This paper analyses students’ preferences for solving open modelling problems and the belief that a mathematical problem includes all the information needed to find a solution. The research questions were: What are students’ preferences, and what do they believe about openness? How are students’ preferences and beliefs about openness related to achievement in mathematics? Does teaching students how to solve open modelling problems affect their preferences and beliefs about openness? Ninth graders (N = 293) were asked about their preferences, beliefs, and grades and were taught how to solve open modelling problems or closed problems. One important finding was that students with lower grades believed more strongly that mathematical problems are not open. Teaching students how to solve open problems improved this belief and their preferences for solving open modelling problems.