When deciding what constitutes students' "on task" or "off task" mathematical communication, teachers and researchers are also making judgements about what is, and what is not, mathematics. In this paper, we question our ability to separate the mathematical from the nonmathematical. We explore intersecting storylines in Grade…

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three­week long solution process by a pair of ninth­-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…

Vicki Zack, a classroom teacher and researcher, returned to the fifth grade classroom in 1989 after more than a decade of teaching in a university faculty of education in order to teach in the changing ecologies of classrooms (with problem-solving approaches in mathematics and literature-based approaches in reading) and to research from the…

In part 1 of this article Zack and Reid offered two examples of students operating with good-enough understandings in mathematics, and related their understandings to features of good-enough understanding identified by Mackey (I997) in the context of reading. Mackey contends that the ability to read further, on the basis of a very imperfect…