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David Maytham

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Speaking of maths…

Today’s teachers are under ever increasing pressure to ensure all children achieve excellent progress and good attainment, regardless of background or SEN. The 2014 maths curriculum is designed to be fully inclusive and aims to ensure all pupils become fluent in the fundamentals of maths, reason mathematically and can solve problems by applying their maths in a range of contexts. In these aims and in children’s maths progression more generally, talk can have a profound and meaningful impact.

Interestingly, these core aims, which on paper seem both realistic and achievable, are actually what teachers across the country find most difficult to develop in their children. Teachers will report that many children lack the ability to rapidly recall facts, which is detrimental to their fluency. They will suggest that children struggle to access and understand core mathematical language, and, for many, it is reasoning, explaining, justifying and problem solving that are major barriers in the classroom.

I believe that for children to be successful they need three key competencies: procedural proficiency, conceptual understanding and language competence. Procedural proficiency refers to them mastering a procedure. For example, a child is able to use their fingers to recall the nine times table, or can successfully follow a column addition procedure to complete addition sums. Procedural proficiency on its own is useful, but without conceptual understanding and an ability to access and understand mathematical language, the child will lack both fluency and the ability to reason to solve problems.

For example, I recently taught Ben, who “knew his times tables up to 12×12”. That is to say, he knew the procedures to recall these facts. However, when I asked him to work out 12 multiplied by 13, he looked at me blankly. Ben had procedural proficiency, but lacked the conceptual understanding to apply his knowledge of multiplication to solve this problem. Conceptual understanding thus refers to a child’s understanding of the underlying mathematical concept. Children who have procedural proficiency, but lack conceptual understanding, will often demonstrate an inability to adapt skills to unfamiliar contexts, will have difficulty reconstructing forgotten knowledge or skills and will compute without meaning. An inability to access mathematical language will often make the development of a conceptual understanding harder.

Of course, some children have the reverse problem. These are the children who have a good conceptual understanding of an area of maths, but will lack the procedure to enable them to solve the problem. When this occurs their computation will be slow, effortful and frustrating, as they grapple with the procedure. Often these children will show an inability to focus on the bigger picture when solving problems and will have trouble progressing to new or more complex ideas.


Understanding procedure and concepts

The use of talk in the maths classroom aims to support children in developing the procedural proficiency alongside their conceptual understanding, while supporting language competence through systematic mathematical language acquisition.

While the use of talk in the maths classroom is not limited to the two principles below, these are the most powerful.


Principle 1: gamifiy your maths lessons

Schools which have introduced the concept of playing short maths games ranging from 60 seconds to ten minutes every single day (across the curriculum and not just as starters) report positive shifts in pupils’ perception of maths, engagement with the lesson content and ability to rapidly recall mathematical facts. The principle behind this is a simple one. In the natural world, young animals learn through play. We are familiar with this as a concept with babies and toddlers; why, then, do we reject this as children begin to grow? When an idea or concept is made into a game – something which children recognise and respond to – children begin to engage with it and take ownership of it. Gamifying learning allows children to generate ideas for themselves, cultivate their creativity, and lay the foundations for fluent learning. 


Principle 2: use mathematical stories

Through centuries of exposure to the story form, our brains have become hardwired to respond to stories. The way our brains work to decipher stories is highly sophisticated, yet evidence proves that children can engage in this process from a very young age. Using mathematical stories is a revolutionary development in the teaching of maths in the twenty-first century classroom. For younger children, stories such as The Hungry Caterpillar could be successfully used as a hook for a maths unit, supporting children with counting to five and learning the days of the week.

However, I highly recommend that teachers write their own maths stories, which contain the mathematical language and concept appropriate to the topic they are teaching. As soon as a mathematical concept is put into a story form it comes alive. It can provide a suitable hook or engagement for a topic and provide purpose and meaning for maths. Crucially, mathematical stories can support children in understanding abstract concepts as well as help them internalise and learn specific mathematical language and facts.

Through engaging with mathematical stories, children will try things out, polish them, come back to them, look at them from a different viewpoint, bring their peers in to support the idea they are investigating, swap roles and find reasons and answers to problems that will sometimes seem impossible. These types of engagement will support procedural proficiency, conceptual understanding and language competence and, ultimately, create a new generation of confident and fluent mathematicians.


Talking the talk

by David Jones, class teacher at St Hugh’s Communication and Interaction Specialist College, Lincolnshire

I have used maths stories in both primary and SEN settings. These stories provide a hook to engage children in new mathematical vocabulary in a real life context. The pupils in both settings have enjoyed writing them and refer back to them to support their learning. The stories have deepened the understanding of pupils and have provided them with skills to teach other children independently.

Short maths games create a buzz in the classroom and provide access for all levels of ability. High quality maths vocabulary is established and the children within my classes have shown vast improvements in retention and recall of key concepts.

Dedicating just one to five minutes to intense quality discussion every day is important and allows the children to consolidate their learning through deeper reasoning skills.

A focus on the key skills of mathematics is important here; children are given the opportunity to move their learning from superficial to a deeper understanding of concepts. They are given an armoury of skills which enables them get rich and meaningful experiences through investigations and applying their skills with fluidity. As pupils’ viewpoints become more critical, they are able to look at particular skills from many angles. These are vital skills which will prepare our pupils to solve problems with confidence and meet the challenges of the wider world.