I can still recall a maths lesson where one of the children in a class I was teaching looked really worried because she didn't understand what was needed to solve a problem. All the rest of the class were cracking on with their work but she was getting nowhere. I asked her what the problem was, as I'd already gone over with the group what was needed to solve the problem.
I quickly realised that the problem wasn't her mathematical skills, it was her lack of mathematical vocabulary and this was something I needed to focus on. Since then I've used a variety of maths vocabulary when teaching to get the children used to the different words that come up in maths lessons.
How does lack of mathematical vocabulary show itself?
There are three main ways in which children’s failure to understand mathematical vocabulary may show itself: children do not respond to questions in lessons, they cannot do a task they are set and/or they do poorly in tests.
Their lack of response may be because:
- they do not understand the spoken or written instructions, such as ‘draw a line between…’, ‘ring…’ or ‘find two different ways to…’
- they are not familiar with the mathematical vocabulary, that is, words such as ‘difference’, ‘subtract’, ‘divide’ or ‘product’
- they may be confused about mathematical terms, such as ‘odd’ or ‘table’, which have different meanings in everyday English
- they may be confused about other words, like ‘area’ or ‘divide’, which are used in everyday English and have similar, though more precise, meanings in mathematics
There are, then, practical reasons why children need to acquire appropriate vocabulary so that they can participate in the activities, lessons and tests that are part of classroom life. There is, however, an even more important reason: mathematical language is crucial to children’s development of thinking. If children don’t have the vocabulary to talk about division, or perimeters, or numerical difference, they cannot make progress in understanding these areas of mathematical knowledge.
How do children develop their understanding of mathematical vocabulary?
Teachers often use informal, everyday language in mathematics lessons before or alongside technical mathematical vocabulary. Although this can help children to grasp the meaning of different words and phrases, you will find that a structured approach to the teaching and learning of vocabulary is essential if children are to move on and begin using the correct mathematical terminology as soon as possible.
Some children may start school with a good understanding of mathematical words when used informally, either in English or their home language. Find out the extent of their mathematical vocabulary and the depth of their understanding, and build on this.
You need to plan the introduction of new words in a suitable context, for example, with relevant real objects, mathematical apparatus, pictures and/or diagrams. Explain their meanings carefully and rehearse them several times. Referring to new words only once will do little to promote learning. Encourage their use in context in oral sessions, particularly through your questioning. You can help sort out any ambiguities or misconceptions your pupils may have through a range of open and closed questions.
Use every opportunity to draw attention to new words or symbols with the whole class, in a group or when talking to individual pupils. The final stages are learning to read and write new mathematical vocabulary in a range of circumstances, ultimately spelling the relevant words correctly.
Using regular, planned opportunities for development
It is not just younger children who need regular, planned opportunities to develop their mathematical vocabulary. All children throughout Key Stages 1 and 2 need to experience a cycle of oral work, reading and writing as outlined below.
oral work based on practical work
Here they can have visual images and tactile experience of what mathematical words mean in a variety of contexts.
other forms of oral work
This will give them opportunities to:
- listen to adults and other children using the words correctly
- acquire confidence and fluency in speaking, using complete sentences that include the new words and phrases, sometimes in chorus with others and sometimes individually
- describe, define and compare mathematical properties, positions, methods, patterns, relationships, rules
- discuss ways of tackling a problem, collecting data, organising their work…
- hypothesise or make predictions about possible results
- present, explain and justify their methods, results, solutions or reasoning, to the whole class or to a group or partner
- generalise, or describe examples that match a general statement
reading aloud and silently, sometimes as a whole class and sometimes individually, for example, reading:
- numbers, signs and symbols, expressions and equations in whiteboard presentations
- instructions and explanations in workbooks, textbooks, online …
- texts with mathematical references in fiction and non-fiction books and books of rhymes during the literacy hour as well as mathematics lessons
- labels and captions on classroom displays, in diagrams, graphs, charts and tables…
- definitions in illustrated dictionaries, including dictionaries that they themselves have made, in order to discover synonyms, origins of words, words that start with the same group of letters (such as triangle, tricycle, triplet, trisect…)
writing and recording in a variety of ways, progressing from words, phrases and short sentences to paragraphs and longer pieces of writing, for example:
- writing prose in order to describe, compare, predict, interpret, explain, justify…
- writing formulae, first using words, then symbols
- sketching and labelling diagrams in order to clarify their meaning
- drawing and labelling graphs, charts or tables, and interpreting and making predictions from the data in them, in mathematics and other subjects
As you can see, using mathematical vocabulary consistently and taking the time to build this into your lessons will enable all of your pupils to take part in all of your lessons and will ensure that no child is left behind because they can't understand the meaning of words.