Supporting language development in the mathematics classroom

My school is having a big literacy push this year. There’s a ‘literacy focus’ poster in every classroom and we’re all getting used to a standardised marking code for correcting SPAG.

This drive has prompted me to put some thought into language development in my lessons, but to be honest I’ve found it hard to apply much of the whole-school guidance to mathematics. The rarity of extended writing tasks limits opportunity for ‘green penning’, for example, and I’ve yet to find a chance to embed the use of connectives in a lesson. So the question is raised: how can we develop literacy in mathematics?

In their best practice case study, Literacy across the curriculum (2012), Ofsted clarify:

Our message is that individual subjects create different language demands, which need to be identified and addressed within those subjects.

So this is the real question: what are the language demands in maths, and how can we address them? I’ll share my thoughts.

Using technical terms

At every level, students need a mathematical vocabulary to access tasks and questions.

  • Whenever a keyword is introduced, draw attention to it. I usually ask students to copy it down with a definition in their books and put a box around it for emphasis. Peers then check each others’ spelling. It’s best if the definition is in their own words.
  • Avoid simplifying vocabulary, even for students working at lower levels. Language is embedded through frequent use. For example, talk about the numerator and denominator of a fraction, rather than the top and bottom. From an exam point of view, students will run into difficulties if they’re used to talking about the ‘bow tie rule’ of circle theorems and ‘Z angles’ in parallel lines.
  • Be particularly aware of technical terms which have a different meaning in maths to their everyday use – called faux amis by Skemp (1972). For example: origin, axes, base, degree, odd, solution, table, term, division.
  • Circle mis-spelt words in books when marking, and allow lesson time for students to copy down the correct spellings collaboratively.
  • Discuss command words regularly. For example, whenever a question starts with “Evaluate…”, “Show that…” or “Write down…”, nominate a learner to remind you what that means.
  • Praise and reward students when they ask for a word to be defined, to encourage openness in language enquiry.
  • Task students with calling out definitions throughout the lesson: “Every time I say ‘relative frequency’, I want you to say “…which means experimental probability”.
  • Game: ‘Splat!‘. Project a jumble of keywords onto the board and invite two students to come up and play. When you read out a definition, the first person to put their hand on the right word wins.
  • Game: ‘Taboo‘. Produce a set of cards, each with a keyword at the top and then four related words underneath. In teams, students must take turns picking a card from the pack and then trying to describe the top word without using it or any of the other words on the card. In a variation to this game, students can begin by creating their own cards for each other.
  • Display posters around the school with keywords and definitions, coloured according to topic (number, algebra, shape, data). Then set a homework where each student is given a colour and needs to find as many posters as possible of that colour. Provide a worksheet where they can note down each keyword and its definition.

Interpreting text

There are many occasions in maths when students need to scan text to extract information. For example, when answering worded problems they begin by identifying the key facts and considering what the question is asking. Manipulating algebraic expressions, they scan to identify like terms and factors.

  • Create opportunities for students to read numbers and expressions out loud. For example, when introducing the quadratic formula, ask pairs to discuss how they would communicate it verbally to another person.
  • Whenever tackling a test or exam paper, start with a pile of highlighters on each table and allow time for students to highlight all the keywords in each question. Sometimes I use green for ‘I know what this means’ and pink for ‘I need a reminder’.
  • A few moments in to every task, ensure that the instructions are understood: “Tell me what you’re being asked to do”. This approach is particularly useful for students with EAL, those with low reading ages and individuals on the autistic spectrum. It doesn’t just apply to written questions; verbal instructions need confirmation too.

Explaining ideas

As I often remind my classes, it’s no use having great mathematical ideas if you can’t communicate them clearly to others. Students need to be able to do this both verbally and in writing.

  • Model great written communication. Once my students have tried the below exam question, for example, I show them a video of my model solution from which we establish success criteria for them to self-assess their own work.
  • Provide the answers up front, to place emphasis on how students communicate their method. This also means time spent going over the answers can be replaced with peer assessment time to review the clarity of working.
  • Use Kagan Structures such as RallyRobin and Timed Pair Share to maximise the time each student spends speaking and listening.
  • Even if a nominated student can adequately explain a concept to the class, extend an invitation for others to paraphrase the idea.
  • Once or twice each lesson, nominate a student to sum up what has been learned so far, so they get into the habit of explaining concepts in their own words.
  • Create a display board of students’ model answers to exam questions. Give students post-its so they can annotate with specific praise (‘What makes this a great answer?’).
  • When setting extended tasks (e.g. stats projects, painted cube), include success criteria for contextualising answers in plain English.

(Thanks to @amdindependent@MrHillMaths@perryclaire and @awi700 for their great advice which I’ve taken on board in preparing this article.)

What have I missed? Please share your ideas in the comments.

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