Aesthetic
considerations in
teacher education
Martin Griffiths
1
. In this paper I consider the potential dilemmas faced by teacher educators wishing both to explore and to highlight aesthetic aspects of their subje
What are our aims here?
First, to explore whether there evidence in our
classrooms for the presence of, or appreciation for, the
various aesthetic aspects of mathematics?
Second, within this context, to consider the potential
dilemmas faced by teacher educators wishing both
to explore and to highlight aesthetic aspects of their
subject areas whilst simultaneously having to satisfy
their students’ perceived needs regarding the
pragmatic business of modern-day teaching.
2
What do we mean by aesthetics?
Yuri Borev gives a very broad definition:
“Any human activity has, besides a purely
utilitarian purpose, the grains of what
makes it universally important for mankind.
It is these grains which lend human activity
its aesthetic flavour.”
3
What about the mathematical
aesthetic?
Aesthetics is often considered a branch of
axiology.
 The perspective I adopt is that a student’s
aesthetic capacity is not simply their ability to
identify formal qualities such as economy,
inevitability, and unexpectedness, but also
comprises their sensibility in combining
information with imagination when making
purposeful decisions regarding meaning and
pleasure.

4
Beauty in method
 Beauty in mathematical results
 Beauty through experience
 Philosophical aspects to beauty

5
Is the mathematical aesthetic an
elitist concept?
"The mathematician does not study pure mathematics because it is useful; he
studies it because he delights in it and he delights in it because it is
beautiful." -- Henri Poincare
"Beauty in mathematics is seeing the truth without effort.“ -- George Polya
"The mathematician's patterns, like the painter's or poet's, must be beautiful.
The ideas, like the colours or the words, must fit together in a harmonious
way. Beauty is the first test: There is no permanent place in the world for
ugly mathematics.” -- G. H. Hardy
"Mathematics, rightly viewed, possesses not only truth, but supreme beauty."
-- Bertrand Russell
"We cannot hope that many children will learn mathematics unless we find a
way to share our enjoyment and show them its beauty as well as its utility."
-- Mary Beth Ruskai
6
Some educators who have written
on the mathematical aesthetic:








N. Sinclair
P. Betts
J. Dewey
A. Mack
G. Gadanidis
C. Hoogland
S. Papert
T. Tymoczko
7
Roles purported to be played by
the aesthetic:
Motivational (intrinsic rather extrinsic)
 Evaluative
 Generative

8
Some questions:



Is test-score-driven schooling having an
effect on mathematics to the extent that
motives are transforming from aesthetic
considerations to more utilitarian ones?
Are we, as a consequence, completely
losing sight of aesthetic values in school
mathematics?
Does it matter?
9
Classroom observations




I have seen some excellent lessons, but even
many of these do not provide real opportunities for
students to experience or explore mathematics in
a way that will allow their aesthetic sensibilities to
develop and flourish.
Complete lack of vocabulary associated with the
aesthetic.
Discourse centres on things such as “The
examiner will be looking for …” or “We are doing
this because you will get asked about it in your
GCSE”, and so on.
A complete absence of any “Aha!” moments
amongst the students.
10
Comments



At present I am merely highlighting some
findings and express concern over what I
perceive to be a potential issue. I am not yet
offering any solutions!
Are we gradually losing sight of the aesthetic
aspects of mathematics; will this affect creativity
of future generations?
Are we becoming ‘mathematical parrots’,
capable only of regurgitating the work of others
as opposed to being creative ourselves?
11




Is the whole thing dangerously selfperpetuating?
Are the curriculum and the accompanying
resources (textbooks, for example) partly to
blame?
If the whole area of the mathematical aesthetic
is seen as elitist by some, then how might we
counter this?
Have we gone beyond the point of no return?
12
Some thoughts on teacher
education
There are some amazing teachers out
there; both trainees and mentors.
 I see the problem as a systemic one.
 How may we, as practicing teachers and
educators, encourage new entrants to the
profession to engage with the aesthetic?

13
Could we incorporate explicitly the notion
of the aesthetic as part of our PGCE
programmes?
 Might we encourage this aspects of our
subjects in lesson plans, for example?
 Might the above steps be counter
productive in the sense that they would
seem to force the issue, and be yet
another aspect of the tick-box culture?

14