A boy is sorting out the coins in
his piggy bank. He put the coins into stacks according to their
value. 1/3 of the coins went into the first stack. They were five
pence coins. 3/4 of the remaining coins were ten pence pieces. The
rest were one penny coins. What fraction of the coins were
If he had six pence in one penny
coins, can you work out how much money he had saved in his piggy
What was your reaction as you read this problem?
How you reacted informs you about your preferred learning style,
or dominant intelligence. But do you have to be strong in
mathematical-logic intelligence to be able to have a strategy to
tackle and solve such problems? A question such as this is not an
'open' question, it does not have several possible solutions, but
it does have several possible ways of being solved and it allows
for pupils of different intelligences to engage with the
Let's see some of the possible opportunities for children who
operate from different intelligences to be involved in what seems
like a typical maths problem that would be solved by the
conventional, taught procedure.
Verbal-linguistic - as
these learners enjoy and are skilled at interpreting 'word'
problems and their imaginations are captured by the power of
stories this mathematical 'story' is within their domain. They can
contribute their interpretation and inference skills to a group
effort. They will probably be able to say pretty quickly that there
are three piles of coins.
Spatial-visual - this
learner style responds to visualizing or using colourful diagrams
to illustrate mathematical problems and performs especially well
when using space is part of the investigation. Using paper, or
another concrete device, will help them see a way around this
problem. Here is one way of allowing children to visually and
physically interact with the problem:
This diagram (paper) represents the coins divided into
In labelling the intelligences, Howard Gardiner offered a new
map of learning based on a theory that there is not just one way to
define and be intelligent but multiple ways. Just as there is a
call to expand our understanding of what it means to be
intelligent, so too is there a need to redefine our idea of how
mathematical-logical intelligence 'looks' in use. We need to
broaden our perception of how mathematical-logical intelligence is
used. We need to move beyond the picture of a mathematician proving
a theorem and include bushmen drawing complex conclusions based on
observing animal tracks; to incorpotate ideas of a detective, or
reader, solving a mystery by piecing together the clues; to
recognise the skills used by a lottery player figuring out his
share of the winnings; and to acknowledge the high level of logical
intelligence demonstrated by pupils playing strategy games.
Knowledge of multiple intelligences is not a call for the
radical rewriting of the curriculum. It is a framework that can be
used to construct curriculum, to support the instructional choices
we make and to strengthen our understanding of the learners in our
Our job is to open mathematics to all, to tap the skills and
talents of other intelliegences so as to create mathematics "Aha!"
moments for every learner.