As David Pimm, author of the influential book Speaking Mathematically, wrote in the early 1990s: “Mathematics education begins and proceeds in language, it advances and stumbles because of language, and its outcomes are often assessed in language.”
We all know however that getting pupils to use meaningful maths language, particularly orally, is hard to do.
There is of course a symbiotic relationship between a pupil’s conceptual understanding in maths and their confident use of mathematical language to demonstrate that understanding. Conceptual understanding and proficiency in mathematical language progress together, hand-in-hand.
The national curriculum agrees and highlights the need to help children use language to support clear, structured thinking. It states: “The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof.
“They must be assisted in making their thinking clear to themselves as well as others and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.”
The importance of language and communication is reflected in the not-for-profit Mathematics Mastery approach – which was created within a small group of schools in 2012. Indeed, language and communication is included as one of the programme’s three “dimensions of depth”.
On the Mathematics Mastery programme, the dimensions of depth – which are language and communication, conceptual understanding, and mathematical thinking – are the three key ingredients used to help teachers reach the end-goal of improving pupils’ ability to solve mathematical problems.
We have a suite of tools and tactics for improving language and communication and they align to a new framework that has been built on research to guide teachers towards best practice. We have distilled our framework down into five top tips for Headteacher Update to help you consider ways that your classroom practice might be improved.
Tip #1: Opportunities to talk in every lesson
There should be opportunity in every maths lesson for pupils to get talking. We use Talk Tasks. Pupils have five to 10 minutes in every lesson to explicitly practise using the new language that they have learned in the day’s maths lesson, either in pairs or small groups.
The opportunity to talk about what they have learned helps them become aware of what they now know, which enables them to clarify, explore, consolidate and reorganise their new knowledge.
Pupils will respond differently. Less confident children often struggle to discuss mathematical ideas while more confident children might feel that they can get “the answer” on their own. All of them, however, will benefit from mathematical talk, as they practise using words and sentence structures that embed a more complete understanding of mathematical concepts.
We recommend putting children in mixed-attainment pairs for this kind of activity as this helps everyone to participate.
Tip #2: Make sure everyone feels listened to
This is easier said than done but a selection of ground rules and certain types of support can level the playing field for everyone to get talking on equal terms. We insist that all students speak in full sentences, often giving pupils scaffold phrases to help them begin their sentences. In a year 2 classroom, a simple exchange between teacher and pupil might go something like this:
- Teacher: What is five multiplied by six?
- Pupil: Thirty.
- Teacher: Five multiplied by...
- Pupil: Five multiplied by six is equal to 30.
The insistence on full sentences, with support to get students started, creates a classroom ethos that empowers all pupils to talk meaningfully which, in turn, helps all pupils feel heard.
Tip #3: Teach mathematical language meaningfully
Mathematics does have a precise formal language which is distinct from our everyday language. It is important to know what these words mean when teaching maths. For example, in maths, a “product” is not something you make or buy and a “sum” is more specific than it seems. Insisting on the use of “star words” – key words that underpin that day’s learning– helps lead to the correct use of precise vocabulary.
It is also important, however, to let pupils connect their own informal use of language to the more formal mathematics register. Once the words and scaffold phrases have been introduced, pupils should use exploratory, often informal, talk in paired activities to get to grips with what they are learning. Teachers should listen to help their pupils refine their own definitions to avoid overlaying “correct” explanations and definitions which can leave students with a disconnected, shallow understanding.
Tip #4: Listen openly to your pupils
We can all find ourselves listening for the answers we expect to hear rather than really listening to answers. When we listen, however, we deepen our understanding of where the pupil is coming from. A teacher can only tackle misconceptions and help to build understanding if they really listen and resist jumping on answers as either “right” or “wrong”.
It is a teacher’s job to pick out the maths from the jumbled words a pupil says and by doing this start to unpick misconceptions.
As Beka Goh, the design project lead at Mathematics Mastery, writes in a recent blog post on formative assessment: “By listening to pupils’ explanation, teachers gain useful insights into their understanding, as well as being able to probe them with timely questioning. This dialogue can then inform the teacher’s next move: which questions to ask (and to whom), which tasks to choose, and which examples to give.” (Goh, 2019)
Tip #5: Use words to make connections
Learners extend and deepen their understanding when they find that the words they understand in one context also apply in another context. The words become the bridge, connecting mathematical ideas. For example, saying 0.8 out loud as “eight-tenths” helps learners to see that 0.8 can be represented as a fraction. A structured approach to language for mathematics helps to introduce words in a coherent order to aid cumulative mastery of vocabulary and a deeper understanding of maths itself.
Conclusion
I hope that these top five tips help you think of ways to improve the use of language and communication in your classrooms to help children explain how they know things and to improve their ability to reason verbally.
Helen Drury, founding director of Mathematics Mastery, said that when it comes to focusing on pupils’ use of language and communication, schools have found that it is not just children’s mathematics that is improving – but that they are having an impact on children’s literacy too.
She explained: “Better use of language and communication gives children a level of confidence that is born through being able to fully understand and make up their own sentences. Their deep understanding of constructing sentences soon begins to show through in all subjects.”
- Joe Sarchet-Winters is head of external relations at English and Mathematics Mastery, Ark Curriculum Partnerships. Mathematics Mastery is a non-profit organisation dedicated to transforming mathematics education in the UK. Launched within a small group of schools in 2012, it has now grown to work with hundreds of schools across the UK. Email partnerships@mathematicsmastery.org
Further information & resources
- Formative Assessment: Understanding students’ misconceptions, Goh, Mathematics Mastery, August 2019: http://bit.ly/2ksiOwg
- Mathematics Mastery: www.mathematicsmastery.org