For the Learning of Mathematics,
Vol. 28, No. 2 (Jul., 2008), pp. 26-32
Published by: FLM Publishing Association
Stable URL: http://www.jstor.org/stable/40248605
Accessed: 06-10-2015 18:45 UTC
This paper explores repetition and poetic structures in mathematics discourse.
One means of highlighting this parallelism relies on indentation (Hymes, 1981):
2 Cos every fifth one
3 from William
4 is going to be
5 a white,
6 and every fifth one
7 from the next person on
8 is going to be
9 a red
10 and every fifth one
1 1 from the next person
12 is going to be
13 a green
Selection 1: Cuisenaire rods (Pimm)
The mathematical pattern is expressed through the grammatical pattern of parallelism. In this example, the discourse structure is identical to the mathematical argument.
Parallelism allows a speaker to recognize an existing idea and modify it in a way that is concise and easy to understand.
Despite differences in subject matter, there are theoretical resonances between the studies of oral traditions and of mathematics discourse. Just as literate expressions are often valued more highly than oral ones, the formal register of our discipline is sometimes valued more highly than the legitimate ways in which learners express mathematical ideas (Barwell, 2005; Street, 2005)
Why do students express mathematical ideas using forms of discourse that can, in other contexts, be poetic? We can see this by considering that in Jakobson’s perspective, poetic speech is inherently organizational. Indeed, he called parallelism a poetic functiond eliberately,b ecause it maps related ideas into an established grammatical structure. This sorting and arranging of ideas based on similarity and contrast is arguably a mathematical way of thinking.
But further, the form of the message establishes relationships among ideas that are not always expressed explicitly.
The transformation of one unit of meaning into another is quite literally a linguistic construction of mathematical ideas. Parallelism is a multi-functional feature of language that allows people to “think out loud” about the relationships among ideas.