Teaching approaches is a key factor that contributes to the improvement of learner achievement. Moreover, learning mathematics through activities helps learners to develop mathematical thinking which is the foundation for development and a basis for sustainable development in mathematics. In this study, 77 third year pre-service mathematics teachers at Makerere University were provided with an experience of utilizing the activity based heuristic approach in making connections between patterns, sequences and graphs with the intention of developing their mathematical thinking. The participants were subjected to a whole-class discussion after which they reflected on the discussion. The whole-class discussion was videotaped and data were collected through observation of the video and making reflective notes. Having used observation narratives and thematic analysis of reflections from the whole-class discussion through the lens of the conversational framework, it was observed that learning mathematics through activities helps learners to develop mathematical thinking which is the foundation for their development and a basis for their sustainable development in mathematics. The learners are engaged in the learning process and besides, develop several other competences like communication, creativity and innovation, presentation and working in a team. From the pre-service teachers’ perspective, the major implication of activity based heuristic approach is the need for an exigent change of the pedagogical training approaches for Makerere University’s pre-service mathematics teachers.