In our investigation of preservice secondary teachers' understanding of irrational numbers we focus on how different representations influence participants' responses with respect to irrationality. As a theoretical perspective we use the distinction between transparent and opaque representations, that is, representations that "show"…

This paper describes the current debate over developmentally appropriate teaching practice. The paper presents the perspective of multicultural educators, who argue that developmentally appropriate practice is biased toward white, middle-class values, and the perspective of special educators, who argue that modification of developmentally…