Campus Review Volume 28 Issue 12 December 2018 | Seite 20

policy & reform
campusreview.com.au
Turning a minus into a plus
How to help students
with ‘maths trauma’.
By Daniel Mansfield
M
aths trauma, the issue
highlighted in the US edition
of The Conversation, is real.
If a student never masters irrational
numbers, then when they come to
trigonometry (which involves lots of
irrational numbers), they will receive
a constant bombardment of negative
reinforcement, and sooner or later even
the most confident student will have
to acknowledge the overwhelming
evidence: they are “no good at maths”.
The path through mathematics is full of
such pitfalls, and sadly many who fall by
the wayside do not return. How can we
restore maths confidence in those who
have lost it? I don’t believe there is a single
answer to this question, but here are some
thoughts.
Someone who is traumatised by
mathematics cannot simply be expected to
just try again, but this time try harder, and
reminding them that they will need this skill
in the real world will just compound the
shame of failure. So, instead of trying to put
them back onto the same road, find them a
different road.
I teach first-year maths students, and
I recall one student in particular who was
traumatised by simultaneous equations. He
would flatly refuse to apply the standard
high school methods. But he would gladly
solve simultaneous equations using a
matrix. The matrix method is technically
excessive, but for him, it had the single
important advantage of being different.
Now, let’s imagine a student who is
unable to perform arithmetic. Arithmetic
is the goal, and the fastest path is
memorisation. But the student’s experience
on this path has been traumatic, and now
the student reasonably believes that further
attempts along these lines will only lead to
failure. How could a teacher help?
You might like to pause for a moment
and consider what you would do or have
done to help such a person. Here are some
ideas that could work in this situation:
• Teach them to use an abacus. Arithmetic
can be understood as the purely physical
activity of moving beads on a frame.
Addition, subtraction, multiplication
and division can all be performed by
repeating a pattern with your hands.
• Teach them binary arithmetic. Binary
arithmetic looks strange to decimally
minded people, but it is actually the
simplest form of arithmetic. The idea
of learning the binary number system
might be both achievable and palatable
because it is does not immediately
reignite traumatic thoughts.
Other ideas would be to use Cuisenaire
rods, or modular arithmetic. These are just
some of the many paths to understanding
the fundamentals of arithmetic, and I’m
sure there are many others.
Mastering a different strategy doesn’t
teach arithmetic as directly or easily as
memorisation. The advantage, however,
is that the student can circumvent
trauma by finding a different path to
understanding.
The real question is matching the person
to the path. Students do not need to stay
and suffer on a path that does not work for
them; they can and should get off and try
something different.
While arithmetic may be fundamental
and even universal, it is a concept
understood by humans, and this human
element permits an unlimited number of
different and legitimate understandings.  ■
Dr Daniel Mansfield is a lecturer in the
School of Mathematics and Statistics at
UNSW Sydney.
11