A White Rose Maths approach to language

Kate Henshall is a Primary Mastery Specialist Lead and works closely with White Rose Maths to help ensure the quality of their resources. Kate came to speak with Learning by Questions about mathematical language and what practical advice she has for filling the language gaps.

“There has been a lot of research into the issues surrounding language deficiency, and its effect on maths cognition. Hart and Risely (1995) found that children from lower socio-economic backgrounds knew and used fewer words than children from professional backgrounds. Not only that, but they continued to add words at a much slower rate, extending the gap even further as time went on. The conclusion of this study was that there is a 3 million word difference - a child from a higher-income family is likely to experience 3 million more words in the first four years of their life in comparison to a child from a low-income family.

3 million words: of course, a number of words of this size has huge implications for the learning journey children take, not to mention the impact such implications also have on wider life chances and mental health.

Low literacy levels and the impact on maths

Academic studies have taken place to look into the issues low levels of literacy have on the development of mathematical ability.

“...an association between mathematical ability and spoken language skills…

...spoken language skills may be important in the drive to reduce educational inequality.”

S. Spencer, J. Clegg, J. Stackhouse (2010)

“Children with better language will tend to develop better reasoning, inference and pragmatic skills.”

A. Theakston, J. Law, J. Charlton, J. Dockrell, M. Gascoigne, C. McKean

Off the back of this, I have collated ideas that I have seen used in the classroom or used myself where mathematical language has been the focus.

Generate discussion in maths

There has to be time set aside for constructive discussion about mathematics, and as teachers, we have to provide those opportunities. Encourage pupils to spot links between representations at the beginning of the lesson, at the beginning of a unit or the end of teaching a particular concept to see how much has been remembered.

Throughout the activity below, we started with simple, basic everyday language to label both columns, for example “rolls” and “doesn’t roll” through to “Less than 8 vertices or no vertices” and “8 or more vertices”. By adding more examples, we began to use more precise language whilst simultaneously generating discussion. Not only that, through this rich discussion and the use of precise mathematical language, children could deepen their conceptual understanding.

Use real-life examples

Real-life examples provide an opportunity for deeper thinking and also give an all-important context for pupils to see why maths is valuable beyond the classroom. Discussion is also made easier if teachers choose examples that children will see and can relate to. However, careful thought should go into these examples. Often, real-life examples can be misleading unless we explore them in detail. Take train tracks as an example of parallel lines. Sometimes we can see lines within train tracks that are not parallel but some that are. It is therefore important we distinguish this with the children and draw out the essential characteristics of a concept.

Address homonyms

Consider the following words:

• Mean

• Ruler

• Odd

• difference

These are all words that are commonly used in mathematics, but they also have completely different meanings in different contexts. It might seem obvious to us as experienced readers, but as a pupil who has not realised a change in context, the meaning of these words could become very muddled.

Be wary of the language you use in the classroom and aim to emulate the kind of language you hope your pupils use. For example, using “the bottom number and the top number” is quite confusing when you consider a whole fraction itself is a number. Using less formal language exposes students to less correct mathematical language that may not help develop their language and in turn, their maths skills.

Incorporate stem sentences

Once children have had the opportunity to discuss freely and draw out essential characteristics of a concept, I often encourage them to spot patterns and to start to make generalisations. Providing scaffolding for effective mathematical discussion takes the pressure off thinking about how to correctly formulate a response and develops reasoning and understanding. Provide students with example stem sentences to aid partner discussion such as:

I think… because…

I disagree because…

I know… so I also know…

If… then…

All… Some… None…

It must be… It might be… It can’t be…

Additionally, you may want to use stem sentences to help children with mathematical rules or generalisations that they can then apply in other ways. For example, ‘ an odd factor x odd factor = odd product and an even factor x odd factor = even factor’

Of the same ilk, when you ask a question in class, ensure the answer returned is in a full sentence; this will help students to gain more confidence in more complex language and sentence construction in mathematics as well as support other children. If other children hear answers in full sentences it allows them to consolidate their understanding or hear something with its full meaning. A one-word answer may not make sense if a child has not heard the question."

Using LbQ to improve language use in maths

Learning by Questions addresses the issue of low literacy in maths head-on:

• Mathematical language is interwoven throughout Question Sets to ensure the perfect balance of understanding and exposure to more complex terms.

• Feedback for incorrectly answered or misunderstood mathematical terminology provides students with a simpler explanation for the term.

• Reasoning questions with sentence stems that provide students with a starting point for their answers are included in all Mastery Question Sets.

• Real-life examples are used throughout Question Sets to ensure pupils are provided a context that relates to them.

You can find Kate on Twitter @Henshie1