Mathematical Dragons
D R A G O N S T O D A Y . A U T U M N 2 0 1 1
Making Sense of Maths:
Understanding, Enjoyment
and Challenge
The Mathematics Department at the
Dragon aims to give all pupils as authentic
an experience of maths as possible. At every
level, there is an emphasis on understanding
and practice. All children are encouraged
to try – and to understand that ‘wrong’
answers are central to learning, comprehend-
ing, and ultimately enjoying, maths. The
aim is to convince children that maths is not
a ‘black and white’ subject; the goal is not
the answer but the process. The aim for all
young Dragon mathematicians is that they
become critical thinkers – they are always
encouraged to ask ‘why’. Dragon pupils
investigate their own questions, test their
own hypotheses and explain their solutions;
in short, they are encouraged to behave like
real mathematicians.
The key to maths learning at the
Dragon is ‘firm foundations’ with an
emphasis on understanding through expla-
nation, whether individually, in small
groups or as a whole class. Key ideas are
revisited and built on, year on year, to
give children the opportunity to refresh
their ideas and draw connections between
different areas of maths. Theoretical and
technical ability are developed through this
‘spiral’ curriculum which spins out into
new areas while constantly returning to core
principles. Open-ended questions and proj-
ects develop thinking skills and deepen the
understanding of process as children select
and apply techniques, remember concepts and
make associations for themselves. Confidence
develops as children try, and sometimes fail,
in order to learn. They work with numbers,
graphs, measure, shape and statistics, and are
encouraged to generalise and abstract. Algebra
features strongly from Year 6 but verbal and
written explanations are also encouraged to
develop essential mathematical vocabulary.
All maths teaching at the Dragon revolves
around the interdependent concepts of under-
standing, enjoyment and challenge. Without
understanding, children are uncomfortable and
unlikely to enjoy maths; without enjoyment,
even the most studious will be uninspired and
reluctant to rise to a challenge; without chal-
lenge, enjoyment is short lived. With all these
in place, though, maths intrigues, inspires and
makes real sense
The aim for all young
Dragon mathematicians
is that they become
critical thinkers – they
are always encouraged
to ask ‘why’
Try your skill:
Four numbers have a mean of 7, a median
of 8 and a mode of 9. What are the four
numbers? Answer on page 8.
Why do we teach maths? Some
areas of maths are clearly useful in
everyday life, but when was the last
time you used Pythagoras’ Theorem,
drew a quadratic graph, or proved
that the sum of the first n integers is
½n(n+1)? The main reason for teaching
maths is because by behaving like
a mathematician, you are learning
crucial life skills. Mathematicians
are logical, they deconstruct difficult
problems into simpler ones and work
systematically, searching for patterns,
drawing connections between
ideas and generalising beyond the
particular case. These real life skills are
transferable to every part of life; any
time you make a reasoned decision
you are being a mathematician. They
may sound daunting, but I sum them
up to the children at the Dragon as
follows: mathematicians are lazy. We
look for short cuts and break things
down into small pieces to make them
easier. We have even invented our own
language, algebra, so we can explain
our ideas in the shortest way possible.
Communication is the part of maths
many children find the most challenging,
either explaining in words or trying to
transfer their thoughts to paper. I think
the most useful way parents can help
their children with their maths is to ask
them to explain it to them. You do not
have to be a skilled mathematician
yourself to ask children ‘what did you
do in maths today?’. They may find this
a difficult question to answer, but keep
asking, because in explaining maths to
you they are explaining it to themselves.
Dr Emily MacMillan
Head of Maths
Dragons enter local and national
maths competitions, frequently winning
certificates and qualifying for testing
‘Olympiads’ with the brightest in the
country. Several pupils have made the
UK Top 50 in recent years and the Year
8 team has regularly finished as top
Oxfordshire Prep School.
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