This study examines the beliefs of 33 preservice teachers (PSTs) from the U.S. have about using different types of real-world contexts in the mathematics classroom. Qualitative data about the participants' reactions to specially designed word problems that varied in contexts from "neutral" to controversial were collected. A thematic analysis of the responses indicated that they could be arranged into three typologies on a continuum based on their openness towards the use of controversial issues in the mathematics classroom. Drawing on the analysis of PSTs' responses and the literature, a fourth typology was inferred. The typologies can be useful to teacher educators and education programs as they seek to prepare PSTs to work with increasingly diverse students in their future mathematics classes. The study also highlights the potential of using word problems as a tool to understand PSTs' beliefs.