Paper folding and equivalent fractions—bridging a gap

Abstract

Much emphasis has long been placed on the value of using concrete models and manipulative devices in the early stages of the development of mathematical ideas. As Johnson suggests, however, it is entirely possible for a teacher to use instructional aids and get little benefit from them. “Some use them but fail to take students from the concrete representation to the concept behind it. Others use an inadequate or inappropriate aid” (Johnson 1967, p. 20). Brownell emphasizes that the processes children use at the concrete and semiconcrete levels must be closely related to the processes they will use later in dealing with abstract symbols (Brownell 1928, p. 24).