Abstract
The persistent educational challenges that fractions pose call for developing 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 34 second-graders who attended the intervention (intervention group) and 15 children who did not participate in any sessions (control group). As attendance at the intervention sessions was irregular (median = 15.6 sessions, range = 1–24), we specifically examined the effect of the number of sessions completed on their non-symbolic proportional reasoning. Our results showed that children who attended a larger number of sessions increased their ability to compare non-symbolic continuous proportions. However, contrary to our expectations, they also decreased their ability to compare misleading discretized proportions. In contrast, children in the Control group did not show any change in their performance. These results provide further evidence on the malleability of non-symbolic continuous proportional reasoning and highlight the rigidity of counting knowledge interference on discrete proportional reasoning.
Highlights
Learning fractions is an arduous and protracted process for students
Continuous Proportional Reasoning While there were no improvements in the control group, children in the intervention group improved in line with the number or sessions attended (Figure 3)
We hypothesized that by training proportional reasoning with a particular focus on a continuous magnitude, children would improve their ability to compare continuous proportions and discrete ones. Contrary to this hypothesis, children who completed the 24 sessions of the intervention showed a decline in their ability to compare discrete quantities, in contexts where whole-number information interfered with the proportional one. These results beg the question if proportions are processed in a modalityindependent manner (Matthews et al, 2016; Park et al, 2020), why do gains in continuous proportional reasoning not transfer to discrete quantities? We offer two potential explanations: one related to our intervention’s instructional structure and the other to the developmental trajectory of discrete proportional reasoning
Summary
Learning fractions is an arduous and protracted process for students. Even after four years of instruction, less than a third of eighth-graders (∼30%) show an understanding of fraction addition (Carpenter et al, 1980; Lortie-Forgues et al, 2015). Fraction arithmetic is just one example of students’ persistent difficulties with. Cuisenaire Rod Proportional Reasoning Intervention fractions (Siegler and Lortie-Forgues, 2017; van Hoof et al, 2018). Recent efforts from researchers and educators to develop novel methods involving non-symbolic representations to teach fractions are beginning to bear fruit. We examined the effects of an intervention using Cuisenaire rods to improve non-symbolic proportional reasoning, a building block for symbolic fraction knowledge
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
