Learning outcomes
After studying this chapter, you should be able to:
• recognise the importance of language in the teaching and learning of mathematics
• identify the elements of the mathematics register in English and other languages and discuss the impact on learning
• reflect on the appropriate use of language by the student and the teacher in the mathematics classroom
• write mathematics correctly (technical communication).
Introduction
In a typical mathematics classroom, students read, write, listen and speak mathematics. In a typical secondary mathematics classroom there is a lot of listening to the teacher speaking the mathematics, but is this the best way for students to learn? In addition, in these four language modes there are particular issues in the context of mathematics. Consider the following:
1 There are just four numbers, after unity, which are the sums of the cubes of their digits. The word ‘diameter’ and the word ‘radius’ are closely related. In Chinese, diameter is 直径 [zhíjìng], literally meaning ‘straight path’, with radius being 半径 [bànjìng], meaning half path.
2 Recently a pre-service teacher commented: ‘I think at this stage I'd make a poor maths teacher because I've never spoken this language. I read it at school, but never “said it aloud” BIG difference’ (Galligan & Hobohm, 2013, p. 328).
3 A student says: ‘I can see this bit here has to be timesed by 3 outside the brackets, and then take away the bits in the brackets …’
4 In solving the simultaneous equations
a student wrote as an answer:
Each of these scenarios highlights some of the language issues in teaching and learning mathematics. These issues fall into a number of categories:
1 The mathematics register (i.e. the words, phrases and associated meanings used to express mathematical ideas). This includes the etymological view of the words of mathematics as well as the syntax, semantics, orthography and phonology of the language itself and its impact on understanding mathematics.
2 Language in the classroom: the use of language by teachers to communicate ideas and the dialogue used by students to communicate and learn mathematics.
3 Technical communication: i.e. the accepted standard use of language and symbols to communicate mathematical ideas, both orally and in the written form.
In this chapter we will highlight these issues, ask you to reflect on particular problems and offer activities that can be used in the secondary classroom.