O. Yevdokimov: Teaching mathematics as relationships between structures

O. Yevdokimov, Notes about teaching mathematics as relationships between structures: A short journey from early childhood to higher mathematics, The De Morgan Journal, 2 no. 1 (2012),  69-83.

From the Introduction:

No matter at which level, from mathematics related activities in kindergarten, to studying mathematical courses at university, many learners consider contents they are dealing with in a prescriptive way as a set of direct instructions. Following instructions they are able to complete some tasks. In most cases, however, such a performance is shadowed by their inability to deal with any other task that does not follow exactly the same prescriptive way.

The scope of this paper is bound within reflections about one teaching approach that may help to address this issue.

This approach focuses on understanding relationships between different structures. Under structures here I mean, in a wider context, any mathematical object or set of objects and/or their properties, including any statement or visual representation, i.e. anything which can be considered from a mathematical point of view and related to a certain level of cognitive development.

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