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…

The algebraic expertise that mathematics education is aiming for includes both procedural skills and conceptual understanding. To capture the latter, notions such as symbol sense, gestalt view and visual salience have been developed. We wonder if digital activities can be designed that not only require procedural algebraic skills, but also invite…

Presents a number of transcript examples of correct and incorrect transferences by children. Considers the objects of transference including spoken words, written symbols, models and diagrams, arithmetic procedures, and structures. Discusses the use of transference in arithmetic education. (YP)

Analyzes two transcripts of children's mathematical behavior to observe the nature of recursive levels and interrelationships among them. Describes several levels of the recursions. (YP)

Describes basic problem-solving skills and presents a protocol of a student solving a problem. Discusses some of the difficulties in obtaining a correct solution. Lists basic prompts for problem solving. (YP)