Published February 2011.
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 pennies?
If he had six pence in one penny coins, can you work out how much money he had saved in his piggy bank?
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 problem.
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 thirds.
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 charge.
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.