Defence mechanisms operating in
mathematics selection and assessment
The psychoanalytic take: Maths operates either as
an instrument of defence against anxiety or as
something onto which anxiety is displaced and
which we then defend ourselves against.
How far can we get in understanding mathematical
identities if we use this approach?
Specifically, how do selection and assessment fit
into this?
Laura Black & Yvette Solomon, with Margaret
Brown, Heather Mendick, Melissa Rodd
Jaques Nimier (1993): One psychoanalytic
account
“Phantasy can be taken as the mental expression of
instincts, but also as a means of escape - an escape
from confronting external reality or the frustrated
reality within” – so that either
(1) the anxiety and its associated phantasy are
displaced onto mathematics, and defences are
directed against mathematics, so directly containing
the anxiety; or
(2) anxiety is contained in some other way and
defences are mounted against this anxiety,
mathematics serving as an instrument of this defence.
Defence mechanisms against mathematics:
phobic avoidance
Q1 I feel there is something that keeps me from getting at the
problem, a barrier I can't get across.
Q3 At the start of a mathematical problem, I feel as if I'm in front
of a black hole.
Q11 Doing maths is doing something which, to me, seems
impossible.
“The
cannot
theseparates
mathematical
It isstudent
as if there
was aapproach
veil... which
me fromobject,
what is
something
him orI her
it -it's
barrier,
hole,it or
there, if... separates
I look into space,
don'tfrom
know,
faraway...
has
impossibility. No blame is placed on mathematics itself…. The
already given me this impression... evidently, I don't think
student is looking for a way of avoiding mathematics because
maths, when
I look
at theself-protectively
stars; but there, I prefers
am
of immediately
the anxiety of
it provokes.
The
student
that
it represents something
similar,
I don't
know.
To look
to aware
classify
mathematics
as impossible
rather
than
confront
it.
at something
and
reach a time
when you known
can no longer
see,
This
is a matter
of then
the defence
mechanism
as phobic
close your eyelids,
avoidance.”
(p.30) there is the veil which prevents us from
penetrating any further, from reaching it... I think it's that.
Defence mechanisms against mathematics:
repression
Q 9 Doing maths, it represents nothing, it's absurd.
Q10 It is something that you are told to do and which you
repeat, a bit like a machine.
Q13 It is doing something obligatory, something imposed.
“…mathematics
doesn't
represent
anything.
If it is done at
The x's and the y's,
they represent
nothing,
it's completely
all,
it is because it is compulsory; the student is so
abstract.
uninvolved
feels
mechanical.
drive towards
You have tothat
copyit out
theorems
that areAllcompletely
idiotic.
mathematics
is missing
and
is repressed.
Therefigures,
is no longer
I don't know what
is really
concrete.
You calculate
you
anything
positive
forend,
these
students,
rather
"indifference".
do anything!
In the
anything
... to but
me that
seems
If nonsensical.
they are forced
into remember
mathematics,
it becomes
negative
(or
.. I don't
anything,
it is precisely
because
absurd)
for them.”
(p.31)
it is absurd
that I don't
remember anything
Defence mechanisms against mathematics:
projection
Q16 In mathematics there is no place for personality; all that you
do has been done before, everything has been seen already.
Q18 Mathematics sometimes risks bringing destruction, you
only have to think of the atomic bomb.
Q23 When one is deep in maths work, it's difficult to get out of it,
that's why it doesn't do to get involved with it.
Q24 Doing maths oversimplifies everything, it takes the poetry
out of things.
Q25 Those who do too much mathematics some times risk not
having your feet on the ground.
I know
shepherd.
…He nocan
longer
life. …of He
“Theafeeling
of danger
onlyknows
comeanything
from a about
projection
studies…
is now, enclosedThe
in a danger
laboratory
doing calculations.
the self here
ontohe
mathematics….
is inside
the
Heindividual;
suffocates in
He thinks
mathematically.
Well, I don't
to figures
protect...yourself
you
project the danger
outward
know,
... weThere
are mad
wethe
are danger
mad. … of
Fortunately,
there's
ontoultimately
an object….
is ...
also
losing your
little
chance
of our
going mad, …
because
not many
us become
own
physical
boundaries,
of losing
one’sofway”
(p.31)top
mathematicians.
Defence mechanisms against mathematics:
reparation
Q2 I have the impression I am creating something when I am
solving a problem.
Q8 It means doing something basic which is the key to everything
else.
Q12 It is constantly discovering something new.
Q19 Mathematics brings you the pleasure of creating something.
Q20 Mathematics means another world in which I feel at home.
“Construction
leads you
to the
of new and
important
.. by doing maths,
arediscovery
making something
for yourself.
Youthings
are
(‘the
key tosomething.
everything
else’),
even
the construction
of ‘another
making
Well,
it's for
thattoreason
... that we enjoy
it;
world’.
This reparation
could
be the I‘wish
the capacity
for the
everybody
likes to make
something,
think,and
because
if one doesn't
restoration
the good
object,
and
is the
manage toofmake
something,
ininternal
the end to
findexternal,
... to findthat
peace,
to
basis
ofprecisely
the ego'sthecapacity
to maintain
and
relationships
have
joy of having
done it,love
I think
that
makes you do
through
conflicts
and
Butcome
reparation
canbut
also
be
more ...
The start
of difficulties’….
a problem doesn’t
from you,
after
fanatical:
‘in that
aim
is tothe
repair
objectsthings
in such
a way
that
doing what
has its
to be
done,
mostthe
important
is that
which
guilt
and
loss are
has
to come
fromnever
you. experienced’. ” (p.32, quoting Segal)
Defence mechanisms against mathematics:
introjection
Q14 Doing maths is a way of training my mind.
Q15 It is trying to find connections between different things.
Q17 Mathematics is a way of getting a strong character.
Q21 Working with mathematics allows you to acquire a wellbalanced personality.
Q22 Mathematics allows you to develop good reasoning.
With
maths, I thinkhelps
that when
to solvestability
something,
you should
“…mathematics
to setone
uphas
a certain
in the
do
it progressively
withoutfor
jumping…
jumping
that way from
personality.
The search
connections,
theindisciplining
of one
the
question
another when
arereasoning
totally different,
youestablish
know ... And
mind, thetoacquisition
of they
sound
help to
a
then,
to seecharacter
how far you
can
although
I don't know
myself!toAnd it's
balanced
and
a go,
strong
personality.
… Failure
respect
mathematics
hinders
of the
preciselythe
that,rules
I amof
searching
for a way
of lifeany
... ause
stability
...Itsubject
is
…certain
students
[make]for
use
of it as a
way
structuring
perhaps because
I am…looking
something
that
willofmake
me stable,
their
personality.
…mathematics
gives
them
because
I know very
well that in myself,
I am
not.some order, .. it lets
them struggle against the instincts they consider bad..” (p.32)
Defence mechanisms against mathematics:
reversal into the opposite
Q4 If I can't find the solution, I feel defeated.
Q5 When I work something out, I feel like a void is being filled.
Q7 If I find the solution straightaway, I feel really at peace.
When you
do something,
it's not
that could
it isn't possibly
normal, it's
“[There
is] acan't
disagreeable
feeling
which
benot
that you have
a grudgeaagainst
it ...
it when we're
taught is
neutralised
whenever
solution
toIaenjoy
mathematical
problem
something,
when
something
to do.
To be ablewound’
to do it...and the
found….
[This
is] we've
a reminder
of the
‘narcissistic
Because
to be able toof
dothis
it: itfeeling
has to be
your
level.
search
foryou
thehave
transformation
intoatits
opposite:
You'reinto
given
it, youlack
haveinto
to bereplenishment,
able to do it! Otherwise,
as soon
defeat
victory,
disagreeable
feeling
as there's
something
can't do or youoften
say, What's
into
feelingaatsnag,
peace.
Failureyou
in mathematics
calls into
going on?
can'tthat
I doyou
it? I'm
stupid,
it's no good!'
... students
That's
question
theWhy
image
have
of yourself.
… For
how
it is.
When
given of
something,
you have
to understand
know how to
like
this
there
areyou're
two sorts
people, those
who
do those
it. That's
how
it is in
the course,
in ‘you're
class: some
cangood
do it,or bad at
and
who
don't.
They
also say
either
others can't.
maths’".(p.33)
Why does mathematics take this role so
powerfully and frequently?
“So mathematics, through its rigour, that is to say
through its constant refusal to entertain ambiguity, will
more than any other discipline revive anxieties arising
from noticing individual differences.” (Nimier, 1993: 33)
But there’s also a powerful set of discourses
surrounding mathematics….
Lucey et al., 2003: 286: “social and cultural analysis
needs an understanding of emotional processes
presented in a way which does not reduce the psychic
to the social and cultural and vice versa, but recognises
their interweavement”
Psychosocial approaches to identity allow us to focus
on how people work and are worked by these
discourses.
We looked for a fit with Nimier’s picture in our
own relationships with maths
Similarities in our accounts:
• a focus on ability and its markers
• discourses of maths and cleverness
• competition with others (both academic and
personal)
• gender themes.
We looked for a fit with the defence mechanisms –
• we can see them up to a point
• but the major mathematical discourses are also
important
• gender and institutional practices of assessment
and selection seem to be highly relevant in
understanding our relationships with mathematics.
Competition – projection?
..my brother. He also did maths and got his PhD in the
end. I always thought he was cleverer than me (I think
he always thought that I was cleverer than him). ... I
had a massive discussion/row with my brother about
how come he found it so easy to say he was good at
maths and I didn’t. The happy ending was that me and
my brother still get on, .. and I can now say I’m good
at maths. There must be sibling projective
identifications like mad going on around maths.
Comfort mathematics: Reparation?
Introjection? Reversal into the opposite?
… the puzzle is definitely the motivating factor when
doing Sudoku (and all those algebraic equations
years ago) – solving the puzzle gives me a good
feeling, like I’ve sorted something out in my head
and that life and the world is much simpler now
because there are only numbers.
I guess that maths was more of a direct line to pure
abstraction and also instant gratification really in
terms of the achievement aspect of the thing.
Mathematics as protective – introjection?
Maybe I have used maths as a defence against
other anxieties – I do recognise ‘introjection’ in
the sense of using maths as a defence against
teenage and maybe adult emotional
involvements – somewhere you can feel safe in
the stability of rules and structure and away
from the emotional uncertainties of life.
Selfhood and change – defences and
assessment discourses
Processes of introjection: I had a neo-Platonic view of
maths, I thought it was discovered rather than created, cos
that was how it felt to me. It went in the first year of my
PhD…. my sense of who I was and my place in the world
shifted and so I acted different and was different. I had to lose
maths as special and to lose myself as special too.
Reversal into the opposite: Had I stayed at A I’d have been
in ‘honours’ maths so I enrolled in ‘honours’ courses at B. A
different league – the thought of those first few analysis
classes still brings out anxiety. I stayed on for graduate
school. Passed my qualifying exams for PhD. But I was so
out of my comfort zone, so stretched by daily difficulties of
doing it that hard maths stuff. B as doctoral student were
extremely anxious times and it is strange how rigid my
thinking about maths became.
Anxiety about how others see us –
reversal into the opposite?
I’m always scared I can’t do it and make some terrible
error which makes me look really stupid.
I also recognise ‘reversal into the opposite’ – the
frustrations of failure and the relief at reaching
resolution – and the fact that failure is made worse by
the knowledge that it will demean you in the eyes of
others as someone who is stupid, since mathematics
is aligned so strongly with intellectual capacity!
I got my first though it was a close one and so I didn’t
feel that I’d succeeded at maths. … I felt that I’d
crossed the first barrier by learning stuff rather than
doing the hard questions. My relationship with maths
was never fully secure after that. I still loved it though
and it still functioned as a safe space.
The presence of collective influences gender issues
I admit that choosing to do Mathematics, Further Mathematics
and Physics for A-level was partly a matter of feeling that this
was a bit exotic/esoteric for a female and separated me out
from the crowd. It also had a cachet of intelligence referred to
by Jacques N. I also think I was fully aware at the time that it
would give me privileged access to a wide range of males at
university; the female competition would be tougher in arts
subjects..
On reflection, I guess my interest in maths education has been
influenced by all these successful men in my family who do or
have done maths…. I don’t see maths as impossible – it’s not
the knowledge itself which has made maths seem impossible to
me but other external or pragmatic circumstances (but maybe
I’m in denial!) … It does seem that my interest in maths ed
could be a defence mechanism against other events in my
family life but I’m not really sure about this.
Individual disposition versus collective
influences
There appears to be a distinction between the
unconscious phantasies identified by Nimier and the
collective discourses evident in our maths biographies
(including discourses about mathematics).
For example, gender relations seemed to feature in all
our stories about our relationships with mathematics –
whether we do it and how it is valued. Comparison
with others via selection and assessment also
featured, and institutions played a part.
But how/why does this happen, and how does
individual experience fit into large structural influences
such as gender ?
Mathematics Discourses in ‘self-authoring’
We use Discourses which are constructed and perpetuated
using devices such as assessment and selection to position
ourselves:
I got my first though it was a close one and so I didn’t feel that
I’d succeeded at maths. … I felt that I’d crossed the first barrier
by learning stuff rather than doing the hard questions.
Unlike any other thing I’ve ever done, maths is the thing I want
to score hundred percent in. … I’m not actually good at maths.
… I never feel as though I really truly understand what I’m
doing. … And I really do think that a lot of my understanding is
somewhat ritualistic in that I don’t know how to apply it to new
situations, so to me that means that I’m not really very good at
maths.
Selection/assessment as a positioning device
Institutional Policy – audit/performance Discourse:
“I got really engaged in solving the equations – page
after page in the textbook. I remember being so
engaged that I didn’t eat my lunch….I quite enjoyed
doing maths at school and was planning to carry on
doing it for A level as I decided that I wanted to be an
engineer. However, when my mum and I went to the
open evening to discuss my potential A level subjects
my maths teacher told us that I wasn’t good enough at
the subject to carry it on after GCSE (despite the fact I
got a B at GCSE).”
Sometimes other things such as institutional policies
position us in a way which prevents us from acting on
our dispositions…..
Conclusions & questions
Do we need to invoke Nimier’s defense mechanisms
in understanding how people relate to maths?
If we accept Nimier’s basic position that it is useful to
identify and understand the varied psychosocial
dispositions towards/against mathematics, how might
we best integrate these with collective discourses
such as assessment and performance?
What can Socio Cultural theory and Discourse theory
offer? How do they differ in their contributions?