[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…