The teaching of socioscientific issues (SSI) holds promise for advancing functional scientific literacy, promoting critical thinking, and providing an interesting context for learning required science content, but few teachers actually employ this teaching method in K-12 classrooms. One common reason cited by teachers is their concern about the controversial aspects of teaching these topics. This study attempts to better understand these tensions by exploring preservice secondary science teachers' ideas, concerns, and approaches for teaching SSI as they move through a semester-long science methods class that specifically addresses teaching about controversial and SSI. Classroom artifact data and individual interviews were used to explore the science concepts deemed most controversial by preservice secondary science teachers and their preferred approaches for teaching these topics. The findings revealed several topics that are deemed controversial, including evolution, climate change, nuclear energy, and reproduction. Preservice teachers also eagerly adopted the methods course's discussion strategies for teaching about controversial issues. However, preservice teachers did not distinguish between the appropriateness for using different discussion-based, multiple-perspectives approaches for different types of issues. Specifically, preservice teachers often conflated SSI (societal issues that have both scientific and ethical elements) together with societally denied science for which the "teaching" is controversial (evolution, anthropogenic causes of climate change). Implications of these findings for methods courses and future research are discussed.