Qualitative research methods were employed to investigate characterization of preservice teachers' mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren's (1994) model of growth of mathematical understanding. Five elementary and special education preservice teachers were the focus of this study. Analysis showed that preservice teachers demonstrated different levels of mathematical understanding. The nature of the mathematical tasks they completed in class provided contexts for their developing understanding. (Contains 23 figures.)