Intuiting the fundamental theorem of arithmetic

Our aim here was to explore, via a specific instance, the potential for learners to develop mathematically as a consequence of the interplay between intuition and indirect classroom experience rather than through explicit tuition. A significant aspect of this study is the recognition of the possibility for learners to be able to thematize schemata associated with the fundamental theorem of arithmetic without formal knowledge of either the theorem or its consequences. Our findings would suggest that some learners, by way of a series of key intuitive episodes or concrete classroom experiences, do indeed possess the capacity to create meaningful mathematical structures that, though perhaps imperfectly formed, may in some sense mirror schemata.