Why is it that, in many schools, the work we plan for those children who are slower to grasp maths has either a lack, or complete absence, of reasoning and problem-solving activities? 

The rationale usually goes along the lines of, “well, if they’re not fluent, how are they going to be able to use their mathematics?”. I don’t buy that. 

Becoming truly fluent in mathematical concepts and procedures can only happen when they are applied to different contexts, and withholding these types of activities further hinders the learners who find mathematics most difficult.

The organisation of the national curriculum expectations suggests that fluency is separate from reasoning and problem-solving, and it is easy for teachers to teach it as such. It is as important for pupils to be fluent in their problem-solving strategies and ability to apply their procedural skills as it is to recall them, if not more so. 

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Maths fluency 

I would argue that true fluency in an area of mathematics comes not from reproducing a procedure or performance style, but in the ability to know what procedure to use when at different stages of problem-solving. 

By having fewer (or in some cases, no) opportunities to apply the procedural knowledge that they do have, this knowledge never becomes fully embedded in the long-term memory for lower-attaining students, and therefore the child never becomes fully fluent with the concept.

The importance of modelling

There is a further issue. When the prevailing model is to say, “You’ve got the fluency, now apply it to a problem,” without any extra modelling, pupils often don’t know the strategies they need to solve the question.  

This situation is exacerbated in the cases of many slower-grasping children, who often aren’t even introduced to problem-solving, let alone given strategies to support their solving of said problems.  

This can show up most keenly at Year 6, where the separation of arithmetic from problem-solving can cover up some of the issues pupils have with a lack of strategy. There should be no surprise at the slower-grasping pupils’ inability to solve, or even break into, a problem when they have never been taught the strategies to do so. 

Rosenshine’s Principles, while not flawless, contain some lessons as to the dangers of abandoning problem-solving for lower-attaining pupils. Providing worked models for these pupils, especially modelling expert thinking out loud, is vital to support pupils’ understanding of the strategies required to solve different types of problems. 

As we so often see, what works best with the slowest-grasping pupils, works effectively with all pupils.

Vocabulary issues

A final issue is vocabulary. All vocabulary in mathematics has a specific meaning, often a different one to that which pupils have encountered before (the word “difference” being one example that immediately springs to mind). 

However, as much as the specific vocabulary itself, the phrasing of questions and problems in mathematics can pose a significant challenge for those pupils with communication or language difficulties, who may otherwise have a solid understanding of procedural mathematics. 

Once again, the modelling of these problems, including the written and spoken language, is key to helping pupils become proficient problem-solvers. Stem sentences (providing structure for understanding problems) can be a useful tool in supporting these pupils, as well as carefully planned examples that use the same language over and over again to build confidence and understanding. 

As with all modelling, if you want pupils to become proficient in a certain area then try not to cognitively overload them - make the object of your practice specific, with slight variations, rather than introducing a wide variety of vocabulary and phrases with fewer opportunities to practice at once.  

Aligned with this is my intense dislike of RUCSAC (read, understand, choose, solve, answer, check), a method of solving one particular type of problem that relies so heavily on the “read and understand” part of the question that, if you get stuck here, you have no chance of the solve, choose, answer, check part ever happening (not to mention that it is almost useless for solving any non-linear problems).

Primary maths: how to help struggling pupils

Taking all this into consideration, this would be my blueprint for supporting pupils struggling with maths in primary:

1. When planning, ensure that pupils at all stages of understanding are given sufficient exposure to reasoning and problem-solving activities. Pupils will become no more proficient at these tasks if they have no chance to engage with them.

2. Ensure that you consider in depth the modelling of problems that pupils require. Expert modelling, guided practice and independent practice are all vital for pupils to develop their understanding of strategies to solve problems.

3. Consider the cognitive load. Different types of problems require different strategies, so model how to solve one particular type of problem, with sufficient consolidating practice, before introducing a different type of problem that will require different strategies to solve.

4. Ensure that enough attention is spent on the vocabulary of problem-solving, including the phrasing of questions. Stem sentences and prompts can help slower-grasping pupils to scaffold their understanding.

5. Even if pupils are taking longer to embed the procedural and calculation aspects of their mathematics, remember that modelled reasoning and problem-solving application of the concepts they have been studying will only help to secure their fluency.

Jon Parsons is deputy headteacher at White Meadows Primary Academy. 

This was originally published on 28 July 2020