Arithmetic mean is a concept which, although simple in form, is quite complicated to fully understand. The purpose of this study was to examine how experts understood arithmetic mean in order to provide articulations of their understandings. Additionally, the articulations of conceptions of arithmetic mean could give a research-based foundation to future studies done to examine how to develop understanding of arithmetic mean. Five participants, each with expertise with arithmetic mean, were interviewed to probe into how they were thinking of arithmetic mean. Analysis of the interviews led to an articulation of two distinct conceptions of arithmetic mean: understanding the algorithm for arithmetic mean and understanding arithmetic mean as a mathematical point of balance. The experts did not have a readily-available description of how these conceptions were connected. However, follow up interviews led to a hypothesized connection between the conceptions through the use of leveling-off. This hypothesis lays a foundation for future studies on how children may develop a fuller and connected understanding of arithmetic mean.

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