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?

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.

Here we have dealt with and can remove a third of the 'coins' which we know are five pence coins. What is left of the coins is divided into quarters - because we have information about three of the quarters. They were ten pence coins.
What we now know is that we have a small fraction of the original number left. It becomes easy to see what fraction of the whole it is. Knowing that these are penny coins and that the boy had six helps solve the original, more complex problem.

Bodily-kinesthetic - children with this dominant intelligence learn by constructing models and manipulating objects, so to be able to fold and tear the paper representation will enable them to engage with the problem in a very hands-on way.

Musical-rhythmic - as pattern recognition, creation and extension are important for these learners they will be seeking to find a repeat sequence. In repeating the folds in the paper a pattern will begin to emerge and estimates of "what comes next" can be made.

Naturalistic - identifying attributes, sorting and classifying parts to the whole are skills of this intelligence. Therefore, seeing the relationships and being able to name the fraction of the whole as one sixth is in the nature of this type of learner.

Intrapersonal - this is the intelligence for whom thinking about feelings is very important. So time for reflection, planning and the opportunity to work individually allows these children to decide upon best strategies. To assist them, ask questions about how they felt when encountering the problem and if they feel they understand the problem better with the strategy of using a concrete object.

Interpersonal - there is a preference for this intelligence to learn in social situations. They become more involved when there is a cooperative effort from a group work. This task lends itself to group work, to the sharing of ideas and perspectives, it is an opportunity for learning from each other.

Unless other intelligences are seen in operation, we will not learn how to use or develop them all. Using one intelligence helps develop others - so, for example, spatial learners are developing their mathematical-logical intelligence as they employ the visual skills in engaging with maths tasks and investigations, especially if good modeling of mathemaical thinking is taking place. When creating cooperative work groups are we making sure that the various intelligences are represented?

We are all curriculum designers, as such we have to ask ourselves if we are structuring problems and tasks that allow for the full spectrum of intelligences to be brought into play? As intelligence can be expressed in a multitude of ways we have to ask if the learning opportunities we design and provide have enough scope for all children to demonstrate what they know. Do we allow students to reveal their own areas of expertise by encouraging, valuing and rewarding a variety of outputs?

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.