We are beginning to identify problems that children and adults have in constructing the notion of average. In addition, we are examining the mathematical and organizational concepts that are needed to successfully solve averaging problems. Even though we are in the midst of this research, we know enough at this point to question the methods usually used to teach averaging in the 4th grade. Children no doubt can be taught to do the appropriate calculation, but our research shows that understanding of central tendency is far more complex. Given a good deal of experience in working with data sets, children do show a deeper, although by no means a complete, understanding of average. Experiences in which children are given more opportunities to connect their informal strategies with their formal mathematical knowledge seem to facilitate this deeper understanding.