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…

Although basing instruction on learning trajectories (LTs) is often recommended, there is little direct evidence regarding the premise of a LT approach--that instruction should be presented (only) one LT level beyond a child's present level. We evaluated this hypothesis in the domain of early shape composition. One group of preschoolers, who were…

Although basing instruction on learning trajectories (LTs) is often recommended, there is little direct evidence regarding the premise of an LT approach--that instruction should be presented (only) one LT level beyond a child's present level. We evaluated this hypothesis in the domain of early shape composition. One group of preschoolers, who were…

Sarah Black wanted to remedy Year 9's lack of knowledge about nineteenth-century politics. With just five lessons to work with, she decided to devise a sequence on Gladstone and Disraeli, shaping the sequence with an enquiry question that invited argument about change and continuity. Black analyses the status and function of different layers of…

"The Oxford Handbook of Deaf Studies, Language, and Education, Volume 2," is an updated edition of the landmark original volume. A range of international experts present a comprehensive overview of the field of deaf studies, language, and education. This area has grown dramatically over the past forty years. From work on the linguistics…