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Abstract
This comparative study aims to identify the philosophical underpinnings of the principles of two approaches to the teaching of primary mathematics, the English Numeracy Strategy and the Dutch Realistic Mathematics Education and to discuss pedagogical implications. Philosophical views of knowledge as personal'subjective' and culturally'constructed' are considered in relation to inter subjectivity as a state of shared knowledge within a community of mathematicians. The didactics of the teaching of mental calculation strategies from the two approaches are used to illustrate a key epistemological difference in the mathematics that is presented to children.