[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] We argue that teaching learning sequence (TLS) design needs to be further developed through the explicit articulation of methodology, which comprises the theoretical commitments regarding research and how those give rise to methods for design,…

This paper describes a study in which we investigated relationships between defining mathematical concepts--increasing and decreasing infinite sequences--explaining their meanings and classifying consistently with formal definitions. We explored the effect of defining, explaining or studying a definition on subsequent classification, and 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…

Being adaptive to the individual novice teacher is considered a condition for effective teacher mentoring. The aims of this study are therefore to explore (1) mentoring activities through which mentors intend to adapt to the individual novice teacher and (2) characteristics of adaptive mentors. Information was collected through on-site,…