This paper presented various issues about pedagogical and cognitive aspects of problem solving and explored ways to lessen the heavy cognitive load of a problem solving task. It established a problem type schema for students at different levels. It recognizes the role of modern technology as a cognitive tool that promotes learning mathematics with…

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…