Children's Developing Understanding of Place Value: Semiotic Aspects

This article is devoted to two interrelated semiotic aspects of the placevalue system: multiplicity of value and composition of values. Both aspects involve the basic characteristic of the placevalue system-the differentiation between face value and complete value. We explored whether a system that is intermediate between the written place-value system (multiplicity of value) and the base-10 manipulatives (no multiplicity of value) helps children understand the place-value system. The intermediate system that we designed, called FVCV (for face value and complete value), has a pseudomultiplicity of value. We report and discuss evidence that instruction and practice in the FVCV system helped children (a) to differentiate between the face value and the complete value of the digits in a multidigit place-value number representation and (b) to grasp that the complete values of the digits in a multidigit placevalue number representation add up to the total value.