The use of language and vocabulary in mathematics
Mathematics cannot be learnt without language
Whilst mathematics might be considered to be a language in its own right the demands it makes of the use of language by learners can be considerable.
Main Section
Language is essential to the learning of mathematics. It provides a means for learners to express their understanding, negotiate meanings, to develop their thinking further and to share their findings with others. Language is necessary for the transition of problems between the real world and mathematics and mediates between the teacher and learner and between learners. It helps to expose understanding and develop meaning.
The language demands for learners of mathematics can be considerable. In particular, vocabulary provides a significant challenge for students. Learners need vocabulary to classify mathematical objects, to understand mathematical ideas and to articulate and communicate their mathematical reasoning.
However the relationship between the mathematical register and everyday language is not simple. Some words have the same meaning in mathematics and everyday language. Other words have a meaning only in mathematics and could be considered to be the technical vocabulary of mathematics, for example, place value, divisor, congruent. Finally there are also some words that have a different meaning in mathematics than they do in everyday English, for example, round, value, factor.
Students use language in a multitude of ways in mathematics lessons. The language demand of mathematics questions is often high and there are few contextual clues to assist pupils in decoding them. Pupils are also expected to reinterpret their solutions in the context of the original problem. A student’s vocabulary is also drawn on when they explain their work to others, ask or answer questions, and work in a group. For example, this may include describing something. For this they may also use metaphor, language that is based on a shared understanding outside of the classroom, image creating language as well as language mathematics teachers would consider as mathematically incorrect such as ‘diamond’ for a square in a particular orientation.
When students are learning something new in mathematics they often also have to learn new vocabulary which increases the level of challenge faced by learners. Often this new vocabulary refers to abstract and complex concepts and it can be difficult to discern a student’s understanding if they are having difficultly with the related vocabulary.
Probes & Prompts
How good are you at using mathematical vocabulary correctly?
Do you make the meanings of words and the different meanings in different contexts explicit?
How do you provide learners with the opportunity to develop their use of language in mathematics? Taking Action
A fantastic way to help children learn and remember the appropiate words for a maths topic is to play 'Just a Minute'. Copy, laminate and cut out the vocabulary they should be using for their year group. Give a set to mixed ability groups of four or five children. The most confident child starts. They describe the words on the cards without actually saying them. When the group guesses the word, the 'describer' places it face up on the table (important to do this as some children will look at it and be able to remember the word by seeing it). They guess words for a minute, then the 'describer' collects the words they guessed, counts them and places them at the top of the pile and hands them to a second person who becomes the 'describer'. They begin with the words previously guessed and then move on to new words. This continues until everyone has had a chance to be the 'describer'. The children get quite competitive and in my experience really love the game. It is a brilliant method for learning and remembering vocabulary. It also works for other things e.g. tables facts. fraction/decimal/percentage equivalents.
Case Studies
I observed a game of 'Just a minute' in a Year 1 class recently. The children were using picture and word cards for the shapes and their properties that they needed to learn. It was great to watch, the children were all participating and really enjoying themselves.
I also observed a game in Year 3 at another school. The children were enthusiastic and competitive and did so well with their explanations of the measures vocabulary that they were using.
Try it, its a great way to rehearse vocabulary!
Research Sources
Durkin K. and Shire B. (eds) (1991), Language in Mathematical Education: Research and Practice. Milton Keynes: Open University Press.
Pimm, D. (1987), Speaking Mathematically. London: Routledge.
Categories
FAQs, Obstacles, Pedagogy