Notations, Conventions, and Constraints: Contributions to Effective Uses of Concrete Materials in Elementary Mathematics

Twenty fourth-grade children were matched according to performance on a whole-number calculation and concepts pretest and assigned at random to one of two groups: wooden base-ten blocks and computerized microworld. Instruction in each group was designed to orient students toward relationships between notation and meaning. Instruction given the two groups was based upon a single script that extended whole number numeration to decimal numeration, and emphasized solving problems in concrete settings while inventing notational schemes to represent steps in solutions. Neither group changed in regard to whole-number notational methods. Blocks children understood decimal numerals as if they were funny whole numbers; Microworld children attempted to give meaning to decimal notational methods, but were largely in a state of disequilibrium at the end of the study.