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 curriculum for eleven-year old students in the United Kingdom, currently adopted by most schools, includes solving linear equations with the unknown on one side only before moving onto those with the unknown on both sides in later years. School textbooks struggle with the balance between developing algebraic understanding and training…

Presents the reactions of a mathematics educator and a mathematician to a seven-year-old student's response for finding square numbers. Reflects on the mathematician's focus on the mathematics of the problem and the mathematics educator's focus on the student's systematic way of working, and discusses the common focus of student creativity. (MDH)