Research has been conducted on the role and importance of visualisation in many fields, including psychology, but very little has been done to extend its role to mathematics education in particular. Furthermore, much research has been done on the importance of critical thinking. However, to date not much has been done to clarify the fact that visualisation is a very important component of critical thinking. In this paper I investigate visualisation for the purpose of examining its role in developing critical thinking for a better understanding of mathematics by Grade 9 learners. In order to achieve this, I provide a qualitative examination from a master's dissertation of some thought processes used during visualisation when Grade 9 pupils engage in mathematics tasks. In order to support the derived thought processes data, audio-taped interviews were conducted with the students. A framework of four stages of visualisation was adapted for the collection and analysis of data. Several roles of visualisation were identified, which revealed that visualisation encourages critical thinking which further leads to a better understanding of data handling.