Art and Mathematics in Education

We begin by asking a simple question: To what extent can art education be related to mathematics education? One reason for asking this is that there is, on the one hand, a significant body of claims that assert that mathematics is an art, and, on the other, work in art that has a mathematical basis. Observations of these kinds are not trivial. They have significant implications for the teaching of these areas of the curriculum in at least two ways. First, there is the methodological issue of the extent to which we should teach mathematics and art separately, and second, the teleological question of why they appear in the curriculum at all. So the relationship between the nature of mathematics and art, perceived or real, bears down on questions of the individuation and the justification of these disciplines, or, in other words, upon pedagogy and purpose. Although in principle both the pedagogy and the purpose of any discipline are distinct, there are important connections between them, as we shall draw out.

As far as mathematics goes, it has been stressed that the purposes of even rudimentary aspects of mathematics such as counting do need to be made explicit to pupils. ¹ What have been seen as errors in understanding are internally linked with pupils' ideas of the purposes of counting. Anna Sierpinska discusses a similar situation within the broader aspect of what she calls "theory" in higher mathematics. ² More generally, John Passmore, in his analysis of pupils' understanding includes the case where a pupil sees no need to understand since he or she cannot understand the point of learning the subject. ³ If the purposes of art and mathematics are strikingly similar then there is reason to suppose that certain pedagogical approaches that follow from this will improve understanding of both mathematics and art, and therefore understanding of reasons for engaging in math-based and art-based activities.

In schools we see what appears to be some evidence of connections between art and mathematics in cross-curricular work, such as that described in Jacqueline Cossentino and David Schaffer. ⁴ Apart from providing much-needed motivation, an important value of this approach toward mathematics is that it can illuminate pupils' understanding of some of its purpose by, at the very least, allowing them to recognize instances of mathematics at work, often in unsuspecting contexts. In particular, by facilitating some transference of knowledge pupils can appreciate the so-called "power" of mathematics in its widespread application to the world of artefacts produced by themselves and others.

Can we go further than displaying connections between these disciplines? Can we treat mathematics itself as art? In particular, can we suppose that pupils can make mathematics just as they can make artefacts? Some writers seem to imply this by invoking the notion of creativity as a common property between the two disciplines. ⁵ Leaving aside the ironic sense of creativity in, for example, the case of "creative accountancy" pupils must indeed "make" sense of mathematics and they must originate mathematical assertions of their own that have not been directly taught. In both respects mathematics is similar to the learning of a language. Further than this, we value pupils' inventiveness in their approaches to areas of mathematics, calculations for example.

The linking of mathematics and art via creativity has its most persuasive force in the change of attitude toward axiomatic foundations. ⁶ The story is familiar: for centuries Euclidean geometry was (wrongly) supposed to offer truths of the actual space in which we lived, since its axioms were thought to be confirmed by our intuitions of space. However, when it was found that consistent and useful axiomatic systems could be constructed by making certain alterations to these axioms, it became clear that mathematics was not simply discovered. It involved a significant measure of creativity. Yet one thing is clear: the sense that children make of mathematics, the original utterances they make...