# Mathematical language

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Effective teachers shape mathematical language by modelling appropriate terms and communicating their meaning in ways that students understand.

#### Guidance for effective practice:

1. Work with ākonga to connect mathematical symbols with the meaning of those symbols in spoken and written language.
Viliami is aware that the language of mathematics is sometimes confusing for his students, especially those for whom English is a second language. He knows that confusions about words and symbols can also lead to misconceptions. He begins the unit on multiplication and division by asking his studentsabout the meaning of three sentences displayed on the whiteboard:
“Five multiplied by six equals thirty.”
“Siali has three times as many pencils as Repeka.”
“Our class of 24 students is divided into groups of four.”
Viliami underlines words and terms that he thinks might have other, non-mathematical meanings in real life. His students offer their ideas about the words.
Ellie: Multiplied by is like “it gets bigger”, right?
Repeka: Times is about clocks, usually. I think it means Siali has more pencils than me.
Tyrese: Groups are bands that play music or dance, I think. I belong to a pātē group that beat drums.

Vilami recognises that students’ existing meanings, such as multiplication makes bigger, may lead to over-generalisations. He also sees that everyday contexts, like Tyrese’s illustration of groups, may help students relate to the mathematical meaning. He asks his students to draw a diagram, and write a mathematical equation for each sentence, to show what the sentence means.

During the discussion that follows, Vilami explicitly draws students’ attention to the ×, ÷, and = symbols to negotiate their meaning. For example, several students have drawn “five multiplied by six” as six sets of five. Vilami records 6 x 5 = 30 and asks for the meaning of each symbol. Students decide that the x symbol means ‘of’ as in six sets of five.

2. Collectively create and share a list of important mathematical terms with your ākonga and provide them with access to an age-appropriate mathematics dictionary, either in book or digital form.
Andreas creates a list of important terms during the first lessons of a unit on symmetry with his Year 6 class. The list is displayed on the mathematics wall along with student work. As a ‘stock take’ of the students’ understanding of the ideas, he asks them to work in pairs to write or draw examples of each term (e.g., line of reflection, translation, point of rotation, etc.). Later, the class shares their illustrations and chooses the clearest examples to go on the wall display.

For terms that are uncertain, such as regular hexagon, students look up their dictionary and agree on the meanings, e.g., regular as having equal angles and side lengths, not the standard size or consistently occurring, as in real life.