A Cognitional Theory for Mathematics Methodology on an Initial Teacher Education Programme

This paper suggests that the philosophical work of Bernard Lonergan comprises a powerful resource particularly suited to underpin and inform the practice of action learning in the context of a mathematical methodology for initial teacher education. It is proposed that the cognitional theory of Bernard Lonergan provides a framework that is uniquely suited to guiding this dynamic interplay, concerned as it is with what Lonergan calls the realms of meaning of theory, practice and interiority (Lonergan 1972; D. Coghlan, 2010; D. Coghlan, 2016) and which can be adopted for mathematics teacher education. The three-fold Action Learning strategy presented reorients education away from the transmission of pre-formulated concepts and towards the engagement of the pure desire to know of each student as it draws the pre-service teacher through the levels of cognitional process. Lonergans emphasis, like a teachers, is on the act or event of insight in the learners mind. Practical and higher order thinking and reflection, promoted by encouraging problem solving skills, is best supported by valuing and elucidating reflexively the process of inquisitive and creative enquiry (Mason, 1998). Mathematical problems provoke spontaneous common-sense enquiry. With tutor guidance, enquiry moves into the realm of theory, or scientific knowing, an approach which offers a rationale to students for learning mathematical topics (Hiebert et al., 1996; Prusak, Hershkowitz, Schwarz, 2013) and lastly to reflection and critical knowing. Lonergans approach focusses on the students framing fruitful questions rather than always reaching right answers. The cognitional theory provides teachers, preservice teachers and students with a guide to bring cognitional process into conscious awareness (Carley, 2005; Colleran, 2002; Connolly, Murphy, Moore, 2008) and can be adopted for the mathematics ITE programmes.