: Building the architecture: Developing pupils’ mathematical problem-solving strategies How explicit teaching of problem-solving strategies helps KS2 pupils tackle unfamiliar mathematical challenges with confidence.

In the first blog of our Grand Architecture series, Problem Solving in Early Years – Laying the foundations, we explored how the foundations of mathematical problem solving are established in the Early Years. Through play, exploration and rich mathematical talk, children develop the early number sense, reasoning skills and mathematical curiosity that form the bedrock of future learning. Once these foundations are secure, the next stage of construction can begin.

In Key Stage 2, pupils encounter increasingly complex mathematical challenges that require more than knowledge alone. The EEF’s Improving Mathematics in Key Stages 2 and 3 guidance report highlights this in Recommendation 3: Teach strategies for solving problems. Just as a cathedral requires a strong structure to rise above its foundations, pupils need a range of strategies that support them when faced with unfamiliar mathematical problems.

Raising the walls

The walls of a cathedral give shape and form to the building. Similarly, problem-solving strategies provide structure to pupils’ mathematical thinking. The EEF recommends that pupils are explicitly taught a range of strategies and representations that can help them approach unfamiliar problems. These might include drawing diagrams, using bar models, organising information in tables, looking for patterns, working backwards or breaking a problem into smaller steps.

Rather than leaving pupils to discover these approaches for themselves, effective teaching makes them visible and purposeful. By developing a toolkit of strategies, pupils are better equipped to make sense of a problem before attempting to solve it, giving them confidence when the route to the solution is not immediately clear.

Positioning the pillars

Strong walls require strong pillars. In mathematics, these pillars are built through explicit teaching and modelling. The guidance emphasises the importance of demonstrating not only what to do, but also why a particular strategy has been chosen.

When teachers think aloud, they make the invisible processes of problem solving visible. Comments such as, ​“A diagram might help me represent the information more clearly” or ​“I think a table will help me organise what I know” allow pupils to see how experienced mathematicians make decisions. Through carefully chosen worked examples, teachers can model how different strategies can unlock different types of problems, helping pupils understand that successful problem solving is often about choosing an effective approach rather than applying a memorised procedure.

Connecting the arches

The arches of a cathedral connect different parts of the structure, creating strength and stability. In the same way, pupils need opportunities to connect and compare different problem-solving strategies across a range of mathematical contexts.

The guidance recommends exposing pupils to multiple strategies and encouraging discussion about their effectiveness. A problem may be solved using a diagram, a table or a numerical approach and comparing these methods helps pupils develop a deeper understanding of the mathematical structures underpinning the problem. By discussing which strategies are most efficient and why, pupils become more flexible thinkers who can select appropriate approaches when faced with new challenges.

Preparing for the spires

As the structure rises, it prepares the way for the final stage of construction. The foundations laid in the Early Years, and the strategies developed throughout Key Stage 2, provide the support pupils need for the more sophisticated mathematical thinking that awaits in Key Stage 3.

By explicitly teaching problem-solving strategies, modelling their use and encouraging pupils to compare and evaluate different approaches, we help to construct a rich network of mathematical knowledge. It is this that will support pupils as they move towards the higher levels of reasoning, reflection and independence that will be explored in the final stage of our cathedral’s construction.

In the final blog in our Grand Architecture series, From Foundations to Independence: Problem Solving in Secondary Mathematics, we’ll explore how the foundations laid in the Early Years and strengthened in Key Stage 2 enable students to become increasingly independent, strategic and resilient mathematical problem solvers.