Making mathematical purpose explicit: why Maths Horizons is arguing for greater specificity and coherence within the programme of study

Maths Horizons has identified four areas of change that we believe will support the goal of a richer maths curriculum with problem solving at its heart. 

Suggested changes
Curriculum	1	Rebalance content from upper primary to lower secondary, allowing more time for knowledge to be secure and flexible, including opportunities for problem solving and reasoning for all students
	2	Greater specificity and coherence within the programme of study about the mathematical meaning and purpose of what students are taught
	3	Make problem solving and reasoning accessible to all by identifying the mathematical content from prior years required to solve problems in a variety of contexts
Assessment	4	Incentivise the teaching of problem solving and reasoning by increasing the proportion of marks allocated to problem solving and reasoning in key stage 2 SATs and GCSEs.

Greater specificity and coherence within the programme of study about the mathematical meaning and purpose of what students are taught

In the current programme of study, procedures are named, but the purpose of learning these procedures is often left implicit. This means that pupils may meet curriculum expectations by reproducing techniques accurately, without reliably demonstrating the kinds of mathematical thinking those techniques are intended to support. Over time, this can limit pupils’ opportunities to develop and apply key capabilities, such as judging the plausibility of results, recognising and explaining patterns, constraining possible solutions, generalising relationships, and justifying conclusions. Making these expectations explicit in curriculum language is therefore important for securing rigour, consistency and progression, and for ensuring that procedural fluency functions as a tool for mathematical thinking rather than an end in itself.

This matters for all pupils. Maths Horizons’ analysis indicates that reasoning and problem solving should be treated as a shared entitlement, made explicit in the curriculum language itself, and grounded in the specific mathematical structures of each sub-domain. 

But effective problem solving is grounded in a deep understanding of the underlying content. Richer mathematical knowledge includes understanding why procedures work and when it makes sense to use them. Without these foundations then pupils will lack the tools that allow them to tackle unfamiliar problems and apply their knowledge flexibly in non-routine situations.

Building foundations for problem solving

To equip all pupils with the richer mathematical knowledge that they need to experience success with problem solving, greater specificity is needed about the meaning and purpose of the mathematical content they are learning. This is not about adding new or extra content. Rather it is about ensuring that there is shared understanding of why mathematical procedures have a place in the curriculum, how they are connected and sequenced to build a progression of knowledge, and why understanding how procedures work and can be flexibly applied is as important as being able to perform them fluently. What could this look like? 

Example: Year 5 rounding

Current Year 5 content

• round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000

• solve number problems and practical problems that involve all of the above

This wording risks separating skill from purpose. Pupils can learn to round accurately without understanding when, why, or how rounding helps them think. In practice, rounding can become a checklist item, with “problem solving” bolted on afterwards and interpreted very differently across classrooms.

Proposed Year 5 content: 

• use rounding of whole numbers to estimate, compare and evaluate the reasonableness of results, selecting an appropriate degree of accuracy and reasoning about scale to eliminate implausible solutions

This revised statement makes the mathematical intent explicit. Rounding is positioned as a tool for estimation, judgement and justification, not an end in itself. 

The following examples illustrate how this wording better equips pupils to apply this knowledge when problem solving and reasoning.

• Identifying and using structure and scale 

  Which is the best estimate of 4,983 + 2,017? (6,000; 7,000; 8,000; 9,000) 

  Pupils must reason about magnitude and place value to judge plausibility, rather than calculate exactly. 

• Constraining solution space 

  A number rounds to 800 when rounded to the nearest hundred. Which of these could be the number? (749, 802, 851, 912) 

  This task is not about performing rounding; it is about eliminating impossibilities and reasoning about ranges.

• Justifying judgement in context 

  A charity prints 4,763 leaflets. Each box holds 200 leaflets. Without calculating exactly, explain how you know they need fewer than 25 boxes. 

Here, rounding supports estimation, but the core demand is explaining why an answer makes sense

Why greater specificity matters

The shift in wording is important. It communicates the purpose of the mathematical content. It builds the foundations for reasoning, embeds problem solving within the mathematics itself, and protects intent in teaching and assessment. Pupils must demonstrate mathematical judgement - judging the plausibility of results, recognising and explaining patterns, constraining possible solutions, generalising relationships, and justifying conclusions.

Maths Horizons therefore argues that greater specificity about the meaning and purpose of mathematical content is essential if the National Curriculum is to secure depth, coherence, and equity. By specifying the reasoning that matters in each area of mathematics, we ensure that all pupils are entitled not just to do mathematics, but to think mathematically.

Maths Horizons is an independent programme drawing on an extensive evidence base to inform and support system change in maths education.