This research study was conducted to identify core practices of enacting effective mathematics pedagogy with GeoGebra, a software application for teaching and learning mathematics. Eleven Ghanaian in-service mathematics teachers were engaged in a twelve-month professional development programme where they developed GeoGebra-based mathematics lessons, which they taught to their peers and subsequently to students in the classroom. The teachers' actions and views about using GeoGebra to enact mathematics lessons were examined with the aim to specify the core practices of effective mathematics pedagogy. Data was collected through interviews, focus group discussions, lesson plans, and lesson observations. The results provided evidence that teachers were able to enact core practices, to different degrees, within five central themes of effective mathematics pedagogy: creating a mathematical setting, providing worthwhile mathematical tasks, orchestrating mathematical discussions, making mathematical connections, and assessing students' learning. Further analysis of the data provided evidence for theorising 31 core practices across these central themes of effective mathematics pedagogy. Following their engagement in the professional development programme, the teachers enacted these practices to greater or lesser extent. However, it was problematic for most teachers to effectively engage their students in a deep mathematical discussion. The findings from this study have implications for high school mathematics curriculum, effective mathematics pedagogy literature, and professional development for technology integration in teaching and learning.