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1. Art and Mathematics in Education
Richard Hickman, Peter Huckstep
The Journal of Aesthetic Education, Volume 37, Number 1, Spring 2003, pp.
1-12 (Article)
Published by University of Illinois Press
DOI:
For additional information about this article
[ Access provided at 26 Sep 2020 13:15 GMT from Durham University ]
https://doi.org/10.1353/jae.2003.0001
https://muse.jhu.edu/article/39812

2. Richard Hickman is course leader for the University of Cambridge PGCE Art & De-
sign course and Director of Studies for Art History at Homerton College. He is editor
of Art Education 11-18: Meaning Purpose & Direction. Other recent publications include
articles in The International Journal of Art & Design Education, Art Education, and the
Journal of Aesthetic Education.
Peter Huckstep is Lecturer in Mathematics Education at The Faculty of Education,
University of Cambridge, UK. His recent publications include an article in Mathemat-
ics in School and a chapter in Research in Mathematics Education, Volume 3, The British
Society for Research into Learning Mathematics.
Journal of Aesthetic Education, Vol. 37, No. 1, Spring 2003
©2003 Board of Trustees of the University of Illinois
Art and Mathematics in Education
RICHARD HICKMAN and PETER HUCKSTEP
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. Obser-
vations 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 peda-
gogy 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 learn-
ing the subject.3
If the purposes of art and mathematics are strikingly simi-
lar then there is reason to suppose that certain pedagogical approaches that

3. 2 Richard Hickman and Peter Huckstep
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 be-
tween 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 transfer-
ence of knowledge pupils can appreciate the so-called “power” of math-
ematics in its widespread application to the world of artefacts produced
by themselves and others.
Can we go further than displaying connections between these disci-
plines? 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 cre-
ativity in, for example, the case of “creative accountancy” pupils must in-
deed “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 mak-
ing 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 and the inventive methods that often charac-
terize their work, takes place within a fairly stable system, which, apart
from exceptional cases, pupils could not create for themselves.7
Although the traditional version of creativity involves, literally, the mak-
ing of something, the concept is broader than this and has also come to mean
simply imaginative thinking and problem-solving. Since imaginative prob-
lem-solving is central to mathematics, a fully engaged mathematician is in-
escapably creative. This is all well and good provided that we do not sup-
pose that in this respect mathematics may be likened to the arts. It may well
be true that the mathematician “creates” solutions to problems and it is also

4. Art and Mathematics 3
possible that in much rarer cases the nature of the creating is of a similar
kind to that in art, at least at the conceptual level. However, there is an erro-
neous assumption that creating is central to art making in a way which is
absent from other areas of the curriculum. To provide opportunities for cre-
ative activities in mathematics is not necessarily to treat them like art, but
simply to attend to an aspect which has hitherto been absent.
There are many aspects of good practice in art education that can be
transferred to other subjects; in doing so it provides enrichment rather than
making them more “artistic.” Nevertheless, even if invoking creativity does
not get us very far in attempting to annex mathematics and art, there are
other similarities between the disciplines that should be considered. Just as
many artists have traditionally tried to “imitate” the properties of nature so
the application of mathematics involves a careful representation of the ex-
tra-mathematical world in what is called a mathematical model. The idea of
a mathematical model is broad: it can range from the simple idea of a
number line to full-blown theories in mathematical physics. One suggestion
might be that this provides a means of uniting mathematics and art. There
are, however, notable differences between the principles which underpin
the working practices of the artist and those of the mathematician that
severely threaten the analogy. In the first place it is typically, though not
exclusively, the quantitative relationships that concern the applied math-
ematician. The artist has enormous scope, compared to the mathematician,
for choosing which aspects to draw out from nature. Second, the mathe-
matician’s model is constructed to meet certain functional requirements not
considered essential to art. For example, it will need to be predictive or ex-
planatory. Third, while the artist’s product is essentially sensuous and pro-
duced for enjoyment or for some didactic purpose, these are only of second-
ary concern to the mathematician. Of course he or she will want to meet
certain aesthetic criteria — economy and elegance for example, but this is
true in many other areas of life including such as the making of speeches.
So the purpose of the mathematical model and the artists’ depiction of
nature diverge too much to make this analogy any more than a marginal
connection.
Not all art, of course, is representational. An artist may be more con-
cerned with formal properties internal to a work. As we have suggested,
the same is true of pure mathematics. The “pure” indicates that internal co-
herence is of primary concern rather than correspondence. Moreover, it is
not uncommon for mathematicians and writers to stress the importance of
aesthetic ideals of mathematics. So that beauty, or more modestly, elegance
is sought in mathematical argument as it is in art. Thus pleasure of a similar
kind to that which is often found in art can to some extent be found in math-
ematics. What is also very important to point out is that such pleasure need
not be created. Just as pleasure can be found by contemplating the art of

5. 4 Richard Hickman and Peter Huckstep
others, so one can derive pleasure from exploring existing properties of
mathematics, such as pattern. Whether of course mathematics is the best,
or even an ideal, source for such pleasure depends upon its accessibility,
distinctiveness, and scope compared with other disciplines. So the justifica-
tion for learning mathematics on the strength of its internal properties re-
quires careful judgment.
There is, then, an undeniably aesthetic dimension to mathematics, and
this is not simply confined to the notion of an “elegant solution” to a
problem. At a fundamental level, aesthetics is concerned with perception,
with viewing things in a particular way with a particular (aesthetic) attitude
that Jerome Stolnitz called “sympathetic disinterested attention.”8
Yet
Stolnitz is quick to point out that such perception is not confined to what is
sensuous, and is available within mathematics:
There is another kind of “awareness” that occurs, though relatively
infrequently, in adult experience. This is “intellectual,” nonsensuous
knowledge of “concepts” and “meanings” and their interrelations: such
knowing takes place in abstract thinking, such as logic and math-
ematics….this kind of apprehension can also be aesthetic…anything
at all, whether sensed or perceived, whether it is the product of
imagination or conceptual thought, can become the object of aesthetic
attention.9
It should be noted however, that, in rebutting Stolnitz’s notion of disinter-
est, George Dickie argued that being in the “aesthetic attitude” is simply
“attending closely to a work of art,” which implies that “attending closely
to” a particularly elegant mathematical solution, for example, would not be
considered an aesthetic act.10
We feel that mathematics does have aesthetic
properties and that one can have an aesthetic experience through math-
ematics, while acknowledging that aesthetics is not confined to artistic
activities.
At least one writer, Morris Kline, has indicated that mathematics also
has an emotional or expressive facet to it — this aspect of art often being the
sticking point for those arguing that math is, or is an aspect of, art.11
There
is an assumption here that art is inextricably bound up with expression,
more particularly the expression of feeling. Kline realizes that the usual as-
sumption that art has an emotional element that is missing in mathematics
is a potential stumbling block in trying to bring mathematics and art to-
gether. He attempts to overcome this difficulty by identifying an emotional
element in mathematics, on the one hand, and by diminishing the impor-
tance of emotion in the fine arts, on the other. With regard to the emotion
in mathematics he writes:
No doubt many people feel that the inclusion of mathematics among
the arts is unwarranted. The strongest objection is that mathematics
has no emotional import. Of course this argument discounts the feel-
ing of dislike and revulsion which mathematics induces in some

6. Art and Mathematics 5
people. This argument also undervalues the delight experienced by
creators of mathematics when they succeed in formulating their ideas
and in erecting ingenious and masterful proofs. Even the student of
elementary mathematics is pleased by his success in proving stereo-
typed exercises and by his ability to see light, meaning, and order
where formerly there was obscurity and confusion (MWC, 521).
It must be said that this is a very weak attempt at showing that mathematics
has an emotional element. The negative feelings that Kline refers to are not
intrinsic to mathematics. The positive feelings, on the other hand, which are
experienced in the production of mathematics, do have something in com-
mon with those experienced by artists. But whereas the artist can addition-
ally, intentionally, express emotion in his or her work, this is not true of the
mathematician. Moreover, to say that the students are “pleased” with their
efforts may have very little to do with the mathematics; the same pleasure
could arise from any demanding activity. So Kline’s case has not yet been
made, and this much he concedes. Perhaps his attempt to remove the kin-
ship of emotion and art will fare better, although in doing so he entrenches
himself firmly in the “Emotionalist” camp. His first move in this direction is
to admit that “a person is logically able to insist that the primary function of
art is to arouse emotions and stir feelings” (MWC, 521). But he points out
that this function cannot be sufficient to pick out works of art since a “dra-
matic photograph” with no pretensions to being great art might move us
more than certain great works of art from the accepted canon. It appears to
Kline that the arousal of emotions is not necessary to the arts either. He
presses this point by giving precise examples of works of fine art which he
believes do not satisfy this requirement:
The still-life paintings of Picasso, impressionistic studies, such as
Monet’s, of atmospheric and light effects, the work of Seurat and
Cézanne, and the “arrangements” of the Cubists would also fail to sat-
isfy the requirement. In fact, the pure art of modern times puts em-
phasis on the theoretical and formal side of painting, on the use of
line and form, and on technical problems. Such work appeals much
more to the intellect than to the emotions (MWC, 521).
But while it might be true that these works do appeal to the intellect to
some extent, to say that they appeal more to the intellect than the emotions
seems to be loading the die too much in favor of Kline’s own position on
mathematics. For Kline, moreover, the emotional aspect of art is largely at-
tributable to the work of the Renaissance. This is clearly an exaggeration.
Even if it were true of paintings, it is false of music. Surely no one would
deny that nineteenth century music was devoid of intense emotion. One
only needs to think of the works of Chopin, Brahms, or Tchaikovsky. Some
contemporary music may indeed be referred to as “cerebral,” but the West-
ern concept of music does not appear to have changed dramatically. There
is still an overriding demand for works of emotional content in our concert

7. 6 Richard Hickman and Peter Huckstep
programs, and as we try to come to grips with a new music concept — even
that which consists solely of silence — there are insufficient grounds for
concluding that emotion is minimal in the arts even if it is missing in some
of them.
However, Kline does more than stress the negative point that since emo-
tion and art are only contingently connected, mathematics cannot be ruled
out as a fine art in this respect. He sets out a positive reason why mathemat-
ics is art, namely, that it is an “outlet for the creative instinct of man.” But as
we have seen, the concept of the creative has different versions and these
versions tend to highlight the difference between artist and mathematician
rather than draw them together. Kline adds no more to the concept of “cre-
ative” to convince us otherwise. Indeed he makes the important point that
creativity alone is not sufficient, and that the mathematician must produce
work with “design, harmony, and beauty” (MWC, 522).
Although “expression” is an important aspect of work in art, both in
schools and in contemporary practice, the majority of art activity is not
concerned with expression in this way. While Modern art has moved away
from imitationalist and to some extent expressivist (or emotionalist) theo-
ries of art toward formalism, contemporary art has in many cases moved
away from both formalist and emotionalist theories and toward a more so-
cially oriented view of the world and the place of art in it; the importance of
the process of art making and the context in which it is viewed often over-
riding that of the product. There continues to be a strong formalist tradition
in schools as well as a clear commitment to imitationalism. Moreover, is-
sues-based practice, characteristic of contemporary art, is seeping into class-
room practice, and so we have an emergence of a school art which is con-
cerned with social comment rather than on the expression of individual
feeling. It is possible that there is an expressive or even emotional content to
math, but this does not in itself justify the claim that mathematics is closely
allied to art.
Even if the connections between the two subject areas of math and art
are sound, we can only justify the learning of mathematics as an art if the
educational value ascribed to art can be transferred to mathematics. But
perhaps another approach is possible: Suppose that we elucidate the educa-
tional value of art and then see whether mathematics could fulfill a similar
function — perhaps this would show how the one can be assimilated some-
what into the other. In an overview of rationales for art education, Richard
Hickman points out that there is an evolving notion among reconceptualist
art educators toward the notion of art as a means to an end (the end being
social change) rather than as an end in itself.12
There would appear to be no
parallel move among math educators. Several reason for studying the arts
have been set out by John White.13
By “arts” White indicates that he means
paintings, poetry, music, and literature, and hence not mathematics. In-

8. Art and Mathematics 7
deed, at one point when he does refer to mathematics it is to make some-
thing of a contrast with art. First, White acknowledges that art enlarges our
options for obtaining enjoyment in life “so immediately and often with so
little struggle — as compared with so many other intellectual or practical
activities” (EGL, 155). More specifically, he adds, “we take pleasure in exer-
cising our powers in a spontaneous, unfettered, way. In satisfying these de-
sires so deeply implanted in us, art contributes directly to our well-being”
(EGL, 155).
As we have seen, there is no reason to suppose that mathematical activ-
ity could not be conceived in this way to some extent. What comes next,
however, seems out of the range of mathematics. It concerns our desires.
We not only have desires, but conflicts amongst them that call for some pri-
oritizing through developing strength of will. But in some cases the arts can
help us come to terms with such conflicts. As White explains:
it can do this by working on our imagination: we experience the ten-
sions in what we see as the artist’s soul, or in those of the characters
he or she creates. In this way we approach our own conflicts by con-
templating their counterparts in others; and here we do not merely
contemplate them, but experience them within the framework of the
work itself. The work contains them and enables them to co-exist within
a unity, a formal structure. This helps us to reconcile ourselves to the
ineluctability — we see our tensions as something we have to live with,
something we can hold together within the framework of our life. A
work of art comes to stand proxy for our own life (EGL, 156).
White also outlines what he calls a more “conservative” role for art. It
seems that art allows us to reflect upon our common values, which are of-
ten difficult to justify. One of art’s roles is to reaffirm these values. In this
way it contributes toward our self-knowledge. So White writes:
In its power to reveal ourselves to ourselves, and thereby to confirm
us in what we take ourselves most deeply to be, and also in our sense
that our values are not idiosyncratically our own, but shared with
countless others across space and time, art is an unparalleled vehicle
of self-understanding, and so of education (EGL, 159).
There is a certain exclusivity in this last remark that is especially pertinent
for our enquiry. White emphasizes this by claiming for the arts that “Their
intimate connection with self-knowledge and personal well-being give
them a curricular importance which mathematics, say, or science could not
hope to rival” (EGL, 160). Despite what he says, some writers have never-
theless argued that mathematics can contribute to self-knowledge. So even
if it could not rival the fine arts it may at least equal them. J.W.N. Sullivan
makes the bold claim that “Art which is worthy of the name reveals to us
some aspect of reality” (MA, 2021). A similar revelation, he believes, arises
in mathematics:

9. 8 Richard Hickman and Peter Huckstep
Mathematics, as much as music or any other art, is one of the means
by which we rise to a complete self-consciousness. The significance of
mathematics resides precisely in the fact that it is an art; by informing
us of the nature of our own minds it informs us of much that depends
on our minds (MA, 2021)
Here is a clear statement that mathematics is a fine art since it provides us
with a particular kind of self-knowledge. However, we should note from
the start that Sullivan’s notion of self-knowledge is much more restricted
than that set out by White for whom self-knowledge includes knowledge of
common desires and feelings. Sullivan it appears is concerned solely with
knowledge.
Much of Sullivan’s main argument rests upon the notion of the creativity
of axiomatic systems discussed above. So he notes that “the mathematician
is entirely free, within the limits of his imagination, to construct what world
he pleases” (MA, 2020). However, the connections between this created
mathematics and what we might call the external world, but which Sullivan
simply refers to as “experience,” presents him with a problem. He rightly
says:
If he [the mathematician] can find, in experience, sets of entities
which obey the same logical scheme as his mathematical entities, then
he has applied his mathematics to the external world; he has created a
branch of science (MA, 2020).
However, he is clearly not satisfied with the idea that the mathematician
has hereby simply created “science,” rather than art. He therefore invokes
the creativity aspect once again: “Since…mathematics is an entirely free ac-
tivity, unconditioned by the external world…it is,” he concludes, “more just
to call it an art than a science” (MA, 2020). But there is a price to pay for this
realignment: mathematics-as-an-art cannot, it seems, give us the kind of
knowledge that it was once thought that the axiomatic systems could. The
moment we use these created “mathematical models” for understanding
the external world, we are engaging in science. Many would agree that this
is indeed the state of affairs with respect to pure mathematics and science.
But perhaps because the creative nature of mathematics does not seem suf-
ficient for classifying mathematics as an art, Sullivan goes much further and
boldly asserts that: “art which is worthy of the name reveals to us some as-
pect of reality. This is possible because our consciousness and the external
world are not two independent entities” (MA, 2021). He has therefore as-
similated mathematics into art only by taking on something rather like an
idealist position in order to side-step the dualism implicit in mathematics as
it is applied in science. From then on he reiterates his earlier point:
Mathematics, as much as music or any other art, is one of the means
by which we rise to a complete self-consciousness.…the real function
of art is to increase our self-consciousness; to make us more aware of

10. Art and Mathematics 9
what we are, and therefore of what the universe in which we live
really is (MA, .2021).
But to say that mathematics provides essential self-knowledge, and to
say that art does this too, is not sufficient to show that mathematics is art.
This would be to commit the fallacy that If A is S and M is S, then M is A.
Nevertheless, in his concluding lines this is precisely what Sullivan does:
it is certain that the real function of art is to increase our self-con-
sciousness; to make us more aware of what we are, and therefore of
what the universe in which we live really is. And since mathematics,
in its own way, also performs this function, it is not only aesthetically
charming but profoundly significant. It is an art, and a great art. It is
on this, besides its usefulness in practical life, that its claim to esteem
must be based (MA, 2021).
There is therefore something formally wrong with Sullivan’s argument.
Even if we could accept that a certain kind of self-knowledge was a neces-
sary and sufficient condition of the arts, it is not clear that this would clinch
the matter. As we have already mentioned, the particular kind of self-
knowledge, which Sullivan believes that mathematics can provide, is much
narrower in scope than that which is obtained from the arts.
Brent Davis has made a different case for justifying mathematics as a
form of self-knowledge. He makes no links to art but there are traces of
Sullivan’s argument there. Davis is particularly concerned with what he
calls the categorical discourse of mathematics. The supposed absence of
fuzziness and vagueness that normally preclude a reflective approach to
the nature of mathematical utterances. However, in studying certain pupils’
responses he highlights instances where we should ponder on mathemati-
cal discourse, and allow children to challenge its black and whiteness. So,
while Davis does refer to the cases where revisions in the way mathematics
have been conceived occur, such as the non-Euclidean revelation, he is
more concerned with the process involved in challenging the way we speak
about the prestigious area of mathematics. The reason for this is that math-
ematics holds some kind of pride of place in our perception and thus to be
self-conscious about its assertions is to come perceive things differently. He
views his observations as a mathematical anthropology. Davis’s arguments
are far-flung and difficult to take up as a simple pedagogy though they do
seem worth further consideration.
More recently, Anthony O’Hear argues for the particularity of arts and
their basis in perception as a way of marking off art from science.15
By
adapting them slightly, we find that an additional, powerful distinction can
be made between mathematics and the fine arts which shows us conclu-
sively that mathematics cannot be regarded as fine art. A significant part of
his argument goes as follows: human perception is central to the arts, and is
treated there as an end in itself, whereas, for science, the way things seem to

11. 10 Richard Hickman and Peter Huckstep
be is never sufficient. Indeed an important aspect of science is its claim that
commonsense perception of the world is illusory. The object that concerns
science is the world-in-itself rather than the world as-it-is-perceived. So that
even if science begins from human perception, it necessarily transcends this
in order to attain some kind of independent view, unbiased by the way hu-
mans contingently are, and aims at asserting information about how things
are in themselves. Perception is not the usual source of mathematical in-
sight, but widespread use is made of so-called “intuition,” and it seems to
us that intuition does play an analogous part in mathematics to the part that
human perception plays in the sciences. Thus we can inquire whether intu-
ition must at some point part company with mathematics in a similar way
to which human perception departs from physics, but not from the arts. In-
tuition is central to much arts activity, indeed works of art have been de-
scribed, by Benedetto Croce as “examples of intuitive knowledge.”16
Other
commentators have asserted that art and intuition are inextricably linked;
Herbert Read wrote:
As for that mental activity called intuition, by which we do not mean
any super-sensational faculty of the mind, but the apprehension of
abstract quantities and relations (size, shape, distance, volume, sur-
face-areas, etc.) it is the basis of a fourth type of art which…consists in
the effective juxtaposition of surfaces, solid forms, colours and tones.17
Hans Hahn gives several examples of what he calls the “failure of intu-
ition.”18
He shows quite conclusively that there are many occasions where
what seems to be intuitively true turns out to be false through the applica-
tion of mathematics. He writes: “It was believed that a curve must possess
an exact slope, or tangent, if not at every point, at least at an overwhelming
majority of them.”19
Hahn goes on to discuss the famous blancmange curve,
by applying rigorous mathematical techniques to which it can be shown to
have no tangent anywhere. The similarity of his example to O’Hear’s ex-
ample of the “vault of heaven” is striking: “One stands, let us say, on a clear
night beneath a moonless sky in the Mediterranean, and the sense that there
is a vault above one filled with stars is overwhelming. One knows that there
is no such thing, that the sky and heaven’s vault are illusions.”20
In both cases what seems to be true from a human point of view turns
out to be false within disciplines that somehow go beyond such a human
perspective. So, by using O’Hear’s argument, and drawing at least one par-
allel between mathematics and science, an important distinction between
art and mathematics can be made which suggests that they are radically
different in an important respect. O’Hear writes:
What modern science aims to do is, in the name of a wider objectivity
of view, to displace the human being and his modes of perceiving the
world from the centre of the picture, and to present the human being
and his modes of perceiving the world as incidental parts of the

12. Art and Mathematics 11
picture. From this point of view, the human being is seen as part of
a wider and more inclusive causal process, and, from the point of
that view, of no more significance than any other incident in the
development of the cosmos.21
Clearly, O’Hear does not feel that “modern science” subscribes to the no-
tion that phenomena are socially constructed; while modern art, or at least
contemporary art is, as noted above, fundamentally concerned with social
issues rather than issues concerned with perception. In education, there has
been a move toward a more cerebral approach to art in schools, not least
evidenced by the advent of Discipline Based Art Education. This can be
seen as an aspect of scientific rationalism, with art having the status of a
discipline with its own methods of inquiry. Elliot Eisner has for many years
advocated a certain epistemological status for art education, based on the
notion that art is a way of knowing with its own characteristics and which
provides a route to latent cognitive processes.22
Eisner has also noted the
arguments for the idea that learning in art can boost achievement in other ar-
eas of the curriculum.23
There appears to be no conclusive evidence to sup-
port the notion of transference; in any case, as has been asserted elsewhere,
we ought to be concerned with the extent to which other subjects (such as
mathematics) can help raise achievement in art.24
We see that while some
mathematicians and mathematics educators are making a case for their sub-
ject area to be an art, there are art educators making claims for their subject
to be seen as, if not mathematical in nature, then at least as more of a science.
With the increased use of Information and Communication Technology
among art makers, it is likely that there will be a greater overlap between
the arts and sciences. This does not mean, however, that one discipline can
be subsumed within the other. Mathematics can be seen as having a similar
aim to science, even though this aim is perhaps not so far-reaching, since
there is not so much of a commonsense view of intuition in mathematics to
override. All the same, once we turn our intuition onto mathematical ob-
jects, a similar kind of correction must sometimes be made to such intuition
as it is to sense perception in science. This is in strong contrast to the way
matters are in art and gives us an important reason for seriously question-
ing whether mathematics could ever be conceived of as an art in any thor-
ough-going way. We conclude therefore that any apparent relationship be-
tween art and mathematics in an educational setting is superficial, and that
the two disciplines have no more in common than any other arbitrarily
chosen fields of human experience.
NOTES
1. Penny Munn, “Children’s Beliefs about Counting,” in Teaching & Learning Early
1, ed. Ian Thompson (Buckingham: Open University Press, 1997).

13. 12 Richard Hickman and Peter Huckstep
2. Anna Sierpinska, Understanding in Mathematics (London: The Falmer Press,
1994).
3. John Passmore, The Philosophy of Teaching (London: Duckworth, 1980), 198. For a
fuller discussion see Peter Huckstep, “The Utility of Mathematics Education:
Some Responses to Scepticism” in Learning of Mathematics 20, no. 2 (2000).
4. Jacqueline Cossentino and David Shaffer, “The Math Studio: Harnessing the
Power of the Arts to Teach across Disciplines,” in Journal of Aesthetic Education
33, no. 2 (1999): 99-109. The project was inspired by the work of M.C. Escher and
aimed to create “a learning environment that combines serious mathematics
with genuine artistic thinking.” Another project entitled Islamic Art and Maths
which is based on developing designs for bowls derived from Islamic geometry
has been introduced successfully into some art lessons in UK schools by Sharon
Wildsmith, through the University of Cambridge school partnership.
5. Rena Upitis, Eileen Phillips, and William Higginson, Creative Mathematics:
Exploring Children’s Understanding (London: Routledge, 1997).
6. J.W.N. Sullivan, “Mathematics as an Art,” in The World of Mathematics, ed. J.R.
Newman (New York: Simon Schuster, 1956), 2015-2021. This article will be cited
as MA in the text for all subsequent references.
7. Peter Huckstep and Tim Rowland, “Creative Mathematics: Real or Rhetoric?”
Educational Studies in Mathematics 42, no. 1 (2000): 81-100.
8. Jerome Stolnitz, Aesthetics and Philosophy of Art Criticism (Boston: Houghton,
1960).
9. Ibid., 26-27.
10. George Dickie, “The Myth of the Aesthetic Attitude,” in Introductory Readings in
Aesthetics, ed. John Hospers (London: Collier Macmillan, 1969), 44.
11. Morris Kline, Mathematics in Western Culture (Harmondsworth: Penguin, 1972).
This book will be cited as MWC in the text for all subsequent references.
12. Richard Hickman, “Meaning Purpose and Direction,” in Art Education 11-18:
Meaning Purpose and Direction, ed. Richard Hickman (London: Continuum,
2000).
13. John White, Education and the Good Life (London: Kogan Page, 1990). This book
will be cited as EGL in the text for all subsequent references.
14. Brent Davis, “Why Teach Mathematics? Mathematical Education and Enactivist
Theory,” Learning of Mathematics 15, no. 2 (1995).
15. Anthony O’Hear, The Element of Fire: Science, Art and the Human World (London:
Routledge, 1988).
16. Benedetto Croce, “Art as Expression” (1909), in Readings in Art Education, ed.
Elliot Eisner and David Ecker (Lexington, Mass.: Xerox, 1966), 37.
17. Herbert Read, Education Through Art (Faber and Faber: Macmillan, 1947).
18. Hans Hahn, The Crisis in Intuition, in Newman, World of Mathematics.
19. Ibid., 1962.
20. O’Hear, Element of Fire, 8-9.
21. Ibid., 15.
22. Elliot Eisner, Cognition and Curriculum Reconsidered, 2d ed. (New York: Teachers’
College Press, 1994).
23. See for example Elliot Eisner, “Does Experience in the Arts Boost Academic
Achievement?” Journal of Art & Design Education 17, no. 1 (1998): 51-60.
24. Ibid.