Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they are going to use them in their classroom activities. However, there is a limited evidence of what beliefs they hold on their intended actions of using technological tools in teaching mathematics. This study presents two preservice high school mathematics teachers' actional beliefs related to their intended actions in teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised of a series of five task-based qualitative interviews with each of two senior undergraduate preservice teachers at a medium-sized public university in the Rocky Mountain Region of the United States. This study used a radical constructivist grounded theory (RCGT) with five assumptions—symbiosis, voice, cognition, adaptation, and praxis as a theoretical framework to guide the study process. The thematic findings of the study included four in vivo categories of their beliefs associated with actions of teaching GTs with GSP – assessment of student learning, engaging students in a group activity in exploring GTs with GSP, engaging students in individual activity in exploring GTs with GSP, and exploring GTs with GSP as 'suck it up and do it.' Pedagogical implications of these categories have been discussed.

Bring your own device (BYOD) policy implementation in schools worldwide has allowed students to learn subjects, including mathematics, using personal mobile devices (PMDs). PMD use has enhanced students’ mathematics enjoyment by bridging the gap between theoretical mathematics concepts and their practical applications, which makes mathematics more meaningful and leads to improved results. Nonetheless, students in Namibian basic education are not authorised to learn with PMDs in school. While students’ PMD use in school remains a topic of debate, there remains a need to investigate its impact on students’ mathematics learning and teachers’ perceptions of BYOD in mathematics classrooms. This study evaluated the perceptions and intentions of 209 Namibian mathematics teachers from the Omusati and Khomas regions regarding students’ mathematics learning using PMDs in schools. Data were collected through an online survey. A structural equation model revealed teachers’ positive intentions towards students’ use of PMDs through BYOD in learning mathematics in school. Perceived usefulness (PU), perceived ease of use (PEoU), and price value (PV) factors directly affected the teachers’ behavioural intentions (BI) towards students learning mathematics through BYOD. PEoU significantly affected teachers’ PU, and PV significantly affected teachers’ PEoU and PU. PU significantly mediated the relationship between PEoU and teachers’ intentions. PV significantly indirectly affected teachers’ intentions through PU. PEoU non-significantly mediated the PV and intention relationship. Practical implications are discussed, and recommendations are offered for the Namibian Ministry of Education, Arts and Culture and teacher training institutions.