Juggling mathematical understanding

This paper presents a theoretical model for the teaching for understanding of school mathematics. After describing two categories of understanding, it develops a continuum between rote and insight. In the process of describing the model, it articulates the assumptions underpinning the model and presents a process whereby a teacher can move the teaching strategies towards the development of insight within the students. It will argue that the development of insight should be the goal of all school mathematics classrooms. And that in order to achieve this goal the classroom teacher must become an expert juggler by simultaneously applying teaching strategies that develop student proficiency with skills, positive attitudes towards mathematics and deep connected conceptual knowledge.