This study explores the ways in which eleven preservice elementary teachers used a web-based teacher resource to apply a mathematical definition, to correct a procedural error in arithmetic, and to make sense of a story requiring the multiplication of fractions. In our analysis we propose a framework to compare the behaviors and values expressed by our participants with the values and norms of the mathematical community. This analysis suggests that many preservice elementary teachers are profoundly mathematically unsophisticated. In other words, they displayed a set of values and avenues for doing mathematics so different from that of the mathematical community, and so impoverished, that they found it difficult to create fundamental mathematical understandings.