Preservice teachers understanding of the mean: Moving beyond the arithmetic average

The principal objective of this study was to gain insight into preservice elementary teachers understanding of the mean. Specifically, the research focused on identifying preservice teacher conceptions of the role and function of the mean as a statistical measure. Multiple data sources and data collection methods were utilized in an effort to provide rich insights into preservice teachers' mathematical understandings. A questionnaire consisting of six tasks was administered to the sample of 263 preservice teachers. When solving the tasks, participants were asked to provide an explanation of the reasoning surrounding their choice of strategy. Following analysis of the data, a sample of preservice teachers participated in individual clinical interviews. The results highlighted that 57% of the participants correctly utilized the mean to compare two data sets, 21% provided an accurate answer to a weighted means problem, and 88% constructed a data set to reflect a pre-given mean value. Approximately one fourth of the students indicated some form of conceptual understanding of the mean, with the remaining demonstrating limited computational-based understanding. Almost 25% confused the mean with the mode in either narrative description of the mean or through identification of the mean on a graphical representation. The complexities of trying to distinguish procedural and conceptual understanding of the mean are examined. Implications for preservice teacher education are discussed. © Springer Science+Business Media, Inc. 2006.