ABSTRACT
In his 1991 plenary address to the International Group for the Psychology of Mathematics Education, Dreyfus urged mathematicians and mathematics educators to give increased importance to visual reasoning—not to elevate it above analytic reasoning but on an equal level with it. Visual reasoning plays a far more important role in the work of today’s mathematicians than is generally acknowledged (Hadamard, 1949; Sfard, 1994). He cited examples of mathematicians actually hiding the diagrams and visual arguments in presenting their lectures and proofs. Other research, for example, Battista, Wheatley, and Talsma (1989), Brown (1993), Brown and Wheatley (1989, 1990, 1991), Clements and Sarama (this vol.), Reynolds and Wheatley (1992), Wheatley, Brown, and Solano (1994), has shown the power of image-based reasoning in mathematics problem solving. Students who used images in their reasoning were more successful in solving nonroutine mathematics problems than those who approached the tasks procedurally.
