Problem-posing/problem-solving dynamics in the context of a teaching-research and discovery method. (English)

Singer, Florence Mihaela (ed.) et al., Mathematical problem posing. From research to effective practice. New York, NY: Springer (ISBN 978-1-4614-6257-6/hbk; 978-1-4614-6258-3/ebook). Research in Mathematics Education, 355-372 (2014).

Summary: Problem posing is practiced in the context of an integrated teaching/research methodology which has become known as TR/NYCity methodology (Teaching-Research/New York City methodology) [{\it Czarnocha} and {\it Prabhu}, “Teaching-research NYCity model", Dydaktyka Matematyki 29, 251‒272 (2006)]. This approach has been utilized in mathematics classrooms in the New York area for a decade. Problem solving turned out to be an essential teaching strategy for developmental mathematics classrooms of Arithmetic and Algebra, where motivation in learning, interest in mathematics, and the relevance of the subject is unclear to adult learners. Problem posing and problem solving are brought into play together so that moments of understanding occur, and a pattern of these moments of understanding can lead to self-directed discovery, becoming the natural mode of learning. Facilitation of student moments of understanding as manifestations of their creative capacity emerges from classroom teaching-research practice and its relationship with the theory of the act of creation [{\it A. Koestler}, The act of creation. New York, NY: Macmillan (1964)] as the integrative element leading to discovery. Discovery returns to the remedial mathematics classroom, jumpstarting reform.