The educational benefits of challenge- or problem-based approaches to learning are now well established. Action Research (AR) and Action Learning (AL) together provide educators with an ethic, a research methodology and a pedagogical strategy for harnessing and developing the motive power of purposeful activity for reflective enquiry in teaching and learning. However it is argued here that AR and AL implementation demands a sophisticated epistemological awareness on the part of the teacher-researcher. This paper suggests that the cognitional theory of Bernard Lonergan comprises a powerful resource particularly suited to underpin, inform and orient the practice of AL applied to the teaching of mathematics through practical problem solving. In this paper, aspects of Lonergan's thought are outlined and brought to bear on the development of an AL approach for teaching mathematics and its applications through collaborative practical problem solving. Lonergan's thought, as well as offering a theoretical framework of great clarity, when brought to bear on the development and implementation of AL strategies, has the potential to guide researchers, teachers and students in the design and implementation of such strategies and worth incorporating in practice. Also most beneficial for students as they negotiate the complex and dynamic epistemological territory that characterises AL.