In this article we compare two frameworks for analysing young children's responses to the task of copying and extending a 6-dot triangle pattern. We used Mulligan & Mitchelmore's Awareness of Mathematical Pattern and Structure (AMPS) and then Biggs & Collis' SOLO taxonomy, both of which provide criteria for assigning levels. In comparison…

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…

Applying and adapting a variety of appropriate heuristic strategies is one of the accepted standards of problem solving (NCTM, 2000). Thinking through a solution to a non-routine mathematical task, experts in problem solving call into play many sophisticated strategies (almost) without conscious efforts, while novices need to be taught how to do…

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…