We report on students’ thinking regarding entropy in an introductory calculus-based physics course. We analyzed students’ responses to a variety of questions on entropy changes of an arbitrarily defined system and its surroundings. In four offerings of the same course we found that before instruction, no more than 6% of all students could give completely correct responses to relevant questions posed in both general and concrete contexts. Nearly two-thirds of the students showed clear evidence of conservation-type reasoning regarding entropy. These outcomes were little changed even after instruction. Targeted instruction that guided students to recognize that entropy is not a conserved quantity appears to yield improved performance on qualitative questions related to this concept.