In this article, I examine how a focus on preciseness in the mathematics classroom could affect group activity. The preciseness relates to the ways mathematical concepts, in this case angles are described in discourse between students. In this context, I consider how 'micro-invalidations', can limit students' opportunities to learn in a social and…

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…