Fraction Block as a Tool for Learning & Teaching Fraction and Its Experimental Use in an Elementary School

Abstract

This paper proposes “fraction block” as an educational reifications of fraction. Fraction block reifies characteristics of “ratio fraction” as a pair of numerator block and denominator block. The length of the blocks can be changed by keeping the ratio of numerator block to denominator block. By using the fraction block, a quantity represented as a length of tape is derived from another quantity represented as another length of tape. This deriving operation is a reification of multiplication or division with a fraction. We have implemented a learning environment where a learner is able to directly operate the fraction block in order to derive a quantity from a quantity. Experimental use of this environment in an elementary school is also reported in this paper.