From non-symbolic to symbolic proportions and back: a Cuisenaire rod proportional reasoning intervention enhances continuous proportional reasoning skills

Abstract

The persistent educational challenges that fractions pose call for the development of novel instructional methods to better prepare students for fraction learning. Here, we examined the effects of a 24-session, Cuisenaire rod intervention on a building block for symbolic fraction knowledge, continuous and discrete non-symbolic proportional reasoning, in children who have yet to receive fraction instruction. Participants were 40 second graders divided into three groups: the Full intervention group who attended nearly all the sessions (n = 14), the Partial intervention group who participated in a small number of sessions (n = 11), and Control group (n = 15). Children in the Full intervention group increased their ability to compare non-symbolic continuous proportions in representations in which they did not receive any practice (annulus-shaped figures). However, contrary to our expectations, children in this group also decreased their ability to compare misleading discrete proportions. In contrast, children in the Control group did not show any change in their performance, and children in the Partial intervention group showed a similar, but not significant pattern of effects as the Full intervention group. These results provide further evidence on non-symbolic continuous proportional reasoning’s malleability and highlights the rigidity of counting knowledge interference on discrete proportional reasoning.