There is a lack of research that explores teachers’ perspectives on teaching highly able pupils (HAPs) in the diverse ability classroom. Instead, pupils’ perspectives are common, such studies often concluding that teachers need more professional development or that they fail to support HAPs. Consequently, previous research does not support teachers in how to implement teaching that includes HAPs. This thesis aims to harness teachers’ perspectives of pedagogical possibilities that enable learning opportunities for mathematically highly able pupils (MHAPs). By comparing pupils’ (n=264) relative achievement on two different tests, traditional and non-traditional, the first part of this thesis explores teachers’ possibilities to recognize MHAPs. The results show that pupils who achieved highly on the non-traditional test, but not on the other, have higher problem-solving competence compared to pupils who achieved highly on the traditional test instead. The second part presents a teacher-initiated investigation of pupils’ perceptions of challenging mathematical tasks. The findings indicate that the developed tool can help teachers find suitable tasks for MHAPs. The final part uses positioning theory to analyze teachers’ (N=17) discussions and probe their perceptions on orchestrating teaching MHAPs. The findings show that the teachers have knowledge of how to recognize and support MHAPs. Specifically, the teachers express possibilities with challenging tasks and differentiated education to meet MHAPs’ learning needs. Furthermore, the teachers perceived fewer rights than duties to orchestrate teaching for MHAPs’, for example, to continuously asses them. The studies in this thesis support teachers to orchestrate teaching including MHAPs in the diverse ability classroom. Both practice and research can be guided by what the teachers in these studies perceived as possible to do to orchestrate such teaching. Thereby support is given to teachers, from teachers, through research.

This thesis harnesses teachers’ perspectives of pedagogical possibilities that enable learning opportunities for mathematically highly able pupils (MHAPs). Firstly, teachers’ possibilities to recognize MHAPs through assessment are explored. The results show that pupils with high problem-solving competence can achieve highly on a non-traditional test, whereas they do not on traditional tests. Secondly, a teacher-initiated investigation of pupils’ perceptions of challenging mathematical tasks is presented. The findings indicate that a developed tool can help teachers find suitable tasks for MHAPs. Finally, teachers’ (N=17) discussions are analysed and their perceptions on orchestrating teaching MHAPs are probed. The findings show that the teachers have knowledge of how to recognize and support MHAPs. Specifically, the teachers express possibilities with challenging tasks and differentiated education. Furthermore, the teachers perceived they have knowledge and competence to orchestrate teaching for MHAPs. The findings show that their knowledge is consistent with previous research on teaching highly able pupils (HAPs) to meet their learning needs. This thesis gives support, on orchestrating teaching that includes HAPs in learning, to teachers, from teachers, through research.