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This paper discusses the educational issues of a model of the Making Change Problem which requires you to pay a given amount using as few coins as possible. In general people know how to derive the correct solution to this problem but do not know the logic they are using in selecting the appropriate coins. The model allows the user to make a meaningful connection between the mathematical logic and their empirical experiences of these actions.
The model allows the users to learn about the dependencies between the total amount to pay and the quantity and denominations of the coins. By changing the denominations the user is able to investigate the behaviour of the greedy algorithm.
This paper also discusses the roll of empirical modelling as an educational tool. It can be argued that learning through experimental interaction with the artefacts, as opposed to learning from written materials or teaching, can be more effective. The paper introduces the related philosophical theories of the empiricists and their beliefs that man can only know what they have learnt through their own observation.