Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this…

A cognitive-based system of analysis of spoken discourse was designed to provide details about the way pupils think and talk about issues arising from prose material. Written and spoken responses were analyzed to examine the effects of intellectual ability, differences in the stimulus passage, and prior small group discussion. (Note: Page…