Mathematics Education: Exploring the Culture of Learning

By Barbara Allen; Sue Johnston-Wilder | Go to book overview

8

What is the role of diagrams in communication of mathematical activity?

Candia Morgan


Introduction

In investigating the ways in which teachers assess pupils' texts, 11 experienced teachers were asked to read and assess three piece of student's coursework on tasks set by LEAG (LEAG, 1991). Six of the teachers read work on the 'Inner Triangle' task (investigating the relationship between the dimensions and the area of trapezia drawn on isometric paper) while the rest read work on the 'Topples' task (investigating the point at which piles of Cuisenaire rods starting with a small rod and adding successively larger rods will topple over). All of the children's texts on both tasks contained diagrams of one sort or another. It is the ways in which teachers read these diagrams and the values that they placed on them that I intend to address in this paper.


Diagrams as a 'good thing'

The first point to note is that all the teachers at some point expressed approval of diagrams. This approval was several times expressed in general terms, suggesting that diagrams are valued in their own right, regardless of their contribution to the solution or communication of the particular mathematical problem. Charles described his approach to assessment in these terms:

Well, shall I say we would do the thing like this, OK? Have a look for children being systematic in their approach, I've got a couple of things written down here… putting down, tabulating results, perhaps drawing diagrams, putting down ideas, putting forward hypotheses, testing out ideas, um what else?…perhaps coming up again eventually at the other end with algebraic formulas, things like that…

(Charles: 4-8)

Such lists of features are typical of the descriptions teachers gave of their practice. There is little distinction drawn between items related to the act of solving the problem (like hypotheses, testing ideas) and those to do with the form in which the work is presented. According to Charles' self reports of his practice, tables and diagrams, like ideas and hypotheses, do not need any context in order to justify their existence.

While actually reading the children's texts, individual diagrams were, on the whole, ascribed meanings and sometimes values within their contexts; when considering the whole text, however, the mere presence of diagrams in the text appears to be significant in coming to an overall evaluation. Thus, in summing up their evaluations of

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