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.