The goal of this study was to examine prospective primary school teachers’ views of computational estimation and its teaching in primary school. Data was gathered through questionnaires administrated to 113 Greek pre-service teachers regarding the value they accredit to computational estimation and their suggestions for teaching it followed by interviews of 10 pre-service teachers regarding their understanding about computational estimation and skills needed to be developed. Results revealed that the majority of prospective teachers believe in the importance of computational estimation for both daily life and school. In the tasks they propose for teaching computational estimation, they incorporate context that relies on children’s out-of-school experiences, indicating their willingness to relate these experiences to computational estimation and, in general, to mathematics. Educational implications are discussed with regards to the need for computation estimation to be further acknowledged and implemented in the classroom as well as instruction to be provided to teachers.