Rational and Fractional Numbers as Mathematical and Personal Knowledge: Implications for Curriculum and Instruction
Thomas E. Kieren
Abstract
This chapter considers alternatives that have been and are being raised as bases for fractional and rational number instruction. It considers approaches in which an analysis of the mathematics of fractional numbers serves as a basis for the development of experience for children. As suggested by the analysis and literature reviewed earlier in the section of the chapter, the study of fractions presents an opportunity to build and use a wide variety of such patterns. There have been research and curriculum work with children in which it was assumed that the child built up or constructed his or her own mathematics from given experiences that can be taken to relate to the aforementioned personal knowledge theories. Hasemann found that with 100 Hauptschuler in Germany, whereas 52% of the students could compute 16 x 34, only 30% could shade in one sixth of the shaded portion of a circle representing 3/8.