ABSTRACT
Relative thinking is critical in initial fraction instruction. In fraction instruction, relative thinking is entailed in the understanding of several important notions. The children's responses to the opening question about the trees demonstrates how difficult it is for children to move away from the additive thinking with which they are so familiar and to begin to think relatively. Measurement lies at the very heart of human activity; humans have always been preoccupied with measuring their universe, and the units and methods of measurement are essential to science. In mathematics, partitioning is the act of dividing a set or a unit into nonoverlapping and nonempty parts. When using the word partitioning in reference to fractions and measurement, we further require that the subparts be of equal size. Part of understanding measurement is also knowing when counting and taking direct measurements are inadequate.
