Studies measuring teachers' beliefs quantitatively by using self-report Likert scale instruments often face methodological difficulties. Such difficulties might be due to the fact that those instruments often provide less or no contexts. Whereas, several studies have shown that contexts at school, particularly contexts related to students' abilities, may influence teachers' beliefs. To overcome such difficulties, we offer an approach by using rank-then-rate items instead of Likert scale items and by explicitly taking into account students' abilities within a questionnaire. In this study, we had 43 Indonesian teachers answering this questionnaire to investigate how students' abilities influence teachers' beliefs about teaching and learning of mathematics and problem solving as well as the interrelation between these beliefs with their beliefs about mathematics. The results suggest that teachers may elicit different beliefs about teaching and learning in the context of students' abilities. Furthermore, we found that teachers' beliefs about mathematics correlate with their beliefs about teaching and learning in the context of low ability students, but not in the context of high ability students.