Complexity of operating beyond naïve empiricism when proving a conjectured formula for the general term of a geometrical pattern

Abstract

Three student teachers have collaborated on expressing the general term of a geometrical pattern. Their underlying logic of generalisation is naïve empiricism. They are then given the task of proving the conjectured formula. This paper deals with the complexity of understanding the disparity between formulas being conjectures based on empirical examples and formulas resulting from utilisation of structural relationships. The research question is: What is important for the development of an attitude of proof of generality in geometrical patterns?

Complexity of operating beyond naïve empiricism when proving a conjectured formula for the general term of a geometrical pattern