Didactic transposition theory asserts that bodies of knowledge are designed not to be taught but to be used. Discusses didactic transposition, the transposition of knowledge regarded as a tool to be used to knowledge as something to be learned in mathematics textbooks. (14 references) (MDH)

Presents examples and reflections hinting at the role of formal thought in the process of knowledge growth. Discusses proof, language, and mathematics; knowledge as form versus development; the difference between concept and object; how mathematical texts can be improved; and geometry and the idea of diagrammatic reasoning. (Contains 36…

Proposes a framework that identifies the components of number sense and the attributes of students who possess it. Discusses various aspects of three areas where number sense plays a key role: number concepts, operations with numbers, and applications of number and operation. (MDH)