On students' conceptions of arithmetic average: The case of inference from a fixed total

There is more to understanding the concept of mean than simply knowing and applying the add-them-up and divide algorithm. In the following, we discuss a component of understanding the mean - inference from a fixed total - that has been largely ignored by researchers studying students understanding of mean. We add this component to the list of types of reasoning needed to understand mean and discuss student responses to tasks designed to elicit this component of reasoning. These responses reveal that inference from a fixed total reasoning is rare even in advance high school students.