Concreteness fading fosters children's understanding of the inversion concept in addition and subtraction

This study examined the effectiveness of various instructional strategies that aimed to enhance children's understanding of the inversion concept. One hundred and forty kindergartners were randomly assigned to each of the groups namely: (a) concrete-only, (b) abstract-only, (c) concreteness fading, (d) abstract-to-concrete, (e) control. They participated in a pre-test, two training sessions, an immediate post-test, and an 8-week delayed post-test. All the intervention groups showed significantly greater progress than the control group in solving the inversion problems in the post-tests. Concrete representations were more effective than abstract representations to promote knowledge transfer for children with lower prior knowledge. The superior benefits of concreteness fading appeared more prominent in the delayed post-test for children with lower prior knowledge. This study suggests that (1) concrete representations should not be avoided in teaching mathematics to children and (2) the order of presentation for various representations is a key for successful learning.