in Years 5 and 6 often struggle with formal fraction calculations. While students in Key Stage 2 may be able to perform these calculations procedurally, their understanding is often too shallow to apply effectively in later problem-solving.

Updating the secondary maths curriculum to improve learning for all

Mathematics education across Key Stages 3 and 4 should ensure that:

1. All pupils master fundamental mathematics, enabling them to apply maths across the secondary curriculum, for work and life, and to equip them to progress to further studies, including Core Maths, that require the application of fundamental mathematics post-16.
2. Many pupils also further develop their mathematical understanding, equipping them for post-16 study that can enable them to access higher education and/or careers in disciplines that require high levels of expertise in maths and data analysis. 
3. All pupils develop a positive attitude towards maths, appreciating both its beauty and its utility.

The current secondary maths curriculum and assessment structure means that, for many pupils, these functions are not fulfilled well. 

The mastery of fundamental mathematics for life and work aligns with the purpose of the current Foundation tier in GCSE Maths, but the current Foundation tier curriculum is too large, containing topics such as solving quadratic equations and the use of trigonometric functions, which do not align with this purpose. The impact of this curriculum overload is that teaching and learning are often rushed and shallow, preventing many pupils from mastering fundamental mathematics. Pupils can experience maths as an ever-expanding set of rules and instructions to memorise, rather than as a logically coherent, connected discipline.

We recommend some slimming of the mathematical content that all pupils must study. Alongside an overall curriculum reduction for these pupils, we would add the use of spreadsheets, which are ubiquitous in work and everyday life and support a practical understanding of algebra. We would also add basic understanding of risk, and applications of maths in personal finance. Such a curriculum can still be demanding and rigorous, and properly mathematical, as shown by MEI’s work on potential reform of GCSE Maths resit ⁱⁱⁱ.

To prepare for disciplines that require high levels of expertise in maths and data analysis, many pupils should also develop mastery of a wider secondary maths curriculum, which should be reviewed to ensure its content develops the mathematical and data skills needed to underpin post-16 study in disciplines requiring a high level of quantitative knowledge and skills. 

As part of the overall curriculum review, the maths curriculum and the curricula of other quantitative subjects should be aligned to ensure coherence and consistency, and emphasise the transferable nature of mathematical skills. Examples include rearranging equations, and interpreting data and graphs. The Royal Society’s Mathematical Futures report emphasises the importance of coherent mathematical and data education across the curriculum ^iv. The curriculum, and how it is taught, should highlight the usefulness of maths knowledge and skills, so that pupils see the value of studying maths beyond just passing an examination. 

Developing deep mathematical understanding is inspiring and engaging, stretching pupils’ thinking and helping them to appreciate the beauty of maths, as well as its utility. Examples include relationships between fractions, decimals and percentages, links between equations and their graphs and how trig functions relate to the unit circle. 

Allowing more space in the curriculum for pupils to develop a secure, connected understanding of maths and emphasising its usefulness in other subjects, and for work and life, would help pupils to develop positive attitudes towards maths. This would improve attainment and increase progression to Core Maths and AS/A level Maths and Further Maths post-16.

Conclusion

• Moving formal calculations with fractions from the KS2 curriculum to the KS3 curriculum would support deeper mathematical learning by allowing more time in primary school to master other aspects of the KS2 curriculum. This would improve pupils’ mathematical transition from primary to secondary school. 
• Reducing the curriculum content in the Foundation tier of GCSE Mathematics would allow more time to ensure all pupils can master the fundamental maths needed by all, helping to increase young people’s mathematical confidence.
• The usefulness and application of mathematical knowledge and skills should be emphasised, ensuring the curriculum is relevant to work, life and further study in a world that is increasingly driven by maths and data. 
• A curriculum that emphasises developing a deep and connected understanding of maths, and an appreciation of both its beauty and its usefulness, would support pupils to develop positive attitudes to mathematical study.

We know that assessment often drives teaching in the secondary maths classroom ^v. The reform of the secondary maths curriculum must be considered alongside its assessment. To support young people to achieve a deep, connected understanding of maths, assessment should enable pupils to demonstrate their mathematics knowledge and skills, and their ability to use maths to solve problems in context. In Part 2 we will explore how secondary maths assessment could be revised to support the development of secure, transferable knowledge and skills.

ⁱ XTX Markets - Maths Excellence Pathways

ⁱⁱ Learning fractions shouldn't be difficult (NCETM)

ⁱⁱⁱ A new mathematics GCSE curriculum for post-16 resit students (MEI)

^iv Royal Society Mathematical Futures programme

^v Coordinating mathematical success: the mathematics subject report (Ofsted).