Summer 2004

Talking Maths

Numeracy Is Every Teacher's Business

Students need a sound understanding of mathematics if they are to make the most of their education and their future lives, argues STEVE THORNTON. Teaching numeracy through other learning areas can deepen their understanding of both the subjects at hand and of mathematics.

I THINK THERE ARE four contexts and purposes for doing maths at school. The first two are familiar: learning maths concepts in maths lessons, and applying them to solving problems. It is critically important that we teach maths concepts well, that students learn them well and that they learn to apply their mathematical knowledge effectively. Whether mathematical concepts have an obvious use in life (such as measurement, statistical ideas or mental computation), or are less obviously useful (as in number theory), understanding them is vital to students’ development as learners and doers of mathematics. Whether our curriculum is structured around traditional subject boundaries or some kind of integrated structure, we cannot escape our responsibility to teach maths well and to help students to develop a deep understanding.

The third context and purpose is more open ended. It is using a context outside of the mathematics lesson as a spring-board for learning mathematics. In my own teaching of mathematics to first year undergraduate primary teachers, I have used a CD called Problem Pictures. The CD has some 150 photographs from all over the world of objects that have a mathematical aspect to them. I use the photographs as a springboard to ask students to explore more and deeper mathematics.

For example, one of the photographs is of two men standing in front of a giant’s foot at a theme park. The question on the photograph asks students to estimate the height of the giant. Two of my students took the idea further and asked how much material it would take to make the giant’s sock, or how much the giant would weigh. They asked themselves why you could not simply multiply by the linear scale factor to find surface area and volume. In asking this question they were doing a lot of maths through a context in which they were engaged and interested. The purpose was to learn more maths.

I think there is a subtle difference between this assignment and what we frequently do in maths lessons, which is to ask students to use their math-ematical knowledge in a context. Here I was really saying ‘I want you to find out some new maths that you didn’t know before and show me that you understand it’. I wonder if this sort of experience might help to make school maths a more joyous experience for some of those students who don’t ever really get to see that maths is everywhere because they don’t know the maths in the first place. Perhaps instead of teaching the maths then applying it to problems around us, it might sometimes be better to look around us and see if the environment prompts the learning of some new maths.

The fourth context and purpose for mathematics is different again. It is what is often called ‘numeracy across the curriculum’; however this term is seldom well understood or implemented. Sue Willis¹ described being numerate as, at the very least, having the competence and the disposition to use mathematics to meet the general demands of life at home, in paid work, and for participation in community and civic life. I think that, for students at school, the general demands of life include the demands of other learning areas. After all, school is a huge part of children’s lives and most of their school life is not spent in maths lessons.

The difference between this way of looking at maths out of the maths lesson and the previous one is that the purpose here is not to learn maths, nor even to apply maths to another context. The purpose is to do geography, science, music or language better. My claim is that without numeracy you actually can’t do good English, physical education, woodwork, etc.

In particular, I want to suggest that understanding mathematical ideas is crucially important in understanding how the world works. Lynn Steen, an American mathematician who has been instrumental in drawing attention to the need for quantitative literacy, says If individuals lack the ability to think numerically, they cannot participate fully in civic life, thereby bringing into question the very basis of government of, by, and for the people.

To take a fairly recent example, the media rightly gave a great deal of attention to the issue of boys’ education. The Canberra Times² claimed, for example, that year 3 and 5 literacy tests show boys perform up to five percentage points worse than girls. However, what the article failed to do was explain what this really means. In fact, it does not mean that on average boys gain 5% fewer marks than girls. What it means is that whereas in most states and territories some 90% of girls achieved the literacy benchmark, only around 85% of boys met the benchmark. This is still a good result for most boys. However, if the figures are looked at differently it shows that 15% of boys do not reach the benchmark, compared to 10% of girls. So the real worry with boys’ education, as almost all teachers will confirm, is not that boys generally are doing badly but that there is a significant and worrying cohort of boys for whom school can be an alienating experience, and who opt out of learning as a result. Much of this perspective was lost in the general debate about boys’ education, yet a more informed look at mathematics would have significantly enlightened the situation.

In the school setting, it is critical that all teachers address the numeracy demands and opportunities in the subject area they are teaching. While this could mean planning to incorporate numeracy, it is equally likely to include dealing with ‘numeracy moments’ as they arise.

A year 5/6 class in the ACT was reading Day of the Triffids by John Wyndham. Rather than glossing over the measurements of the triffids given in the novel, their teacher dealt with the numeracy of the situation by asking how big these triffids really were. The children then made a full-sized model of a triffid, and suddenly realised how terrified the people must have been. This added enormously to their appreciation and enjoyment of the novel. So the purpose was not to learn measurement, but to understand English literature better by appreciating the numeracy.

By looking at maths not only in but out of the maths lesson, we can challenge the way students view mathematics. In the process, we can add to students’ enjoyment of, and connection with, mathematics (and all other areas of schooling), and give them skills essential for participation in a democratic society.

1. Willis, S (1992). Being numerate: Whose right? Who's left? Literacy and Numeracy Exchange, Autumn 1992

2. Falling Behind, Canberra Times, October 22, 2002

Steve Thornton lectures in Mathematics Education at the University of Canberra. For the past two years he was president of the Australian Association of Mathematics Teachers.

The author owns the copyright in this article. For information related to the reuse of this work in any form please contact the publisher denise.quinn@curriculum.edu.au